Conor.Murphy.Delamination.Fatigue.2016

Determination of the Fatigue Properties of

High Performance Composite Materials

Conor Murphy

The thesis is submitted to University College Dublin in part

fulfilment of the requirements of the degree of ME in Mechanical

Engineering

School of Mechanical and Materials Engineering

Supervisor: Dr Neal Murphy

April 2016

i

Declaration

I declare that this dissertation is entirely my own work, carried out at University College

Dublin, and has not been submitted for a degree to this or any other university and that

the contents are original unless otherwise stated.

Signed: ______________

Date: ________________

ii

Acknowledgements

I have received a lot of help and support over the course of this project, of which I am very

grateful. Firstly, I would like to thank Dr Neal Murphy for his role as a patient and

approachable supervisor. His dedication of time and effort into the project is much

appreciated. There are a number of members of UCD staff and alumni who have been of

tremendous help, and in particular I would like to acknowledge the support of Clémence

Rouge and John Gahan. Clémence guided me through almost all experimental aspects of

my project, from composite manufacture to the use of test software. John Gahan was

incredibly patient and willing to help, despite the large number of students relying on his

help. I would also like to thank Dr Steffen Stelzer and Dr Andreas Brunner for their support

regarding fatigue test protocol and calculations. Finally, I would like to thank my parents

Ger and Siobhán for their kind and supportive attitude throughout my time in UCD.

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Table of contents

Contents 1 Introduction ............................................................................................................................... 1

1.1 Background......................................................................................................................... 1

1.2 Motivation .......................................................................................................................... 3

1.3 Project Scope & Objectives ................................................................................................ 4

1.4 Thesis Structure .................................................................................................................. 4

2 Literature Review ...................................................................................................................... 5

2.1 Composite Delamination .................................................................................................... 5

2.1.1 The Achilles Heel of Composite Structures ................................................................ 5

2.1.2 Interlaminar Reinforcement ....................................................................................... 7

2.2 Fracture Mechanics Applied to Delamination .................................................................... 7

2.2.1 Modes of Fracture .................................................................................................... 12

2.3 Experimental Test Standardisation .................................................................................. 13

2.3.1 Quasi-Static Test Standardisation ............................................................................ 13

2.3.2 Cyclic Fatigue Delamination Test Standardisation ................................................... 14

2.4 Crack Shielding Mechanisms ............................................................................................ 20

2.4.1 Stress Ratio Effect & Crack Closure .......................................................................... 20

2.4.2 Fibre Bridging ........................................................................................................... 21

2.4.3 Describing shielding mechanisms individually ......................................................... 24

2.5 Delamination Growth Representation ............................................................................. 24

2.5.1 Threshold Behaviour ................................................................................................ 24

2.5.2 A Variant of the Hartman Schijve Equation ............................................................. 25

3 Materials and Methods ........................................................................................................... 28

3.1 Materials .......................................................................................................................... 28

3.1.1 Carbon Fibre Prepreg ............................................................................................... 28

3.1.2 Storage ..................................................................................................................... 29

3.2 Manufacture of Specimens .............................................................................................. 29

3.2.1 Layup Procedure....................................................................................................... 29

3.2.2 Curing Procedure ...................................................................................................... 31

3.2.3 Machining of DCB Dimensions ................................................................................. 33

3.2.4 Preparation of DCB Specimens ................................................................................ 34

3.3 Theory for Beam Analysis ................................................................................................. 35

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3.3.1 Simple Beam Theory ................................................................................................ 35

3.3.2 Corrected Beam Theory ........................................................................................... 37

3.3.3 Modified Compliance Calibration ............................................................................. 39

3.3.4 Back-Calculated Flexural Modulus ........................................................................... 40

3.4 Mode I Fracture Toughness Test ...................................................................................... 40

3.4.1 Preparation ............................................................................................................... 40

3.4.2 Precracking ............................................................................................................... 41

3.4.3 Re-Loading ................................................................................................................ 41

3.4.4 Initiation Points ........................................................................................................ 42

3.5 Fatigue Testing ................................................................................................................. 44

3.5.1 Instron 8502 Servo Hydraulic Test System ............................................................... 44

3.5.2 Load Cells .................................................................................................................. 47

3.5.3 Fatigue Testing Protocol ........................................................................................... 49

3.5.4 WaveMatrix Dynamic Testing Software ................................................................... 52

3.5.5 Methods of Crack Length Determination ................................................................. 53

3.5.6 Calculation of da/dN ................................................................................................ 54

3.6 Flexural Modulus Test ...................................................................................................... 56

4 Results and Discussion ............................................................................................................ 57

4.1 Flexural Modulus Tests..................................................................................................... 57

4.2 Mode I Fracture Toughness Test ...................................................................................... 60

4.3 Fatigue Testing of UCD Specimens ................................................................................... 62

4.3.1 Early Testing ............................................................................................................. 62

4.3.2 Testing of UCD Specimens ........................................................................................ 63

4.4 Fatigue Testing of ESIS Specimens ................................................................................... 67

4.4.1 Results of 250N Load Cell Tests ................................................................................ 67

4.4.2 Collated ESIS Results ................................................................................................ 75

4.5 Comparison of Crack Length Calculation Methods .......................................................... 79

4.6 Crack Shielding ................................................................................................................. 81

5 Conclusions .............................................................................................................................. 84

6 References ............................................................................................................................... 87

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Abstract

This project analyses the mode I fatigue delamination behaviour of a unidirectional carbon

fibre reinforced polymer, Hexcel 8552/AS4. Double cantilever beam specimens were

manufactured from prepreg material and subjected to displacement control fatigue testing

using an Instron 8502 servo-hydraulic testing machine. Five specimens of the same

material were then received from Imperial College London as part of a round robin test

conducted by the European Structural Integrity Society. The aim of the round robin is to

further develop a standardised test method for fatigue delamination evaluation of

composite laminates. A draft test procedure was followed, and the strain energy release

rate was calculated using a compliance based method, involving periodic visual

determination of the crack length using a travelling microscope, and continuous

measurement of load and crosshead displacement values. Early testing was conducted

with the use of a 5kN load cell, and the ESIS specimens were tested using a 250N load cell.

The aim of the procedure is to produce test durations of under 24 hours, however it is also

of interest to attempt to observe threshold behaviour of the material, which occurs at low

crack growth rates. Two samples were tested to 500’000 cycles, however it is apparent that

much longer test durations are required. Experimental challenges in the form of a stiffening

effect on beam arms, load measurement resolution and observer-dependant visual crack

measurement contributed to scatter in forming delamination growth curves for each

specimen. As an alternative to the use of a Paris law power representation, an attempt was

made to represent fatigue delamination growth using a Hartman-Schijve approach, which

involves obtaining the threshold value of the strain energy release rate, Gth. Despite

obtaining similar slopes for each specimen, significant scatter was present due to the

sensitivity of the load measurements to small deviations, environmental effects and

experimental phenomena such as crack closure and fibre bridging.

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List of Figures

Figure 1-1: High specific strength of CFRP compared to metals ........................................................ 1

Figure 1-2: Transverse tensile failure occurring at the fibre-matrix interface. ................................. 2

Figure 2-1: Transverse shear stress distribution in beams ................................................................ 5

Figure 2-2: Fatigue simulation conducted on an F/A-18 carbon fibre epoxy wing skin. .................. 6

Figure 2-3: Paris plot displaying typical fatigue crack growth regions. ............................................. 9

Figure 2-4: Modes of Loading .......................................................................................................... 12

Figure 2-5: A comparison of displacement and load control tests.. ................................................ 15

Figure 2-6: Scatter and inaccurate load application in load controlled testing. .............................. 16

Figure 2-7: Comparison of the relative stability of load and displacement controlled tests........... 17

Figure 2-8: Comparison of effective crack length values and crack lengths obtained from

compliance calibration. .................................................................................................................... 18

Figure 2-9: The effect of data reduction on raw data ...................................................................... 19

Figure 2-10: Fibre Bridging as a shielding mechanism in CFRP composite. ..................................... 21

Figure 2-11: Different damage from quasi-static and fatigue delamination. .................................. 22

Figure 2-12: Correlation between rate of cyclic energy release and crack growth rate on a linear

scale. ................................................................................................................................................. 23

Figure 2-13: Linearity of the Hartman-Schijve representation of ESIS TC4 round robin data ......... 26

Figure 2-14: Stress ratio-independent Hartman–Schijve representation of delamination growth in

DCB tests using a unidirectional composite laminate. ..................................................................... 27

Figure 3-1: Debulking Layup ............................................................................................................. 30

Figure 3-2 Curing Layup .................................................................................................................. 31

Figure 3-3: Cure Cycle ...................................................................................................................... 32

Figure 3-4: Machining of DCB specimens ........................................................................................ 33

Figure 3-5: Double cantilever beam specimen with load blocks. ................................................... 35

Figure 3-6: Corrections applied to correct for assumptions of simple beam theory....................... 38

Figure 3-7 Linear fit to calculate the correction factor for beam root rotation .............................. 38

Figure 3-8: Double cantilever beam mounted on Hounsfield tensile testing machine ................... 41

Figure 3-9: Load-displacement curve of quasi static test ............................................................... 43

Figure 3-10: Fatigue testing of a double cantilever beam specimen ............................................... 44

Figure 3-11: Tuning of the PI controller. .......................................................................................... 45

Figure 3-12: Upper fixture replacement .......................................................................................... 47

Figure 3-13 Obtaining the maximum displacement to be used in fatigue testing .......................... 50

Figure 3-14: Fatigue testing of ESIS Specimen. ................................................................................ 51

Figure 3-15: Visual representation of WaveMatrix program stages................................................ 53

Figure 3-16: A typical a vs N graph under displacement control .................................................... 55

Figure 4-1: Load-displacement curve for flexural modulus calculation .......................................... 57

Figure 4-2: Load-displacement curve of ESIS specimens ................................................................. 58

Figure 4-3 Brittle-ductile failure interface through the beam thickness ........................................ 59

Figure 4-4: Load Displacement Curve .............................................................................................. 60

Figure 4-5: Comparison of initiation points across the three tested specimens ............................. 61

Figure 4-6: Load-displacement curve showing adjustment for thermal drift .................................. 64

Figure 4-7: MCC plots of UCD Specimens ........................................................................................ 65

Figure 4-8 Comparison of beam theory methods for ESIS A1 ......................................................... 68

Figure 4-9: Comparison of beam theory methods for ESIS A2. ....................................................... 68

Figure 4-10: Drop in load observed in ESIS A1 Specimen at 9000 cycles ......................................... 70

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Figure 4-11 Paris power law fit ........................................................................................................ 71

Figure 4-12 Hartman-Schijve linearity plot ...................................................................................... 72

Figure 4-13: Hartman-Schijve representation of ESIS A1 ................................................................ 73

Figure 4-14: Hartman-Schijve representation of ESIS A2 ................................................................ 73

Figure 4-15 Delamination growth curve of ESIS specimens ............................................................ 75

Figure 4-16: Hartman Schijve linearity of ESIS Specimens ............................................................... 77

Figure 4-17 Hartman-Schijve representation of ESIS specimens ..................................................... 78

Figure 4-18: Comparison of crack length determination methods ................................................. 79

Figure 4-19: Comparison of crack length determination methods on delamination growth curve 80

Figure 4-20: Varying delamination front in ESIS A1 ......................................................................... 81

Figure 4-21: Minimum load undergoing compressive loading after approximately 10’000 cycles . 82

Figure 4-22: Crack Shielding Phenomena. ....................................................................................... 83

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List of Tables

Table 3-1: Amplitude capability of Instron 8502 ............................................................................. 46

Table 3-2: Summary of WaveMatrix program ................................................................................. 52

Table 4-1: Flexural Modulus Calculation of UCD Specimens .......................................................... 57

Table 4-2: ESIS Specimens Flexural Modulus Calculation ................................................................ 58

Table 4-3: Sample 1 Fracture Toughness Results ............................................................................ 60



Table 4-6: Fatigue test parameters for UCD specimens ................................................................. 64

Table 4-7: ESIS Specimen dimensions and testing parameters tested with 250N load cell ............ 67

Table 4-8: Parameters used in Hartman-Schijve calculations .......................................................... 74

Table 4-9: Properties of power law fits of ESIS specimens .............................................................. 75

Table 4-10: Parameters used in Hartman-Schijve calculations for ESIS specimens ........................ 78

1

1 Introduction

1.1 Background

Due to the impressive strength to weight properties of composite materials, and the

relative ease with which complex components can be manufactured, such materials have

been favoured as a cost effective alternative to metals in a wide range of industries. The

properties of composite structures can be customized in the form of different fibre

orientations and matrix formulations to suit individual design requirements. Redesign of

components of complex geometries that previously incorporated less versatile materials

has resulted in lighter designs that boast excellent surface finish and corrosion resistance.

The manufacture of Fibre Reinforced Polymers (FRPs) for structural application gained

traction in the 1940’s, where new moulding methods found application in the motor and

marine industries. During the 1960’s the marine industry was the largest consumer of fibre-

reinforced composite materials, and in subsequent years composites have become

preferred materials in many aspects of aircraft and spacecraft construction.

Figure 1-1: High specific strength of CFRP compared to metals. Data obtained from the

CES materials database.

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The opportunity for significant weight reduction has been seized by the aerospace industry

as the cost of fuel rises. Notable aircraft in which composites are largely incorporated

includes the recently introduced Boeing 787 Dreamliner, 50% of the composition of which

is fibre reinforced polymers – far higher than any other civilian airliner at the present time.

The use of composite materials as a replacement for traditional steel and thermoplastic

materials has brought with it a number of challenges. The use of different fibre orientations

and matrix formulations requires the ability to accurately and consistently predict the

mechanical properties of such materials under a variety of modes of loading. At the present

time, many important mechanical properties are accurately known, however it is

important to characterise composites’ behaviour in all forms of fatigue loading. Ideally

loads occur in the same plane as the fibres, however an inherent weakness in the layered

structure of composite laminates is its weakness to loading in the plane perpendicular to

the fibres. Under fatigue loading conditions, delaminations can initiate and grow to a

critical length, significantly reducing the structural integrity of the material, leading to

failure. A standardised test method exists for the composite material’s mode I fracture

toughness under quasi-static loading conditions [1], however no such standards exist for

experimental determination of its behaviour under fatigue loading conditions, which is the

most common cause of failure in the material.

Figure 1-2: Transverse tensile failure occurring at the fibre-matrix interface. From [2]

3

1.2 Motivation

Fatigue delamination of composite materials is a subject that has received much research

attention in recent years. The European Structural Integrity Society Technical Committee

have conducted several round robin tests [3, 4, 5] with the aim of establishing a

standardised test procedure, the results of which have presented a number of

experimental challenges. Among the challenges faced have been in and inter-laboratory

scatter due to load measurement resolution, observer-dependent visual determination of

crack growth, testing mode choice and the effect of different stress ratios on the

delamination growth curve obtained. The choice of specimen geometry is the double

cantilever beam, which is also employed in quasi-static testing. Emphasis has been placed

on establishing a procedure of relatively short test duration (8-10 hour minimum) however

it is also necessary to characterise the threshold behaviour of the material – its behaviour

at short crack growth rates. This requires longer test durations under displacement control.

The empirical use of the Paris law power relationship in representing crack growth in

composites as a function of the strain energy release rate has been based on its correlation

with crack growth in metals, provoking research into alternative forms of crack growth

representation. A model for crack growth representation that shows potential is a variant

of the Hartman-Schijve equation, which requires observing the crack growth as it reaches

near-threshold behaviour. This project contributes to a 7-laboratory round robin, the

results of which are reported to ESIS.

4

1.3 Project Scope & Objectives

Composite structures can consist of continuous and non-continuous fibres, combined in a

stacking sequences comprising of varying fibre orientations. This project is limited to the

observation of mode I (opening) fatigue delamination fatigue properties of Hexcel

8552/AS4 unidirectional carbon fibre reinforced polymer. The objectives of the project are

as follows:

To manufacture unidirectional CFRP layup using prepreg supplied by Bombardier

and prepare double cantilever beam specimens for delamination fatigue analysis.

To conduct interlaminar fracture toughness and flexural modulus tests on CFRP

beams.

To create satisfactory conditions for the employment of a draft test procedure

prepared by ESIS TC4.

To conduct five fatigue tests on Hexcel 8552/AS4 double cantilever beam

specimens supplied by ESIS using a 250N load cell.

To investigate the use of a variant of the Hartman-Schijve equation to represent

delamination fatigue growth.

1.4 Thesis Structure

This thesis consists of five chapters. The Literature Review provides an overview of the

application of fracture mechanics to describe delamination growth in composites, and

presents up-to-date developments in experimental standardisation and crack growth

representation. The Materials and Methods chapter presents a comprehensive procedure

for the manufacture of double cantilever beam specimens from unidirectional prepreg

material, the test procedures followed, and necessary theory for analysis. Results from

testing are presented and discussed in Chapter 4. In the final chapter, the project

conclusions are presented.

5

2 Literature Review

2.1 Composite Delamination

2.1.1 The Achilles Heel of Composite Structures

Composite laminates consist of layers of fibre reinforcement bonded by a thermoset

polymer matrix, such as epoxy resin. Such materials are susceptible to delamination (or

interlaminar fracture) where the separation of plies occurs. The propagation of

delamination is confined to the matrix material bonding them, following the path of least

resistance. Delamination is perhaps the most common cause of failure in composite

structures; the separation of the resin-rich interface between the layers of fibre

reinforcement results in a significant decrease in the stiffness and strength that contribute

to the structural integrity of the material [6], and can ultimately result in structural collapse

via fibre breakage or buckling. In comparison with other engineering materials, composites

exhibit a very high strength to weight ratio, or specific strength, however in spite of the

materials high effective elastic modulus in the fibre direction, its transverse shear modulus

is significantly lower. Delamination of the material is caused by transverse shear stresses,

which are parabolic in magnitude through the thickness of a beam – greatest at the centre

[7, 8].

Figure 2-1: Transverse shear stress distribution, acting in a parabolic nature through the centre of a beam. From [7]

6

High interlaminar stresses are naturally likely to occur at sections in the structural design

that require discontinuity of the composite material, such as cut-outs, holes [9], joints [10]

and ply-drops [11]. The differences in Young’s Moduli of the fibre and matrix is the cause

for the high local stresses present at the interface of the two. In aircraft, considerable use

is made of composites in components that are subjected to low strain levels, such as skins,

stabilisers and fins – the primary structural components are still metallic, however. In such

composite components fatigue delamination is a major concern, and at the time of writing

a ‘no-growth’ design approach is taken to composite materials, in which design does not

allow for any visible defect to occur. Even so, there are a number of examples in which

delamination were seen to have grown during service life in spite of this restriction. A

service report, [12] examining Boron/epoxy doublers (patches) used for reinforcement of

metallic structures in RAAF F-111C aircraft reported several instances of debonding in

boron/epoxy doublers on the upper surface of wing-pivot fittings. The delaminations were

found to have been detected 759 to 1233 service hours after installation, determined by

fractographic evidence to be fatigue induced. At the time, inspection of the doublers was

scheduled every 2025 flight hours, so these findings were decidedly unsettling. This

brought attention to the need to design a fatigue threshold for composite delamination

growth and predict its behaviour so that inspection intervals can be designed accordingly.

Figure 2-2: A fatigue simulation conducted on an F/A-18 carbon fibre epoxy wing skin. The above delamination propagated over a period of 1633 simulated flight hours to approximately 150-300mm in size. From [13]

7

2.1.2 Interlaminar Reinforcement

A number of methods have been employed in attempts to increase the delamination

resistance of composite materials. Among them, Z-pinning has been shown to improve the

bonding strength of composite joints. Z pinning is a through-thickness reinforcement,

employing the use of z-pins that act as fine nails that provide support in the direction

normal to the plies through a combination of adhesion and friction, and is employed in

some composite aircraft structures. The pins are usually constructed of titanium, steel or

fibrous composite – the latter has shown to be the most effective [14]. Z-pinning has shown

to largely improve composites interlaminar properties, showing increases in through-

thickness modulus as a large scale bridging zone is created, as reviewed in [15]. Surface

treatments and their effect on the fracture resistance of composites have also been

investigated. Studies of the effects of surface treatment with Ar+ irradiation [16] and the

more environmentally friendly oxygen plasma [17] have observed an increase in

interlaminar fracture toughness of a carbon/epoxy prepreg by 24% and 20% respectively.

2.2 Fracture Mechanics Applied to Delamination

Several methods have developed for the analysis of interlaminar fracture. One such

method is a stress/strain approach, however this is more applicable for static delamination,

and will not predict the crack growth rate. Cohesive zone modelling is another method,

employing finite element analysis to model an interface between two layers using cohesive

zone elements [18]. Over the past 30-40 years, it has become respectable practice to use

fracture mechanics methods for the characterisation of the onset and growth of

delamination. Delamination fracture is a zone which can be treated as a crack, and is thus

a rare instance where fracture mechanics can be globally applied to fibre-reinforced

composite materials. Delamination crack growth is self-similar, and continuum theory is

applicable [19].

8

Fracture mechanics is the study of crack propagation in materials in order to predict their

failure load or remaining lifetime. A requirement for this method is that little or no plastic

deformation occurs - matrix materials tend to undergo brittle fracture, so this method can

thus be applied to delamination of composite materials. Fatigue failure is the fracture of a

material due to brittle crack propagation under repeated cyclic loading, where the stresses

experienced by the material can be considerably below the yield stress limit of the material.

In composite materials it is rare that catastrophic failure occurs without warning, however

it tends to progress over time, as the aforementioned subcritical stresses are dispersed

throughout the material [19]. During certification of the AIRBUS A320 vertical fin, Schön

et al. [20] stated:

“No delamination growth was detected during static loading. The following fatigue loading

of the same component had to be interrupted due to large delamination growth. The

delamination grew due to out-of-plane loads.”

Griffith [21] began the field of linear elastic fracture mechanics (LEFM) when he was faced

with two seemingly contradictory facts – the stress required to fracture bulk glass is

approximately 100MPa, yet in theory the stress required to break the atomic bonds is

approximately 10GPa. He suggested that these low fracture values were a result of

microscopic flaws in the material. The stress intensity factor is a constant that describes

the stresses and displacements that are occurring ahead of a sharp crack tip, a result of

Irwin et al. [22] building upon Griffith’s research. In 1961, Paris and Erdogen [23] proposed

an equation to describe a linear relationship between the crack growth rate in metals

under cyclic loading, da/dN, and the stress intensity factor (SIF), K, presented in equation

2.1. The SIF is seen as ‘the controlling variable for analysing crack extension rates’ [24].

da/dN =B(ΔK)m (2.1)

9

Where B and m are constants of a power law, and ΔK is the range of K as it oscillates

between the application of maximum and minimum loads. For metals this method has

allowed for computation of the structural lives of complex geometries. A Paris plot is a

sigmoidal curve that describes three regions of fatigue crack growth in metals. The curve

(see Figure 2-3 below) shows two periods of crack growth rate acceleration - the threshold

(or crack nucleation) value of K occurs at very low crack growth rates, and its critical value

occurs at the point at which fracture subsequently occurs. These two regions are separated

by a log-linear region. Cracks may nucleate quite early in the fatigue life of a material,

however it is relatively more difficult at stress levels near the fatigue limit [25].

Figure 2-3: Paris plot displaying typical fatigue crack growth regions. From [26]

10

Due to difficulty in calculation of the SIF for an inhomogeneous layered material, the Strain

Energy Release Rate (SERR) derived by Griffith is preferred for characterising delamination

growth in composites. It is denoted G, and is defined as the amount of energy dissipated

during the fracture of a newly created fracture surface area. It is also referred to as the

“crack driving force”.

𝐺 = −1

𝑏 (

𝑑𝑈

𝑑𝑎) (2.2)

Where b is the specimen width, U is the potential energy for crack growth. Details on the

calculation of G using elastic beam theory will be provided in Section 3.3. A strong

correlation has been shown between the SIF and SERR [22], therefore Equation 1.1 is

usually rewritten in terms of the SERR when characterising delamination growth rate

prediction:

da/dN = C(ΔG)n (2.3)

Where C and n are still power law constants and ΔG is the range of the strain energy release

rate – the difference between maximum and minimum values of G. The SERR can be

calculated analytically, or by Finite Element Analysis, the most common method for which

is the virtual crack closure technique (VCCT) [27]. Experimentally, it can be calculated with

relative ease by monitoring the change in compliance (the inverse of stiffness) with crack

length – a technique employed in this project.

11

The Paris relation (Equations 2.1 and 2.3) has been used in attempts to describe fatigue

delamination in composites. Gmax is also commonly used in this relationship in the place of

ΔG – both have been seen to correlate with delamination growth, however recent

literature disputes the use of ΔG, suggesting it is not a suitable crack driving force, and that

√ΔG is a more suitable parameter [28], where:

√ΔG = √𝐺𝑚𝑎𝑥 − √𝐺𝑚𝑖𝑛 (2.4)

The use of this term will be further discussed in Section 2.5.2. At low stress ratios, the use

of Gmax is preferable to ΔG to minimise the effects of crack closure, as will be discussed in

Section 2.4. It’s worth noting that the use of the Paris relation to describe delamination in

composites is not based on the physics of the problem, but rather on correlation obtained

with experimental observation. An engineering approach has been taken to the use of the

strain energy release rate as opposed to a scientific one; it appears that once similitude has

been established in literature, many studies follow this approach without challenging the

fundamentals of the relationship. Obtaining a greater understanding of the complex stress

states present in the material would shed some light on the power-law relationship

between SERR and the growth of delamination, and allow for corrections to be made in

areas where the parameter cannot currently explain. An excellent critical review of

developments regarding fatigue delamination growth representation in composites has

been published by Pascoe et al [18]. Extensive literature is also available on theoretical

modelling of quasi-static and fatigue delamination growth, reviewed in detail by Tay [29].

The latter is beyond the scope of this project, as this project focuses on experimental work.

The development of a standardised experimental test procedure is the subject of much

recent research, which will be reviewed in Section 2.3.

12

2.2.1 Modes of Fracture

A crack can be subjected to three modes of loading in any combination. These modes were

introduced by Irwin [26] as Mode I (opening) loading, Mode II (in-plane shear) and Mode

III (anti-plane shear). In reality, fatigue failure of a composite structure is a result of a

mixture of all three of these modes being applied to propagate a crack, however Mode I

loading is of particular interest. Experimentally, Mode I loading generally outputs the

lowest fracture toughness values when compared to the other pure or mixed modes of

loading [30,31]. Considering this, characterising mode I fatigue behaviour is the first step

in alleviating the no-growth design approach being applied to composite materials, as it

can then provide a conservative (or lower limit) estimate for all three modes of loading,

even though it may be impossible to observe pure mode I loading in real application. This

project is limited in scope to the analysis of Mode I cyclic loading, employing the double

cantilever beam test method originally developed by J.G Williams [32] for which detailed

beam theory will be supplied in Section 3.3.

Figure 2-4: Modes of Loading, from [19].

13

2.3 Experimental Test Standardisation

2.3.1 Quasi-Static Test Standardisation

Development of standardised test procedures for quasi-static and fatigue delamination

growth in fibre-reinforced polymers has been the subject of extensive research in recent

years. Such work has resulted in a number of standards being published, including an

international Standard for quasi-static determination of interlaminar fracture toughness

utilising a Double Cantilever Beam specimen geometry with crack starter insert [1]

published in 2001 as a result of the combined efforts of the Japanese Standards

Association, American Society for Testing and Materials, and the European Structural

Integrity Society (ESIS) Technical Committee 4. A detailed overview of ESIS developments

in polymer fracture testing methods from 1980-2000 [30] discusses progression in the

development of this standard by means of multiple round robin tests.

2.3.1.1 Limitations and Open Problems

The limitation of available test protocols for delamination to unidirectional orientations

has been due to instances of multiple cracking forming in multidirectional laminate tests

[33], or ‘crack jumping’ occurring, where the crack shifts from the propagation plane, which

invalidates the test, according to the ISO standard [1]. The interlaminar fracture of

multidirectional specimens was investigated by ESIS during which cracking was seen to

propagate in neighbouring 0/90o and within the 90o mid-layer [34]. As the majority of

composite structures do not use unidirectional layups, it is necessary to fully characterise

cross-ply behaviour as well, as delamination fracture toughness of composite materials

depends on the stacking sequence of plies and their fibre direction. [35] Another reason

for testing being mainly confined to unidirectional specimens is that they appear to provide

lower (conservative) measurements of energy release rates compared to cross-ply

specimens, thus their use is of the same reasoning as the choice of Mode I as a conservative

estimate for all three modes of loading.

14

2.3.2 Cyclic Fatigue Delamination Test Standardisation

The only standard that has been published for mode I fatigue loading is the determination

of fatigue delamination growth onset [36] The focus of substantial effort in composite

fracture testing at the present time is on developing a standardised test for cyclic fatigue.

Much ground has been gained in the last 10 years on this subject; the Double Cantilever

Beam test method has been adapted for this application, with cyclic tensile loads being

applied via servo-hydraulic testing machines that apply cyclic tensile loading at speeds of

up to 10Hz. The objective of this project is to supply fatigue testing data to members of the

ESIS Technical Committee, namely A. Brunner and S. Stelzer as part of a 7 laboratory round

robin test. The mentioned names are responsible for the state of the art in this subject,

and have conducted multiple round robin tests through which some clear progress has

been made on the subject [3, 4, 5]. Among the experimental challenges faced have been

load measurement resolution, in and inter-laboratory scatter, and the choice between load

and displacement controlled testing, all of which will be discussed.

2.3.2.1 Test Control Mode (Displacement vs Load Control)

The first ESIS round robin testing on mode I delamination propagation was conducted in

2008 [4] across three laboratories. Emphasis was placed on defining test set-up,

measurement and data acquisition for application in an industrial environment. The CFRP

laminate chosen for the test was IM7 fibre, reinforced with 977/2 epoxy. The specimens

were quasi-statically precracked as per ISO 15024, and were first conducted under

displacement control, beginning at a value just under GIC obtained from quasi-static

precracking. This produces a plot of decreasing Gmax – as the applied load drops for the

same displacement, the specimen compliance increases. The definition of this initial value

of Gmax was investigated, and it was concluded that it was suitable to use the last

displacement value obtained from the quasi-static test as the maximum displacement in

the fatigue test. This produced a Gmax value approximately 90% of the GIC value, and

conveniently defined the displacement to remain fixed for the cyclic test. Testing under

displacement control results in an initially large crack rate (da/dN) that decreases as the

test progresses, following a power law distribution. After the displacement control test,

each specimen was then subjected to testing under load control. Subjecting the DCB

15

specimen to a fixed load limits the observation of delamination growth rate to relatively

high rates - the delamination continues until complete fracture of the specimen. In order

to maintain the fixed load, the crosshead displacement must increase over the course of

the test. There were a number of issues found with load control testing, as difficulty was

encountered with the choice of initial load. Values ranging from the last load value

measured during pre-cracking to around 90% of this value were investigated, however if

this value is too high, the specimen may fail before sufficient data is collected for the Paris

plot representation of the data. If the value is too low, there is the issue of test durations

being of impractical/unpredictable length. Figure 2.5 shows evidence of delamination

arrest, showing limitation in the da/dN range to about one decade for the full Gmax range

for testing in which a low value was chosen.

Figure 2-5: A comparison of displacement and load control tests. Evidence of delamination arrest can be seen in specimens B3 and B5, but not in A5, suggesting the fixed load chosen for A5 was more suitable for testing. From [4].

16

A more recent paper published by A.J Brunner et al [37], also supports the consensus that

load control is an unsuitable method of fatigue testing. To compliment the findings in [4],

it was observed that scatter tended to increase as crosshead displacement increased.

While displacement control has been shown to produce data that is reasonably well

smoothed with a power law fit, load control is not as easily smoothed. Furthermore, as the

compliance of the specimen rapidly increased towards the end of the test (before failure),

there was some difficulty in applying an accurate load. Figure 2-6 illustrates a sudden

increase in applied load that is intended to remain fixed. It is mentioned that this may be

resolved with sufficiently tuned load control settings, however the ends do not seem to

justify the means in this case, when displacement control offers a more consistently stable

alternative. Sufficiently optimising the load control settings would require further tests to

evaluate the machine settings, so difficulty arises in formulating a universally applicable

procedure as a result. Another point to note is that displacement control can allow for the

calculation of the threshold strain energy release rate Gth at which low crack growth rate

occurs – see Figure 2-3. This is an important parameter that needs to be consistently

obtainable.

Figure 2-6: Scatter and inaccurate load application in load controlled testing. From [37]

17

Figure 2-7: Comparison of the relative stability of load and displacement controlled tests, from [37]

2.3.2.2 In and Inter-Laboratory Scatter

A five laboratory round robin published in 2014 [5] investigated three different approaches

to the calculation of the strain energy release rate – simple beam theory (SBT), corrected

beam theory (CBT) and modified compliance calibration (MCC). It was found that CBT and

MCC generally observed more conservative calculations of Gmax than SBT. This is possibly

due to the lack of load block correction factors employed in SBT. It is also preferable to

incorporate the more conservative method for design purposes. A 7-point averaging

method was employed in the calculation of da/dN as described in [1]. Three methods of

obtaining the crack length a used in this calculation were compared:

1) Visual determination using a travelling microscope.

2) Use of visually obtained crack lengths in a compliance based power law fit:

𝑎 = (𝐶

𝐵)

1

𝑚′ (2.5)

Where C is the specimen compliance, and B and m’ are power law constants.

18

3) An effective crack length method, derived from corrected beam theory which back-

calculates crack lengths based on compliance data and experimental measurement of the

flexural modulus Ef, independent of visual measurement of the crack length:

𝑎𝑒𝑓𝑓 = ℎ

2(

𝐸𝑓𝐶𝑏

𝑁)

1/3

(2.6)

Where h is the specimen half-thickness, Ef is the flexural modulus, b is the specimen width

and N is a load block correction factor. The results from this method combined with MCC

calculation of Gmax showed less scatter than methods 1 and 2. The values obtained for the

effective crack length were lower than visually measured values The scatter in raw data

between the five laboratories was evaluated, and found to be significant (upwards of two

decades) in the calculation of delamination propagation da/dN and up to 21% in Gmax due

to errors in measurement. This scatter was shown to depend on the laminate used – it was

lower for CF-Epoxy and higher for the more compliant CF-PEEK specimens, and was largely

attributed to the extrapolation of the linear plot of the cube root of compliance versus

delamination length.

Figure 2-8: Comparison of effective crack length values and crack lengths obtained from compliance calibration. The lower value of aeff was suggested to be a result of the use of an average flexural modulus value, as opposed to individual specimen measurements. [5]

19

2.3.2.2.1 Data Smoothing

Data reduction was necessary to reduce scatter in da/dN – one method used that involved

deletion of data corresponding to less than a 0.1mm crack growth increment, however any

spike in the sensitive compliance data could still yield scatter in da/dN. Another means to

smooth the data was applying second order power law fit (see Figure 2.9), and only

accepting the fit if it met the arbitrarily chosen criterion of a coefficient of determination

R2 > 0.95. Using this criterion yielded lower scatter values. A major factor in the presence

of this scatter was the variation in load measurement, which could be attributed to

inaccuracy in load cell resolution (error of +/- 1.25N with an average load of 31N), and the

issue of the observer dependence of visually measured crack lengths.

Figure 2-9: The effect of data reduction on raw data, from [5]

20

2.4 Crack Shielding Mechanisms

2.4.1 Stress Ratio Effect & Crack Closure

The stress ratio, or R-ratio, is the ratio of the maximum to the minimum crosshead

displacements during fatigue loading. It is well documented that the R-Ratio has an effect

on the position on the Paris plot – testing with higher R-ratios results in a higher fracture

surface roughness and a resulting higher calculation of the SERR, as determined

experimentally and by SEM fractography [38]. Considering this, the choice of a low R-Ratio

(0.1) is logical as it will provide conservative curves. It has been proposed by Ras et al [39]

that the effect of stress ratio can effectively be removed by use of an effective strain energy

release rate (see Equation 2.4). ESIS round robins have decided upon a compulsory fixed

R-Ratio of 0.1 across all current round robin tests [37].

The fibre-epoxy interface comprises of a number of effects that need to be considered in

order to have complete understanding of delamination growth. One such effect is a

plasticity zone wake ahead of the crack tip, known in metals as crack closure. It is the

general opinion that crack closure is the primary cause of the stress ratio effect. This is a

crack shielding phenomenon, where the crack driving force (in this case SERR) actually

experienced at the crack tip differs from the applied driving force [40]. This effect on mode

I fatigue loading has been experimentally investigated by Khan et al [41] using a

compliance-based technique. Crack closure was shown to reduce the cyclic load amplitude

by increasing the effective minimum load at the crack tip, however it was stated that crack

closure is not the only cause for the stress ratio effect, but that it is also due to an increase

in cyclic energy, ΔU.

ΔU = 1

2(𝐹𝑚𝑎𝑥𝛿𝑚𝑎𝑥 − 𝐹𝑚𝑖𝑛𝛿𝑚𝑖𝑛) (2.7)

This is consistent with that given in [28] where Jones et al. showed that the effect of stress

ratio can be accounted for by examining the change in SERR relative to its threshold value

– implying that crack closure does not need to be examined to obtain a master curve for

21

delamination propagation. This can be represented by a variant of the Hartman Schijve

equation, which will be discussed in Section 2.5. Results from other studies have also

shown similar stress ratio effects, however significant degrees of plasticity were not

observed, supporting the opinion that this stress ratio effect cannot be fully explained by

crack closure.

2.4.2 Fibre Bridging

The nesting of fibres between adjacent plies is a phenomenon known as fibre bridging. It

is another important mechanism in fatigue delamination testing, and is responsible for a

decrease the crack growth rate as the delamination length increases. The fibres absorb

some of the strain energy, and their contribution to the R-Curve generally manifests itself

as an increase in SERR after the onset of crack growth in quasi-static testing. This does not

provide detailed information on the contribution of fibre bridging to the stresses

experienced at the crack front, however. The R-Curve depends on specimen geometry,

and thus cannot be seen as a material property. It is difficult to fully characterise the

bridging phenomenon, and the exact contribution of fibre bridging to delamination growth

resistance calculations in experimental testing is the topic of a sizeable amount of research.

Literature is available on modelling of composite fracture with bridging using cohesive zone

and bridging models [42], which is beyond the scope of this discussion.

Figure 2-10: Fibre Bridging as a shielding mechanism in CFRP composite. From [43]

22

Regarding experimental research, attempts have been made to use quasi-static results to

normalise the contribution of bridging in fatigue loading [44,51], however this has been

disputed by Yao et al. [43], who observed that there is a distinct difference between the

contribution of fibre bridging due to fatigue and its effect on quasi-static loading. This was

observed by means of a specific test procedure to distinguish the two. A DCB specimen was

fatigue tested under displacement control several times at the same R-Ratio until the

delamination growth rate had decreased with decreasing SERR to a near-asymptotic value.

Each subsequent test was conducted at an increased displacement until the capacity of the

test machine was reached. This procedure allowed for multiple delamination resistance

curves corresponding to different precrack lengths to be obtained. Another specimen was

then quasi-statically precracked to the same delamination length, and the results from

both tests were compared. The results indicated that the amount of bridging depends on

loading type, and thus quasi-static results should not be used to normalise fatigue results.

Figure 2-11: Different damage from quasi-static and fatigue delamination. Specimens consisted of a 0//0 plie interface with 50mm precrack length. From [50]

23

The same publication found that the delamination growth curve depends on initial

delamination length, stating that the contribution of bridging increases as the delamination

surface contact is increased between tests. Yao presented fatigue experimental data in a

new format as da/dN vs dU/dN, and the author stated that in this format, bridging fibres

actually have little permanent contribution to SERR, but rather periodically store and

release strain energy upon loading and reloading. It was suggested that only in the case of

fibre failure or pull-out that strain energy is permanently released. In this format the

derivative of strain energy with respect to the number of cycles is:

𝑑𝑈

𝑑𝑁=

𝑑𝑈

𝑑𝑎

𝑑𝑎

𝑑𝑁 (2.8)

In this case dU/da represents an average rate of strain energy release Gav, which is not the

same as the calculated SERR. [46]

Figure 2-12: Correlation between rate of cyclic energy release and crack growth rate on a linear scale. Data from [43], presented in this form in [46]

24

2.4.3 Describing shielding mechanisms individually

The use of SERR in characterising a number of complex mechanisms together introduces

difficulty in understanding the crack extension alone, as well as the behaviour of individual

shielding mechanisms. As an alternative approach the investigation and establishment of

a fatigue delamination prediction model based on the correct energy balance has been

advised. Relating to the aforementioned work by Yao on fibre bridging [43, 47] and the

work of Pascoe on cyclic strain energy [45] it has been recommended by Anderlieson et al.

[46] to separate the SERR into terms describing shielding mechanisms individually – for

example using Ga = dUa/da to relate only to crack extension, and GPL = dUPL/da to relate to

plasticity formation. By separating the terms, the crack extension due to Ga could then be

tied to a single material characteristic.

2.5 Delamination Growth Representation

2.5.1 Threshold Behaviour

As seen in Figure 2-3, the fatigue crack propagation threshold defines a loading criterion

below which significant crack growth will not occur. From an engineering design

perspective, the logical approach is to avoid subjecting a material to loading above

threshold values in the interest of prolonging the service life of a component. Near-

threshold crack propagation is generally defined as taking place at crack growth rates

below 10-9 m/cycle [48]. In practical terms, if the slope in the near-threshold region is lower

there is more time in which to inspect a component for the onset of crack growth. In

addition, if this slope is lower it is easier to describe growth behaviour, because errors in

the load applied will lead to small errors in the calculation of da/dN. In order to have

complete understanding of fatigue delamination (or fatigue crack growth in any structure)

it is important to understand threshold behaviour. This is a benefit of the use of

displacement control testing in which G decreases towards an asymptotic ‘zero slope’ that

indicates the threshold value, Gth. As shown by results of ESIS round robins, no definitive

threshold value has been obtained despite testing of over 19 million cycles, which

25

corresponds to 22 days of testing at 10Hz. Specimen compliance was still observed to

increase past this point [4].

2.5.2 A Variant of the Hartman Schijve Equation

When Paris law power relationships between the strain energy release rate and the

delamination growth rate can involve a very large exponent – denoted m in equation 2.3.

It is not uncommon to observe a value higher than 10 for this exponent. This means that

any error in the applied load can lead to very large error in the calculated crack growth

rate. Composite materials’ inhomogeneous nature means that there are inherent small

sub-mm defects that can be the cause of such load measurement errors. This has resulted

in the ‘no-growth’ design approach currently applied to composite structures, which has

forced the use of high safety factors and excessively heavy structures as a result. R. Jones

et al [49, 50] have recently proposed an alternative to the Paris power law representation

in the form of a variant of the Hartman-Schijve equation. This equation suggests a

relationship between the extent to which the crack driving force exceeds its threshold

value, ΔK – Kth and the delamination growth rate increment da/dN. Its variant for

composites can be found below:

𝑑𝑎

𝑑𝑁= 𝐷 (

√𝐺𝑚𝑎𝑥−√𝐺𝑡ℎ

√1−√𝐺𝑚𝑎𝑥−𝐴

)

𝛽

(2.9)

Here the constant exponent β is between 2 and 3, significantly lower than those found in

power law representations based on Paris’ law. Gmax is the SERR corresponding to the

maximum cyclic load, Gth is its threshold value, D is a proportionality constant related to

the flexural modulus, and A is seen as a toughness parameter. In [58] this was taken as the

value of GIC obtained during quasi static testing. The term inside the brackets in equation

2.9 correlates linearly on a log scale with da/dN, and the Hartman-Schijve variant appeared

26

to provide a good fit not only for mode I loading conditions, but for mode II and mixed

mode II/III. The values of D and β also appeared to be independent of mode.

Figure 2-13: Linearity of the Hartman-Schijve representation of ESIS TC4 round robin data From [49]

A recently published paper by Jones et al [28] has shown that the Hartman Schijve equation

is capable of collapsing experimentally measured data onto a single linear ‘master’ curve,

regardless of R-Ratio. The approach has also shown potential for reducing the previously

mentioned effect of initial delamination length on the growth curve, which was

investigated by Yao et al [43]. The use of the term 𝛥√𝐺 (Equation 2.4) was suggested as a

unifying and valid term for the crack driving force, showing promise in allowing the Federal

Aviation Administration (the national aviation authority of the United States) to reliably

certify composite and adhesively-bonded designs.

27

This would allow for evaluation of delamination damage tolerance of in-service aircraft,

and alleviation of the no growth design approach to composite materials as it currently

stands.

Figure 2-14: Stress ratio-independent Hartman–Schijve representation of delamination growth in DCB tests using a unidirectional composite laminate.

28

3 Materials and Methods

This chapter will first discuss the properties of the carbon fibre reinforced polymer used,

followed by the procedures followed in the manufacture of double cantilever beam

specimens from a prepreg roll. It is then appropriate to provide theory for the analysis of

double cantilever beams under mode I loading, in preparation for the proceeding sections

detailing the procedures for quasi-static interlaminar fracture toughness testing, cyclic

fatigue delamination testing and flexural modulus measurement.

3.1 Materials

3.1.1 Carbon Fibre Prepreg

When a thermoset epoxy resin is impregnated into fibres such as carbon or glass in an

uncured state, this is referred to as a prepreg material. Prepregs are commonly used in

aircraft structures, and constitute over 50% of the airframe of the Boeing 787 aircraft. An

epoxy matrix supports the fibres, maintaining their correct plie orientation and ensuring

load transfer to them. The matrix consists of a toughened epoxy resin, curing agents and

additives such as tougheners, accelerators to reduce cure time, and flame retardants.

Prepregs are supplied in single fibre layers in roll form.

The manufacture of composite specimens for this project involved the use of a high

strength Hexply© 8552/AS4 (carbon/epoxy) material. Hexply 8852 is a toughened epoxy

resin which is combined with carbon fibres of unidirectional plie orientation. Hexcel

recommends the use of this epoxy matrix in structural applications where high strength,

stiffness and damage tolerance are required. The 8552/AS4 carbon fibre prepreg was

supplied by Bombardier in 50m rolls. This material contains a nominal fibre volume of

57.42%. Due to the unidirectional nature of the plies, the mechanical properties of this

prepreg are anisotropic. At room temperature this material typically has a 0° tensile

modulus of 130-140 GPa (in the direction of the plie orientation), and a 90° tensile modulus

of 10 GPa. The curing temperature of the prepreg is 180°C. [53]

29

3.1.2 Storage

The storage temperature of this material should be kept low to prevent premature curing

of the epoxy. The roll was stored in a freezer at -18°C, sealed in a plastic bag. Allowing the

roll to lie flat for long periods of time is to be avoided. Prior to commencing the layup

process, the appropriate number of layers were cut from the roll and allowed to thaw

overnight in a sealed plastic bag. The bag was allowed to reach room temperature before

it was opened – keeping the prepreg above dew point temperature of air is important to

avoid moisture contamination, as literature has shown that this can significantly reduce

joint strength. As suggested by Parker [54], effects of pre-bond moisture present in the

manufacture of adhesively bonded composite joints can include voiding, a plasticising

effect on the adhesive used, and a reduction in the strength of the interfacial adhesion .At

room temperature (23°C, 55% RH), carbon-fibre reinforced epoxy laminates are capable of

absorbing 0.5-1% w/w of atmospheric moisture. Regarding the effect of prepreg storage

humidity, literature presents findings that suggest that fracture toughness under mode I

and II loading decreases as humidity increases. [55]

3.2 Manufacture of Specimens

Over the duration of the project, two prepreg composite layups were completed in order

to produce double cantilever beam specimens for fracture toughness testing, and to

become proficient in fatigue testing in anticipation of the arrival of ESIS round robin

specimens. This section will provide a detailed account of the manufacturing procedure

that was followed. The procedure followed is as recommended by Hexcel, and has been

developed for application in UCD by Dr Joseph Mohan who has written a comprehensive

thesis on composite-to-composite bonding. [56]

3.2.1 Layup Procedure

28 layers measuring 200 x 300mm were cut from a prepreg roll directly after removing it

from a freezer. The layers were placed into a sealed plastic bag and left to defrost

overnight. With the prepreg at room temperature, 13 layers* of the prepreg were laid

30

down on a protective sheet of PTFE film on the base plate of the aluminium mould. A layer

of non-adhesive Teflon film insert of thickness 13μm measuring 65 x 300mm was then

placed on the 13th layer of prepreg. This introduces an intentional weakness in the layup at

that point that inhibits adhesion, allowing the specimen to be centrally pre-cracked from

the insert during testing. The insert was placed with its edges protruding from the edge of

the layup, so that it could be easily identified after curing. The 65mm insert length was

chosen to accommodate the longer insert requirement associated with fracture toughness

tests – the length of the sample was reduced to then accommodate the shorter insert

length used in fatigue testing. The remaining 13 layers were then laid down as before, and

another layer of PTFE film was placed on the top. Breather fabric was placed down to cover

this and the two vacuum holes in the baseplate, in order to enable the vacuum. Sealant

tape was then laid around the layup and the vacuum holes, and a sheet of bagging film was

placed around the sealant tape. A vacuum was applied via a plastic hose through a brass

fitting to the layup, and was checked for any leaks between the film and the tape. The

vacuum was applied for 45 minutes. The debulking process squeezes out air and any

volatiles that may be present in the layup, preventing the development of an uneven

surface, and promoting optimal adhesion.

Figure 3-1: Debulking Layup

Vacuum

Aluminium Baseplate

Prepreg containing insert PTFE Film Bagging Film Sealant Tape Breather Fabric

31

* This corresponds to a thickness of approximately 4mm. To produce a thickness of 3mm

similar to that of the supplied ESIS specimens, fewer layers should be used.

3.2.2 Curing Procedure

After the completion of debulking, a layer of release film was placed on either side of the

prepreg. This is a slightly porous material that allows for just air and volatiles to pass

through it. An edge dam was placed tightly against the prepreg in order to prevent any

undesirable flow of resin from the layup during curing. A layer of PTFE film was placed

under the bottom layer of release film, and above the top layer to protect the reusable

materials. A rubber caul pad was placed down next to assist in giving a good distribution of

pressure on the layup, also protected on either side by PTFE film. Above this, breather

fabric was placed. The bagging film was placed above this and pressed against the sealant

tape. A layer of outer sealant tape was then placed around the outside of the baseplate.

The top lid was placed on the baseplate, making contact with the outer sealant tape. As

compressed air was later applied through the top lid, it was important to ensure a good

seal was present.

Figure 3-2 Curing Layup

32

The plate was inserted into the pressclave with the brass inlets for the vacuum and

compressed air application facing forward. The press was then lowered until it was

touching the plate. The vacuum tube was attached to the baseplate, and the compressed

air tube was attached to the top lid fitting. The program controlling the thermocouples was

initiated, and the pressure was increased slowly to 500kg.The vacuum was turned on, and

the compressed air was increased over 15 minutes to 6 bar. If the air pressure is increased

too quickly there is the possibility that the seal between the top lid and baseplate can

break.

The pressclave is heated by 4 thermocouples which are connected to the back of the

aluminium mould – two in the top lid and two in the bottom lid. The thermocouples were

programmed to ramp up to 110°C over a period of 30 minutes, to maintain at this

temperature for an hour, to then increase to 180°C over 40 minutes and dwell for 2 hours

before turning off, allowing the mould to cool. Upon reaching 80°C the 500kg load was

relieved, and the air and vacuum inputs turned off. Figure 3-2 below shows the cure cycle

used, with an approximated cooling time shown.

Figure 3-3: Cure Cycle

0

100

200

300

400

500

600

0

20

40

60

80

100

120

140

160

180

200

0 100 200 300 400 500

Load

(kg

)

Tem

per

atu

re (

°C)

Time (minutes)

33

When the mould had cooled to room temperature, compressed air at 2 bar was applied,

and a chisel was used to pry the mould open. This is best achieved by using a Stanley blade

to cut along the outer sealant tape. Once the layup was removed, the mould was then

cleaned using a scraper and mould release spray.

3.2.3 Machining of DCB Dimensions

Machining of composite specimens requires extensive protective equipment, as carbon

fibre dust is harmful to inhale, and irritating to the skin. Full overalls, a full face ventilator,

ear protection and 2 pairs of latex gloves taped around the sleeves of the overalls were

used. Before cutting the specimens the occupiers of the next room were notified and the

extractor was turned on. At the edge of the layup on each side for up to 15mm there is an

uneven section where not all of the layers were placed evenly. This was marked and cut

using a diamond saw of blade width 2.5mm to ensure that only DCB specimens of uniform

thickness were produced. 9 specimens of width 25mm and length 150mm were produced

in the first manufacturing session. It should be noted that in fatigue testing where the

objective is observing threshold behaviour (crack growth rate lower than 10-6 mm/cycle) a

longer specimen length than 150mm will assist in achieving this. The length of the received

ESIS specimens was 185mm. In the second manufacturing session, specimens of 20mm

width were produced to emulate the dimensions of the ESIS samples. The thickness of the

specimens was ~4.1mm.

Figure 3-4: Left: Marked layup before machining. Right: Machined DCB specimen

34

3.2.4 Preparation of DCB Specimens

Each DCB specimen was polished on the sides using sand paper to produce a smooth

surface upon which correction fluid was applied to easily identify the crack length during

testing. For the first round of tests, aluminium load blocks of 25x25x25mm were attached

to samples of 25mm width. ISO 15024 recommends 15mm as the maximum value of l3 (see

Section 3.3) so 10 load blocks of 20x20x15mm were machined from an aluminium beam

for the second round of tests, where the recommended width of the DCB specimens is

20mm. A hole of 6mm diameter was machined through the centre of the 15x20mm face.

The load blocks were abraded slightly and attached using a tough room temperature cure

glue and were weighed down and allowed to cure over a period of a few hours.

35

3.3 Theory for Beam Analysis

This section provides details on three methods of calculating the strain energy release rate

providing theory for the proceeding quasi-static and fatigue testing methodologies. The

three methods, which are detailed in ISO 15024 for quasi-static determination of GIC [1],

are also used in the calculation of G in the fatigue testing protocol draft (October 2015)

written by Brunner et al. of ESIS TC4 [57]. A method to back calculate the flexural modulus

is also described.

3.3.1 Simple Beam Theory

This section will cover beam theory proposed by Williams [63] to calculate the strain energy

release rate, G, for fibre reinforced polymers in mode I loading conditions. Provided the

bond gap is small, it can also be applied to adhesive joints. The Mode I fracture toughness

can be calculated using the double cantilever beam (DCB) test. The DCB specimen is a

centrally cracked beam, symmetrically subjected to tensile loading by means of adhesively

bonded load blocks in this case, but piano hinges may also be used.

Figure 3-5: Double cantilever beam specimen with load blocks. From [1]

36

The strain energy release rate G, is the sum of its mode I, II and III components. Its critical

mode I (opening) component, GIC , for a double cantilever beam is given below, calculated

using simple beam theory:

𝐺𝐼𝐶 =𝑃2

2𝐵

𝑑𝐶

𝑑𝑎 (3.1)

Where:

𝑑𝐶

𝑑𝑎=

8

𝐸𝐵(

3𝑎2

ℎ3 +1

ℎ) (3.2)

Therefore:

𝐺𝐼𝐶 =4𝑃2

𝐸𝑓𝐵2 (3𝑎2

ℎ3 +1

ℎ) (3.3)

Where:

𝐺𝐼𝐶 = Mode I critical strain energy release rate

P = Load (N)

a = Crack length (m)

C = Compliance (δ

𝑃) (m/N)

δ = Crosshead displacement (m)

Ef = Flexural Modulus, determined experimentally by a three-point-bend test

B = Specimen width (m)

h = Specimen half thickness (m)

37

3.3.2 Corrected Beam Theory

Simple Beam Theory does not take into account effects of the experiment that can

influence the parameters used to calculate the G. Williams [32] derived correction factors

to account for this. The first of these effects takes the shortening of the moment arm.

The moment applied by the beam arm is shorter than the measured distance from the

crack to the load line; due to the bending of the beam arm, the perpendicular distance

from the load line to the crack is reduced. This can be seen in Figure 3-6, where a is

corrected to a’. The large displacement correction factor F takes this into account:

𝐹 = 1 − 3

10(

𝛿

𝑎)

2

− 3

2(

𝛿𝑙1

𝑎2) (3.6)

The second correction factor takes into account the stiffening effect that the load blocks

have on the arms of the beam:

𝑁 = 1 − (𝑙2

𝑎)

3

−9

8[1 − (

𝑙2

𝑎)

2

] [𝛿𝑙1

𝑎2 ] −9

35(

𝛿

𝑎)

2

(3.7)

Where 𝑙1 is the distance from the load line (the centre of the load block) to the centre of

the beam arm, and 𝑙2 is the distance from the centre of the load block to its edge.

38

Figure 3-6: Corrections applied to correct for assumptions of simple beam theory

The third correction is to account for beam root rotation. Simple beam theory assumes

that the beam arm is perfectly built in, however shear deformation occurs at this point.

The correction factor |∆| can be calculated by plotting (C/N)1/3 vs a, and taking the x-axis

intercept of the line of best fit, as seen in Figure 3-7.

Figure 3-7 Linear fit to calculate the correction ∆ in corrected beam theory. The VIS initiation point may be excluded from this fit. See Section 3.4.4 for initiation points.

39

The critical strain energy release rate using corrected beam theory can therefore be

calculated by:

𝐺𝐼𝐶 =3𝑃𝛿

2𝐵(𝑎+|∆|)

𝐹

𝑁 (3.8)

3.3.3 Modified Compliance Calibration

Modified Compliance Calibration (MCC) is a method that involves plotting the width-

normalized cube root of the compliance (bC)1/3 , or in this case (bC/N)1/3 due to the use of

load blocks, as a function of the thickness normalized crack length a/2h. The slope of this

graph is m.

𝐺𝐼𝐶 =3𝑚

2(2ℎ) (

𝑃

𝐵)

2

(𝐵𝐶

𝑁)

2/3

𝐹 (3.9)

A travelling microscope is used to measure the crack length a, and compliance values based

on the load and displacement values corresponding to each crack length allow for the

creation of the MCC plot. Once the slope and intercept of this plot are established,

continuous load and displacement values throughout the test can be used to calculate GIC

at any point in the load-displacement curve.

40

3.3.4 Back-Calculated Flexural Modulus

As a means of checking the validity of the test, the flexural modulus can be back-calculated

from experimental data. If it is found to change significantly, it is an indication that the

beam arms are experiencing plastic deformation, invalidating the test. It is calculated as

follows:

𝐸𝑓 = 8(𝑎+|∆|)3

𝐵ℎ3 𝑁

𝐶 (3.10)

3.4 Mode I Fracture Toughness Test

A delamination fracture toughness test was carried out as per ISO 15024 [1] on 3 DCB

specimens. There are a number of benefits of carrying out this test in a project primarily

concerned with delamination fatigue testing. Obtaining the critical strain energy release

rate GIC allows for comparison with the rate at which G reduces over the course of fatigue

testing. Attempts have been made in literature to normalise the bridging effect in fatigue

testing using results from such quasi static tests [44, 51].

3.4.1 Preparation

Prior to testing, each specimen was marked at 5mm intervals for a length of 50mm beyond

the insert tip. Additionally, each specimen was marked at 1mm intervals in the first 10mm,

and the last 5mm. A Hounsfield tensile test machine was used for the fracture toughness

test, employing a 10kN load cell. The test involves applying a crack opening load to a DCB

specimen, applied perpendicular to the delamination plane under displacement control –

the rate of change of crosshead displacement was kept constant.

41

3.4.2 Precracking

The load cell of the Hounsfield testing machine was calibrated prior to placing the DCB

specimen in the grips, and the specimen was loaded at a crosshead displacement speed of

1mm/min, to a delamination precrack length of 3-5mm. The load and crosshead

displacement were continuously recorded during this time. A travelling microscope was

used to monitor the crack growth. An Excel macro file with a timer built into it was used to

note the time at which each 1mm delamination increment occurred. This file is used

together with the known crosshead displacement speed to calculate the applied load at

each delamination length. The timer and the test were started simultaneously. Once the

precrack length was reached, the specimen was unloaded at a rate of 25mm/min.

3.4.3 Re-Loading

The specimen was re-loaded at the same crosshead displacement speed, and the excel file

was used to note the time at each marked increment, as before. The specimen was

unloaded after the crack had propagated the desired 50mm beyond the tip of the insert.

Figure 3-8: Double cantilever beam mounted on Hounsfield tensile testing machine

42

3.4.4 Initiation Points

The load displacement curve obtained from this test was used to obtain several initiation

points, which are defined below. An indication of typical locations of such values can be

seen on a load displacement curve in Figure 3-9.

VIS - Point at which there is visual confirmation of crack propagation. This was noted during

the test by visual inspection with the microscope.

NL - Non Linearity onset, the point at which the linear region ceases to behave linearly. A

section in centre of the linear region of the load displacement curve was selected, and a

line of the same slope was created. It is usually the point at which the lowest value of GIC

occurs, and can be seen as a conservative estimate By taking the difference between this

new line and the curve, its point of onset of non-linearity can be determined. The standard

states to choose a consistent criterion, a value at which it is decided that the curve is no

longer linear. In this case, a deviation of +/- 0.5N was chosen to the NL point. Results from

a round robin [58] suggest that the determination of this value is quite operator

dependant, with approximately 10% variation.

C0 + 5% - The point at which the specimen compliance has increased by 5% from its initial

value. By taking a line of 5% greater compliance than C0, it is located at its point of

intersection with the load displacement curve.

Max – The maximum force applied to the specimen. In some cases the NL point has been

seen to coincide with this value, when stick-slip behaviour is observed.

GIC was calculated using simple and corrected beam theory [See section 2.3] for the

initiation and propagation points discussed above.

43

.

Figure 3-9: Load-displacement curve, where: 1- Crack initiation followed by unloading 2- Crack propagation 3- Crack propagation markers

44

3.5 Fatigue Testing

This section will cover the preparation undertaken to conduct fatigue delamination testing

under displacement control, and the test procedure followed. This includes the operation

of the Instron 8502 Servo hydraulic testing machine and associated software packages,

preparation and modification of fixtures used, the use of a 5kN load cell and associated

issues, the use of a 250N load cell, and the fatigue testing procedure itself, which follows a

draft protocol prepared by A. Brunner, S. Stelzer and G. Pinter [57].

Figure 3-10: Fatigue testing of a double cantilever beam specimen

3.5.1 Instron 8502 Servo Hydraulic Test System

Servo-hydraulic systems are capable of performing a wide range of low and high cycle

fatigue tests. This 8502 system operates by attaching a load cell to the upper grip and

keeping its position fixed, and the motion of the lower grip is controlled. The system

45

requires a flow of coolant supplied by a coolant tower through pump. This system uses

approximately 50kW of power regardless of the test being conducted. Due to its high

running cost, there is talk of the introduction of a new more efficient system.

3.5.1.1 Actuator Performance

The performance of the actuator for each particular test depends on the proportional-

integral-derivitive controller (PID) settings of the machine. This controller continuously

calculates the difference between a desired setpoint (load or displacement, for example)

and the measured value of that variable. It then attempts to minimize this error to achieve

the desired setpoint with as little deviation as possible. Manual tuning is required,

particularly in the case of load control tests where the system requires an indication of how

the test material behaves so that it can efficiently and accurately reach the desired load.

Tuning involves adjusting Kp, Ki and Kd– proportional, integral and derivative gains

respectively to achieve the desired balance of rise time, overshooting and settling of the

response variable [59]. The figure below shows effects of varying these parameters.

Figure 3-11: Tuning of the PI controller. From [60]

46

It is obvious that in the case of a load control test, overshooting the desired load is a major

concern. This project involves subjecting a DCB specimen to a displacement control cyclic

loading, so the system’s ability to consistently and accurately achieve the desired

amplitude at as high a frequency as possible is of importance in this case. The system was

found to contain a clear upper limit on the amplitude that it was capable of achieving

depending on the frequency – essentially testing could not be conducted at frequencies

above 5Hz due to compromises in amplitude as well as accuracy. Testing was conducted to

determine the frequency achievable by the machine in order to prevent the invalidation of

specimens due to incorrect amplitude application. Table 3-1 presents the capabilities of

the machine at the time of writing.

Table 3-1: Amplitude capability of Instron 8502

Frequency (Hz) Max Amplitude (mm) Error (mm)

3 0.83 0.02

4 0.765 0.02

5 0.675 0.02

3.5.1.2 Fixture Preparation

The fixtures used consist of simple steel grips each containing a 6mm diameter hole, the

same diameter as the load blocks. The load blocks are secured to the grips with a pin. The

pin was sanded so that it allows rotation of the load block, but provides a tight enough fit

to avoid any free movement of the load block. Such movement would introduce

unfavourable dynamic loading of the specimen. In early testing, a large upper fixture was

used, which was 50cm in length and 2kg in weight. It had previously been used to allow

specimens to be heated before testing. It was apparent after the first fatigue test that the

size and mass of this grip had a negative inertial effect on the loads experienced by the

specimen, as the results produced by the tests were inconsistent and scattered. It was

subsequently replaced by a smaller, lighter upper fixture. Reduction in the mass of the

upper grip has been suggested as a means of reduction of inertial effects in an application

report produced by Instron. [61]

47

Figure 3-12: Dissatisfactory upper fixture, subsequently replaced by the lighter, shorter fixture to its right.

3.5.2 Load Cells

A load cell is a transducer that outputs a voltage proportional to the force it experiences.

Two load cells of different ratings were used to measure the load exerted on the DCB

specimens during the course of this project. The load signal has a large impact on scatter

present in results, therefore a lower capacity load cell was employed for round robin

testing.

3.5.2.1 5 kN Load Cell

Early testing was conducted using an Instron 2518-103 load cell with a +/- 5kN dynamic

capability. The accuracy rating of this load cell is equal to 0.025% of the cell rated output.

This implies that there is approximate error of +/- 1.25 N associated with each data point,

which is a significant in fatigue testing where load measurement can be as low as 20N, and

small decreases in the measured load are important.. A thermal drift was discovered in

the load cell at the beginning of fatigue testing, in which both Pmax and Pmin began to

significantly drift after approximately 5000-10000 cycles. This is possibly due to the load

cell becoming damaged in recent years, resulting in a fault that is easy to discover in

displacement control testing with low loads. It's worth noting that the displayed load in

48

load control tests using this load cell may not be accurate as a result of this - despite its

displayed value remaining constant. Both load measurements drifted with the same slope,

so an attempt to correct the thermal drift was made by making an approximated

assumption that the minimum load should remain roughly constant - therefore the

adjusted value of the maximum load could be obtained by:

Pmax_adjusted = Pmax - Pmin (3.11)

Where:

Pmax_adjusted is the new adjusted value of Pmax to be used in data analysis. Although Pmin is

generally observed to decrease over the course of the test, the most reasonable

approximation for this purpose is that it remains at zero. This is supported by results using

the 250N load cell, showing minimum values ranging from 3 to -2N. When the initial value

of Pmin is higher, it was assumed to remain at that value.

3.5.2.2 250N Load Cell

A new 2527-131 load cell rated +/- 250N was ordered from Instron during this project,

where its improved accuracy was used for the testing of the ESIS specimens. It was

mounted via an M6 hole in both the top (inactive) and bottom (active) sides. The top fitting

was attached to the 5kN load cell, which was left mounted on the machine. To attach the

upper grip to the active side, an M6 hole was tapped into the fixture, and it was secured to

the load cell carefully with a bolt. Unfortunately the load cell became damaged during

testing – in spite of the limits being set on the machine, the load cell can suddenly undergo

relatively large compressive loads when placing the bolt through the load block without

the awareness of the user. Two of the five ESIS specimens were tested using this load cell,

and as a result of this irreparable damage the remaining three were tested using the 5kN

cell, data from which did not contribute to the round robin.

49

3.5.3 Fatigue Testing Protocol The fatigue testing protocol was written by Andreas Brunner and Steffen Stelzer, members

of the ESIS TC4 Committee and co-ordinators of the round robin testing. The goal of this

procedure is to move towards establishing a standard testing method to compare the

mode I fatigue delamination behaviour of different unidirectional composite laminates.

Doing so will allow for further research into different matrix formulations, and the

establishment of critical energy release rates for use in structural design. The protocol is

intended to produce a standardised test that runs for a minimum of 8 hours per specimen,

and generally intended for test durations of less 24 hours in duration for practical reasons

in industry. That said, observation of threshold behaviour is an optional component of this

procedure – the behaviour of the material as the crack growth rate slows to under

10-6 mm/cycle.

3.5.3.1 Quasi Static Mode I Precracking

As per ISO 15024, a precrack was prepared at a fixed crosshead speed of 1mm/min. The

precrack length was stopped before a delamination length increment of 3-5mm was

exceeded. The procedure aims at keeping the precrack length under 30mm from the load

line, however a crack too close to the load line increases the stiffening affect on the beam

arms. With this in mind, the load blocks were placed so that the load line was 25mm from

the tip of the insert – after precracking, this produced a crack length of 28-30mm. The

crosshead displacement value at this point was noted and the specimen was unloaded, but

not removed. The crosshead displacement display on the console was closely monitored

during testing to ensure no deviation from the desired displacement values.

3.5.3.2 Fatigue Testing

The last crosshead displacement value from the quasi static precrack was taken as the

maximum displacement for the fatigue test, and is denoted δmax - See Figure 3-13. An R-

Ratio of 0.1 was used, which is the ratio of the maximum to the minimum displacements:

δmax / δmin = 0.1.

50

Figure 3-13 Obtaining the maximum displacement to be used in fatigue testing

A cyclic fatigue test was conducted at 5 Hz beginning at the mean displacement, and

continued until a crack growth rate of 10-6 mm/cycle was reached, at which threshold

behaviour is observable. The mean displacement is found by

δmean = δmax+ δmin

2 (3.12)

As previously mentioned, the Instron 8502 when testing at 5 Hz is limited to producing an

amplitude of approximately 0.675mm at the time of writing. This implies that the

maximum value of δmax that can safely be used is approximately 1.5mm, above which the

test would have to be conducted at a lower frequency. A compromise needed to be found

between precrack lengths from the load line and test frequency - a shorter precrack allows

for a faster test as it enables a higher frequency to be used, however it also increases the

stiffening effect due to the load blocks. In any case, a crosshead displacement higher than

1.8mm (the upper limit for 3 Hz at R=0.1) would not be possible due to time constraints in

the project. Should a displacement of such a magnitude be found, it is advisable to reduce

the precrack length.

δmax

51

Figure 3-14: Fatigue testing of ESIS Specimen. Elastic bands were used to ensure that slippage of the pins did not occur

The test was stopped at mean crosshead displacement at least 5 times between 0 and

100'000 cycles ( e.g. 1000, 5000, 10'000, 20'000, 30'000, 50'000 cycles) and at least 5 times

between 100'000 and 1'000'000 cycles to visually measure the crack length a using an

optical or digital microscope. A digital microscope was beneficial for observing crack

growth that was difficult to track. Stopping the test for a short period at this crosshead

displacement has no effect on crack growth, however leaving the specimen in this state for

a prolonged period of time may affect the crack length and load measurement, and is thus

better avoided. Pmax and δmax were recorded for the last cycle before each planned stop.

The loads Pmax, Pmin and displacements δmax and δmin were recorded for each cycle for one

specimen, and for every 100 cycles for the remaining specimens.

52

3.5.4 WaveMatrix Dynamic Testing Software

The Instron 8502 is an 8800 retrofit, which upgrades the systems digital electronics and

enables use of the WaveMatrix and BlueHill 2 software. WaveMatrix is a flexible material

testing software system that allows both static ramps and cyclic waveforms to be

generated. It displays the stages of each test in a graphical form - clearly showing static

ramp stages and cyclic loading stages. A program was written for use in this fatigue test

that consists of 2 static ramping stages proceeded by a number of cyclic load stages that

depends on the number of intended pauses in the test. The waveform starting phase was

set to a 0o sine wave. A summary of the procedure followed can be found below.

Table 3-2: Summary of WaveMatrix program

Stage Name Action Data

Recorded

How Often Data

is Saved

Static Ramp to δmin Displacement checked on console. N/A N/A

Static Ramp to δmean Displacement checked on console.

Crack length visually measured for

N = 0 cycles.

a N/A

N = 1 - 1000 Cyclic loading at 5 Hz , then pauses

at δmeanto allow for visual crack

length measurement.

Pmax,Pmin,δmax,

δmin, N, a

Every 10 cycles

N = 1001-5000 " " Every 100 cycles

N = 5001-10000 " " "

N = 10001-20000 " " "

... " " "

N = 900001-1000000 " " "

Static Ramp to δ = 0mm End of test None N/A

53

During the running of the test, the sine wave indicating the measured displacement was

visible, and a load-displacement curve was displayed. The displacement sine wave was

checked to be sure that the correct amplitude was consistently being applied during the

test.

Figure 3-15: Visual representation of ramping stages, followed by cyclic waveform generation for a sample maximum displacement of 1mm, at an R Ratio of 0.1.

3.5.5 Methods of Crack Length Determination

As previously mentioned, the crack length is determined visually at several planned stops

in the test. The compliance data is be used to back-calculate the crack lengths in between

the visually determined lengths using the load and displacement values that were

continuously recorded:

𝑎 = (𝐶

𝐵)

1

𝑚 (3.13)

Where C is the specimen compliance, B is the intercept of the MCC plot, and m is its

slope. Another method by which the crack length can be determined, as mentioned in

Section 2.3 is the ‘effective crack’ method, which uses a measured value of the crack

length to calculate the crack length corresponding to load and compliance data.

54

This method is independent of visual measurement, and thus has potential to reduce

scatter by eliminating the need to stop the test. The effective crack length is calculated by

the following:

𝑎𝑒𝑓𝑓 = ℎ

2(

𝐸𝑓𝐶𝑏

𝑁)

1/3

(3.14)

Where h is the specimen half-thickness, Ef is the flexural modulus, b is the specimen

width and N is a load block correction factor.

3.5.6 Calculation of da/dN

The strain energy release rate associated with the maximum load applied in each cycle,

Gmax, was calculated using compliance-based beam theory. The delamination growth rate

was calculated using a 7-point averaging method, as detailed in ASTM E 647 [62]. It is an

incremental polynomial method, which involves fitting a second order polynomial fit to

sets of (2m+1) successive data points, where m is 1, 2, 3 or 4. The regression parameters

of the fit are determined by the method of least squares. For the second and second last

data points a 3-point method is used, where a polynomial fit is applied to three successive

values of a, and the value of da/dN is evaluated for the medium (second) point. A similar

process is followed using a 5-point method for the third and third-last data points, and all

further values of a are evaluated using a 7-point method. The first and last data points are

evaluated using a secant technique that involves calculating the slope of the straight line

connecting two consecutive values of a. For the round robin test, a macro written in a

Microsoft Excel workbook supplied by Dr. Brunner was used to perform this calculation.

55

Figure 3-16 A typical a vs N graph under displacement control, illustrating the calculation method for da/dN

56

3.6 Flexural Modulus Test

To determine the flexural modulus, E, of the manufactured and ESIS specimens, sections

were cut from the un-cracked DCB specimens after fatigue testing and subjected to three

point bend testing as per ISO 14125 [65]. Three specimens from each group were tested.

The thickness and width were measured at three points along each specimen before

testing. In both cases, a span of 64mm was used for specimens of 80mm length and 20mm

width.

The total deflection of the beam is:

𝛿 =𝐹𝐿3

4𝑏ℎ3𝐸+

3𝐹𝐿

8𝑏ℎ𝐺 (3.15)

Where F is the applied bending force, E is the flexural modulus, G is the shear modulus, h

is the beam thickness, L is the span (the distance between the centres of the two support

points) and b is the beam width. In this test the deflection and force were continuously

measured, so with this information the flexural modulus can be calculated in the following

way:

𝐸𝑓 = 𝐿3𝑚

4𝑏ℎ3 (3.16)

Where m is the slope of the linear plot of F vs 𝛿. The use of units of mm for length

measurements yields a value of Ef in MPa.

57

4 Results and Discussion

4.1 Flexural Modulus Tests

Three-point bend testing was conducted on three specimens manufactured in UCD, and

three ESIS specimens. The manufactured specimens are denoted U1, U2, and U3. The ESIS

specimens are denoted E1, E2, and E3.

Figure 4-1: Load-displacement curve used for the calculation of the flexural modulus of UCD specimens

Table 4-1: Flexural Modulus Calculation of UCD Specimens

Specimen

b (mm) h (mm) L (mm) m Ef (GPa)

U1 20.09 4.12 68 1750.35 99.698

U2 20.05 4.11 68 1764.12 100.358

U3 20.08 4.12 68 1767.08 100.431

Mean Ef 100.162

SD 0.404

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4

Load

(N

)

Displacement (mm)

U1

U2

U3

58

Figure 4-2: Load-displacement curve of ESIS specimens

Table 4-2: ESIS Specimens Flexural Modulus Calculation

Specimen

b (mm) h (mm) L (mm) m Ef (GPa)

E1 20.01 3.00 68 764.374 111.270

E2 20.00 3.01 68 724.117 105.410

E3 20.02 3.00 68 739.241 107.612

Mean Ef 108.097

SD 2.960

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6

Load

(N

)

Displacement (mm)

E1

E2

E3

59

The mean calculated value of Ef for the UCD specimens of 100.16 GPa is considerably lower

than the values of approximately 130GPa stated by Hexcel [53], and the measured values

of 121 +/- 2GPa calculated by Dr Joseph Mohan [56] who employed the same

manufacturing process in UCD. This can possibly be attributed to a number of factors. After

removal from the freezer, during the time that the 28 layers were cut and the time they

were placed in a sealed bag, some moisture could have accumulated on the cold surface

of each layer. As previously stated, moisture contamination between prepreg layers can

reduce the adhesive strength of the material. Furthermore, one of the heating elements in

the press clave is known to function in a lower capacity to the others, and there is a lag in

one of the four thermocouples that was unknown during the curing process. It is therefore

advisable to increase the dwell stage by approximately 25 minutes above the

recommended level to ensure that the layup is uniformly subjected to a temperature of

1800 C during this stage. The mean calculated value of the ESIS specimens was also below

the expected value. This provokes the thought that the span was greater than the marking

measured below the two supports. An increased in span of 1mm on each support would

produce a calculated value of Ef that is approximately 10GPa higher – an error in

measurement that is easily made. Furthermore, IS0 14125 [65] recommends that the

supports used be of radius 5 +/- 0.2mm for beams of thickness h ≥ 3mm. The apparatus in

place in UCD consists of triangular supports that do not comply with this standard.

Figure 4-3 Brittle-ductile failure interface through the beam thickness

60

4.2 Mode I Fracture Toughness Test A mode I fracture toughness test was carried out for 3 Hexcel 8552/AS4 specimens

manufactured in UCD, denoted Sample 1, Sample 2 and Sample 3. Initiation points were

determined as per IS0 15024, which can be found in Figure 4-4 below. In each case, the

critical strain energy release rate GIC was determined from an average of the entire R-

Curve.

Figure 4-4: Load Displacement Curve

Table 4-3: Sample 1 Fracture Toughness Results

GIC SBT (J/m2) GIC CBT (J/m2) Ef (GPa)

MEAN 190.19 222.85 118.11

SD 20.53 7.64 5.53

CoV 10.79 3.43 4.53

0

10

20

30

40

50

60

70

80

90

0 0.005 0.01 0.015 0.02 0.025

Load

(N

)

Crosshead Displacement (mm)

Sample 1

Sample 2

Sample 3

61



MEAN 220.33 235.87 109.44

SD 20.12 7.70 4.5

CoV 9.13 3.26 4.11



MEAN 203.77 245.32 97.72

SD 17.62 4.78 2.31

CoV 8.65 1.95 2.37

Figure 4-5: Comparison of initiation points across the three tested specimens

The average value of GIC obtained across the three samples using corrected beam theory

was 235 J/m2. As mentioned in (initiation points section) often the location of the NL

initiation point was seen to coincide with the MAX point. The back calculated flexural

modulus outputted values were similar to the calculated values from three-point bend

testing – the low standard deviation in this value adds validity to the fracture toughness

0

50

100

150

200

250

300

NL C +5% MAX VIS

GIC

(J/m

2)

Initiation Points

Sample 1 Sample 2 Sample 3

62

calculations. The intention of this test was to use the obtained value for the critical strain

energy release rate for comparison with fatigue delamination results, and to normalise the

delamination growth curve for the effects of fibre bridging. As fatigue testing of specimens

from the same layup proved to be largely effected by stiffening effects, it became apparent

that the latter investigation could not be carried out. This conclusion was further

strengthened by recent research suggesting that the contribution of fibre bridging is

different between quasi static and fatigue loading [43,47]. Nonetheless, it is a useful

parameter to compare to the maximum values of the strain energy release rate observed

in fatigue testing of ESIS specimens, which were comprised of the same material, Hexcel

8552/AS4.

4.3 Fatigue Testing of UCD Specimens

4.3.1 Early Testing From the first layup manufactured, just one sample produced usable results. The use of

large load blocks and a short test insert in this test increases the stiffening effect of the

load block on the moment arm. The other four specimens that were made available for

testing from the first layup did not produce satisfactory results. Two of the samples

experienced large inertial effects from the heavy upper grip which was subsequently

replaced, and two were invalidated by the application of the incorrect amplitude. The latter

is due to the issue of frequency limitations of the Instron 8502. The frequency the machine

is capable of achieving depends upon the amplitude requirements of each test, which in

itself depends upon the compliance of the material in question. PEEK specimens, for

instance, require a larger crosshead displacement to precrack. The maximum amplitude

achievable by the machine was determined to be 0.83 mm at 3 Hz, with an error of

0.02mm. This corresponds to a maximum achievable crosshead displacement of 1.8mm.

Higher displacements can be achieved at lower frequencies, which were not investigated.

63

4.3.2 Testing of UCD Specimens

From the second layup, six samples were tested to between 50’000 and 200’000 cycles. In

three cases, visual crack growth did not coincide with the measured reduction in load. A

crack growth increment greater than the previous recorded increment was observed in

some cases, despite a relatively small increase in specimen compliance. Back calculation of

the flexural modulus in such cases yielded larger values by upwards of a factor of four.

Taking an MCC log plot of crack length vs compliance in such cases did not yield satisfactory

degrees of linearity, and further analysis and calculation of the strain energy release rate

would be fruitless. This is a typical example of an experimental challenge associated with

the sensitive measurement of fatigue delamination growth. Although the upper and lower

grip require perfect alignment, and the load recorded when mounting each specimen did

not increase (which would represent torsion or compression being applied to the

specimen), it is still possible that such specimens were asymmetrically loaded. In one case,

another delamination was observed in a separate plane, arresting delamination growth

and invalidating the test, which can be seen in Section 4.6.

Testing of the other three UCD specimens were conducted with the use of the 5kN load

cell, in which MCC linearity was satisfactory. They shall be referred to as UCD 1, UCD 2, and

UCD 3. As mentioned in Section 3.5.2, a thermal drift had to be accounted for when

recording the maximum load. Despite this obstacle, the adjusted value of Pmax in most

cases could be well represented by a power law fit, as observed in previous round robin

attempts to smooth data when load measurement resolution was an issue. Power fits with

a coefficient of variance R2 ≥ 0.925 were generally observed. Due to the error in load

measurement resolution of +/- 1.25N associated with the 5kN load cell, values directly from

the power law fit were used for the calibration equation. Sensitivity of the calibration of

the MCC plot to small errors in the measured load was presented as a significant cause of

scatter, as the decreases in load were lower in absolute value than the error associated

with the load cell. If the power law representation were not used, a false increase in load

would no doubt be recorded, despite the trend indicating a consistent decrease in load.

This would manifest itself as an apparent decrease in compliance and hence a decrease in

crack length relative to the previous point, resulting in significant scatter in data.

64

Figure 4-6 below shows a plot of the maximum and minimum load outputs from the load

cell, and the adjusted plot of its value used in compliance calibration calculation of Gmax.

Figure 4-6: Load-displacement curve showing adjustment for thermal drift

Table 4-6: Fatigue test parameters for UCD specimens

Specimen L (mm) B (mm) 2h (mm) a0 (mm) δmax (mm)

R-Ratio Cycles

UCD 1 150 20 4.12 25 1.27 0.1 200’000

UCD 2 150 25 4.05 20 0.84 0.1 100’000

UCD 3 150 25 4.08 20 0.75 0.1 50’000

y = 77.739x-0.039

R² = 0.943

0

10

20

30

40

50

60

70

80

90

0 50000 100000 150000 200000 250000

Load

(N

)

Cycles

UCD 1

AdjustedPmax

Pmin

Pmax

Power(AdjustedPmax)

65

Figure 4-7: MCC plots of UCD Specimens

Each specimen was precracked to 4 +/- 0.2mm from the insert. Despite obtaining a good

correlation between the crack length and compliance of each specimen, there were

indications from the results that the UCD samples experienced stiffening effects due to the

size of the load blocks and the short distance from the load line to the insert relative to the

thickness of the specimens. This is further supported by consistent back-calculated flexural

modulus values of 180 GPa, 230 GPa, and 362 GPa for specimens UCD 1, UCD 2 and UCD 3

respectively. A recent paper has shown that the delamination growth curve

Regarding load block size, the load blocks used were 25mm3 for beams of 25mm width,

and 20mm3 for the beam of 20mm width. The standard for mode I fracture toughness test

(ISO 15024) states that the length of the load block in the direction parallel to the beam

length (l3) should be 15mm or less. ESIS TC4 fatigue protocol [57] also advises to follow

this requirement. At the time that these tests were conducted, no load blocks of these

dimensions were available. They were later manufactured to the correct dimensions.

Another requirement stated in ISO 15024 test is that the minimum distance from the edge

of the insert to the edge of the load block should be at least 45mm, to minimise the

stiffening effect due to the load blocks. In comparison, the ESIS test protocol states that

R² = 0.9883

R² = 0.9648

R² = 0.9871

-2.1

-2

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

1.35 1.4 1.45 1.5 1.55 1.6

log

C

log a

UCD 1

UCD 2

UCD 3

66

the initial delamination from the load line after precracking of 3-5mm from the load line to

the insert should be less than 30mm. For a load block of 20mm3 in volume, this corresponds

to a distance approximately 15mm from the edge of the load block. The choice of this short

distance a0 by ESIS is to accommodate as wide a range of testing machines as possible,

which are limited in their displacement capabilities. A trade-off can be easily seen: A

shorter value of a0 allows for lower crosshead displacement, therefore higher test

frequency, but a longer value of a0 is also beneficial, as it decreases the stiffening effect

inherent with the use of load blocks. Regarding thickness, ESIS TC4 recommended that the

thickness be enhanced compared to the 3mm advised in IS010524 to reduce specimen

compliance. This advice was followed, and beams of thickness 4.1mm were produced,

similar in dimension to those produced in [4]. In combination with the factors discussed

above, the enhanced thickness further increased the stiffening effect. The ESIS specimens

that were later received were 3mm in thickness.

The Paris plot shown in Figure shows similar slopes obtained for the three specimens. In

each case, data was reduced so that load measurements corresponding to a crack growth

increment Δa = 0.005 were taken. UCD 1 was observed to contain the lowest degree of

y = 2E-36x15.962

R² = 0.9268

y = 5E-29x12.809

R² = 0.6967

y = 2E-23x9.442

R² = 0.636

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 10 100 1000

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

UCD 1MCC

UCD 2MCC

UCD 3MCC

67

scatter, and the highest slope. The high slopes of UCD 1 and UCD 2 specimens are further

evidence of the aforementioned stiffening effect.

4.4 Fatigue Testing of ESIS Specimens In preparation for testing of ESIS specimens, load blocks measuring 20x20x15mm were

manufactured. In each case the distance from the load line to the tip of the insert was

25mm, which complies with the maximum allowable distance stated by the protocol after

3-5mm of quasi-static precracking. As the stiffening effect was reduced, the crosshead

displacement required to precrack the specimens increased relative to the ucd specimens.

In each case, the maximum displacement was within the determined limits of the machine

to allow for testing at 5 Hz. Of the five specimens, two were tested using a 250N capacity

load cell, and are named as ESIS A1 and ESIS A2. As the load cell was accidentally

overloaded during mounting of one specimen, it was subjected to an unknown

compressive load, which is sufficient to invalidate any results obtained. Nonetheless,

testing on this specimen with the use of the 5kN load cell produced interesting results. A

significantly larger crosshead displacement was required to precrack the specimen, and

significant crack branching was observed. As this effectively produces a second

delamination, observation of this phenomenon was also sufficient to invalidate the test.

The two remaining specimens were tested using the 5kN load cell, and are denoted ESIS

B1 and ESIS B2.

4.4.1 Results of 250N Load Cell Tests Specimens ESIS A1 and ESIS A2 were tested to 500’000 cycles in an attempt to observe near

threshold behaviour, which is represented by delamination growth rate of below 1x10-6

mm/cycle. The properties of each DCB specimen are presented in Table 4-7.

Table 4-7: ESIS Specimen dimensions and testing parameters tested with 250N load cell

Specimen L (mm) B (mm) 2h (mm) a0 (mm) dmax (mm)

R-Ratio Cycles

ESIS A1 185 20 3 24 1.44 0.1 300’000

ESIS A2 185 20 3 25 1.39 0.1 500’000

68

4.4.1.1 Comparison of Beam Theory Calculation Methods

Figure 4-8 Comparison of beam theory methods for ESIS A1, showing almost identical results across the three methods

Figure 4-9: Comparison of beam theory methods for ESIS A2. More conservative growth curves were obtained using CBT and MCC methods.

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

100.00

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS A1

MCC

CBT

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

90.0000

da/

dN

(m

m/c

ycle

)

Gmax (J/m2 )

ESIS A2

MCCCBTSBT

69

The appearance of scatter in the order of almost 2 decades in da/dN for a given value of

Gmax can be seen in the delamination growth representation of ESIS A1 at values of Gmax <

150 J/m2, as presented in Figure 4-8. Referring to Figure 4-10 below, a drastic drop followed

by a rise in the measured load was observed between 9000 and 10000 cycles. While small

deviations in the load were recorded after pausing the test (at 20’000 cycles, for example)

to visually determine the crack lengths, pausing the test was not the cause for this drop, as

the test was paused at 5’000 and 10’000 cycles. The recorded crack length increase in this

period was 1.0mm. The calculation of da/dN in this region is affected significantly by events

such as this. The calculated crack lengths based on the observed increase in compliance

are used in the calculation of da/dN. In this case, as the relationship between log a and log

C locally deviates from the linear fit, the calculation of the crack growth rate is scattered.

As the calculation of da/dN is based on a 7-point average method, the polynomial fit for

the da/dN data points adjacent to this region will not compare favourably with the

calculated compliance curve obtained from visual observation at set intervals. Local load

spikes can also affect delamination growth calculation in a similar manner. Despite data

reduction that involves deleting data points that do not meet the requirement of a chosen

crack growth increment, load measurement points can be chosen that are not

representative of the trend. This said, such points cannot simply be deleted from analysis

without consistent data reduction criteria. Referring to Figure 4-8, the calculation of the

parameter |Δ| for ESIS A1 was very low, at 0.61mm, placing MCC and CBT almost

identically with SBT in the calculation of Gmax. By comparison, the slope of the compliance

fit for ESIS A2 was lower, calculating lower values via MCC and CBT relative to SBT. SBT has

also been seen to shift in either Gmax or da/dN in previous round robin testing. In [5], a shift

in SBT calculation of similar magnitude to that of Figure 4-9 was observed, leading to the

conclusion that safety factors based on CBT or MCC would lead to more conservative

designs.

70

Figure 4-10: Drop in load observed in ESIS A1 Specimen at 9000 cycles, contributing to scatter in calculation of Gmax

4.4.1.2 Paris Representation

The use of a Paris-like representation of delamination growth as a function of the strain

energy release rate can be seen in Figure 4-11. This power law fit was shown to correlate

reasonably well with delamination growth, with R2 values of 0.933 and 0.977 for ESIS A1

and ESIS A2 respectively. The slopes in each case show very high exponents around 10.7,

typical of the high exponents that have provoked research into alternative representations

of delamination growth. Errors in the measurement of applied load will provide further

amplified errors in corresponding delamination growth rate if this representation were

applied. The Paris relation as below above proves to only be an accurate approximation for

the linear region of crack growth, and is seen not to correlate well as near-threshold

behaviour is reached at low rates of crack growth.

71

Figure 4-11 A Paris power law fit applied to the delamination growth curve of specimens ESIS A1 and ESIS A2

4.4.1.3 Hartman Schijve Representation

The aforementioned large exponent and poor representation of threshold behaviour

associated with Paris representations of delamination growth have been shown to be

improved upon through use of a variant of the Hartman-Schijve equation for composites,

previously discussed in Section 2.5.2. The toughness parameter A in each case was taken

as the maximum value of Gmax that occurred at the beginning of the test. The threshold

value Gth for each sample was the lowest calculated value of Gmax observed, which occurred

at the end of the test. It is preferable to obtain a value corresponding to an asymptotic

‘zero slope’ in order to fully comply with this equation, however that would require a much

longer test duration. Regarding ESIS AS1, the specimen had originally been tested to

y = 9E-28x10.687

R² = 0.9333

y = 1E-27x10.715

R² = 0.9771

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

10.00 100.00

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS A1 (MCC)

ESIS A2 (MCC)

Power (ESIS A1(MCC))

Power (ESIS A2(MCC))

72

500’000 cycles, however a large spike was seen directly after pausing the test at 300’000

cycles. In this case the test was paused for too long a duration (almost 30 minutes due to

a miscalculation of stage duration), and the crack was maintained at mean amplitude for

too long. As a result, only values up to 300’000 cycles were taken. Gmax values calculated

using modified compliance calibration were used. In each case the Hartman Schijve term

was plotted on a log scale against the calculated 7-point da/dN. A linear fit was taken of

this term vs da/dN in order to determine the value of β, which is typically between 2 and

3, and the proportionality constant D. As seen in Figure 4-12, D and β values were obtained

from the equation of this linear plot. Despite its assumed linearity, the data does tend to

contain some non-linearity. As advised by Dr Brunner, a best fit of the “top” section of this

plot was taken. Further analysis of the round robin data will be required to determine a

consistent fitting procedure for these constants to yield minimum inter-laboratory scatter,

however. Figures 4-13 and 4-14 compare da/dN calculated using the seven-point method

with the Hartman-Schijve representation of delamination growth.

Figure 4-12: Hartman Schijve linearity of ESIS A1 and ESIS A2

y = 5E-09x2.1514

R² = 0.9101

y = 4E-09x2.1469

R² = 0.977

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1 10 100

da/

dN

(m

/cyc

le)

(√(Gmax )− √(Gthr ))/√(1− √(Gmax/A)) (√J/m2)

ESIS A1

ESIS A2

73

Figure 4-13: Hartman-Schijve representation of ESIS A1

Figure 4-14: Hartman-Schijve representation of ESIS A2

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

50.00 500.00

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS A1

Modified Compliance Calibration

Hartman-Schijve Representation

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

50 500

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS A2

Modified Compliance Calibration

Hartman Schijve Representation

74

Table 4-8: Parameters used in Hartman-Schijve calculations

Specimen Gth (J/m2) D A (J/m2) β

ESIS A1 107.52 5.0 x 10-9 222.4 2.1514

ESIS A2 97.21 4.0 x 10-9 208.52 2.1469

The scatter present in delamination growth curve for ESIS A1 can be seen to affect the

linearity of the Hartman-Schijve term, as seen in its relatively poor correlation with da/dN

upon comparison with ESIS A2. The slopes of the linearity plots yielded values consistent

with the value of approximately 2 stated by Jones et al [49,50]. Fitting parameters D were

between 4 x 10-9 and 5 x 10-9 to fit the data, however more research is required to fully

establish the relationship of this constant with the material in order to provide consistent

values for delamination prediction. The Hartman-Schijve equation assumes the use of a

threshold value corresponding to a load measurement that is not expected to decrease

significantly beyond that point. As ESIS A1 and ESIS A2 were tested to 300’000 and 500’000

cycles respectively, there is a degree of inaccuracy associated with the stated Gth value due

to the limitation in time available for use of the machine. As the threshold value Gth was

approached, the value of the term (√𝐺𝑚𝑎𝑥 − √𝐺𝑡ℎ) (and hence the calculated da/dN)

approached zero, as can be seen in the calculation of very low crack growth rates in the

Hartman Schijve plot. If each test had been conducted to a larger number of cycles, the 7-

point calculation method of da/dN would be placing a more accurate value of Gth in the

region below 10-7 mm/cycle, as this is the location that the Hartman-Schijve representation

assumes it lies. Regarding ESIS A1, the threshold value can be seen to be almost 10 J/m2

higher than that obtained for ESIS A2 due to its shorter test duration, and therefore shorter

amount of time for the crack growth to decrease further. The approximation was seen to

provide a good fit for ESIS A2, despite the absence of a test duration of sufficient length to

obtain a satisfactory threshold value. A better linear fit of the Hartman Schijve

representation would no doubt provide a more accurate value of D for ESIS A1 in this case,

however the aforementioned scatter had a negative impact in that regard.

75

4.4.2 Collated ESIS Results This section will present the data obtained from all four ESIS specimens. As previously

mentioned, the load measurements for specimens ESIS B1 and ESIS B2 were obtained

using a 5kN load cell, and values taken from a power law fit of the load-cycle curve were

used for the calibration equations for MCC in a similar manner to that of the UCD

specimens. In the case of all ESIS specimens, back calculated flexural moduli were

observed to lie consistently in the range of 100-112 GPa.

Figure 4-15 Delamination growth curve of ESIS specimens

Table 4-9: Properties of power law fits of ESIS specimens

Specimen Slope R2

ESIS A1 10.687 0.933

ESIS A2 10.715 0.977

ESIS B1 10.897 0.845

ESIS B2 12.634 0.8935

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

10.00 100.00

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS A1MCC

ESIS A2MCC

ESIS B1MCC

ESIS B2MCC

76

In spite of the greater degree of scatter inherent with the use of this load cell, ESIS B1

exhibited a similar slope in its Paris representation to the previous two specimens, as

presented in Figure 4-15. A higher slope was observed in the plot of ESIS B2 than the other

specimens, despite exhibiting a similar range of values of Gmax. The higher slope is a result

of plateaus in the plot of P vs N, further exacerbated by the error with the load cell. Where

an increase in crack length may have been visually observed regions where a plateau in

load was presented, the calculated change in a based on the change in compliance would

be relatively small due to little or no observed change in load. Thus, similar Gmax values are

spread across a wide range of da/dN. In this specimen, the crack was seen to reform ahead

of the original crack tip in the same defect plane, later joining the original crack, offering

possible explanation to the resistance of the material to a decrease in load. This is discussed

in further detail in Section 4.6.

Due to the variation in threshold values obtained, scatter in the order of 2 decades of

da/dN could be observed at low crack growth rates between specimens. It should be noted

that in the late stages of each test, visual determination of crack growth proved to be

especially difficult, as crack growth increments decreased. A combination of an optical

microscope and a digital microscope was used to determine the crack length, however this

is no doubt observer-dependent to a certain extent.

4.4.2.1 Hartman-Schijve Representation

Figures 4-16 and 4-17 present Hartman-Schijve representations of the four ESIS specimens.

The aforementioned large slope in the Paris representation of ESIS B2 can be easier seen

in this form, also reflected in the relatively high β value of 2.585. The scatter in Gmax found

at low crack growth rates can once again be explained by the accuracy of Gth values

obtained. The use of the linear plots of the Hartman-schijve term to determine D and β

appears to be reasonably consistent, although a good linear fit is essential. While A is

usually taken as the quasi-static value GIC, it was found not to have a large effect on the fit,

even when the parameter was varied by +/- 20%. In this case, consistently taking the first

value for Gmax at the start of the test proved to provide a good fit. The effect of the use of

the 5kN with the comparatively crude method of obtaining the maximum load value can

77

be seen in the scatter of Hartman-Schijve linearity seen for ESIS B1 and ESIS B2, and the

variation in D measurement as a result. With the exception of the aforementioned issue

with the slope of the delamination curve for ESIS B2, the slope parameter β for the

remaining three specimens proved to be very consistent. Overall it appears that if an

insufficient value of the threshold value Gth is obtained, the Hartman-Schijve

approximation will, of course, be inaccurate in its approximation of delamination growth

in for short crack growth rates, however it still provides a good fit of the linear region of

crack growth. ESIS A2 is deemed to have been the most successful of the four tests in

obtaining this value, and is the best suited to this approximation as a result.

Figure 4-16: Hartman Schijve linearity of ESIS Specimens

y = 5E-09x2.1514

R² = 0.9101

y = 4E-09x2.1469

R² = 0.977

y = 5E-09x2.5849

R² = 0.9028

y = 1E-08x2.1527

R² = 0.8712

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1 10 100

da/

dN

(m

m/c

ycle

)

(√(Gmax )− √(Gthr ))/√(1− √(Gmax/A)) (√J/m2)

ESIS Specimens

ESIS A1

ESIS A2

ESIS B1

ESIS B2

78

Figure 4-17: Hartman-Schijve representation of ESIS specimens

Table 4-10: Parameters used in Hartman-Schijve calculations for ESIS specimens

Specimen Gth (J/m2) D A (J/m2) β

ESIS A1 107.52 5 x 10-9 222.4 2.151

ESIS A2 97.21 4 x 10-9 208.52 2.147

ESIS B1 111.61 3 x 10-9 231.34 2.158

ESIS B2 104.52 5 x 10-9 212.08 2.724

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

50.00 500.00

da/

dN

(m

m/c

ycle

)

Gmax (J/m2)

ESIS Specimens

ESIS A1 Hartman-Schijve

ESIS A2 Hartman-Schijve

ESIS B1 Hartman-Schijve

ESIS B2 Hartman-Schijve

79

4.5 Comparison of Crack Length Calculation Methods The effective crack length method involves the use of a measured value of the flexural

modulus with compliance to calculate the crack length, taking into account a zone of

plasticity ahead of the crack tip. This method is independent of visual determination of the

crack length, and can thus remove the starting and stopping aspect of the test, which

contributes to scatter in the MCC method. The issue encountered with the use of this

method was that values of the effective crack length were typically lower than the visually

observed crack lengths. This was also observed in [5] (See Figure 2-8) where a possible

explanation was offered of an average value of the flexural modulus being used, as

opposed to individual specimen measurements. In this case, testing showed values lower

by almost 1mm than the measured crack length for ESIS A2. The same approach provided

higher values for aeff for other specimens, depending on the difference between the back

calculated flexural modulus and the measured value. The same explanation for the lower

values can be offered as was offered by Stelzer et al, supplemented by the aforementioned

uncertainty associated with the validity of the three point bend test results. If, for example,

a value of 120 GPa or above were assumed for the material, in each case a larger effective

crack length than the measured value would be observed.

Figure 4-18: Comparison of crack length determination methods

24

26

28

30

32

34

36

38

40

0 100000 200000 300000 400000 500000 600000

Cra

ck le

ngt

h (

mm

)

Cycles

ESIS A2

A calculated (MCC)

A effective

A visual

80

-

Figure 4-19: Comparison of crack length determination methods on delamination growth curve

It is important to note that in order to perform a proper analysis of the scatter associated

with the effective crack length approach, a test would have to be performed that does not

stop for visual determination of crack length. In any case, the results are compared in

Figure 4-19 above for testing MCC back calculation of crack length and the effective crack

length calculations. It is also suitable at this point to note that the visually observed crack

length was not always representative of the extent of the delamination for each specimen.

Delaminations were observed to propagate in an uneven manner through the material in

some cases. Figure 4-20 seems to suggest that asymmetrical loading took place in ESIS B1.

In light of this information, it is advisable to measure the crack length on both sides of a

DCB specimen in future tests.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

50 500

da/

dN

(m

m/c

ycle

Gmax (J/m2 )

ESIS A2

With Aeff

A calculated via MCC

81

Figure 4-20: Varying delamination front in ESIS B1

4.6 Crack Shielding Gmax was chosen as the parameter to represent delamination growth for a number of

reasons. As observed in literature at R-Ratio crack closure can have a greater effect on the

load measurement. For this reason taking the load value at the maximum displacement is

preferable, whereas the use of ∆G can be more reliable for higher R-Ratios. Unlike the 5kN

tests, testing with the 250N load cell provided an accurate reading for the minimum load

in testing, which was seen to reduce to compressive readings ranging from 0 to -3N after

5000 to 10’000 cycles. In this sense the crack front is not in a complete state of cyclic

tension, as the surface roughness is seen to increase over the course of the test. As stated

in ASTM E-647 [62], residual stresses in the material can lead to partly compressive cycles,

exacerbating the crack closure effect. The apparent tension-compression behaviour in

testing results in an inability to use the successfully employed crack driving force 𝛥√𝐺 (See

section 2.5.2) investigated by Jones et al [28] as it assumes cyclic tension at all times.

82

Figure 4-21: Minimum load undergoing compressive loading after approximately 10’000 cycles

Over the course of numerous fatigue tests a number of fracture phenomena were observed

- in some cases providing increased delamination resistance in the form of bridging fibres,

and in other cases invalidating tests completely. As previously mentioned, separation of

the crack front occurred in ESIS B2, absorbing some of the cyclic energy. It is not completely

clear to what extent this phenomenon must be observed to invalidate a test, thus the

results were analysed and compared to the other samples, and a larger slope can be clearly

seen in its delamination growth curve. Crack branching was observed in the

aforementioned compressively loaded ESIS Sample, which was seen to continue for

approximately 1.5mm before re-joining the original crack, as shown in Figure 4-22.

Obviously this is means for invalidation, as the intention of the test is to characterise the

growth of a single crack.

Compression at 10'000 Cycles

-2.136543 N

-10

0

10

20

30

40

50

60

0 50000 100000 150000 200000

Load

(N

)

Cycles

ESIS A1

Pmax

Pmin

83

Figure 4-22 Top: Crack Branching, invalidating the test. Left: A separate delamination propagating, absorbing cyclic strain energy and also invalidating the test. Right: Separation of the crack front.

84

5 Conclusions Results have been presented of fatigue delamination testing that was carried out on a

thermoset epoxy polymer reinforced with unidirectional carbon fibres as part of a round

robin test. The scatter present in the results is representative of the difficulties with in and

inter-laboratory scatter than have been restricting the development of a recognisable

standard for damage evaluation of delamination fatigue crack growth in composite

materials. Large changes in the crack growth rate, da/dN were observed for small changes

in the strain energy release rate, which is highly sensitive to load measurement resolution.

Before delamination fatigue tests can be applied to the design of composite structures,

such sources of scatter must be investigated using data from multiple laboratories in order

to gain a greater understanding of their source, and make efforts to reduce them.

Stiffening effects due to short insert lengths, the effect of specimen thickness and large

load block size placed a limit on the analysis of manufactured specimens in this project.

Literature has shown the huge impact on results of the relative load measurement

capabilities of different laboratories on the scatter of data on the delamination growth

curve [5], the implications of which were observed first-hand in this project through the

use of load cells of differing resolutions. The presence of a thermal drift in the higher

capacity load cell had an effect on the validity of results obtained, however correction was

applied to the load output that allowed for analysis and acquirement of crack growth

representations that were comparable to their higher resolution counterparts, despite the

inherent scatter in the outputted readings. Slopes of Paris plots were obtained that were

typically in the order of 10, consistently of similar values with the exception of one

specimen that underwent noticeable crack shielding. The latter (ESIS B2) should practically

be omitted from consideration in this regard, due to the presence of a separate crack front

in results and a noticeable absorption of strain energy as a result.

The discussion of slope values begs the question of whether a low slope in a Paris plot is

preferable or not. When considering a Paris-representation of crack growth that assumes

a power-law fit between the crack growth rate and the strain energy release rate, a low

slope implies that the delamination can be detected and monitored with some space for

error in measurement, however it also implies that delamination will propagate from a low

85

value of Gmax. Structural components in aircraft are primarily metallic, and composite carry

low loads in components such as wing panels, stabilizers etc., yet delamination has still

been seen to propagate during service life [12,49]. A higher slope would indicate that a

higher load needs to be applied for delamination to initiate and grow, however it also

implies that acceleration of the crack growth rate would occur over a small range of applied

load. This not only makes it very difficult to characterise crack growth without significant

scatter in da/dN calculation for a given value of Gmax experimentally, but practically it

implies that delamination would be very difficult to monitor, which has potentially

catastrophic consequences for aircraft.

The inappropriate nature of the Paris relation can be seen in this regard, as well as the need

to definitively measure threshold behaviour of composite materials. The measurement of

threshold values has proven to be an immense challenge in previously conducted tests

.Near-plateaus in load measurement have indicated near-threshold behaviour after

approximately 20 million cycles (280 hours at 10 Hz) [5], however even longer test

durations are required to obtain a definitive measurement. The measurement of threshold

behaviour involves identification of small decreases in applied load, while eliminating

environmental factors that can affect its measurement, such as temperature and relative

humidity. Temperature regulation alone presents a challenge, as higher frequencies cause

heating effects in the material – therefore lower frequencies (implying even longer test

durations) must be applied. With the current issue of in and inter-laboratory scatter

emerging in results of round robin testing, an overly conservative design of composite

structures would be a result, even if a definitive threshold strain energy release rate could

be obtained for each material. The results of this project have presented the difficulty in

obtaining such a value – the minimum value of the strain energy release rate (which was

assumed to be the threshold value) showed no signs of reaching an asymptotic ‘zero slope’

value indicative of threshold behaviour.

Literature has presented a Hartman-Schijve approach to delamination representation

which is a function of this threshold value. It has been shown to be a suitable approach to

characterising all modes of loading using fixed constants obtained from linear plots [49,

50]. It has also been shown to be independent of the effect of stress ratio on delamination

growth curves with a favourably lower exponent than that observed in Paris law

86

representations [28]. Investigation of the use of this approach has led to the observation

of delamination curves similar to that observed in metals, and what would be a better

characterisation of small crack growth. The limiting factor in this investigation was the

aforementioned inability to obtain satisfactory threshold values in order to make a more

informed observation on its applicability, however. There is little doubt as to its huge

potential in alleviating the no growth design approach currently taken to composite

structures, and its applicability remains to be determined by further analysis. Round robin

testing is therefore a valuable tool, enabling analysis of large data sets in order to find a

consistent and reliable method to evaluate the fatigue delamination damage tolerance of

composite materials.

87

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