DEGREE PROJECT IN MECHANICAL ENGINEERING,
SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2018
Failure Modeling of
Curved Composite Beams
Numerical Modeling of Failure Onset and
Propagation in L-Profile Beams
SUHAS GURURAJ SHETTY
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ENGINEERING SCIENCES
i
This thesis work was carried out as a part of degree project of the Master’s programme in
Aerospace Engineering – Lightweight Structures at KTH Royal Institute of Technology.
The author takes full responsibility for the Master Thesis work presented in this report.
GKN Supervisors - Olofsson Niklas and Tsampas Spyros
KTH Supervisor/Examiner - Stefan Hallström
ii
Abstract
The high strength/stiffness-to-weight ratio that composite materials exhibit has led to the
utilization of composites as alternative to traditional materials in weight-critical applications.
However, the highly anisotropic nature of composites renders the strength prediction under
complex loading challenging. To efficiently predict the failure of composite structures
especially in cases where out-of-plane stresses are dominant, the modeling of damage onset
and propagation plays an essential role in accurate strength predictions.
Firstly, in this Thesis work the analysis of a composite L-profile, which is loaded such that
significant out-of-plane stresses are generated in the curved region, is conducted. However,
the inherent heterogeneity at the micro/meso scale is not modeled for the stress analysis.
Secondly, in this project the target was to accurately predict the initiation of failure at the ply
level, modal based Puck’s matrix failure criteria have been implemented to the failure
analysis. Maximum stress failure criteria were however retained to check the possible fiber-
based failure which is not directly captured with in Puck’s failure criterion.
Thirdly, Cohesive Zone Material Model has also been employed to model the growth of
interlaminar damage (delamination). The delamination study is based on the Inter Fibre
Fracture crack initiation and doesn’t include other causes like edge effects, voids,
manufacturing defects etc.
Finally, the attempt to validate the analysis results with the available test results was made.
Further development of the existing model and several tests are required to be carried out for
material characterization and complete validation of the developed damage model for
composite structure.
iii
Acknowledgments
This master Thesis work was written as a part of the master’s degree programme in Aerospace
Engineering under Lightweight Structures track at Kungliga Tekniska Högskolan. The work
has been carried out at GKN Aerospace Engine Systems in Trollhättan, Sweden during the
spring term of 2018. Firstly, I would like to thank my supervisors Olofsson Niklas, Tsampas
Spyros and Stefan Hallström for their time and continuous support during the project. I would
substantially like to thank them for their valuable feedbacks which motivated me to
understand further down the line in the world of composites. Special gratitude to all the
employees at the R&T- department for their warm welcome and nice work environment who
kept me propelled throughout the project especially due to their helpful nature and patience
with my questions.
I would like to thank Erik Marklund, Thomas Bru and Fredrik Ahlqvist at Swerea SICOMP
who guided me with the initial input for the project, despite their busy schedule. I would also
like to thank ANSYS and Hyperworks technical support team for their valuable response
during this Thesis work. This Thesis work would have been impossible without the inputs
from the Journals, Text Books and other technical papers published in the related topics and
hence I would also like to thank all the authors for publishing their articles which indirectly
helped me to carry out my Master Thesis work. I would like to dedicate this master Thesis
work to all teachers and professors who had upskilled me till date. Last but not the least I
would like to thank my family, friends and relatives for continuously reinforcing me during
the Thesis work.
- Suhas Gururaj Shetty
Trollhättan, July 2018
iv
List of Symbols
€ : Euros (Currency)
ρ : Density
E : Elastic Modulus
�̂� : Tensile Strength
b : Width of Specimen
t : Thickness of Specimen
δ : Applied Displacement
σ n(θ) : Normal Stress Component on Action Plane
Ͳ nt(θ) : Component of shear stress on Action Plane
Ͳ n1(θ) : Other component of shear stress on Action Plane
θ : Action plane search angle
θfp : Fracture angle
fE(θ) : Local Stress Exposure
σmax : Maximum Normal Traction
δnc : Normal displacement jump at the completion of debonding
Tmax : Maximum Tangential Traction
δtc : Tangential displacement jump at the completion of debonding
v
List of Abbreviations
UD : Unidirectional
NCF : Non-Crimp Fabrics
RTM : Resin Transfer Moulding
LR : Long Range
GE : General Electric Company
OMC : Organic-Matrix Composites
MMC : Metal-Matrix Composites
CMC : Ceramic-Matrix Composites
PMC : Polymer-Matrix Composites
WWFE : Worldwide Failure Exercise
FE : Finite Element
VCCT : Virtual Crack Closure Technology
CTE : Crack Tip Element Method
CZM : Cohesive Zone Modeling
M1 : Module 1
M2 : Module 2
M3 : Module 3
CTE : Coefficient of Thermal Expansion
T : Tension
C : Compression
LC : Loading Case
IFF : Inter Fiber Fracture
vi
List of Figures
Figure 1: Locations with complex geometry [6]. ....................................................................... 2
Figure 2: Typical T-profile cross Section [7]. ............................................................................ 3
Figure 3: GEnx-1B Engine [4]. .................................................................................................. 4
Figure 4 : Gantt Chart of Thesis work. ....................................................................................... 6
Figure 5: Generic workflow of the thesis work and modeling process (marked in the blue
frame). ........................................................................................................................................ 7
Figure 6: Example of a composite material in nature [9]. .......................................................... 8
Figure 7: Classification based on reinforcement [10]. ............................................................... 9
Figure 8: Chipped stone tool in paleolithic age [9]. ................................................................. 10
Figure 9: Three modes of Fracture [9]. .................................................................................... 11
Figure 10: Illustration showing different damage in composites [13]. .................................... 12
Figure 11: Example of L-shaped laminate showing section loads and delamination [16] ...... 13
Figure 12: Three major analysis modules. ............................................................................... 16
Figure 13: GKN Workflow. ..................................................................................................... 17
Figure 14: Relevant scale for composite analysis [25]............................................................. 18
Figure 15: L-Shaped specimen used in this thesis work [7]. ................................................... 19
Figure 16: Layered Solid Model. ............................................................................................. 20
Figure 17: Mesh quality check. ................................................................................................ 21
Figure 18: General Hooke’s Law [25]. .................................................................................... 21
Figure 19: Laminate and transformation of co-ordinate system [26]. ...................................... 22
Figure 20: Material Properties at the ply level. ........................................................................ 22
Figure 21: Global co-ordinate system and Local co-ordinate system [26]. ............................. 23
Figure 22: Tool setup used for testing the specimen in Tension and Compression [7]. .......... 24
Figure 23: Out-of-plane stress components. ............................................................................ 25
Figure 24: Out-of-plane stress components at δ = 0.6 mm. ..................................................... 26
Figure 25: Out-of-plane stress components at δ = 0.7 mm. ..................................................... 26
Figure 26: Stresses in UD-Laminae [27]. ................................................................................. 28
Figure 27: Inter Fiber Fracture [28]. ........................................................................................ 29
Figure 28: Stresses on the action plane [28]. ........................................................................... 29
Figure 29: Searching for fracture plane angle [28]. ................................................................. 30
Figure 30: Initiation of failure for LC Tension and LC Compression. .................................... 31
Figure 31: Schematic showing crack bridging tractions in cohesive zone [29]. ...................... 32
vii
Figure 32: Various typical cohesive traction-displacement curves: (a) Triangular, (b)
exponential, (c) trapezoidal, (d) perfectly plastic and (e) linear/Polynomial [29]. .................. 33
Figure 33: Schematic diagrams of different formulations of interface elements [29]. ............ 33
Figure 34: Mode 1 and mode 2 dominated Bilinear CZM law [24]. ....................................... 34
Figure 35: Typical CZM mesh introduced into the existing model. ........................................ 35
Figure 36: Example illustrating bilinear behavior check. ........................................................ 36
Figure 37: At δ = 0.9 mm. ........................................................................................................ 37
Figure 38:At δ = 1.45 mm. ....................................................................................................... 37
Figure 39: At δ = 2 mm. ........................................................................................................... 37
Figure 40: At δ = 0.9 mm. ........................................................................................................ 38
Figure 41: At δ = 1.45 mm. ...................................................................................................... 38
Figure 42: At δ = 0.9 mm. ........................................................................................................ 38
Figure 43: At δ = 1.45 mm. ...................................................................................................... 39
Figure 44: Experimental test rig [7]. ........................................................................................ 40
Figure 45: Failure strains in Tensile tests. ................................................................................ 41
Figure 46: Failure strains in Compressive tests. ...................................................................... 41
Figure 47: Failure displacement in tensile tests ....................................................................... 42
Figure 48: Failure displacement in compressive tests. ............................................................. 42
viii
List of Tables
Table 1: Lifetime data for LR A330 [5]. .................................................................................... 3
Table 2: Estimation for composite fan case [5]. ......................................................................... 4
Table 3: Mechanical properties of some UD fiber composites [8]. ........................................... 5
Table 4: Pre-study on modeling approaches in composite structures. ..................................... 15
Table 5: Dimensions of the four test specimens....................................................................... 19
Table 6: Defined Boundary Conditions [7]. ............................................................................. 24
Table 7: Results based on max stress failure criteria, using small deformation analysis......... 27
Table 8: Results based on max stress failure criteria, using large deformation analysis. ........ 27
Table 9: IFF failure criteria for LC Tension and LC Compression. ........................................ 30
Table 10: Mixed mode bilinear material model input [24]. ..................................................... 35
Table 11: Max stress failure criteria for all load steps ............................................................. 51
ix
Table of Contents
Abstract ...................................................................................................................................... ii
Acknowledgments ..................................................................................................................... iii
List of Symbols ......................................................................................................................... iv
List of Abbreviations .................................................................................................................. v
List of Figures ........................................................................................................................... vi
List of Tables ........................................................................................................................... viii
Table of Contents ...................................................................................................................... ix
1 Introduction ........................................................................................................................ 1
1.1 Background and Origin of Thesis ................................................................................ 1
1.2 GKN Aerospace Sweden Presentation ........................................................................ 1
1.3 Aims and Objectives of Thesis Work .......................................................................... 2
1.4 Why do we need Composites? ..................................................................................... 3
1.5 Flow Chart for the Thesis Work .................................................................................. 5
2 Literature Review ............................................................................................................... 8
2.1 Brief Introduction to Composite Materials .................................................................. 8
2.2 Application of Composite Materials ............................................................................ 9
2.3 Brief Introduction to Fracture Mechanics ................................................................. 10
2.4 Failure Mechanisms in Composite Structures ........................................................... 11
2.5 Failure Criteria in Composite Structures ................................................................... 12
2.6 Brief introduction to Composite Curved Beams ....................................................... 13
2.7 Modeling Approaches in Composite Structures ........................................................ 14
3 Methodology .................................................................................................................... 16
3.1 FEM Software used ................................................................................................... 16
3.1.1 Hyperworks ........................................................................................................ 16
3.1.2 MATLAB ........................................................................................................... 17
3.1.3 ANSYS ............................................................................................................... 17
x
3.2 Material and Component Testing at Swerea SICOMP .............................................. 17
4 Numerical Modeling of Composite Structures ................................................................. 18
4.1 Module 1 – Stress Analysis ....................................................................................... 18
4.1.1 L-profile Geometry Modeling ............................................................................ 19
4.1.2 Pre-Processing .................................................................................................... 20
4.1.2.1 Meshing ....................................................................................................... 20
4.1.2.2 Material and Properties ............................................................................... 21
4.1.2.3 Loads and Boundary Conditions ................................................................. 23
4.1.3 Processing ........................................................................................................... 24
4.1.3.1 ANSYS Solver ............................................................................................ 24
4.1.4 Post-Processing .................................................................................................. 25
4.1.4.1 3D Stress Field ............................................................................................ 25
4.2 Module 2 – Failure Analysis ..................................................................................... 27
4.2.1 Max Stress Failure Criteria ................................................................................ 27
4.2.2 Puck’s Failure Criteria ....................................................................................... 28
4.2.2.1 Introduction to Puck’s action plane fracture criteria ................................... 28
4.2.2.2 Algorithm for Puck’s failure criteria ........................................................... 30
4.2.2.3 Results from IFF failure analysis ................................................................ 30
4.3 Module 3 – Progression Analysis .............................................................................. 31
4.3.1 Introduction to delamination modeling with cohesive interface elements ......... 32
4.3.1.1 Implementing Bilinear CZM Model to existing model .............................. 34
4.3.1.2 Post-processing for Progression Analysis ................................................... 36
5 Comparison with Experimental Results and Validation .................................................. 40
6 Discussions and Conclusions ........................................................................................... 43
7 Suggestions for Future Work ........................................................................................... 46
8 References ........................................................................................................................ 47
Appendix - 1 ............................................................................................................................. 50
xi
Appendix - 2 ............................................................................................................................. 51
Appendix - 3 ............................................................................................................................. 52
Appendix - 4 ............................................................................................................................. 56
Appendix - 5 ............................................................................................................................. 59
Appendix - 6 ............................................................................................................................. 61
1
1 Introduction
Failure of fiber-reinforced composite laminates is a complicated process and because of that,
failure prediction models become overly simplified since accounting for all the different
physical phenomena occurring in the failure process would be very complex [1]. In this
Thesis, composite failure modeling has been studied with the major focus in out-of-plane
direction. It is vital to know how the structure responses to the applied load, before it is
further developed and implemented in the design and manufacturing. Interpreting the failure
onset and propagation in composite structures is very important. Hence, it is important to
understand and appreciate the difficulties prior so that the limitations of these can be
understood properly [1].
Non-planar complex composite structures are prone to out-of-plane loading which might lead
to catastrophic failure due to for example delamination must be avoided when designing such
lightweight structures. Accordingly, it is necessary to precisely predict the initiation by using
suitable failure criteria. Finally, the model was developed to study how delamination grows
by introducing cohesive elements. Hence, the major objective of Thesis work is to develop a
suitable composite failure modeling approach.
1.1 Background and Origin of Thesis
GKN Aerospace Sweden has for several years been exploring the potential of using composite
materials in aero-engines to reduce weight without compromising the overall performance.
For complex thermo-mechanical applications like aero engines, composites with high
temperature capability can play an important role in enabling the use of composites in such
applications. To optimize such composites for aero-engine applications and predict their
structural performance, numerical simulations are performed. In this project, failure modeling
has been carried out on curved L-profile geometries with the aim to validate the analysis
results with the test results from a previous development program. However, to accurately
predict with accounting for all the different phenomena further work is needed in all the major
modules of the developed composite failure modeling.
1.2 GKN Aerospace Sweden Presentation
GKN Aerospace is the aerospace operation of GKN plc, serving a global customer base. With
sales of £3.6 billion in 2017, the business is focused around 3 major product areas –
aerostructures, engine products and transparencies and several specialist products like electro-
thermal ice protection, fuel and floating systems and bullet resistant glasses. The business has
2
significant participation on most major civil and military programs. GKN Aerospace is a
major supplier of integrated airframe and aero-engine composite structures. GKN also offers
one of the most comprehensive capabilities in high performance metallics processing. GKN is
also the world leading supplier of cockpit transparencies and passenger cabin windows [2].
1.3 Aims and Objectives of Thesis Work
In the General Electric GEnx engine, fan blades and the fan case are made of fibre-reinforced
composites that enable a significant reduction in the overall weight [3] [4]. Such lightweight
fan blades and fan case can effectively lead to reductions in the operational cost by a notable
amount [5]. Similarly, the replacement of frame structures in the compressor module by
composites as shown in the Figure 1 can further reduce the weight, and thus cost and CO2
emissions. The complex geometries of the modules result in new challenges where the effects
due to out-of-plane loading cannot be neglected. L and T-joints are typical examples of such
complexity (Figure 2). To predict the behavior of composites in such complex geometries due
to out-of-plane loading there is a need for accurate composite failure modeling.
Figure 1: Locations with complex geometry [6].
The aims of this Thesis are briefly listed below:
• Numerical modeling of composite structure, capable of handling the stress analysis of
the composite laminates at the ply level
• To predict onset of inter-laminar damage by using suitable failure criteria
3
• To study how delamination grows and develops by introducing cohesive elements
• To validate the analysis with the help of available test results
Figure 2: Typical T-profile cross Section [7].
This Thesis however is limited to prediction of the damage of simple L-profile composite
geometries instead of T-profiles (to reduce the computational time due to geometrical
complexity) and to develop the suitable modeling techniques. The proposed modeling
approach is also capable of handling multidirectional laminates provided the inputs are
carefully defined. However, in this report the major focus is on failure modeling for
Unidirectional (UD) non-crimp fabrics (NCF), Resin Transfer Moulding (RTM6) composite
material system [7]. The model is in-between the meso and macro scale, thus in this study the
effect of glass yarns and the fiber waviness is not included.
1.4 Why do we need Composites?
Despite several complexity involved in handling composites over other conventional material
system it is important to understand why there is a need for alternate material system. To
understand this further let us consider lifetime data for LR A330 as given by SAS airlines,
tabulated in Table 1 [5].
Table 1: Lifetime data for LR A330 [5].
Total fuel consumption One billion liters of jet fuel per engine
Average fuel prize € 0,40/L
4
The presented data is statistical and thus have variation based on the flight cycle which is
dependent on the airliner and the fuel prize which is also varying. However, from the above
data, 1 kg of structural weight reduction should save around 4000 – 5000 L of fuel which
could be further estimated to € 1,000 – 2,000 direct cost saving per kg of structural weight [5].
GEnx engines have replaced fan blade with composite which weighs 10-15% less than a
hollow-core titanium blade [3]. A typical GEnx engine is presented in Figure 3 for reference.
Since, the blades are lighter, they also explored the possibility of building a lighter fan case.
The resulting fan case which is made of composites is in total 158 kg less weight per engine
[3]. So, from the statistics mentioned above one could quickly estimate lifetime fuel and cost
saving as tabulated in Table 2:
Table 2: Estimation for composite fan case [5].
Fuel saved 700,000 – 800,000 L per engine
Cost saved € 200,000 – 320,000 per engine
Firstly, from the above study one could infer that the run time cost plays a vital role when the
cost modeling is done for structures involving composites. Also, from the above statistics it is
Figure 3: GEnx-1B Engine [4].
also clear (and a well-known fact) that composites could be one of the possible solutions to
reduce operating costs for an airliner.
Secondly, composites can be tailored in such a way that better mechanical properties or any
other desired properties can be achieved, which is further discussed in Section 2.1. At the
material selection stage, an engineer working to reduce weight must investigate specific
5
stiffness and strength properties. Typical mechanical properties of some UD fiber composites
with other conventional materials is given in Table 3 [8]:
Table 3: Mechanical properties of some UD fiber composites [8].
Material ρ (kg/m3) E (GPa)1 �̂� (MPa)2
Mild Steel 7800 206 250-500
Stainless Steel 7900 196 200
Aluminum alloy 2024 2700 73 300
Titanium alloy 4500 108 980
UD3 - Carbon/Epoxy 1600 180/10 1500/40
UD3 – Glass/Epoxy 1800 39/8 1060/30
UD3 – Kevlar/Epoxy 1300 76/6 1400/12
Note: 1 - Elastic modulus in/perpendicular to fiber direction, 2 – Tensile strength in/perpendicular to fiber direction and 3 – Prepregs with
high fiber volume fraction
From the table one should note that it is possible to make a material system with higher
specific mechanical properties. Thus, with the major goal of reducing weight in aero-engine
one must overcome the barriers created due to non-planar complex composite structures as
mentioned in Section 1.3. Hence there is a need for accurate numerical modeling of composite
structures which will be discussed in the upcoming chapters.
1.5 Flow Chart for the Thesis Work
Composite Failure Modeling is a vast topic by itself. Hence, there was a need for the plan
before going ahead with the Thesis work. A detailed work plan of the thesis work is illustrated
in Figure 4 and overall workflow of the thesis work is also shown in Figure 5.
6
Figure 4 : Gantt Chart of Thesis work.
7
Figure 5: Generic workflow of the thesis work and modeling process (marked in the blue
frame).
8
2 Literature Review
The purpose of this chapter is to summarize the literature relevant to this work investigated in
a survey that was carried out in an early stage of this thesis work. One must note that the
sections included in this chapter are brief and the main aim is to revisit some basic concepts.
2.1 Brief Introduction to Composite Materials
Composite material is defined as ‘‘A macroscopic combination of two or more distinct
materials into one with the intent of suppressing undesirable properties of the constituent
materials in favor of desirable properties’’. In a material science perspective, a composite
material is thus composed of several different distinct materials [1].The application of
composite materials is not a unique invention by mankind. Other species excel in making
composites, and they have benefited from it for millions of years. For example, the nest of the
Chinese bird shown in Figure 6 uses a similar concept as advanced carbon fiber reinforced
composites from a mechanical point of view. Clay basically plays the role of a matrix that
holds intact the reinforcements and protect them from being affected by the environment [9].
Figure 6: Example of a composite material in nature [9].
Composites are used not only for their structural properties, but also for their electrical,
thermal, tribological and environmental properties. They are usually optimized to achieve a
balance of properties based on applications and are commonly classified in two major levels.
The first level of classification is usually made with respect to the matrix constituent. This
level of classification includes: organic-matrix composites (OMC), metal-matrix composites
(MMC) and ceramic-matrix-composites (CMC). OMCs are further classified to two classes of
composites: polymer-matrix composites (PMC) and carbon matrix composites. The second
9
level of classification refers to the reinforcement form which includes: particulate
reinforcements, whisker reinforcements, continuous fiber composites and woven composites
as depicted in Figure 7 [10].
Figure 7: Classification based on reinforcement [10].
The final category of fiber architecture is formed either by weaving, braiding, knitting the
fiber bundles or also known as ‘tows’ to create interlocking fibers that often have orientations
slightly or fully in an orientation orthogonal to the primary structural plane. This approach is
taken for variety of reasons, including the ability to have structural, thermal, electrical
properties etc. in the out-of-plane direction [10].
Thus, it becomes evident that there are infinite ways by which the composite part could be
built. This is one of the major tasks of any composite engineer to optimize the design with the
right selection of constituent materials.
2.2 Application of Composite Materials
The aim of lightweight construction is to preserve or even expand a product’s functionality
while reducing the overall weight of the product. Some of the existing approaches for
reducing mass include the use of less dense materials such as metal foams and honeycombs,
composite materials etc. or decrease the material volume by reducing wall thickness in
structural components. The main reasons for the application of lightweight composites are
weight savings and possible cost savings. If there are significant weight reductions with
10
improved performance, it will also mean that there is less fuel consumption and CO2
emissions. In addition, there are several other advantages like noise and vibration reduction,
impact resistance and energy absorption capability. Composites can also be tailored to meet
specific design requirements in ways that are not possible for most conventional materials.
This could be done by correctly choosing the constituent materials and the orientation of the
reinforcement fibers. This is of primary importance for performance optimization and hence
lightweight construction could play a vital role in such applications [11].
2.3 Brief Introduction to Fracture Mechanics
Human ancestors made use of fracture phenomena more than 2 million years ago. Brittle
solids, such as flint stones, usually crack in terms of cleavage when they are tapped, and sharp
edges are formed on the stones as shown in Figure 8 which can be used as tools for cutting
food or hunting [9].
Fracture Mechanics is the study of mechanical failures which can be of many different kinds.
A failure is a sudden loss of functionality of a mechanical component or structure by
exhaustion of its load bearing capacity. The failure mechanism is thus the mode by which this
occurs like for instance buckling, fracture etc. This is to be distinguished from the concept of
damage mechanism. Damage is under most circumstances a non-favourable change of the
material properties and the material behavior which in general develops over some time span
or possibly with increasing loading. Failure is often preceded and promoted by damage
formation and sometimes the difference between the two concepts is difficult to perceive [12].
Figure 8: Chipped stone tool in paleolithic age [9].
11
The goal of fracture mechanics is to enable predictions of initiation and propagation of growth
of existing or postulated cracks of given configurations in structures of arbitrary shape. In
general, for three-dimensional elastic crack problems, three stress intensity factors are enough
to fully characterize the state at a point along the crack front. To obtain a visual impression of
the three different modes idealized illustration are provided in Figure 9 [12].
Figure 9: Three modes of Fracture [9].
2.4 Failure Mechanisms in Composite Structures
Composite failure is the result of competition between different damage mechanisms. Failure
mechanisms or modes of failure of a laminated composite can generally be divided into three
types:
1. Translaminar: Through the thickness in which fibers have been broken (Fiber-
dominated failure)
2. Intralaminar: Through the thickness in which only matrix, or fibre/matrix interface
have failed (matrix and fiber/matrix interface-dominated failure)
3. Interlaminar: In the laminate plane, in which the layers (or plies) have been
separated (matrix and fiber/matrix interface-dominated failure). This damage of
laminate is also known as delamination [13]
12
Illustrations of these 3 failure modes are given in Figure 10.
Figure 10: Illustration showing different damage in composites [13].
2.5 Failure Criteria in Composite Structures
In 1991, an ‘Expert Meeting’ was held at St Albans (UK) on the subject of ‘Failure of
Polymeric Composites and Structures’. Two key findings emerged during the meeting are as
follows [14]:
1. There is lack of faith in the developed failure criteria
2. There is no Universal definition of what constitutes ‘failure’ of composite
This meeting later led to the Worldwide failure exercise also known as WWFE [14].
Composite plies and laminates have directionally-dependent strength and they exhibit several
distinct failure modes. These anisotropic materials display more complex interaction of
multiaxial stresses and strains, making the development of reliable failure theories much more
difficult [15]. Failure criteria in a broader sense could be classified into two main categories
as listed below:
1. Interactive Failure Criteria
2. Modal Failure Criteria
Depending on the load case and stress state at laminae, the failure predicted by these criteria
can be fiber-dominated, matrix-dominated and fiber/matrix interface-dominated. In this
Thesis work, Max stress and Pucks matrix failure criteria has been implemented to the failure
analysis.
13
2.6 Brief introduction to Composite Curved Beams
As mentioned earlier in Section 1.3, Composite laminates in a wide variety of shapes start to
replace metallic counter-parts and L-shaped geometry is frequently encountered composite
curved beam. Interlaminar normal stresses are induced at the interfaces between the plies in
addition to the well-known interlaminar shear stresses due to the geometry. Mixed-mode
delamination failure occurs in the curved region of the L-shaped composite laminates under
sectional forces as illustrated in Figure 11 [16].
Figure 11: Example of L-shaped laminate showing section loads and delamination [16]
The origins of such failures can often be associated simply with transverse strength
limitations. When the loading or environmental condition is such that these interlaminar
stresses are tensile, failure may occur at load levels much less than predictions based on the
in-plane strength properties would indicate [17]. The analytical methods to determine load
bearing capabilities of curved beams are under constant development. For example; an
analytical technique suitable for calculating the stresses, strains and maximum load for a
symmetric UD layup is developed by Fu-Kuo Chang and George S. Springer in 1985 [18].
Several Numerical methods are under constant development for the stress evaluation of
curved structures. For example; stress variation along the curved beam’s width in bending
using a 3D finite element analysis was investigated. It was observed that the assumption of
plane strain for the analysis model resulted in a close solution to the 3D analysis in case of
large specimen’s width, while significant errors were obtained with the assumption of plane
stress [19].
14
Delamination research has mostly dealt with the initiation and growth of delamination.
Initiation can be predicted using stress-based criteria with some characteristic lengths.
Methods using fracture mechanics were developed for simulating delamination growth
successfully. Another approach for the numerical simulation of delamination is the cohesive
zone method, in which the framework of damage mechanics and softening is employed.
Delamination is interpreted as the creation of a cohesive damage zone in front of the
delamination front, separating the adjacent plies. This method can handle both delamination
onset and growth [20]. To predict accurately the damage of curved composite structures
damage modeling is thus important.
2.7 Modeling Approaches in Composite Structures
The use of classical (continuum) methods of stress analysis has been developed over many
decades to give techniques that can be applied satisfactorily to a vast range of situations.
Classical methods are however very limited to simple geometries and ‘real structural features’
for example the details of attachment of a stringer to a skin panel, cannot be analyzed. In such
cases one must resort to Finite Element (FE) methods. FE analysis is merely an alternative
approach to solving the governing equations of a structural problem [21]. In this Thesis, a pre-
study was carried out to decide on a suitable numerical modeling for composite L-profile
specimen and is briefly presented in Table 4.
15
Table 4: Pre-study on modeling approaches in composite structures.
Type – Stress
Analysis
Application Advantages Disadvantages
Homogenized solid
model
Useful when the
geometry is complex
and large
Easy to model and
not heavy modeling
files
Only smeared
stresses on laminate
level
Shell model Works for any layup
orientation
Suitable for in-plane
composite analysis
Extrapolated results
for out of plane
stresses
Layered solid model Works for any layup
orientation
3D stress and strains
are obtained at the
laminae level
It might be heavier
model when
implemented on the
large geometry
Type – Failure and
Growth Analysis
Application Advantages Disadvantages
Virtual crack closure
technology (VCCT)
Works for any layup
orientation
Based only on
critical fracture
toughness [9]
Crack tip needs to be
defined
Crack tip element
method (CTE)
Works for any layup
orientation
Based only on
critical fracture
toughness [9]
Crack tip needs to be
defined
Cohesive Zone
Modeling (CZM)
Works for any layup
orientation
Crack tip is not
needed
Extensive input and
mesh size influence
16
3 Methodology
The composite failure modeling carried out in this thesis can be divided into three major
modules as shown in Figure 12 (for detailed workflow of the thesis work refer to Section 1.4).
Module 1 [M1] is the first part of composite numerical modeling where the stress analysis is
carried out to obtain 3D stressing in the ply. The stresses obtained are later input to Module 2
[M2] to perform the required composite failure analysis. Once the initiation of damage is
identified then progression of failure can be simplified in Module 3 [M3] to simulate the
damage growth. It is important to note that all the three major modules are highly inter-
dependent. Therefore, the accuracy of the analysis carried out in M2 and M3 is very much
dependent on the precision achieved in M1 and M2 respectively.
Figure 12: Three major analysis modules.
3.1 FEM Software used
The software used during this thesis as per the GKN specific workflow is given in Figure 13
for the better understanding of subsequent work carried out in the thesis work.
3.1.1 Hyperworks
• HyperMesh: In this thesis HyperMesh was used as the pre-processor tool, due to its
ability to quickly generate quality meshes. The advanced geometry and meshing
capabilities provide an environment for rapid model generation [22].
Stress Analysis
[M1]
Failure Analysis
[M2]
Progression Analysis
[M3]
17
Figure 13: GKN Workflow.
• HyperView: HyperView was used as the post processing tool to visualize results
interactively [22].
3.1.2 MATLAB
MATLAB is a tool which combines a desktop environment tuned for iterative analysis and
design processes with a programming language that expresses matrix and array mathematics
directly [23]. Puck’s failure criteria are implemented in this tool for swift computation.
3.1.3 ANSYS
ANSYS structural analysis software is capable to solve complex structural engineering
problems. In this thesis work, ANSYS was used as the solver in M1 and M3 modules. CZM
pre and post processing were also performed using ANSYS [24].
3.2 Material and Component Testing at Swerea SICOMP
Test results used for comparison were obtained from the tests which were performed at
Swerea SICOMP in Piteå using an Instron 8800 testing machine with a 100 kN load cell
(calibration date 2012-11-26). The fiber preform was a Sigmatex UD weave consisting of
alternating E-glass yarns (13.5 g/m2) and 12K Toho Tenax HTS40 F13 carbon fiber roving
(242 g/m2) in the warp direction and a combi-yarn (areal weight 8.5 g/m2) in the weft
direction. The resin material used is the monocomponent epoxy system RTM6 supplied by
Hexcel corporation [7].
Hyperworksand ANSYS
[M1]
Matlab
[M2]
ANSYS and Hyperworks
[M3]
18
4 Numerical Modeling of Composite Structures
As stated in Chapter 3, this Chapter briefly introduces to all the three modules developed in
this thesis. Numerical Modeling of Composites can be broadly classified as follows;
• Structural analysis of the behavior of a fully consolidated composite structure
• Process modeling; the analysis of the manufacturing and forming of composite
materials and parts [25]
The thesis focuses on the structural analysis of the composite structure and process modeling
is not considered.
4.1 Module 1 – Stress Analysis
Stress Analysis of composites can be categorized as follows;
• Macromechanical approach: This approach involves constructing models strictly at the
global scale. This approach is straightforward in the linear elastic regime
• Micromechanical approach: In the nonlinear regime and when trying to predict
damage and failure, the macromechanical approach becomes problematic. This
approach explicitly considers the constituent materials and how they are arranged [25]
Illustration of the relevant levels of scale for composite analysis is given in Figure 14. Note
that the stress analysis carried out in this work is slightly inclined towards the mesoscale.
With the current model it is possible to obtain the 3D stress field at the ply level.
Figure 14: Relevant scale for composite analysis [25].
19
4.1.1 L-profile Geometry Modeling
As mentioned earlier in Section 1.3, the geometry under consideration is L- shaped. Also, one
should note that L/T – profiles are the typical cross-section of the complex geometry as stated
in Section 1.3. The 2D geometry was created in Hypermesh as per the cross-section
dimensions given in Figure 15. Variation in the dimensions of the four test specimens
manufactured as per this cross section is also listed in Table 5 for reference.
Figure 15: L-Shaped specimen used in this thesis work [7].
Table 5: Dimensions of the four test specimens.
Width of specimen (b in mm) Thickness of specimen (t in mm)
20.20 3.28
20.39 3.43
20.27 3.30
15.68 3.43
20
4.1.2 Pre-Processing
In this step, the composite model is setup for stress analysis. Accuracy of stress output is
controlled at this stage for any typical composite structural analysis.
4.1.2.1 Meshing
Due to simple geometric shape, the results are not sensitive to meshing. Hence, a quadrilateral
mapped plane strain element [22] was created initially by meshing the geometry mentioned in
the Section 4.1.1. This mesh was later extruded in the z-direction as per the width of the
geometry which is illustrated in Figure 16. There was no significant variation in stress results
based on the element type chosen. Finally, the stress analysis was carried out using Solid 185
elements. The element selection should be made in such a way that there are no compatibility
issues when the interface or contact elements is implemented to the existing FE model.
SOLSH190 was also tested for the model which could be alternative to the element type
chosen [24].
Figure 16: Layered Solid Model.
As a general routine in the process of meshing, the quality of the mesh was also checked as
shown in Figure 17 [22] [24]. It was observed that the minimum Jacobian was above 0.98.
Mesh was checked for default hypermesh parameters. The mesh was further refined based on
the quality check. The quality of the mesh could affect the stress and strain outputs which are
the major inputs for failure analysis. However, this check will play a vital role for complex
shaped real structures.
21
Figure 17: Mesh quality check.
4.1.2.2 Material and Properties
Hooke’s Law for a fully anisotropic material (such as fiber-reinforced composites) is shown
in Figure 18. In its most general form, it has 21 independent elastic constants [1] and 6
independent coefficients of coefficient of thermal expansion (CTE) [25].
Figure 18: General Hooke’s Law [25].
For computational purposes, general anisotropic laminae can be simplified using orthotropic
laminae or a transversely isotropic material. As mentioned earlier in Section 3.2 the material
system under consideration is a weave-based lamina. For computational simplicity UD
laminae can be characterized as transversely isotropic materials. But weave-based laminae are
better treated as orthotropic layered (materials with three orthogonal planes of symmetry for
its material properties) [1] and the model is thus developed to run with orthotropic material
input and is characterized by nine independent elastic engineering constants. As of now
thermal aspects are not included in the analysis [25]. With the stable set of inputs (thermal co-
efficient) it is possible to include them to the existing model. For the typical laminate, all the
plies may not have the same ply orientation as shown in Figure 19 [26]. In such cases, the
user must be careful while defining the material properties by controlling the necessary
transformation of the properties to the laminate axes or controlling the element orientation.
22
Figure 19: Laminate and transformation of co-ordinate system [26].
The model developed in this thesis is capable of handling multidirectional laminates by
defining the transformed material properties for each ply. A typical illustration after defining
material properties for composite numerical modeling is shown in Figure 20.
Figure 20: Material Properties at the ply level.
However, in this project the material system under consideration is UD as mentioned in
Section 3.2. Thus, laminate and laminae axes are in the same direction and hence the laminae
axes coincide with the laminate axes. But as mentioned earlier if the model has to be updated
with additional layers, change of orientation of the laminae or in general change the stacking
sequence, then the illustration in Figure 21 is helpful to define the orthotropic material
properties. The tiny blue arrows shown in the image is the out-of-plane direction for the
composite.
23
Figure 21: Global co-ordinate system and Local co-ordinate system [26].
4.1.2.3 Loads and Boundary Conditions
The interaction of tool on the specimen is defined with the help of boundary conditions. An
attempt has been made to reach closer to reality with the help of suitable boundary conditions
as listed in Table 6. Also, as shown in Figure 22, the tool setup is such that the specimen is
ideally restricted to move in the z-direction. However, during testing it was observed that the
displacement in the z-direction is miniscule for the 4 specimens. The load is controlled by
prescribing the displacement in tension (T) or compression (C) respectively as illustrated in
Figure 22 and table 6. It is important to note that tooling is not modeled in the current model.
However, for more accurate stress analysis modeling including the tool is needed.
24
Figure 22: Tool setup used for testing the specimen in Tension and Compression [7].
Table 6: Defined Boundary Conditions [7].
Global directions Horizontal (H) part of L-profile Vertical (V) part of L-profile
X free to roll gripped
Y gripped +/- prescribed δ
Z gripped gripped
4.1.3 Processing
Once the composite FE model is setup in the pre-processing stage, it needs to be processed
with help of a suitable solver. In this project ANSYS was used as the solver as per the GKN
workflow discussed in Chapter 3.
4.1.3.1 ANSYS Solver
ANSYS allows the user to control the analysis settings as per the structure under
consideration. For simple linear static analysis, it is not needed to change any of the solver
settings [24]. But if one needs to consider the incremental load step of 0.12 mm/min which
was applied during the testing [7] then it might be needed to consider large deflections.
Activating large deflection will consider stiffness changes resulting from changes in element
T C
V
H
25
shape and orientation. While small deflection and small strain analysis assume that
displacements are small and the resulting stiffness changes are insignificant. However, a rule
of thumb is that one should use large deflection if the transverse displacements in a slender
structure are more than 10% of the thickness. Due to this uncertainty, analysis was carried out
for both and the significant variation in stress and strain outputs was observed. However, the
computation time is increased when the large displacement setting is switched on [24].
4.1.4 Post-Processing
Post-processing of the stress analysis was done with the help of HyperView. It is obvious to
obtain the stresses or strains to use the suitable failure criteria in Module 2. Post processing in
composite analysis is rather substantial when one considers all the three modules. For better
clarity and to explain the methodology mentioned in the previous Chapter, the results for only
one case is considered (when the specimen is tested in tension). The results for the
compression case are presented in Appendix 4.
4.1.4.1 3D Stress Field
The stress output from linear small displacement stress analysis is illustrated in Figure 23.
Stress (XX) represents the out-of-plane normal stresses and Stress (XY) represents out-of-
plane shear stresses for the curved part of the L-profile when the prescribed displacement is1
mm. The other stress components are also given in Appendix 1 for reference.
Figure 23: Out-of-plane stress components.
26
The stress analysis was carried out with incremental load steps. The most critical sub-step
based on Max stress failure criteria are illustrated in Figure 24 and Figure 25. Some additional
stress output closer to the critical load for both the load cases is given in Appendix 3 and
Appendix 4 for reference.
• Sub step 5: δ = 0.6 mm
Figure 24: Out-of-plane stress components at δ = 0.6 mm.
• Sub step 6: δ = 0.7 mm
Figure 25: Out-of-plane stress components at δ = 0.7 mm.
27
4.2 Module 2 – Failure Analysis
The application of realistic failure criteria for the UD composite layers in laminate design is a
precondition for the successful use of laminated components in lightweight structures. Also,
use of laminated composites as a primary/secondary structural component implies an accurate
assessment of damage initiation, damage mechanisms, failure and post failure behavior. An
attempt has been made to understand and implement suitable composite failure analysis to the
model.
4.2.1 Max Stress Failure Criteria
Based on the stress output obtained in Module 1, Max stress criteria was initially used to
predict the first ply failure due to out-of-plane stresses. Based on linear stress analysis the
failure δ for different Loading Cases (LC) are listed in Table 7. All δ values are given in mm
and all stresses and failure strengths are given in MPa
Table 7: Results based on max stress failure criteria, using small deformation analysis.
Loading case δc
[mm]
δt
[mm]
δs
[mm]
Critical Ply number
LC Tension 3.69 0.36 0.35 8 or 9
LC Compression 2.97 0.44 0.35 9
Out of plane strengths 218 26.3 65
When the large displacement setting is switched on, for the incremental load step the failure δ
comes out as in Table 8. Detailed failure analysis using Max Stress criteria for every sub-step
is given in Appendix 2 for reference.
Table 8: Results based on max stress failure criteria, using large deformation analysis.
Loading case Failure δ [mm] Critical Ply number
LC Tension 0.6 – 0.7 8
LC Compression 0.3 – 0.4 9
As mentioned in the above table it is possible to predict the initiation of failure (the critical
initiation points are marked with the red). However, Max Stress and Strain failure criteria
28
have several limitations and can be used only for the quick estimate of initiation of failure.
Thus, there is need for better failure criteria which account for the mutual interaction of
stresses and for the damage mechanism involved.
4.2.2 Puck’s Failure Criteria
Puck’s failure criteria are modal based matrix failure criteria which have been implemented in
the failure analysis. Puck’s failure criteria constitute one of the competing theories involved in
WWFE-II. These criteria are based on 3D stress formulations and have already proven their
capability under two-dimensional stresses in the WWFE-I [27].
4.2.2.1 Introduction to Puck’s action plane fracture criteria
As mentioned in Section 2.4, delamination is defined as the separation of layers from each
other. This separation is caused by tensile stresses acting in the thickness direction and/or
shear stresses acting in planes which are parallel to the layer interfaces. For better
understanding, nine stresses which could possible lead to failure of the UD-laminae is also
shown in Figure 26. Interlaminar stresses exist close to geometric discontinuities such as free
edges and can be caused both by mechanical and hygrothermal loading. Even more important
for the development of delamination zones are stress concentrations at inner defects such as
tips of Inter Fiber Fracture (IFF) cracks. A figure illustrating a typical IFF crack tip is also
shown in Figure 27. Higher local stresses occur and cause local delamination at each IFF-
crack tip. Also, intensive testing has been carried out by Puck and his colleagues and their
experimental and theoretical investigations even suggest that no delamination can occur in the
absence of impact if no IFF-cracks have been developed in the laminate [28].
Figure 26: Stresses in UD-Laminae [27].
29
Figure 27: Inter Fiber Fracture [28].
For IFF analysis it is reasonable to use an adapted coordinate system. This is done because
IFF can take place on an inclined fracture plane. It is clear from the UD laminae stress state
that shear stresses τ12 and τ13 never lead to inter fiber failure. The interaction of all the stresses
is accounted for in the Puck’s failure criteria. Puck simplifies the UD laminae stress state on
the plane inclined by the angle θ as shown in the Figure 28. In the resolved plane only one
normal stress (σ n(θ)) and two shear stresses (Ͳ nt(θ) and Ͳ n1(θ)) are acting. These three
stresses potentially provoke IFF on their common action plane inclined by the angle θ.
Figure 28: Stresses on the action plane [28].
If fracture occurs on a plane inclined by a certain angle θ this plane is called fracture plane
and the corresponding angle θ is called fracture angle (θfp). A search scheme for the fracture
plane is illustrated in Figure 29 [27].
30
Figure 29: Searching for fracture plane angle [28].
4.2.2.2 Algorithm for Puck’s failure criteria
The failure analysis used in this Thesis is based on universal 3D-formulation of the action
plane related to Puck’s IFF-criteria. To determine the stresses at fracture, it is necessary first
to determine the fracture plane angle (θfp). This can be obtained by carrying out a numerical
search of fE(θ). The fracture plane is characterized as the action plane with the maximum local
stress exposure (fE(θ)) [27] [28].
4.2.2.3 Results from IFF failure analysis
The important results after the numerical search is listed in Table 9 and for better visualization
the results are also illustrated in Figure 30. For further detailed outputs after failure analysis
refer to Appendix 5.
Table 9: IFF failure criteria for LC Tension and LC Compression.
Loading case Critical Failure element ID θfp fE(θfp) Critical Ply number
LC Tension 103988 -83 3.9614 9
LC Compression 90362 85 2.6375 8
31
Figure 30: Initiation of failure for LC Tension and LC Compression.
From the IFF failure analysis the critical failure location could be obtained without any
difficulties which are observed in max stress criteria. From the above results for LC Tension
the initiation of failure happens at ply 9 interface while for the compression the initiation of
failure should happen at ply 8 interface. Prediction of IFF crack initiation gives enough
information needed to carry out the progression analysis in the laminated structure.
4.3 Module 3 – Progression Analysis
The prediction of progression of failure in composite materials is of great importance in the
design of composite structures. However, the prediction of growth of failure in composite
materials is not a trivial matter, because modes and mechanisms of failure are complex and
varied, occurring at multiple-length scales and often interacting with each other to lead to
global failure. As mentioned in the earlier chapters and sections, delamination is widely
acknowledged as one of the most important failure modes and involves both opening and
sliding modes. It can occur at relatively low load levels compared to ultimate failure by fiber
fracture but still with significant consequences for the structural load-bearing capability. It is
also caused by high interlaminar stress levels, which lead to through-thickness debonding of
the individual plies. Within this area there are now several methods for predictions, as
mentioned in Section 2.6 [29].
32
4.3.1 Introduction to delamination modeling with cohesive interface elements
The concept of CZM is based on a presumption of a zone of softening ahead of a sharp crack
tip in the material. Within this zone, the opening is resisted by cohesive tractions as illustrated
in Figure 31. The important assumption in the bilinear CZM formulations is that, the material
remains linear-elastic until it reaches its tensile strength (σ max). After the maximum limit is
reached it degrades linearly to zero at finite displacement. This is the simplest and
numerically most convenient traction-displacement curve. Other shapes could also be
considered for the study; however due to time limitation, the current study was carried out
only on the Exponential CZM model and Bilinear CZM model. Some of the observations and
results related to Bilinear CZM model will be discussed in this subchapter [29].
Figure 31: Schematic showing crack bridging tractions in cohesive zone [29].
Bilinear CZM model is the simplest and numerically most convenient traction-displacement
curve to implement because it is monotonic with no discontinuities. The area under the typical
traction displacement curves is the absorbed energy which is given by
𝐺𝑐 = ∫ 𝜎. 𝑑𝑢𝛿𝑓
0
were σ is the interfacial stress, u is the crack opening displacement and δf is the displacement
at failure. For an assumed shape of curve (see Figure 32), the stress at initiation σmax and
displacement at failure can be set such that the energy absorbed per unit cracked area is equal
to the material’s critical fracture energy, Gc thus preserving Griffith’s energy balance. The
crack thus initiates once the maximum stress criteria are exceeded and has fully propagated
when the stress is returned to zero. This gives CZM an advantage over other fracture
33
mechanics-based methods as mentioned in Section 2.6 since it can predict both initiation and
propagation of a crack [29].
Figure 32: Various typical cohesive traction-displacement curves: (a) Triangular, (b)
exponential, (c) trapezoidal, (d) perfectly plastic and (e) linear/Polynomial [29].
Implementations of interface elements have largely taken the form of planar two-dimensional
elements, which can be either zero thickness with overlapping nodes or have a very small
finite thickness. This is said to represent the thin resin-rich layer between plies. Interface
elements can also be implemented in a discrete form as non-linear springs connecting adjacent
nodes. Figure 33 shows schematically the implementation of such interface elements into a
finite element mesh [29].
Figure 33: Schematic diagrams of different formulations of interface elements [29].
34
4.3.1.1 Implementing Bilinear CZM Model to existing model
Initial first step is taken to implement CZM material model. However, further work is needed
to fully understand the post processing of CZM modeling and improve the module 3 to be
more robust than what could be obtained within this thesis work.
The mode 1 dominated bilinear CZM model assumes that the separation of the material
interfaces is dominated by the displacement jump normal to the interface as shown in Figure
34, while mode 2 or mode 3 dominated bilinear CZM models assume that the separation of
the material interfaces is dominated by the displacement jump that is tangent to the interface
as shown in Figure 34.
Figure 34: Mode 1 and mode 2 dominated Bilinear CZM law [24].
The interface element type Inter 205 [24] is implemented into the existing model as illustrated
in Figure 35. Without failure analysis one could directly implement these elements to all ply
interfaces. But that will then increase the computation time unnecessarily. To minimize the
computation time, it is enough to implement the CZM mesh only at those interfaces which are
closer to the critical ply interface location where there is higher possibility of IFF crack as
observed in Module 2.
Interlaminar fracture energy has been tested for delamination growth in a 0°/0° ply interface
for the material system mentioned in 3.2. This can be used to determine the input parameters
for the bilinear material behavior with tractions and separation distances [24].
For realistic structural applications and loading, it is likely that there will be a component of
mixed-mode loading [13]. Thus, mixed mode debonding which involves both normal
separation and tangential slip is activated by inputting data items as given in Table 10 below
[24].
35
Figure 35: Typical CZM mesh introduced into the existing model.
Table 10: Mixed mode bilinear material model input [24].
Constant Symbol Property
C1 σmax Maximum Normal Traction
C2 δnc Normal displacement jump at the completion of debonding
C3 Tmax Maximum tangential traction
C4 δtc Tangential displacement jump at the completion of debonding
C5 α Ratio of δn* to δn
c or ratio of δt* to δt
c
C6 β Non-dimensional weighting parameter
36
4.3.1.2 Post-processing for Progression Analysis
Post-processing of Module 3 is vast and not trivial like other analysis. The results are very
sensitive to mesh and defined properties. Also, the solution converges only after several
iterations and consideration of certain regularization. The first part in the module is to check
whether the response of the model is the same as expected as per the input defined. One such
illustration to check is shown in Figure 36.
Figure 36: Example illustrating bilinear behavior check.
The study of failure progression can be done either with help of cohesive interface stress or
interface separation distance. One of the observations made here is that, when there is full
separation the cohesive interface stress must approach zero while interface separation distance
should further increase. For simplicity purposes, cohesive interface stress is studied in this
thesis since the post processing of progression analysis involves several iterations and is time
consuming. The simplest LC Tension case with the minimum number of sub step is illustrated
further (see Figure 37 to Figure 43).
37
1. X-Component of interface stress
Figure 37: At δ = 0.9 mm.
Figure 38:At δ = 1.45 mm.
Figure 39: At δ = 2 mm.
38
2. XY-Component of interface stress
Figure 40: At δ = 0.9 mm.
Figure 41: At δ = 1.45 mm.
3. XZ – Component of interface stress
Figure 42: At δ = 0.9 mm.
39
Figure 43: At δ = 1.45 mm.
More detailed results for the critical sub-steps for both LC Tension and LC
Compression can be found in Appendix 5 and Appendix 6.
40
5 Comparison with Experimental Results and Validation
Two tests were carried out for LC Tension and LC Compression respectively. The
experimental rig used for testing is as shown in Figure 44. The test was carried out both
experimentally and numerically as part of the NFFP5 Refact project, which involved
composite damage study and process modeling.
Figure 44: Experimental test rig [7].
Average failure strains (measured by Digital Image Correlation) were compared and there
was some correlation between experiments as illustrated in Figure 45 and Figure 46.
However, more tests need to be conducted to have better representative failure strain which
might result in further tuning of all the 3 modules mentioned in the previous chapter.
41
Figure 45: Failure strains in Tensile tests.
Figure 46: Failure strains in Compressive tests.
It was observed in the experiment that the initiation of failure occurred at the centerline which
was also found in the failure analysis discussed in Module 2. The model also predicts
progression of failure comparable with the experiments. Expected failure displacements
predicted with the help of Module 3 as mentioned in Appendix-5 and Appendix-6 are also
comparable with experimental results as shown in Figure 47 and Figure 48.
0.58 0.592
1.491
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
FE Results Test 1 Test 2
Failu
re S
trai
n
Test Number
Tensile Test 1 and 2
FE Results
Test 1
Test 2
0.58
0.311
0.498
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
FE Results Test 1 Test 2
Failu
re S
trai
n
Test Number
Compressive Test 1 and 2
FE Results
Test 1
Test 2
42
Figure 47: Failure displacement in tensile tests
Figure 48: Failure displacement in compressive tests.
As mentioned in Section 4.1.1 there is a slight variation in geometry between the four test
specimens, which will also affects the FE results mentioned above in the comparison study.
The FE results used in this study are based on the failure δ obtained after progression
analysis. Initially, it was iterative process and computationally heavy. The average of the
geometrical dimensions was used to run the simulation since Module 3 was not very robust.
0.8 0.8
1.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
FE Results Test 1 Test 2
Failu
re δ
in (
mm
)
Test Number
Tensile Test 1 and 2
FE Results
Test 1
Test 2
0.6
0.7 0.7
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
0.72
FE Results Test 1 Test 2
Failu
re δ
in (
mm
)
Test Number
Compressive Test 1 and 2
FE Results
Test 1
Test 2
43
6 Discussions and Conclusions
The composite failure model approach developed in this thesis can handle stress analysis of
fiber-reinforced composite laminates at the ply level. Based on the stress outputs, it is also
capable to predict onset of inter-laminar damage by using a suitable failure criterion.
Depending on the accuracy of results obtained through Module 1 and Module 2, the failure
model is further capable of predicting the growth of delamination by introducing cohesive
elements to the existing model. As discussed in the previous chapter, an attempt was also
made to compare the analysis results with the available experimental results.
Some of the important observations related to composite failure modeling are also listed
below:
1. Firstly, in Module 1 the composite stress analysis was carried out for the L-profile
specimens at the intermediate level between macro and meso scale. If the stress
analysis is more detailed than what it is to date, then it might increase the accuracy of
the entire composite failure modeling. It would be interesting to see if there is any
variation from carrying out the stress analysis at the meso or micro scale. However,
this might lead to very extensive input, higher computation time, pre and post
processing time will be higher than the existing model. The implementation of fracture
plane angle in Module 3 will be more accurate when the model is at the meso/micro
scale. The tooling is not yet implemented to the model. The tooling needs to be
modeled with non-linear contact analysis and with suitable friction co-efficient to
derive more realistic 3D stress states.
2. Secondly, in Module 2 Max Stress and Strain criteria could lead to complex scenarios
in the failure analysis due to their well-known limitations. They could be used as quick
estimates to predict failure, especially for larger components. There are many
advanced failure criteria which could be modified according to the application
requirements. As mentioned in earlier Chapters, Puck’s failure criteria were used in
this thesis work. Nevertheless, the following conditions need to be met before using
Puck’s failure criteria or before modifying as per the requirement:
• It is not a generic failure criterion and mixed-mode fracture is not captured.
• Can be used only for UD (derived for non-woven), might need some modification
and extensive testing for other Layup orientation.
• Six components of stress are needed as input at the laminae level
44
• Sign convention of the stress and strength needs to be considered
• Distinguishing the different shear stress components is necessary
• Three fractural resistance in the action plane must be defined, which could be
estimated for UD laminate when certain conditions are met
• Fractural resistance due to transverse shear strength must be computed
• Validity of inclination parameters must be understood for the given material [27].
3. Finally, in Module 3 a Bilinear Cohesive Zone material model was implemented to the
existing model with inputs based on a cohesive traction separation law. The resulting
FE model has increased computation time. It is important to note that the outputs that
need to be derived from this analysis must be thoroughly understood before running
the analysis. Also, solution controls in ANSYS should be pre-defined as per the
requirement to reduce the computation time. Contact elements could be implemented
instead of interface elements to replace the inputs directly with the help of critical
fracture energy. The developed model is flexible to implement other techniques to
capture the growth of failure. If interface elements are still used in the analysis, then
the input parameters need to be computed with the help of critical fracture energy.
The capabilities of the failure model developed in this master thesis work are as follows:
1. Module 1 predicts 3D stress/strain at laminae level. It can also be used for
multidirectional laminates. For accurate failure analysis, stresses at the laminae level
plays an important role since most of the failure criteria need strengths at ply level as
input.
2. Max Stress and Max Strain failure criteria can be easily determined with the 3D stress
state. This could be the quick way to estimate the failure location. These failure
criteria might come handy for complex geometry with many elements.
3. Module 2 also includes Pucks failure criteria. The advanced failure criteria can predict
accurately the failure location for UD laminates without any major drawbacks as
observed in Max Stress criteria. Inclusion of σ11 to the Puck’s failure criteria is also
implemented in the Module 2.
4. For more accurate failure progression analysis several other inputs are needed for
example fracture plane angle which is also obtained with the help of IFF failure
analysis as mentioned in Chapter 4.
45
5. Along with intralaminar failure initiation, translaminar failure is also considered in
Module 2 since it is important to check when the composite failure analysis is carried
out. Several other check parameters that are needed before using the Puck’s failure
criteria are also included in the Module 2.
6. Module 3 can handle the progression analysis based on input from Module 2. In
relative terms it is quite robust if Module 2 is considered in the failure analysis.
7. The complete package of composite failure models is split into three major modules as
mentioned earlier and hence the failure model developed in this thesis work is robust
to use as three separate modules. This allows the user to perform the necessary
modifications as per the requirement of the analysis.
8. As mentioned in Chapter 5, there is correlation between experiments conducted as a
part of NFFP5 Refact project and the numerical model. Further testing was not
conducted since there was slight delay in the arrival of materials needed for the
testing. However, several tests (at least 5 in each Load Case) need to be carried out to
get more accurate results for complete validation of the model. This might lead to
further tuning of the existing model. By using the suitable statistical methods, it is then
possible to further understand the spread of the experimental results. The scattering of
results could be due to the non-conformance that exist within the test specimens.
46
7 Suggestions for Future Work
Some suggestions for future work based on the observation during this master thesis work are
listed below:
1. Module 1 doesn’t include material non-linearity. For the more accurate stress analysis
this needs to be considered since, the failure analysis is completely dependent on
stress results at the laminae level. Also reducing the scale into meso/micro level so
that the behavior between constituent materials is considered. The material system
considered in this master thesis work is not woven. The effect of alternating E-glass
yarns could be implemented into Module 1.
2. To date, IFF failure analysis in Module 2 doesn’t include all the inclusions. If all the
possible inclusions could be implemented into Module 2 for improved accountability.
Also, there might be need of other advanced failure criteria for the multi-directional
laminates. Max Stress/Max Strain criteria could still be used but Puck is very specific
to UD laminate unless it is modified for multi-directional laminates which will result
in several testing for defining the inputs to run the failure criteria.
3. Due to time limitation and lack of experimental data, complete post-processing of
Module 3 was not carried out since, such a process is time consuming. Detailed in-
depth modification and post-processing of Module 3 could be another important step
in failure progression analysis. Stiffness degradation could also be accounted for in
this module for better accuracy. To date Module 3 is dependent on the input to the
cohesive traction separation law. Robustness of Module 3 could be improved by
directly replacing the traction approach by other CZM modules (with lesser pre-input
calculations) in ANSYS.
4. It is possible to combine all the modules and automate the entire process. This could
save time and lead to a more efficient approach.
5. Additional testing is needed to validate the modeling suggested in this work.
6. Further improvement of the robustness of the composite failure modeling.
47
8 References
[1] D. Zenkert and M. Battley, Foundations of Fibre Composites, Paper 96-10, 2003.
[2] GKN IT Department, "GKN Group," GKN Aerospace, [Online]. Available:
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Manufacturing, Analysis and Performance, J. Njuguna, Ed., Woodhead Publishing, 2016.
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loading: Demonstrator tests and model predictions," GKN Aerospace, Trollhättan, 2014.
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[13] E. S. Greenhalgh, Failure Analysis and fractography of polymer composites, Woodhead
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[14] M. Hinton, A. Kaddour and P. Soden, The world-wide failure exercise: Its origin,
concept and content, Elsevier, 2004.
[15] Marklund, Erik;, "Literature Survey of 3D failure criteria," Swerea SICOMP, Mölndal,
2010.
[16] B. Gozluklu, I. Uyar and D. Coker, "Intersonic delamination in curved thick composite
laminates under quasi-static loading," Elsevier mechanics of materials, no. August 2014,
p. 20, 2014.
[17] K. Kedward, R. Wilson and S. Mclean, "Flexure of simply curved composite shapes," p.
10, 1989.
[18] F.-K. Chang and G. S. Springer, "The Strengths of Fiber Reinforced Composite Bends,"
1985.
[19] J.-H. Kim, K.-H. Nguyen, J.-H. Choi and J.-H. Kweon, "Experimental and finite element
analysis of curved composite structures with C-section," Elsevier, p. 12, 2016.
[20] "Delamination analysis of multi-angle composite curved beams using an out-of-autoclave
material," Elsevier, p. 11, 2017.
[21] F. L. Matthews, G. A. O. Davies, D. Hitchings and C. Soutis, Finite Element Modelling
of Composite Materials and Structures, Cambridge: Woodhead Publishing, 2003.
[22] "Hyperworks Documentation," Altair, [Online]. Available:
https://www.altairhyperworks.com/. [Accessed 19 07 2018].
[23] "Mathworks Documentation," Mathworks, [Online]. Available:
https://www.mathworks.com/products/matlab.html. [Accessed 19 07 2018].
[24] "ANSYS Structural Analysis Documentation," ANSYS, [Online]. Available:
https://www.ansys.com/products/structures. [Accessed 19 07 2018].
[25] J. Aboudi, S. M. Arnold and B. A. Bednarcyk, Micromechanics of Composite Materials,
A Generalized Multiscale Analysis Approach, Elsevier, 2013.
[26] C. Kassapoglou, Design and Analysis of Composite Structures, with applications to
49
aerospace structures, Wiley, 2013.
[27] H. M. Deuschle and A. Puck, "Application of the Puck failure theory for fibre-reinforced
composites under three-dimensional stress: Comparison with experimental results,"
Journal of Composite Materials, 2012.
[28] M. Knops, Analysis of Failure in Fiber Polymer Laminates, The Theory of Alfred Puck,
Springer, 2008.
[29] S. Hallett and P. Harper, Numerical Modeling of Failure in Advanced Composite
Materials, P. P. Camanho and S. R. Hallett, Eds., Woodhead Publishing, 2015.
50
Appendix - 1
• Other 4 stress components in the radial part of the profile for LC Tension
51
Appendix - 2
LC Tension δc δt δs LC Compression δc δt δs
δ1 = 0.1 61.8 6.2 5.9 δ1 = 0.1 28.5 4.551 3.6
δ2 = 0.2 30.5 3.2 2.9 δ2 = 0.2 13.75 2.33 1.8
δ3 = 0.4 20.1 2.2 1.9 δ3 = 0.3 8.8 1.59 1.2
δ4 = 0.5 14.88 1.699 1.4 δ4 = 0.4 6.4 1.21 0.9
δ5 = 0.6 11.76 1.4 1.2 δ5 = 0.5 4.98 0.99 0.8
δ6 = 0.7 9.7 1.2 0.9 δ6 = 0.6 4.04 0.84 0.6
δ7 = 0.8 8.21 1.07 0.8 δ7 = 0.7 3.38 0.73 0.5
δ8 = 0.9 7.1 0.97 0.695 δ8 = 0.8 2.88 0.65 0.5
δ9 = 1.1 6.24 0.897 0.611 δ9 = 0.9 2.5 0.6 0.4
δ10 = 1.2 5.557 0.84 0.544 δ10 = 1.0 2.2 0.54 0.38
δ11 = 1.3 4.999 0.798 0.489 δ11 = 1.1 1.96 0.5 0.36
δ12 = 1.4 4.535 0.7665 0.444 δ12 = 1.2 1.76 0.47 0.33
δ13 = 1.5 4.1445 0.7 0.41 δ13 = 1.3 1.598 0.44 0.3
δ14 = 1.6 3.811 0.73 0.37 δ14 = 1.4 1.458 0.42 0.28
δ15 = 1.76 3.5 0.72 0.34 δ15 = 1.5 1.338 0.398 0.26
δ16 = 1.88 3.26 0.72 0.32 δ16 = 1.6 1.236 0.38 0.24
δ17 = 2 3.03 0.722 0.3 δ17 = 1.7 1.146 0.37 0.22
Out of plane
strengths
218 26.3 65 Out of plane
strengths
218 26.3 65
Critical ply
number
8 9
Table 11: Max stress failure criteria for all load steps
52
Appendix - 3
• Sub step 3: δ = 0.353 mm
• Sub step 4: δ = 0.471 mm
53
• Sub step 5: δ = 0.59 mm
• Sub step 6: δ = 0.71 mm
54
• Sub step 7: δ = 0.82 mm
• Sub step 8: δ = 0.94 mm
55
• Sub step 9: δ = 1.06 mm
56
Appendix - 4
Note: Title of the result file reads tension. This Appendix includes results for LC
compression. It was a renaming error before running the file.
Prescribed δ = 1 mm
57
• Sub step 3: δ = 0.3 mm
• Sub step 4: δ = 0.4 mm
58
• Sub step 5: δ = 0.5 mm
• Sub step 6: δ = 0.6 mm
59
Appendix - 5
• After numerical search, results obtained through IFF failure analysis for LC Tension
when the influence of (σ11) stresses is assumed to be negligible
• After numerical search, results obtained through IFF failure analysis for LC Tension
when the influence of (σ11) stresses is considered
60
• After numerical search, results obtained through IFF failure analysis for LC
Compression when the influence of (σ11) stresses is assumed to be negligible
• After numerical search, results obtained through IFF failure analysis for LC
Compression when the influence of (σ11) stresses is considered
61
Appendix - 6
Progression Analysis cohesive stresses at the radial part of the L-profile between ply 8 and 9
interfaces
LC Tenison: For each sub step cohesive stresses are given in the following order: X-
Component of interface stress, XY-Component of interface stress and XZ – Component of
interface stress (Note: XZ – Component is Zero at majority of location)
1. δ = 0.8 mm (Normal cohesive stress approaches zero at this load)
62
2. δ = 0.96 mm (Tangential XY cohesive stress approaches zero)
63
64
3. δ = 1.28 mm (Full tangential separation)
65
Solution terminates after 17 sub steps, since there is full tangential separation.
LC Compression: For each sub step cohesive stresses are given in the following order: X-
Component of interface stress, XY-Component of interface stress and XZ – Component of
interface stress. (Note: XZ – Component is Zero at majority of location)
1. δ = 0.6 mm (Initiation of XY tangential shear separation at this load)
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67
2. δ = 0.7 mm (Initiation of normal separation since, X- component of cohesive stress
approaches zero at most elements)
68
3. δ = 1.16 mm (Complete tangential separation at this load step)
69
Solution terminates after 13 sub steps, since there is full tangential separation.
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