New concepts for lightweight New concepts for lightweight

composite materials for transport composite materials for transport

aircraftaircraft

Pedro M.P.R. de Castro CamanhoPedro M.P.R. de Castro Camanho

Department of Mechanical Engineering

University of Porto, Portugalpcamanho@fe.up.pt

S. José dos Campos - 2013

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

1. Introduction.

2. Analysis models.

o Micro-mechanical models.

• Representative volume elements of UD and textile composites.

o Meso-mechanical models.

• Smeared crack model for ply damage.

1.Introduction

Contents

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o Macro-mechanical models.

• Finite Fracture Mechanics model for notched strength.

3. Non-conventional laminates.

o Thin ply laminates.

o Variable stiffness laminates.

o Locally hybrid laminates.

4. Conclusions.

2

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions1.Introduction

“Alcoa announced its intention to reduce the cost and weight of its products by 20% in order to

defend the position of metallic aerospace structures against composites.” J. Hinrichsen, “Alcoa

Aerospace – Optimized Solutions Meeting Mission Requirements”, Aeromat Plenary Session

Address, Orlando, Florida, 6 June, 2005.

Airframe structure breakdown by failure mode designing the

structure:

1. Reduction of recurring and non-recurring costs. 2. Improvement of the mechanical response of

composite structures with respect to the main

design drivers.

/413

3. Explore the potential of composite materials as the basis of multifunctional structures.

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions1.Introduction

D. Reys, PhD thesis

Experimental evidence

/414

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions1.Introduction

(Koerber and Camanho,

Mechanics of Materials, Vol. 42,

1004-1019, 2010).

a) dependence of the fracture angle on the applied stress:

Experimental evidence

/415

b) in-situ effect:

(Camanho, et al., Composites-A, 37, 164-175, 2006). (SW Tsai, Stanford University, private communication, 2011).

Same

applied

stress

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions1.Introduction

c) plastic deformation prior to transverse cracking and strain rate effects:

/416(Koerber and Camanho, Mechanics of Materials, 42, 1004-1019, 2010).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

μmMicro

1.Introduction

Bottom-up approach – from material to structure.S&T developments

/417

mm

m

Meso

Macro

(structural)

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions1.Introduction

Top-down approach – from structure to material.Engineering practice

Critical Area Selection Failure Analysis Safety Margins

OptimisationStability AnalysisLoad Case Selection

/418

(Figure courtesy of Dr. Stephane Mahdi, Airbus, Personal Communication)

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions2. Analysis models

• To support the development and validation of the constitutive models for the

homogenised composite material.

• To understand the effects of constituents on the mechanical response of the

composite material – towards the material design.

• To be able to predict the effects of defects on the mechanical response of

composites.

• To lay-out the foundations for multi-scale analysis.

Main objectives of micro-mechanical analysis:

/419

• To lay-out the foundations for multi-scale analysis.

Generation of random RVEs Mesh generation Material models for

the constituents

Application of PBC and

analysis

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Representative volume element of UD composites

• Paraboloidal yield criterion:

• Non-associative flow-rule; flow potential defined as:

Plasticity/damage model for the epoxy resin

• Plasticity model combined with an isotropic damage model.

• Cohesive elements at fiber-matrix interfaces.

2. Analysis models

(N.W. Tschoegl, J. of Polymer Science, 32, 239-267, 1972).

/4110

• Cohesive elements at fiber-matrix interfaces.

(A.R. Melro, P.P. Camanho, International J. Solids and Structures, 50, 1897-1905, 2013).

1-element test:

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Representative volume element of UD composites

2. Analysis models

Computational

Three-dimensional failure criteria (homogenized ply)

/4111

Computational

micromechanics

(mean)

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Representative volume element of 5HS textile composites

Resin: plastic damage model

2. Analysis models

/4112

Composite tows:

transversely

isotropic damage

model

(A. Melro, P.P. Camanho, F. Pires, Computational Materials Science, 61, 116-126, 2012).

Elastic and strength properties of the tows obtained using computational micromechanics

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Representative volume element of 5HS textile composites

2. Analysis models

Damage in the tows Equivalent plastic strain in the resin

/4113(A. Melro, P.P. Camanho, F. Pires, Computational Materials Science, 61, 116-126, 2012).

Damage in the tows Equivalent plastic strain in the resin

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

• To predict the inelastic deformation and fracture of composite laminates, from

first ply fracture to structural collapse.

Main objectives of meso-mechanical analysis:

2. Analysis models

/4114

(Micrographs from: T. Hobbiebrunken, et al.

Composites Part A, 37, 2248–2256, 2006).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Structural tensor of a transversely isotropic solid

with preferred direction a.

Preferred direction

Proposed approach - smeared crack model with uncoupled plasticity

2. Analysis models

Most general invariant form of the yield surface:

/4115

Preferred direction

(Vogler, Rolfes, Camanho, Mechanics of Materials, 59, 50-64, 2013).

(Boehler, Application of tensor functions in solid mechanics, Springer, 1987).

(Spencer, Deformations of fibre-reinforced materials, Oxford, 1987).

Invariants:Decomposition of the stress tensor:

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Preferred direction

Elastic domain:

Proposed approach - smeared crack model with uncoupled plasticity

2. Analysis models

/4116

Preferred direction

(Vogler, Rolfes, Camanho, Mechanics of Materials, 59, 50-64, 2013).

Non-associative flow rule -

plastic potential defined as:

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions2. Analysis models

In-plane shear: Transverse shear:

/4117(Vogler, Rolfes, Camanho, Mechanics of Materials, 59, 50-64, 2013).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Transverse fracture – smeared crack model

Must account for the in-situ effect:

2. Analysis models

Failure criteria (transverse failure):

Must predict the fracture angle:

/4118

Must account for the in-situ effect:

(Camanho, et al.,

Composites-A, 37, 164-175,

2006).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Preferred direction

Additive decomposition of the strain tensor:

Stress-strain law:

Traction tensor:

Transverse fracture – smeared crack model

2. Analysis models

/4119

Preferred direction

Relation between the cracking strain and the displacement jumps:

System of non-linear equations:

solved for

cohesive law that accounts for general loading conditions.

(Camanho, Bessa, Catalanotti, Vogler, Mechanics of Materials, 59, 36-49, 2013).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Longitudinal fracture

Linear softening laws are not suitable to simulate longitudinal cracks.

Shell model of CT Specimen

cohesive elements

2. Analysis models

/412020

0

1000

2000

3000

4000

5000

0 0.5 1 1.5 2 2.5 3 3.5 4

Rea

ctio

n F

orce

, N

Applied Displacement, mm.

Bilinear

Test

Linear

(Dávila, Rose, Camanho, Int. Journal of Fracture, 158, 211-223, 2007).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Off-axis compression θ=15⁰, 30⁰, 45⁰, 60⁰, 75⁰, 90⁰

2. Analysis models

/4121(Camanho, Bessa, Catalanotti, Vogler, Mechanics of Materials, 59, 36-49, 2013).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Effects of size on the strength of notched laminates

Examples

2. Analysis models

[90/0/±45]3s IM7-8552 laminate

/4122

Transverse matrix cracking

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Low-velocity impact

Examples

2. Analysis models

/4123(Lopes, Camanho, et al., Composites Science and Technology, 69, 926-936, 2009).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

ExamplesLow-velocity impact

2. Analysis models

/4124(Lopes, Camanho, et al., Composites Science and Technology, 69, 926-936, 2009).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Low-velocity impact

Examples

2. Analysis models

/4125(Lopes, Camanho, et al., Composites Science and Technology, 69, 926-936, 2009).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

• To perform quick-sizing analysis for preliminary design.

• To enable the optimization of complex composite structures.

Main objectives of macro-mechanical analysis:

2. Analysis models

/4126(Camanho et al., Composites Part A, 43, 1219-1225, 2012).

IM7-8552 CFRP, [90/0/±45]s

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions2. Analysis models

Finite Fracture Mechanics“Both energy and stress criteria are necessary conditions for fracture but neither one nor

the other are sufficient”.

“The incremental form of the energy criterion is the foundation of FFMs”.(Leguillon, European J. of Mechanics A, 21, 61-72, 2002).

/4127(Camanho et al., Composites Part A, 43, 1219-1225, 2012).

Complex Variable Theory

(Lekhnitskii) Finite width correction

factor

, λ 0

, λ=1

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions2. Analysis models

IM7-8552 CFRP

λ=1

/4128

IM7-8552 CFRP

[90/0/±45]s

(Camanho et al., Composites Part A, 43, 1219-1225, 2012).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Thin-ply laminates

3.Non-conventional laminates

1. Improved fibre dispersion and reduced crimp angle.

2. Possibility of using continuous lay-up: mid-plane symmetry no longer required.

3. Improved resistance to delamination.

[(+45n/-45n/0n/90n)r]s

Free-edge delamination

/4129

Skin-stiffener debonding

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Thin-ply laminates

3.Non-conventional laminates

(Amacher et al., ICCM19, Montréal, 2013.)

4. Increased ply longitudinal compressive strength

0

200

400

600

800

1000

1200

XC (MPa)

Ply thickness (mm)

1052

869 848 -19%

0.03 0.10 0.30

/4130

0100200300400500600700800900

UTS (MPa)

Max. ply thickness (mm)

800710

-11%

847 832

595-30%

0.030.100.30 0.08 0.16

UD1 NCF2

5. Increased laminate (QI)

tensile and compressive

unnotched strengths

0

100

200

300

400

500

600

UCS (MPa)

Max. ply thickness (mm)

540465

-14%

0.08 0.16

NCF2

(Mollenhauer el al., Composites – A, 43, 2012).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Thin-ply laminates

3.Non-conventional laminates

6. Open-hole strength:

reduction (quasi-static)

and increase (fatigue).

0.30 mm (thick plies)

0.03 mm (thin plies)

(Amacher et al., ICCM19, Montréal, 2013.)

(SW Tsai, private communication.)

/4131

7.Increase of the bearingstrength

(Amacher et al., ICCM19, Montréal, 2013.)

0

100

200

300

400

500

600

700

σbu (MPa)

Ply thickness (mm)

584 573476

-18%

0.03 0.10 0.30

UD1

(Iarve et al, Composites – A, 36, 2005).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Variable stiffness laminates

3.Non-conventional laminates

/4132(Lopes, Camanho, Gurdal, Int. J. of Solids and Structures, 44, 8493-8516, 2007).

Tow-overlap methodTow-drop methodLinear fibre orientation variation:

Notation: [φ <T0|T1>]

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Variable stiffness laminates

3.Non-conventional laminates

/4133(Lopes, Camanho, Gurdal, Int. J. of Solids and Structures, 44, 8493-8516, 2007).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Locally hybrid composite laminates for heavily loaded bolted joints

3.Non-conventional laminates

Proposed solution: local reinforcement

of the bolted joint using metal layer embedding.

/4134(Camanho, Fink, et al., Composites – Part A, 40, 926-936, 2009).

(Figures courtesy of CASA - Espacio).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Locally hybrid composite laminates for heavily loaded bolted joints

3.Non-conventional laminates

Vega payload adapterAriane V MT-boosters

/4135(Camanho, Fink, et al., Composites – Part A, 40, 926-936, 2009).

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions

Conclusions

4.Conclusions

Advanced computational models (microAdvanced computational models (micro-- and and mesomeso--mechanical):mechanical):

� Micro-mechanical models provide information on the effects of the microstructure on

the global response of a composite material. In addition, such models are useful to

support the development of material models for the homogenized composite.

� Meso-mechanical models do not require pre-cracks or pre-knowledge of fracture planes.

� Different failure mechanisms can be simulated in an integrated approach.

� Energetic regularization is required to avoid mesh-dependency.

/4136

MacroMacro--mechanical models (simplified models):mechanical models (simplified models):

� Provide solutions in a few seconds with a good accuracy.

� Use independently measured material properties defined at laminate level.

� The Finite Fracture Mechanics model reduces the level of empiricism of the traditional

analysis methods – model calibration is no longer required.

1.Introduction 2.Analysis models 3.Non-conventional laminates 4.Conclusions4.Conclusions

NonNon--conventional laminates:conventional laminates:

� Advanced polymer composite materials are currently not used to their full potential.

New concepts, spanning from new types of composite materials to better use of

existing materials, are required to further reduce structural weight and to keep

composites competitive.

� The new concepts proposed have the potential to reduce the weight of composite

structures.

Technology transfer:Technology transfer:

/4137

Technology transfer:Technology transfer:

Acknowledgements

NASA – Langley Research Center, U.S.A.

European Space Agency

Airbus Industries

Daimler AG / Mercedes-Benz

NASA – Langley Research Center, U.S.A.

U.S. Air Force Research Laboratory

Professor Steve Tsai

Chomarat