Interaction of thermal loading on the damage evolution of ...

22ème

Congrès Français de Mécanique Lyon, 24 au 28 Août 2015

Interaction of thermal loading on the damage

evolution of composite materials

M. EL MOUFARI, L. EL BAKKALI

Modeling and Simulation of Mechanical Systems Laboratory, Abdelmalek Essaâdi

University, Faculty of Sciences, Tetouan, Morocco

Résumé

Le but de ce travail est de caractériser et de distinguer les rôles respectifs du gradient de la

température et du chargement mécanique sur les mécanismes d'endommagement des composites

stratifiés utilisés dans l'aéronautique afin de comprendre les mécanismes de dégradation de ce

matériaux due à des interactions entre les contraintes thermiques et mécaniques. Dans cet article,

plusieurs simulations numériques destinées à décrire l'initiation et l’évolution de chaque mode

d'endommagement sont proposées et atteintes pour le composite stratifié Carbone / Epoxyde.

Abstract

The objective of this work is to characterize and discriminate the respective roles of a thermal

gradient, a pressure holding and a cycling loading on the damage mechanisms of composite laminates

used in aeronautics in order to understand damage mechanisms due to interactions between thermal

and mechanical stresses. In this paper several numerical simulations meant to describe initiation for

each damage mode are proposed. The estimation of damage modes contributions is achieved for

Carbone/Epoxy laminates in order to predict the evolution of damage mode transition

Keywords: Composite, Fatigue, High-Temperature, Mechanical loading,

Damage, Hashin’s criterion.

1 Introduction

The damage evolution process in composite materials is one of the important complicated focuses of

fatigue behavior investigation of composite materials and also is the foundation to predict fatigue life

of composite structures for engineering application.

The fatigue of laminated composite structures is preceded by different damage mechanisms involving

fracture initiation and propagation. Fracture in a composite laminate can appear either between two

plies or within a lamina. In the first event, interlaminar fracture or delamination, the crack causes

separation of two adjacent plies and will mainly involve matrix failure or matrix-to-fibre debonding

although some failure of fibers bridging the delamination may also occur. In the second event,

intralaminar or translaminar fracture, the crack is located within the lamina, either parallel to the fibres

(matrix crack) or at an angle (with fibre failure). When an intralaminar crack propagates at a certain

angle to the reinforcing fibres, the fibres bridge both surfaces of the crack, arresting or reducing

further crack opening until the bridging fibres are broken [1].

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The prediction of matrix cracking growth under thermal cyclic variations was not studied as much, as

its mechanical fatigue loading counterpart. Favre et al. [2] studied the damage behavior of various

composite materials, with carbon fibres and thermoset matrices (epoxy, cyanate or bismaleimide),

subjected to thermal cycling.Gotsis et al. [3] predicted the damage initiation and damage growth using

ICAN and CODSTRAN. However, in case of matrix failure, a lot of discrepancy was found between

the predicted and measured failure strengths and strains which were attributed to residual matrix

stiffness and presence of biaxial stress state.

Chang [4] developed an analytical model to predict the failure and response on application of in-plane

tensile and shear loads. Ha [5] investigated micromechanics of failure to predict failure in reinforced

composites using hexagonal arrays and unit square cells. Hashin [6] proposed failure criteria for

unidirectional composites. These criteria consider four different damage initiation mechanisms: fiber

tension, fiber compression, matrix tension and matrix compression. Engblom and Havelka [7]

combined the Hashin [6] and Lee [8] criteria to predict in-plane failure and delamination. Li et al. [9]

analysed the effects of shear on delamination in layered materials. The dependence of deformation in

the notch region on shear was studied. Finite element approaches were used to obtain expressions for

shear components of the energy release rate.

The aim of this study is to create a finite element model of the compact tension (CT) specimen in

order to characterise damage processes in carbon/epoxy laminates submitted to thermal and

mechanical loading. This ambitious objective requires a good preliminary understanding of the

thermal mechanical fatigue and damage mechanisms, their respective ranges of validity and their

interaction.

2. Analytical Model of Damage

The damage development of composite materials can be described by stiffness degradation of

materials in fatigue behaviour investigation.

Since different failure mechanisms occur in tension and compression, Hashin further subdivided

each failure mode into a tension and compression mode. Based on this theory [6], the Hashin

damage model was used for predicting the onset of failure and post failure response of the material.

Strength properties of unidirectional lamina were calculated using Hashin’s equations for the case of

plane stress as follows [6].

Indeed,

Tensile fibre failure for 11 0

2 2 2

12 1311

2

t

f TL

FX S

(1)

Compressive fibre failure for 11( 0)

2

11c

f CF

X

(2)

Tensile matrix failure for 22 33( 0)

13

2 2 221222 33 23 22 33

2 2

t

m T

T L

FY S S

(3)

Compressive matrix failure for 22 33( 0)

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a=26

W=51

e=1

6

t=4

h =

60

x =14

x

y

d=ϕ8

0°

13

2 2 2 221222 3322 33 23 22 33

2 2 21

2 4

cc

m

T C T T L

YF

S Y S S S

(4)

In the above equations, TX : The longitudinal tensile strength; CX : The longitudinal compressive strength;

TY : The transverse tensile strength; cY : The transverse compressive strength;

LS : The longitudinal shear strength;

TS : The transverse shear strength;

is a coefficient that determines the contribution of shear stress to the fiber tensile initiation criterion,

ij are components of effective stress tensor.

3. Geometric model & Material Properties

3.1 Model geometry: The Compact Tension specimen (CT) shown in Fig.1 has been designed to characterize the damage

process in large composite structures as considered in the ASTM standard E399-90 [10]. It is the

samples of the most commonly used test for the determination of the intralaminar fracture toughness

in composite laminates.

The use of CT specimen in composite materials was already studied by Minnetyan and Chamis [11]

who studied the initiation and propagation of the damage by a scaling computational methodology and

a series of experimental tests on carbon-epoxy laminates. The authors have experimentally designated

the modes of the damage distribution and physical locations that appeared in the CT specimen.

As a matter of fact, the energy release rate for this type of specimen is related to the stress intensity

factors as shown in Eq.5 for composites laminates as follows:

2

22

Ic x XIc xy

y XYx y

K E EG

E GE E (5)

The stress intensity factor according to ASTM E399-90 using CT specimens is such that:

( )cIc

PK f a w

t w (6)

Fig. 1: Shape and size of compact tension specimen (dimensions in

mm)

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(6) In (5),

22

2

( )

22

x XIc c xy

y XYx y

E Ef a wG P

E Gt w E E

(7)

Where,

2 3 4

3 2

2 ( )( ) [0.866 4.64( ) 13.32( ) 14.72( ) 5.6( ) ]

(1 ( ))

a wf a w a w a w a w a w

a w

(8)

With t is the thickness of specimen shown in Fig.1, w is the dimension from the load line to

the right hand edge of the specimen. Ѵxy is the major Poisson's ratio, and Ex, Ey, Gxy, are Young's

modulus of the material in x and y direction and the shear modulus respectively.

From this equations, a load-index has been derived taking into account that G is proportional to the

square of the load and, therefore, to the square of the stress. In this way, when the strain energy release

rate on the specimen equals the fracture toughness of the fiber, which implies crack propagation, the

load and stress-state can be obtained as:

c c cP G

P G

(9)

Where Pc and σc correspond to the load and stress-state when G in the specimen is equal to Gc.

3.2 Material Properties The material properties used in this work are those of a high-performance unidirectional carbon fiber

reinforced epoxy Hexcel pre-preg (IM7 / 8552) are shown in Table. 1, measured in a previous

investigation [2], With a nominal ply thickness of 0.25 mm, and the reference stacking sequence

considered in the study is [90-0]8s.

Table 1 : IM7-8552 properties

Elastic ply properties

E1 171.42 GPa

E2 =E3 9.08 GPa

G12 =G13 5.29 GPa

G23 3.98 GPa

ν12 = ν13 0.32

ν23 0.5

UD ply strength

TX 2326.2 MPa CX 1200.1 MPa

TY 62.3 MPa cY 200.8 MPa LS 92.3 MPa

Fracture energies [kJ/m²]

Fiber tension G1+ 81.5

Fiber compression G1- 106.5

Matrix tension G2+ 0.2774

Matrix compression G2- 5.62

4. Finite element modeling and results In this study, the numerical modeling was carried out using commercial software commonly

used for FEM calculations ABAQUS/CAE, which is an engineering tool that is used to solve

various engineering problems ranging from linear to non-linear problems that are complex.

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The compact tension specimen considered in the present study is modeled numerically in 3-D plane

shell with the dimension parameters defined (Fig.1). Due to the symmetry of the problem and load of

the specimens, only one half of the specimen is modeled and a finer mesh was assigned to the region

around the crack tip, during the FE analyses in order to obtain an accurate representation of the

stress/strain fields on that region. .Symmetry boundary conditions are taken in the plane of the crack

ahead of the crack tip. This study included the loading holes modeling to prove that the presence of the

loading hole varies the stress distributions in the specimen, especially for the in-plane shear stress.

This study include both in-phase and out-of-phase thermo mechanical fatigue (TMF) loads as shown

in Fig.4. In order to characterise thermo-mechanical fatigue behaviour from 100 to 500°C, the

specimen was tested under four in-phase tests at maximum stress levels of 244, 367, 441 and 612

MPa, and another four out-of-phase tests at 293, 367, 441 and 612 MPa.

The numerical studies have shown that the stress evolution of the in-phase loading is higher than those

of out-of-phase thermo mechanical loading, which means that the in-phase thermo mechanical loading

is always more severe than the out-of-phase loading .

Fig. 2: The domain of stress distribution in the x-

axis Fig. 3: Evolution of the equivalent stress in

(x,y) plane

Fig. 5: in-phase and out-of-phase stresses as function of r, distance from the crack tip to the point

where the stress is evaluated. o: in-phase loading, 𝛁 :out-of phase

Fig. 4: Thermo mechanical fatigue loads, (a) in phase loading, (b) out of phase loading

0 1 2 3 4 5 6 7

x 10-5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

8

Distance r from crack tip (m)

Stre

ss S

22 a

t dis

tanc

e r (

Pa)

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The evolution law of the damage variable in the post-damage initiation phase is based on the fracture

energy release rate dissipated during the damage process, Gc.

The Energy release rate measured from finite element method which computes the J-integral for

different values of crack length is shown as follows:

This figure the variation of the energy release rate G as a function of the crack length in the specimen

CT subjected to a constant unit load P or unit displacement d under variable temperatures.

5. Conclusion: This work presented a detailed numerical investigation of compact tension specimen subjected to

various thermal mechanical loading, using finite elements method. The continuum mechanics

approach in combination with Hashin’s damage criterion was used for the prediction of damage

initiation and propagation in the composite laminates. This approach allowed us to estimate and

characterize the evolution of the damage modes contributions for Carbone/Epoxy laminates.

The displacement and strain fields obtained using finite element method during the compact tension

specimen analysis of composite laminates may serve as the basis for the rigorous determination of the

location of the crack or kink band tips and for the automatic computation of the J-integral.

References

1. Pinho, S.T., Robinson, P. and Iannucci, L., Fracture toughness of the tensile and compressive

fiber failure modes in laminated composites, Composites Science and Technology,2006; 66:2069-

2079.

2. Favre JP, Levadoux H, Ochin T, Cinquin J. Vieillissement des composites à matrice organique

aux temperatures moyennes. Un premier bilan. In: Baptiste D, Vautrin A, editors. 10emes

Journees Nationales sur les Composites JNC10, Paris, France, AMAC;1996, p. 205–14.

3. Gotsis PK, Chamis CC, Minnetyan L. Application of progressive fracture analysis for predicting

failure envelopes and stress-strain behaviours of composite laminates: a comparison with

experimental results. Compos Sci Technol 2002; 62:1545–59.

4. Shahid, I. and Chang, F.K. (1993). Failure and Strength of Laminated Composite Plates under

Multiple In-Plane Loads, 38th International SAMPE Symposium, pp. 967–977.

5. Ha, S.K., Jin, K.K. and Huang, Y. (2008). Micro-Mechanics of Failure (MMF) for Continuous

Fiber Reinforced Composites, Journal of Composite Materials 2008 42: 1873

6. Z. Hashin, “Failure criteria for unidirectional fibre ;” Journal of Applied Mechanics, vol. 47, no. 1,

pp. 329–334, 1980

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

10 20 30 40 50

a (mm)

G (

kJ

/m2)

P constant

d constant

Fig. 6: Evolution of the energy release rate as a function of the

crack length

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7. J. Engblom and J. Havelka, “Transient response predictions for transversely loaded laminated

composite plates,” AIAA paper no.89-1302-CP, 1989.

8. J. Lee, “Three dimensional finite element analysis of layered fiber-reinforced composite

materials,” Computers and Structures, vol. 12, no. 3, pp. 319–333, 1980.

9. Li S, Wang J, Thouless MD. The eff ects of shear on delamination in layered materials. J Mech

Phys Solids 2004; 52: 193–214.

10. ASTM E399-90, “Standard test method for plane-strain fracture toughness of metallic materials”.

Annual Book of ASTM Standards 03.01, American Society for Testing and Materials, pp 407-528,

1993.

11. Minnetyan, L. and Chamis, C.C. “CT specimen in laminated composite testing”. National

Aeronautics and Space Agency, NTM, No. 4712, 1996.

12. Pinho, S.T., Robinson, P. and Iannucci, L., Fracture toughness of the tensile and compressive

fiber failure modes in laminated composites, Composites Science and Technology, 2006;

66:2069-2079.

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