Computational schemes on the bending fatigue deformation and damage of three-dimensional orthogonal woven composite materials

Computational Materials Science 91 (2014) 91–101

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Computational schemes on the bending fatigue deformation and damage of three-dimensional orthogonal woven composite materials Baozhong Sun, Jinhua Wang, Liwei Wu, Fang Fang, Bohong Gu ⇑ College of Textiles, Donghua University, Shanghai 201620, China

a r t i c l e

i n f o

Article history: Received 8 December 2013 Received in revised form 19 April 2014 Accepted 23 April 2014 Available online 16 May 2014 Keywords: 3D woven composite material Fatigue Finite element analysis (FEA) Damage mechanisms

a b s t r a c t This paper reports a computational scheme on three-dimensional orthogonal woven composites (3DOWC) fatigue behavior under three-point low-cycle bending. Based on three-point cyclic bending fatigue tests, a microstructure model was established at yarn level for predicting the fatigue behaviors. The stiffness degradation and damage morphologies of the 3DOWC were obtained from finite element analysis (FEA) and compared with those from experimental. The stress distribution, energy absorption and damage morphologies in the different parts of the 3DOWC sample were obtained to analyze fatigue failure mechanisms. The influences of warp yarns, weft yarns and Z-yarn systems were discussed. It is found that warp yarn system bears the most cyclic load as well as energy absorption. The stress concentration area was located in the central loading area, especially in the warp yarns that is close to the Z-yarns side and its channels. The triangle damage area was gradually generated from up to down in the stress concentration area as the loading cycle increased. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Three dimensional (3D) textile structural composite materials have been widely applied to the manufacturing of engineering structures in which the high delamination resistance is required [1–3]. As one of the frequently-used 3D structural textile composites, 3D orthogonal woven composites (3DOWC) have high stiffness and strength along warp, weft, and thickness directions due to the noncrimp feature of fiber tows in 3D orthogonal woven fabric (3DOWF) [4]. Furthermore, the unique Z-yarn embedded along the thickness direction leads to the high delaminating resistance and high strength along in-plane direction and through-thickness direction. During the investigations of fatigue behaviors of 3D textile composites, Dadkhah et al. [5] performed compression–compression fatigue experiment of 3D woven composites under load control and found that composite fail by formation of kink band. It was found that as under monotonic loading, the principal mechanism of failure is kink band formation in the primary load bearing tows. Zhu et al. [6] tested low cycle fatigue behavior of 3D orthogonal Tyranno fiber reinforced Si–Ti–C–O matrix composites. The low cycle fatigue tests of an orthogonal three-dimensional (3-D) Tyranno fiber reinforced Si–Ti–C–O (SiC) matrix composites were

⇑ Corresponding author. Tel.: +86 21 67792661; fax: +86 21 67792627. E-mail address: [email protected] (B. Gu). http://dx.doi.org/10.1016/j.commatsci.2014.04.052 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.

conducted with a sine wave form under stress and strain controls at room temperature. It was shown that the asymmetric response of strain or stress occurs between tension and compression. Karahan et al. [7] and Bogdanovich et al. [8] reported in-plane tension– tension fatigue behavior and quasi-static tensile behavior and damage of carbon fiber composite reinforced with non-crimp 3D orthogonal woven fabric respectively. The in-plane tension–tension fatigue behavior of the carbon fiber/epoxy matrix composite reinforced with non-crimp 3D orthogonal woven fabric was tested. It was revealed that the maximum cycle stress corresponding to at least 3 million cycles of fatigue life without failure is in the range of 412–450 MPa for both loading directions. Avanzini et al. [9] investigated fatigue behavior and cyclic damage of PEEK short fiber reinforced composites. Fatigue strength and failure mechanisms of short fiber reinforced composite have been investigated on cyclic creep, fatigue damage accumulation and modeling, particular in presence of both fillers and short fibers as reinforcement. Sun et al. [10] studied the bending fatigue of 3DOWC under different loading stress level. The S–N curve was obtained to illustrate the relationship between applied stress levels and number of cycles to failure. The stiffness variation was recorded to present the degradation of mechanical properties of the 3DOWC during the process of fatigue loading. Yao et al. [11] analyzed static and bending fatigue properties of ultra-thick 3DOWC, and found the residual strength, modulus of both warp and weft direction have a sharp reduction stage in the early part of fatigue cycling and a

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more gradual decrease followed stage. Jin et al. [12] compared quasi-static three point bending and fatigue damage behavior of 3D angle-interlock woven composite with 3DOWC. The S–N curves were obtained to demonstrate the comparison of fatigue life under various stress levels between three-dimensional angle-interlock woven composite and three-dimensional orthogonal woven composite. In 3D woven composite materials, the warp, weft and thickness fiber tows will have different damage and degradation process cyclic loading. How to characterize the composite material’s damage from the preform structure is important to design the 3D woven composite for the cyclic loading application. However, the influence of 3D orthogonal woven preform structure on the cyclic bending fatigue damage mechanisms has not been well studied so far and also not reported in above-mentioned investigations. Here we report the stress distribution, fatigue deformation and damage of the 3DOWC under three-point cyclic bending from a microstructure model approach. A microstructure model at yarn level is established to calculate the fatigue behavior. The stiffness degradation and damage morphologies of the 3DOWC will be obtained from the finite element analyses (FEA) and compared with those from experimental. The bending fatigue failure mechanisms will be analyzed. 2. Experimental details 2.1. Materials (1) Three-dimensional orthogonal woven fabrics (3DOWF). The 3DOWF was prepared with E-glass fiber tows. The specifications are listed in Table 1 and the structure diagram and photograph are shown in Fig. 1. (2) Resin and composite consolidation. Resin (AROPOLTM INF 80501-50), curing agent (AKZO M-50) and accelerating agents (cobalt octoate) were mixed with the proportions of 100:1.5:2 by weight. Using vacuum assisted resin transfer modeling (VARTM) technique, the 3DOWC was cured under 80 °C for 4 h and then room temperature for 24 h. The fiber volume

fraction of the 3DOWC was approximately 43.7%. The size of the coupon was 200  20  9.64 mm (length  width  thickness). 2.2. Quasi-static bending and fatigue tests Both quasi-static bending and fatigue tests were conducted on MTS 810.23 materials testing system. The quasi-static bending tests were performed at a constant speed of 2 mm/min. From Eqs. (1) and (2), the calculated bending modulus (Ef) and the ultimate failure stress rult were 27.58 GPa and 543.0 MPa, respectively. 3

Eb ¼

rb ¼

l DF

ð1Þ

3

4bh Df 3Fl

ð2Þ

2

2bh

where Eb is the bending modulus, rb is bending stress, F is the load at the central of the specimen. DF is the increment of F, Df is the central deflection increment, l is the span between two supporting roller, b and h are the width and thickness of specimen. A sinusoidal wave-form load at 3 Hz was applied to the test species with a stress ratio R (rmin/rmax in one cycle) of 0.1. The tests were performed with the stress level rmax/rult of 60% (the ratio of the applied maximum stress rmax in one cycle to the ultimate static bending stress rult) under the room temperature. The maximum stress rmax equals to 325.8 MPa. 3. Modeling 3.1. Microstructure model Based on the microstructure of 3D woven preform and the impregnated resin, the geometrical model was established and assumed that all the fiber tows were completely wetted by resin during composite consolidation. All the fiber tows were considered to be in fiber/resin form, i.e., the fiber tows were completely impregnated with resins. The geometrical model of warp yarns, weft yarns, Z-yarns, resin and the entire 3DOWC structure are

Table 1 Specifications of 3D orthogonal woven fabric sample. Component

Length (mm)

Width (mm)

Thickness (mm)

Volume (%)

Layers

Linear density/Tex

Density/(ends/cm)

Layers

Fabric size (mm)

Warp Weft Z-yarn

4.00 4.24 –

1.4 1.4 0.4

0.26 0.26 0.1

27.46 30.93 1.11

17 16 –

400  2 400  2 28  2

5 4.7 5  4.7

17 16 –

401 523 –

Fig. 1. Structure diagram and photograph three dimensional orthogonal woven fabric.

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B. Sun et al. / Computational Materials Science 91 (2014) 91–101

shown in Fig. 2. The sizes of the meso-scale geometrical repeating unit cells (RUCs) are listed in Table 1. The entire model was meshed with hexahedron and nodes of coincidence technique, as shown in Fig. 3. The element number of warp system, weft system, Z-yarn system and resin was 68,608, 66,640, 8616, and 246,344, respectively.

2

1 m m 0 0 6 m 1 m 0 0 6 6 6 m m 1 0 0 ½A ¼ 6 6 0 0 0 1 þ m 0 6 6 4 0 0 0 0 1þm 0

3.2. Constitutive models This section briefly discusses the constitutive models before and after damage that are adopted to describe the global and local deformation and damage response of 3DOWC at multi-scale levels, with fiber, yarns and resin. Their mechanical responses are modeled by two different sets of constitutive equations and damage models, respectively. The interface/interphase between the resin and fiber is assumed to bond perfectly. 3.2.1. Resin model The resin is assumed to undergo rate-dependent viscoelastic deformation and failure at maximum strain [13]. The resin is assumed a uniaxial viscoelastic model represented by a finite series of ‘Kelvin–Voigt type’ elements coupled with an elastic spring [14,15] and maximum principal strain failure on the concept of smeared crack [16]. For a uni-axial loading, the nonlinear viscoelastic behavior can be represented by a list of nonlinear ‘Kelvin–Voigt type’ elements and a linear spring element to be connected as shown in Fig. 3. For the system of the serial elements, the global stress–strain relation is expressed by:

fe_ t g ¼ fe_ e g þ fe_ c g

ð3Þ

fr_ g ¼ E½A1 fe_ e g

ð4Þ

where fe_ t g; fe_ e g; fe_ c g; fr_ g are the total strain-rate, elastic strainrate, creep strain-rate and stress-rate vectors (each includes six components, respectively). E is an elastic modulus which is assumed to be constant and [A] is a matrix only related to the value of Poisson’s ratio to be defined by

0

0

0

0

0 0 0 0 0

3 7 7 7 7 7 7 7 7 5

ð5Þ

1þm

The creep strain rate fe_ c g is the sum of the strain-rate of each element fe_ ci g in the serial connection of above-mentioned elements such as

fe_ c g ¼

n  X ½A i¼1

Ei si

frg 

1

si

feci g

 ð6Þ

where si = gi/Ei(i = 1, 2, ..., n) denotes the retardation time. Ei is the spring elastic modulus and gi represents the viscosity coefficient of dashpot for ith Kelvin (Voigt) element respectively. The retardation time si behave a damped exponential character in an exponential-type function from the experimental test [15]. Its value determines the time duration after which contribution from the individual Kelvin element becomes negligible. The number of the Kelvin elements applied in the constitutive equation depends on the required time range. A time factor a is introduced and defined as

si ¼ ðaÞi1 s1

ð7Þ

In this way all si are related by the scale factor a. The span of time is determined by the order of n with n Kelvin elements to be included and the value of a to be 10. The nonlinear viscoelastic response in the current model is realized with the Ei described by the functions of current equivalent stress, req as expressed by

Ei ¼ E1 ðreq Þ

ð8Þ

In the above req is defined as

req ¼

ðR  1ÞI1 þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðR  1Þ2 I21 þ 12RJ 2 2R

Fig. 2. Microstructure model of yarn systems in 3DOWC.

ð9Þ

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x3

x1

x2

(a) Part mesh

(b) Local mesh of assembly Fig. 3. Mesh scheme of geometrical model.

where I1 = r1 + r2 + r3 is the first invariant of the stress tensor, and J2 = SijSji/2 is the second invariant of the deviatory stress and R is the ratio of tensile to compressive ‘yield stress’. Note that when p R= 1, ffiffiffiffiffiffiffi then Eq. (9) reduces to the von Mises equivalent stress, req ¼ 3J 2 . In contrast to a single crack to be predefined in the isotropic material, the complex patterns and discrepant density distributions of cracks in the 3DOWC make it difficult to deal with above-mentioned cracks based on the classical fracture and damage method. The failure criterion for matrix based on maximum principal strain theory is defined by e1 P ecr (ecr is the failure strain of matrix under uniaxial tensile loading). Once the condition is satisfied, a crack in the plane perpendicular to the direction of e1 in the local coordinate system is assumed to have initiated. After the initiation of a crack, the normal and shear stresses are assumed not to be transferred between the surfaces of the crack. In the local (crack) coordinate system, the r1, r12 and r13 approach at zero correspondingly. The subscript 1 denotes the Cartesian axis

perpendicular to the crack plane while 2 and 3 are in the crack plane. The rest of stresses are transferred normally without the effect of the crack formation. The stress and strain vectors in local (crack) coordinate system are defined by {r}cr and {e}cr respectively. The post-damage constitutive model for matrix in the local (crack) coordinate system can be expressed by

fDrgcr ¼ Et ½DfDegcr  v½Bfrgcr

ð10Þ

or written in its full form with 8 8 9 Dr1 >cr bZ 1 > > > > > > > > > > > > > Dr2 > 0 > > > > > > > > < Dr > < 0 = 3 ¼ Et > > Dr12 > 0 > > > > > > > > > > > > > Dr13 > > > 0 > > > > > : : ; Dr23 0

0 Z1 Z2 0 0 0

0 Z2 Z1 0 0 0

0 0 0 bZ 3 0 0

0 0 0 0 bZ 3 0

98 9cr 0 >> D e 1 > > > > > > > > > > > De2 > 0> > > > > > > > > > 0 =< D e 3 = > 0> > Dc12 > > > > > > >> > > > > > 0> > Dc13 > > > > > : ;> ; Dc23 Z3

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8 1 > > > > 0 > > < 0 v 0 > > > > 0 > > : 0

0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0

98 9cr 0> r1 > > > > > > > > r2 > >> > 0> > > > < => 0 r3 = 0> r > 12 > > > > >> > > > 0> r > > > > > ;: 13 > 0 r23 ;

where

Z1 ¼

1m ; ð1 þ mÞð1  2mÞ

Z2 ¼

m ð1 þ mÞð1  2mÞ

;

Z3 ¼

1 2ð1 þ mÞ ð11Þ

Ets is the tensile modulus of the matrix at the instant of damage initiation. b = 0.01Dt is a small number to describe the stiffness degradation in these three particular stress directions and the constant v = 0.2Dt allows the three stress components to decrease to a near zero value in a sufficiently short time duration (Dt is time increment for each iteration). Note that the above Eqs. (3), (4) and (10) are expressed in the local coordinate system. If the local coordinate system is different from the global coordinate system where finite element analyses carry out, the Eq. (6) must be transformed to the global coordinate system as,

fDrggl ¼ ½D0 fDeggl  v½B0 frggl

T

½D  ¼ ½T ½D½T ½B0  ¼ ½TT ½B½T 2

2

l1

6 2 6 l2 6 6 2 6 ½T ¼ 6 l3 6 2l l 6 12 6 4 2l2 l3 2l3 l1

and

m21

n21

l1 m1

m 1 n1

n1 l1

m22

n22

l2 m2

m 2 n2

n2 l2

m23

n23

2m1 m2 2m2 m3 2m3 m1

2n1 n2 2n2 n3 2n3 n1

l3 m3 l1 m2 þ l2 m1 l2 m3 þ l3 m2 l3 m1 þ l1 m3

m 3 n3 m1 n2 þ m2 n1 m2 n3 þ m3 n2 m3 n1 þ m1 n3

3

7 7 7 7 7 n3 l3 7 n1 l2 þ n2 l1 7 7 7 n2 l3 þ n3 l2 5 n3 l1 þ n1 l3 ð13Þ

where limini are directional cosines of the local coordinate axes in the global coordinate system. 3.2.2. Fiber/yarns phase models At the fiber tow level, a post-damage constitutive model for weft, warp yarns and Z-binders with transversely isotropic property is proposed. As shown in Fig. 4, three kinds of cracks are initiated appropriately along fiber yarns direction (Crack 1, Fig. 4(a)) and transversely (Crack 2, Fig. 4(b) and Crack 3, Fig. 4(c)). A crack once created and then its normal stress component perpendicular to surface of crack and shear stress components in in-plane surface of crack are not transferred. For example in Fig. 4(a), the post-damage constitutive model can be expressed with

(a) Crack 1

0

0

C2

C3

C3

C2

0

0

0

0

0

0

0 0 0 0 0 0 0 0 0 0 0 0

98 9cr 0 >> De1 > > > > > > > > > > 0 0 0 > > De2 > >> > > > > > > > > > > 0 0 0 =< De3 = > Dc12 > >> bC 4 0 0 > > > > > > > > > > > > > > > > 0 bC 4 0 >> Dc13 > > > > : ;> ; Dc23 0 0 C6 98 9 0 0 0 >> r1 >cr > > > > > >r > >> > 0 0 0> > > > 2 > > > > > > > > > > 0 0 0 =< r3 = > r12 > 1 0 0> > > > > > > > > > > > > > > > > > r 0 1 0> 13 > > > > > > ;: ; r23 0 0 0 0

0

ð14Þ

where

C1 ¼

C3 ¼

ð12Þ

with 0

8 8 9 Dr1 >cr > bC 1 > > > > > > > > > > > > 0 Dr2 > > > > > > > > > > > > > < Dr3 = < 0 ¼ > > 0 Dr12 > > > > > > > > > > > > > Dr13 > > > > > > 0 > > > > > > : : ; 0 Dr23 8 1 > > > > > 0 > > > > <0 v > 0 > > > > > > 0 > > : 0

E1 ð1  m223 Þ 1  m223  2ð1 þ m23 Þ EE21 m212   E2 m23 þ EE21 m212 1  m223  2ð1 þ m23 Þ EE21 m212

E2 ð1  EE21 m212 Þ

;

C2 ¼

;

C 4 ¼ G12

1  m223  2ð1 þ m23 Þ EE21 m212 and C 6 ¼ G23

;

ð15Þ

E1 is the modulus of matrix impregnated fiber bundles along fiber direction while E2 is transverse directions with E3 = E2. The above three kinds of cracks are damaged independently. The yarn is only damaged partly when one or two of three cracks (Crack 1, Crack 2 and Crack 3) occur. Subsequently, the damage increases and elastic modulus decreases in particular orientations as shown in Fig. 4. For completed damage when all three kinds of cracks occur at same node in finite element analyses, the stress reduces to zero indicating loss of load carrying capacity. 3.3. Fatigue damage criteria Hysteresis energy based on fatigue damage criterion that incorporates both stress and strain terms was used to describe the destruction and expansion of the 3DOWC [17]. The hysteresis loop is formed by the stress and strain change over time. The areas of the hysteresis loop per cycle represent the value of hysteresis energy (DW). The accumulation of hysteresis energy leads to the damage initiation and evolution of material, as presented in Eqs. (16) and (17). And the damage propagation stage starts after the damage initiation criterion is satisfied.

N 0 ¼ k 1 DW m 1

ð16Þ

dD ¼ k2 DW m2 =L dN

ð17Þ

(b) Crack 2 Fig. 4. Crack patterns in matrix impregnated fiber tows.

(c) Crack 3

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where N0 is the number of cycles in which damage is initiated, dD/ dN is the damage rate per cycle in a material, k1, m1, k2 and m2 are material constants, L is the characteristic length. 4. Results and discussions 4.1. Stress distribution and comparisons Fig. 5 shows the status and stress contour diagram of finite element model at four specific times in one bending cycle. The entire deformation procedure and stress distribution of central part of the model in the one bending cycle are presented. The displacement of picture A, picture B, picture C and picture D are 4 mm, 7 mm, 4 mm and 1 mm, respectively. The red and blue lines represent the maximum and minimum stress trend in cyclic loading respectively. It is shown that there is a medium plane in the stress contour diagram where the stress in upper and lower parts is in symmetry. Medium

plane has the minimum stress which is close to 0. From the changes of stress in the four pictures, it is shown that the stress transfers to a large area owing to the straight warp yarns. In order to explain the stress distribution in detail, warp yarns were selected to compare the stress value in different direction with different nodes. Two groups of selected warp nodes along length direction and thickness direction and the results are presented in Fig. 6. The relationship of the stress values are listed as follows:

rNwarp11 > rNwarp18 > rNwarp12 > rNwarp17 > rNwarp13 > rNwarp16 > rNwarp14 > rNwarp15 rNwarp24 > rNwarp23 > rNwarp22 > rNwarp21 It could be found that the stress of the warp yarns declined dramatically within 50 cycles, and then no significant decrease occurs. The stress of warp yarns has a symmetrical distribution through thickness direction. The middle warp yarn carries the minimum

(a) Sinusoidal wave form loading

(b) State at specific points in one single cycle Fig. 5. Stress distribution of the entire model at four specific states during one loading cycle.

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(a) Warp nodes selected along length and thickness direction 900 800

stress (Mpa)

700 600 500 400 300 200 100 0

0

100

200

300

400

500

600

700

800

cycle

(b) Comparison of node maximum stress along thickness direction 1000 900 800

stress (Mpa)

700 600 500 400 300 200 100

0

100

200

300

cycle

400

500

600

(c) Comparison of node maximum stress along length direction Fig. 6. Comparison of maximum stress in different nodes on warp yarns.

amount of stress. The surface and bottom warp yarns carry much more stress than the other parts. In addition, the stress of surface warp yarn is a little greater than that of the bottom warp yarn, which agrees with the experimental that the most serious damage area appeared on the surface of the material. The distribution of stress in weft yarns, Z-yarns and resin are similar to that of warp yarns. In order to understand the structure effect to the stress distribution in the 3DOWC, the specific nodes of different systems were selected, and compared results are shown in Fig. 7. The relationship of different nodes is listed as follows:

rNwarp > rNweft > rNre sin The warp yarns carry the largest amount of load in the three point bending fatigue tests, which is consistent with the stress contour diagram of the entire model. 4.2. Energy absorptions The internal energy was obtained from the numerical results for a better understanding of the structure effect in damage initiation

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while designing the 3DOWC. Resin absorbed a bit more than weft yarn system. The Z-yarn only absorbed a small part of energies. 4.3. Damage morphologies and regions Based on the stress distribution, it could be found that the area with high stress. And the damage area probably begins at this location. Element deleting method was used to describe the damage of material at the high stress sites over 820 MPa. It was found that the initial damage occurred in warp yarn that close to Z-yarns side and its channels, as shown in Fig. 9, which is consistent with maximum stress area obtained from stress distribution. Fig. 10 shows the final surface damage morphologies in the central loading area. The damage distribution is similar to the stress distribution. There is a little difference between the front view and back view of the experimental material damage, owing to the different binding directions of Z-yarn. From the damages both in experimental and FEA, it is shown that triangle damage areas developed in up surface and down surface, and Z-yarn channels are easily damaged. Fig. 11 shows the damage of warp yarns, weft yarns and Z-yarns and resins during cyclic bending, the damages of warp yarns are the most severe while the weft yarns were almost not damaged. This is due to the warp yarns share the most part of cyclic loading. In order to find the fatigue damage modes, the inner layer damage morphology was acquired as shown in Fig. 12. The damage areas were pointed by white arrows. The damages occurred in warp yarns that close to Z-yarn channels because the resin rich region bears less stress than yarn system, which lead to the easy damage of these areas. There is a medium plane where damage morphologies and delaminations occurred in both sides. The damages of upper part and the delamination of lower parts are much severer. The damages of yarns and resins, delaminations of different layers and the growths of triangle damage areas lead to the final failure.

(a) Location of nodes 900 800 700

stress (Mpa)

600 500 400 300 200 100 0

0

50

1 00

150

200

250

300

350

400

450

500

550

cycle

4.4. Stiffness degradation

(b) Stress comparison Fig. 7. Comparison of node maximum stress in different system of material.

800 700

Because the mechanical behaviors of the 3DOWC gradually degrade during cyclic bending, stiffness degradation was selected to characterize the fatigue degradation. The stress and displacement of the 3DOWC under cyclic bending were obtained to calculate bending modulus from Eqs. (1) and (2). Fig. 13 shows the stiffness degradation curve. There is roughly a 14% difference between the two curves which does not correlate well between

600 500 400 300 200 100 0

0

50

100

150

200

250

300 350

400

450

500 550

Cycle Fig. 8. Comparisons of energy absorption.

and development, as shown in Fig. 8. From the internal energy absorption of four parts, we can find that warp yarn system absorbed nearly 60% energy of the whole material. Thus the mechanical behaviors of warp yarn should be paid more attention

Fig. 9. Initial damage area in 3DOWC.

B. Sun et al. / Computational Materials Science 91 (2014) 91–101

99

(a) front surface damage morphology

(b) back surface damage morphology

(c) up surface damage morphology

(d) up surface damage morphology Fig. 10. Surface damage shape comparison of experimental and finite element method simulation.

experimental and FEA. The reasons are probably from that the fiber tows and resin were assumed as transversely-isotropic and isotropic material respectively in the FEA model. And the cracks are propagated regularly based on the failure criteria. While in experimental, the non-simultaneous damage of fiber tows and reins would be occurred.

The stiffness degradations indicate that two stages exist in both the curves: the first stage dropped sharply (0–50 cycles) and the second stage reduced gradually. It is assumed that fiber tows and resin bond perfectly in the FEA model, while crack propagation and the defect originated from the manufacturing of the 3DOWC. Thus the result obtained from FEA is higher than experimental.

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Fig. 11. Damage morphology of different yarn systems.

Fig. 12. Internal failure regions.

32000

5. Conclusions

FEA 30000

28000

26000

24000

22000

0

100

200

300

Cycle Fig. 13. Stiffness degradation curve.

400

500

The fatigue behaviors of 3D orthogonal woven composite (3DOWC) under low-cyclic three-point bending have been investigated with finite element analysis at yarn level. Fatigue damages and failure mechanisms have been analyzed from FEA and compared with those in experimental. The stress distributions in the contact regions and the internal energy absorptions lead to the damages of the woven composite. The resin rich regions along Zyarn channels in thickness direction lead to the damages of these areas. The triangle damage areas were gradually formed up and down in these regions. The non-crimp features of warp, weft yarn and Z-yarn lead to warp yarns share the most part of cyclic load and absorb the most energy. In addition, the top and bottom layers along the thickness direction bear the majority of load during the cyclic bending. And the high stress locations were in the warp yarns near the top surface at central part of the composite beams. The mechanical behaviors of the warp yarns should be paid more

B. Sun et al. / Computational Materials Science 91 (2014) 91–101

attention while designing the 3D orthogonal woven composite materials. Acknowledgements The authors acknowledge the financial supports from the National Science Foundation of China (Grant Number 11272087) and National High-Technology R&D Program of China (863 Program) (No. 2012AA03A206). References [1] A.P. Mouritz, M.K. Bannister, P.J. Falzon, K.H. Leong, Compos. A: Appl. Sci. Manuf. 30 (12) (1999) 1445–1461. [2] M.H. Mohamed, A.E. Bogdanovich, L.C. Dickinson, J.N. Singletary, R.B. Lienhart, SAMPE J. 37 (3) (2001) 8–17. [3] S.V. Lomov, A.E. Bogdanovich, D.S. Ivanov, D. Mungalov, M. Karahan, I. Verpoest, Compos. A: Appl. Sci. Manuf. 40 (8) (2009) 1134–1143.

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