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Composite Interfaces

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Multi-scale analysis of aligned ZnO nanowiresreinforced hybrid composites under three-pointbending

Parisa Marashizadeh, Mohammad Abshirini, Mrinal C. Saha & Yingtao Liu

To cite this article: Parisa Marashizadeh, Mohammad Abshirini, Mrinal C. Saha & Yingtao Liu(2021) Multi-scale analysis of aligned ZnO nanowires reinforced hybrid composites under three-point bending, Composite Interfaces, 28:10, 961-978, DOI: 10.1080/09276440.2020.1833613

To link to this article: https://doi.org/10.1080/09276440.2020.1833613

Published online: 21 Oct 2020.

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Multi-scale analysis of aligned ZnO nanowires reinforced hybrid composites under three-point bendingParisa Marashizadeh, Mohammad Abshirini, Mrinal C. Saha and Yingtao Liu

School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK, USA

ABSTRACTThis paper presents novel multi-scale modeling and failure analysis of hybrid carbon fiber reinforced polymer (CFRP) composites enhanced by zinc oxide (ZnO) nanowires. Vertically aligned ZnO nanowires on CFRP plies create enhancement layers, leading to the increased interfacial properties in composites. A multi-scale model bridging from micro-scale to macro-scale investigates the enhanced interla-minar shear properties in the hybrid composite. At the micro-scale, the effective material properties of the enhancement layer are extracted by the homogenization of an appropriate representative volume element. At the mesoscale, the cohesive zone model is employed to investigate the adhesion bonding and the delamination between the plies. At the macro-scale, the progressive intralaminar failure analysis is developed to explore damage initiation and evolu-tion in fiber and matrix utilizing the user subroutine to define mate-rial behavior (VUMAT). Finite element analysis of a three-dimensional hybrid composite short beam under three-point bending (3PB) load is performed to extract the damage behavior. Numerical results demonstrate that interlaminar shear strength of the hybrid CFRP composites is improved by 43% under 3PB load. The effect of dia-meter and length of ZnO nanowires on the shear strength of the hybrid laminated structure is discussed.

ARTICLE HISTORY Received 11 July 2020 Accepted 5 October 2020

KEYWORDS Multi-scale modeling; hybrid composites; zinc oxide; interlaminar shear strength

CONTACT Yingtao Liu, yingtao@ou.edu School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019 USA

COMPOSITE INTERFACES 2021, VOL. 28, NO. 10, 961–978 https://doi.org/10.1080/09276440.2020.1833613

© 2020 Informa UK Limited, trading as Taylor & Francis Group

1. Introduction

The applications of carbon fiber reinforced polymer (CFRP) composites in industries have been increased rapidly due to their unique properties, such as light-in-weight, high stiffness, and high strength. Although failure analysis of composites has been investigated in the last decade, it is still challenging to accurately predict the initiation and evolution of progressive damage in composites. Transverse loads can result in severe structural damages in compo-site laminates due to their weak interlaminar strength. Therefore, the improvement of interlaminar properties is crucial to enhance the shear strength of composites. Significant efforts have been spent to increase the interlaminar shear strength (ILSS) of laminated composites, including modifying sizing on fibers [1,2], synthesizing functional plates and membranes on the laminates [3–5], and dispersing nanoparticles directly within the laminates [6–8]. Nanoparticles including carbon nanotubes (CNT) and Zinc Oxide (ZnO) nanowires have been used to improve the mechanical, electrical, and thermal properties of hybrid composites in the last decade. CNTs have been synthesized on continuous fibers using chemical vapor deposition to enhance the interlaminar properties [9,10] and interfacial properties [11,12] of fiber/matrix bonding. Most of the CNT synthesis methods require severe heat treatment on structural fibers, resulting in weakened fiber strength [13]. In addition, ZnO nanowires have been employed to enhance interfacial properties and the strength of fiber-reinforced composites [14–16]. Numerical and experi-mental analyses showed that radially grown ZnO nanowires on a structural fiber can increase the interfacial shear strength of single fiber hybrid composites by 99% [17].

Multi-scale analysis is essential to understand the behavior of hybrid composites due to the dramatic differences of micro-scale structural fiber and nano-scale particles in composites. The overall goal of multi-scale modeling techniques for hybrid composites is to combine the mechanical theories at different length scales, including nanoparticles, fiber/matrix interface, and laminates, and to understand their static and dynamic beha-viors under various loads and environmental conditions. In the hybrid composites, the nanoparticles grown on the fiber and embedded in the matrix create an enhancement layer. Micro-scale homogenization has been used to evaluate the material properties of the enhancement layer. Kulkarni et al. [18] have proposed a representative volume element (RVE) for evaluating the effective material properties of nanoparticles aligned on fibers. This technique has been utilized to extract the mechanical and thermal proper-ties of CNTs hybrid fiber-reinforced composites [19,20].

Fiber and matrix interface and the bonding between two stacking plies in composite laminates can be modeled at the mesoscale. Cohesive zone model (CZM) has been widely employed to simulate the traction and separation behavior of the fiber/matrix interface [21–23]. Besides, delamination damage initiation and evolution are modeled by CZM in the laminated composites considering the fracture energies and mixed-mode fracture analysis [24,25]. This meso-scale technique is used in finite element analysis (FEA) employing cohesive elements or cohesive contact to simulate the delamination in the laminated structures [26,27].

At the macro-scale, multiple continuum mechanics models have been developed for the prediction of the intralaminar damage initiation and evolution in composite struc-tures [28–31]. In most of these methods, stiffness degradation is considered for fiber or matrix if stress exceeds the material’s strength. ABAQUS general FEA software developed

962 Y. LIU ET AL.

a built-in damage analysis of fiber-reinforced composite laminates based on the Hashin [32] and Hashin-Rotem [33] theory. However, this model is limited to the 2D analysis utilizing plane stress-based elements, such as shell and membrane elements. Recently, the strain damage model developed by Linde et al. [34] has been widely used in 3D FEA using the user-subroutines for evaluating the failure of composite laminates [35–38].

Most of the multi-scales modeling studies have been focusing on evaluating the material properties of the hybrid composites rather than the damage analysis of these structures. Recently, many research explored the interaction of the interlaminar and intralaminar damage to estimate the failure of laminated composites [26,39,40]. These meso-macro analyses have developed to evaluate the possible damages in the laminated composites, including fiber damage, matrix damage, or delamination. However, to the author’s best knowledge, there is no study in the literature investigating the damage analysis of vertically aligned ZnO nanowires hybrid composites. An appropriate model is essential to make a bridge between the enhancement layer and the intralaminar/interlaminar properties in ZnO hybrid structures.

In this paper, a multi-scale framework is developed to investigate the short-beam CFRP hybrid composite with vertically aligned ZnO nanowires under the three point bending (3PB) loads. The effective material properties of the ZnO nanowires embedded in a matrix are extracted at the micro-scale. The interface between the lamina and the enhancement layer is modeled at the meso-scale using CZM. The ILSS of the hybrid composite is calculated to study the incorporation of the nanowires on the overall improvement of the interlaminar properties. The effect of nanowires’ diameter and length on the ILSS is also explored. The multi-scale framework is explained in sections 2, while the numerical results are described in section 3.

2. Hybrid CFRP composite with vertically aligned ZnO nanowire

A multi-scale model is developed to simulate the hybrid structure containing materials with different length scales. The schematic of the hybrid composite is shown in Figure 1. ZnO nanowires with different diameters (17 nm-450 nm) and multiple lengths (10 µm-30 µm) are vertically aligned on the CFRP plies to enhance the interlaminar shear properties of the composite. The epoxy matrix is filled between the layers to bond the laminates and the ZnO nanowires (Figure 1(b)). The aligned nanowires create

Figure 1. (a) Schematic of a macro-scale hybrid composite under 3PB load, (b) schematic of a meso- scale hybrid composite with vertically aligned ZnO and the interface, (c) schematic of a micro-scale RVE showing ZnO embedded in the matrix, (d) schematic of ZnO nanowire.

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a compact composition, and the enhanced layers are laid up using the epoxy matrix [14,17]. The interface between the enhancement layer and the laminate is simulated using the CZM at the meso-scale. The continuum damage model is utilized to model the failure of the CFRP plies. By taking the properties of these steps into account, a hybrid short beam in 3PB load is simulated at the macro-scale, as shown in Figure 1(a) based on the ASTM D2344 standard [41] to evaluate the improvement of the ILSS by adding ZnO nanowires. The detail of this multi-scale framework is described as follows.

2.1. ZnO/epoxy enhancement layer (micro-scale)

ZnO nanowires with different diameters and lengths are employed to enhance the interlaminar properties of the composite. Based on the theoretical and experimental study performed by Chen et al. [42], the size-dependent modulus of the ZnO nanowires with the core-shell structure (Figure 1(d)) can be extracted from Equation (1).

E ¼ E0 1þ 8Es

E0� 1

� �rs

D� 3

r2s

D2 þ 4r3

sD3 � 2

r4s

D4

� �� �

(1)

where D is the diameter of nanowires in the range of 17–450 nm, Eo is the modulus of the bulk ZnO, Es is the surface modulus, rs is the depth of the core-shell. The calculated values of three parameters are rs = 4.4 nm, E0 = 139 GPa, and Es/E0 = 1.50 [42]. There are two possible types of failure for the ZnO nanowires grown on the fiber laminates and embedded in epoxy. One possible failure type where the nanowires are fractured at the joint between the laminates and ZnO nanowires and the second possible failure types where the nanowires are fractured into two pieces in the matrix. The strength of the ZnO nanowires depends on different parameters, such as the morphology of the nanowires and the atomic interactions. However, based on the experimental analysis performed by Agrawal et al. [43], the axial force on the fiber composites is not enough to fracture the ZnO nanowires with a strength of 3.33 to 9.53 GPa. On the other hand, the interfacial shear strength of ZnO nanowires grown on the fiber and embedded in the matrix is less than 200 MPa, which makes the debonding or delamination of the ZnO and CFRP laminates the most probable failure mode in the hybrid composites [44]. Hence, it can be concluded that in the hybrid composite, the ZnO nanowires and the matrix filled between the plies create a separate layer (enhancement layer) in which the nanowires reinforced the matrix vertically.

Micro-scale homogenization is performed to extract the effective material properties of the ZnO/epoxy enhancement layer. In this regard, a cubic RVE containing a single ZnO nanowire in the epoxy matrix is utilized (Figure 1(c)). The numerical procedure presented by Omairey et al. [45] is implemented in ABAQUS software, and the effective material properties of the enhancement layer with different ZnO diameters (25 nm, 75 nm, 150 nm, 250 nm, 450 nm) are obtained. More detail about the micro-scale homogenization analysis can be found in ref [45,46]. Then, the effective material properties are utilized in the macro- scale FEA to model the enhancement layer as a homogeneous and orthotropic material considering the coordinate systems described in Figure 1(c). (1ʹ-2ʹ-3ʹ) demonstrate the coordinate system of the composite beam with 1 in the fiber orientation, while (1-2-3) show the RVE system with 1 in ZnO orientation.

964 Y. LIU ET AL.

2.2. Simulation of the enhanced interface (meso-scale)

In this study, the interface between the ZnO/epoxy enhancement layer and the laminate is simulated using the CZM. This model can be used in ABAQUS using cohesive contact to define the adhesion between two stacking plies [34,36]. The bi-linear traction- separation law is implemented to model the cohesive contact and the delamination between the layers. Based on this approach, the stress in the cohesive contact increases by applying the load up to the strength of the interface and then degrades linearly to model the separation of the layers. The elastic response based on nodes on the interlayer surfaces is expressed by Equation (2).

t ¼tntstt

8<

:

9=

;¼

Knn Kns KntKns Kss KstKnt Kst Ktt

2

4

3

5δnδsδt

8<

:

9=

;¼ Kδ (2)

where t is the nominal traction stress vector of the cohesive zone, K is the cohesive stiffness, and δ is the separation displacement of the cohesive. The subscripts n, s, and t denote the normal, first shear, and the second shear directions, respectively. The uncoupled traction- separation behavior is assumed in which the cohesive stiffness has the values of Knn, Kss, Ktt. Different experimental studies have been reported the constant interface stiffness number between 106 − 108 N/mm3 [47,48], while some of the researchers assume this number as a function of material properties of the interface [49,50]. In this study, a mathematical model is utilized to define the stiffness of the cohesive model depending on the material properties of the interface. Based on the continuum mechanics, the interface moduli through the thickness has a value between the modulus of the lamina (Ei at r = rply = Eply) and the sounding area (Ei at r = ri = EZnO/epoxy). Several mathematical models

have been used in the literature to define the interface moduli between the fiber and the matrix. Using the power-law variation model shown in Figure 2 and the related boundary

Figure 2. Interface stiffness distribution.

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conditions, the average interface stiffness can be written as Equations (3) and (4) [51,52].

�Ei ¼1ti

ò

ri

rply

Er rð Þdr ¼1

ri � rply� � ò

ri

rply

ArBdr (3)

�Ei ¼Eplyrf

ri � rply� �

Bþ 1ð Þ

ri

rply

� �Bþ1

� 1

" #

(4)

A ¼Eply

rplyB ; B ¼ln E ZnO

epoxy� ln Eply

ln ri � ln rply

Based on the model proposed by Daudeville et al. [49], the penalty stiffness of the interface is a function of the interface elastic moduli and the thickness of the interface, which can be calculated from Equation (5).

Kn ¼2G13

t;Ks ¼

2G23

t;Kt ¼

E3

t(5)

where G13, G23, E3 are the parameters of the interface shear and Young’s moduli, and t is the thickness of the interface. The Quadratic traction criterion is applied to model the damage initiation in the interface. This model has been widely used to simulate the delaminating propagation in composite materials [36,53,54]. As it is shown in Equation (6), the damage initiates in the interface when the quadratic interaction function reaches a value of one.

tn

ton

� �2

þts

tos

� �2

þtt

tot

� �2

¼ 1 (6)

where t(x=n, s, t) shows the traction stress vector in three directions, and the peak value of the contact stress is defined by to when the separation occurs to either of the three directions. The energy-based mixed-mode damage evolution with linear softening is implemented using the power-law fracture criterion. In this method, the energies that cause failure under mixed-mode (normal and two shears) interact based on the power- law relation, as shown in Equation (7).

Gs

Gcn

� �α

þGs

Gcs

� �α

þGt

Gct

� �α

¼ 1 (7)

where α is a material property and assumed as 2 is this study [48]. The critical fracture energies in the normal, in-plane shear and out-of-plane shear directions are demon-strated by Gc

n, Gcs , and Gc

t , respectively. The damage initiation and evolution properties of the cohesive surface are given in Table 1 [35,55].

Table 1. Damage properties of the cohesive surface contact [33,35].to

n(MPa) tos (MPa) to

t (MPa) Gcn(N/mm) Gc

s (N/mm) Gct (N/mm)

70 50 50 0.97 1.72 2.01

966 Y. LIU ET AL.

2.3. Intralaminar damage analysis (macro-scale)

The continuum damage model proposed by Linde et al. [34] is implemented in this study to simulate the damage in the CFRP lamina. The strain-based failure criterion is implemented in the user subroutine to define material behavior (VUMAT) programmed in FORTRAN to explore the damage initiation and evolution in both fiber and epoxy. The composite is assumed as an orthotropic structure with the 6 × 6 constitutive matrix shown in Equations (8) and (9).

σ ¼ Cε ¼

c11c21c31000

c12c22c32000

c13c23c33000

000

c4400

0000

c550

00000

c66

2

66664

3

77775

ε (8)

Cii ¼ Eii�

T1 � 1 � νjkνkj� �� �

; i; j; k ¼ 1to3; i�j�k;

Cij ¼ Eii�

T1 � νji þ νjkνki� �� �

; i; j; k ¼ 1to3; i�j�k; i< j;(9)

T1 ¼ 1 � ν12ν21 � ν23ν32 � ν13ν31 � ν12ν23ν31 � ν23ν13ν21

Based on the Linde approach, the damage in fiber and matrix can be defined using two strain-based functions shown in Equation (10). The damage occurs in the fiber if the fiber failure function (fm) exceeds the ultimate strain in the fiber direction.

ff ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

εt11

εc11

ε11ð Þ2þ εt

11 �εt

11ð Þ2

εc11

!

ε11

vuut � εt

11 (10)

where εt11and εc

11 are the failure strain in the fiber direction in tension and compression, respectively. The damage in matrix initiates when the matrix damage function (fm) shown in Equation (11) exceeds the threshold strain perpendicular to the fiber direction.

fm ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

εt22

εc22

ε22ð Þ2þ εt

22 �εt

22ð Þ2

εc22

!

ε22 þεt

22εc

22

� �2

ε22ð Þ2

vuut � εt

22 (11)

where εt22and εc

22 are the failure strain perpendicular to the fiber direction in tension and compression, respectively. The failure strains can be obtained from Equation (12) con-sidering Xt and Xc as the strength in the longitudinal tension and compression, and Yt and Yc are the transverse failure stresses in tension and compression, respectively.

εt11 ¼

Xt

C11; εc

11 ¼Xc

C11; εt

22 ¼Yt

C22; εc

22 ¼Yc

C22(12)

After damage initiation satisfied, further loading causes the degradation in the lamina stiffness. Based on the Linde failure model, the damage evolution can be defined via the damage parameters for fiber and matrix according to the Equations (13) and (14) [34].

COMPOSITE INTERFACES 967

df ¼ 1 �εt

11ff

e�

C11εt11 ff � εt

11ð ÞLcGf

� �

(13)

dm ¼ 1 �εt

22fm

e�

C22εt22 m� εt

22ð ÞLcGm

� �

(14)

The damage variables can have a value between zero and one. Before damage initiation occurs, the damage parameters have the value of zero, and if this parameter reaches one, the material is failed in that element. The material behavior CFRP lamina after damage initiates assumed to be orthotropic and defined as the degraded conventional constitutive depicted in Equation (15).

σ½ � ¼ Cd½ �: ε½ � (15)

[Cd] is the reduced elastic constitutive matrix depending on the damage variables and can be obtained from Equation (16).

Cd ¼

1 � df� �

c11symsym

000

1 � df� �

1 � dmð Þc121 � dmð Þc22

sym000

1 � df� �

c13

1 � df� �

1 � dmð Þc23c33000

000

1 � df� �

1 � dmð Þc4400

0000

c550

00000

c66

2

666664

3

777775

(16)

2.4. FEA of the hybrid composite short beam in 3PB loading

The progressive damage analysis of the 3D short beam hybrid composite in the 3PB load is performed by the FEA based program ABAQUS Explicit algorithm. For more accurate analysis, the 3D solid elements are used, and the damage model is defined via VUMAT user subroutine. Hence, the CFRP lamina is modeled as 3D orthotropic using an 8-node linear brick, reduced integration (C3D8R), with enhanced hourglass control. The material properties of the composite laminates and epoxy used in this study are depicted in Table 2. The supports and loading nose are simulated based on the ASTM D2344M as cylinder rigid bodies with diameters of 3 mm and 6 mm,

Table 2. Material properties of CFRP [56].Parameter Value

Longitudinal Young’s modulus, E1 (GPa) 140Transverse Young’s modulus, E2 = E3 (GPa) 12.9In-plane shear modulus, G12 = G13 (GPa) 6.90Poisson’s ratio, υ12 = υ13 0.23Longitudinal tensile strength, Xt (MPa) 1520Longitudinal compressive strength, Xc (MPa) 1590Transverse tensile strength, Yt (MPa) 44.5Transverse compressive strength, Yc (MPa) 253In-plane shear strength, S12 (MPa) 107

968 Y. LIU ET AL.

respectively [41]. Based on this standard, the ratio of the specimen length, width, and span to the thickness should be six, two, and four, respectively. Hence, a composite with 20 plies with a thickness of 0.14 mm each is assumed in this study. Considering the total thickness of 2.8 mm, the length and width of the short beam would be 16.8 mm and 5.6 mm, respectively. The shear stress and the normal stress in the composite can be calculated from Equations (17) and (18), respectively. The ILSS can be found by using the maximum load in Equation (17).

Shearstress ¼ 0:75Pbh

(17)

Norman stress ¼ 1:5PL

2bh2 (18)

The contact between the loading nose and first laminate is defined as general contact, and the surface-to-surface contact with small sliding is applied for the supports. The loading nose has movement only through the thickness of the short-beam composite. The ENCASTRE boundary condition is used for supports. The coefficient friction of 1 is introduced in contact behavior for loading nose and supports and 0.3 for the contact between laminates [56].

The VUMAT user subroutine is implemented to investigate the failure analysis and mechanical constitutive behavior of CFRP, which is called for blocks of material calculation points. As shown in the flowchart of VUMAT (Figure 3), the stiffness matrix of CFRP is calculated when the step-time is equal to zero. At times bigger than zero, the subroutine calculates the stresses at each increment for each material point, and the failure functions (ff and fm) are calculated based on the failure criterion. VUMAT can save the failure function as state variables and compare it with the failure displacements to evaluate whether the damage has been initiated or not. If failure starts, the subroutine calculates the damage parameters df and dm and store them as state variables to calculate the degraded stiffness matrix. In the damage evolution state, the stresses will be calculated based on the degraded material properties. The process will end if the damage parameters are equal to or greater than one. Besides the intralaminar damage, the cohesive damage initiation and evolution also is

Figure 3. Flowchart of the VUMAT user subroutine for damage analysis of CFRP.

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controlled to evaluate the interlaminar damage between the layers. The combination of these three damages can cause failure in the composite. However, the delamination is the failure mode if the cohesive damage parameter evolves completely based on the theory discussed in Sect. 2.2 before complete failure occurs in the matrix or fiber.

3. Results and discussion

3.1. ZnO/epoxy enhancement layer

The appropriate RVE containing a single ZnO nanowire embedded in a cubic epoxy is modeled for the homogenization analysis to calculate the effective material properties of the enhancement layer. The related Young’s modulus of the ZnO with different diameters is extracted from Equation (1). The nine parameters of the constitutive matrix for the enhancement layer, including ZnO with the diameters of 17, 75, 150, 450 nm are shown in Table 3. It is observed that by increasing the ZnO diameter, the moduli of the ZnO/ epoxy enhancement layer decreases. Since the ZnO orientation is perpendicular to the fiber direction in CFRP composite, the appropriate material properties are used to calculate the penalty stiffness of the cohesive contact using Equations (3)–(5).

Figure 4. (a) Through the thickness-shear stress distribution at x/L = 0.25, (b) comparing FEA shear stress distribution with theory.

Table 3. The effective material properties of ZnO/epoxy layer with different ZnO diameters.

DZnO (nm) E11 (GPa) E22 (GPa)E33

(GPa) ν21 ν23 ν31 G12 (GPa)G13

(GPa)G23

(GPa)

17 39.0 38.9 149 0.34 0.06 0.06 8.22 13.3 13.375 36.6 36.8 125 0.14 0.07 0.07 7.95 12.6 12.6150 35.8 35.8 116 0.15 0.08 0.09 7.90 12.4 12.4250 35.7 35.8 113 0.15 0.08 0.08 7.86 12.3 12.3450 35.4 35.4 109 0.15 0.08 0.08 7.84 12.3 12.3

970 Y. LIU ET AL.

3.2. Damage analysis of bare and enhanced CFRP

The results of the bare CFRP composite short beam are presented in this section to verify the accuracy of the numerical model. The reaction force at different displacement values (u) is calculated and converted to the interlaminar shear stress using Equation (17). The shear stress distribution through the thickness is illustrated in Figures 4 and 5 at three locations along the beam length (x/L = 0, 0.25, 0.5), and at three different loads (u/ h = 0.025, 0.074, and 0.140). It is obvious that the maximum shear stress is located between the loading nose and support span along the beam length. It can be seen from Figure 4 that the shear stress distribution through the thickness has the parabolic trend in which the maximum is in the middle of the thickness (neutral axis) and reduces to the zero value at the two ends. However, this trend has a sharper gradient at lower loads while at the higher load (u/h = 0.140) it becomes flat in the middle plies as the damage in the cohesive contact is initiated in the critical zone. This distribution at the load of u/ h = 0.025 is also compared to the classical beam theory as depicted in Figure 4(b). A good agreement between the numerical analysis and the theory is observed in this figure, indicating the accuracy of the FEA. The shear stress distribution through the thickness for the location under the support is depicted in Figure 5(a). In this section, the maximum shear stress is shifted to the zone between the middle ply and the support. This trend at the location under the loading nose shows negligible values (Figure 5(b)).

The trend of shear stress from the initial state up to the failure moment is illustrated in Figure 6(a). There are three typical failure modes in the short-beam analysis, including permanent plastic deformation, surface compressive damage followed by the shear fail-ure, and the pure interlaminar shear failure [57]. There is no stress drop until the maximum point in the shear stress distribution extracted from FEA (Figure 6(a)), indicating the valid interlaminar shear failure mode. The failure mode in the composite

Figure 5. (a) Through the thickness-shear stress distribution at x/L = 0, (b) Through the thickness-shear stress distribution at x/L = 0.5.

COMPOSITE INTERFACES 971

with the displacement distribution contour is shown in Figure 6(b). It is clear that the debonding occurs on the middle ply (neutral axis) and extends to the end of the composite in the longitudinal direction, which causes the delamination failure.

As discussed before, the maximum shear stress becomes wider in the neutral axis by increasing the load caused the larger contact areas to exceed the strength. Hence, more cohesive damage is initiated in both directions. However, the damage expands to the end of the composite in the longitudinal directions and results in delamination failure. In addition, although there are few zones in both matrix and fiber that damage has been initiated, these damages are not evolved completely to cause the flexure (compression or

Figure 7. (a) and (b): Fiber damage parameter at u/h = 0.12,0.14; (c) Matrix damage parameter at u/ h = 0.095, 0.14; (e), (f) cohesive contact damage parameter at u/h = 0.116, 0.14.

Figure 6. (a) Shear stress vs. normalized applied displacement and (b) failure mode for the bare CFRP composite short beam.

972 Y. LIU ET AL.

tension) failure modes. For better illustration, the distribution of the damage parameter in the matrix, fiber, and cohesive contact is shown in Figure 7 at two different loads. The first load is the moment that damage initiates, and the second load are the moments of failure. It can be seen in Figure 7(a,b) that the damage in the fiber initiates under the loading nose on the outer ply and expands on the longitudinal direction and then expands to the next ply. However, the damage in the matrix initiates from the area under the loading nose and then expands through the thickness, as shown in Figure 7(b, c). The critical areas for the matrix are close to the loading nose and supports. Besides, the damage in the matrix initiates earlier compared to the fiber.

In order to show the enhancement effect of growing ZnO nanowires on the fiber on the ILSS, the results of the hybrid composite are compared with the bare composite. The damage of the cohesive contact in the middle ply of the hybrid composite at three different loads is tracked along the longitudinal axis, as shown in Figure 8. The damage starts from the area between the loading nose and the supports and expands long-itudinally toward the ends of the beam. The damage reaches the end of the beam at the load of u/h = 0.12 and causes delamination failure. The reaction force trend with

Figure 8. Distribution of the cohesive contact damage parameter along the beam length for three loads.

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increasing the nose displacement from the initial moment until the failure point for the composite with ZnO nanowires are compared with the bare composite in Figure 9(a). It can be observed that similar to the bare composite, the failure mode in the hybrid beam is the interlaminar shear with no obvious flexural damage. The shape of the failed hybrid sample with the cohesive contact damage distribution is depicted in Figure 9(b) indicat-ing the delamination in the middle ply. It should be noted that the thickness of the beam is increased by adding the ZnO/epoxy layer compared to the bare sample, which requires more load to fail the beam. The ILSS for these two samples is calculated using Equation (17) showing the value of ILSS = 69.8 MPa for the bare and ILSS = 100 MPa for the hybrid composite. This result indicates that the interfacial shear strength is improved by 43% by adding the enhancement ZnO nanowire layer in the hybrid composite. These results are captured for the unidirectional fibers with zero fiber orientation angle. The effect of the fiber orientation angle on the interlaminar shear stress is explored by modeling different angles of θ = 0, 15, 30, 35, 60, 75, 90 degrees. The calculated normal strength and ILSS for both bare and hybrid composite with ZnO/epoxy layer are illustrated in Figure 10(a,b), respectively. As it is evident, the strength of the composite beam is decreasing by

Figure 10. (a) Normal strength and (b) ILSS vs fiber orientation angle distribution for bare and hybrid composite short beam.

Figure 9. (a) Comparing the Load vs displacement trend for hybrid composite and bare composite beam, (b) failure mode of the hybrid composite beam.

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increasing the fiber orientation angle for both specimens. The trend in both composites shows abrupt degradation initially (up to 30°) degree, and then it becomes smooth.

The effect of the ZnO nanowire geometry is also investigated in this study. As mentioned before, Young’s modulus of the ZnO nanowire depends on the diameter, which affects the effective material properties of the enhancement layer. Besides, the length of the nanowires can control the thickness of the ZnO/epoxy layer while they do not have any effect on the material properties of the layer. Nanowires with diameters of 17 nm, 75 nm, 150 nm, 450 nm in a unidirectional CFRP with zero degrees fiber orientation are considered. The effective material properties for these diameters dis-played in section 3.1 are used to define the numerical model. The ILSS for each specimen is extracted, as shown in Figure 11(a). It can be observed that the value of ILSS decreases by increasing the ZnO diameter with the parabolic trend. The ILSS is found to be 100 MPa for the ZnO with the diameter of d = 25 nm, while the ILSS is found to be 86.9 MPa for the d = 450 nm. In other words, using thinner ZnO nanowires in the enhancement layer can result in higher shear strength of the hybrid composites. In addition, three typical lengths of the nanowires (L = 10, 20, and 30 µm) are employed to explore the effect of length on the ILSS. The value of the ILSS for each beam is calculated from FEA, as depicted in Figure 11(b). A gradual linear increase in the ILSS is observed by increasing the ZnO length with the values between 100 and 108 MPa. Although longer nanowires can result in higher shear strength from this analysis, this effect is not comparable with the ZnO diameter.

4. Conclusions

The interlaminar shear damage of the hybrid CFRP composite with unidirectional fiber is investigated in this study. The ZnO nanowires with different lengths and diameters are modeled as vertically aligned particles on each ply to improve the shear strength of the composite. A multi-scale numerical model is developed to simulate the damage mechan-ism of a short hybrid composite beam in the 3PB loading. The ZnO nanowires are embedded in epoxy polymer to create an enhancement layer in which the effective material properties are calculated by homogenization analysis of an appropriate RVE.

Figure 11. (a) ILSS of the enhanced composite with different ZnO diameter, (b) ILSS of the enhanced composite with different ZnO length.

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The intralaminar progressive failure in the fiber and matrix is modeled in ABAQUS using the VUMAT user subroutine. The interlaminar shear failure mode is observed from the FEA of both bare and hybrid short composite beam, indicating the appropriate damages analysis of the model. Although damage is initiated in some location in fiber and matrix, the interlaminar shear damage expanded in the middle ply (neutral axis) longitudinally to the end of the sample, causing the failure in the composite.

It is found that by adding the vertically aligned ZnO nanowires on the CFRP layers, the ILSS can be improved up to 43%. It is seen that similar to the bare composites, changing the fiber orientation angle from 0 to 90 degrees reduces the value of the ILSS in the enhanced composite beam with the parabolic trend. The analysis of the hybrid composite with different ZnO geometries shows that the thinner and longer nanowires can improve the shear strength more efficiently. The value of the ILSS for a composite with the ZnO diameter of 25 nm is 15% larger than the one with a diameter of 450 nm with the same length. However, although longer ZnO can result is higher ILSS, the effect of ZnO length is not very remarkable because the typical length of the ZnO range is limited.

Disclosure statement

No potential conflict of interest was reported by the authors.

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