Optimization of the mechanical performance and damage failure characteristics of laminated composites based on fiber orientation

Abstract

In this study, the effect of fiber angle on the tensile load-bearing performance and damage failure characteristics of glass composite laminates was investigated experimentally, analytically, and numerically. The glass fabric in the laminate was perfectly aligned along the load direction (i.e., at 0°), offset at angles of 30° and 45°, or mixed in different directions (i.e., 0°/30° or 0°/45°). The composite laminates were fabricated using vacuum-assisted resin molding. The influence of fiber orientation angle on the mechanical properties and stiffness degradation of the laminates was studied via cyclic tensile strength tests. Furthermore, simulations have been conducted using finite element analysis and analytical approaches to evaluate the influence of fiber orientation on the mechanical performance of glass laminates. Experimental testing revealed that, although the composite laminates laid along the 0° direction exhibited the highest stiffness and strength, their structural performance deteriorated rapidly. We also determined that increasing the fiber offset angle (i.e., 30°) could optimize the mechanical properties and damage failure characteristics of glass laminates. The results of the numerical and analytical approaches demonstrated their ability to capture the mechanical behavior and damage failure modes of composite laminates with different fiber orientations, which may be used to prevent the catastrophic failures that occur in composite laminates.

Graphical abstract

Keywords

fiber orientation / composite laminates / stiffness degradation / analytical approaches / finite element analysis

1 Introduction

In recent decades, lightweight composites have been used in structural components owing to the increasing demand for energy-efficient systems. Composite materials are widely used in various application, such as aerospace, aeronautical, and automotive fields, owing to their high stiffness and strength-to-weight ratio characteristics [1–3]. The most effective materials adopted in these applications are glass fiber, carbon fiber, and Kevlar fiber composites because of their excellent strength properties. However, the high cost of these fibers makes their accountable usage more essential. For instance, the Boeing 707 jet, which was the first commercial aircraft manufactured using a composite structure in the 1950s, in which glass fiber accounted for 2% of the total structure. Furthermore, parts of Airbus A308 that contain GLARE fiber metal laminates were manufactured using S-glass fibers [4]. Moreover, the proportion of glass composites has increased recently by around 50% of their total weight in various aircraft, such as Boeing 787 and Airbus A350XWB. Nevertheless, these composites experience different modes of failure owing to the combined stresses resulting from their brittleness [5]. These damage failures are dangerous considering the safety of composite structures because they cannot be detected visually, leading to catastrophic failures. Many studies [6–14] have reported that failures occur due to tensile and compression loadings, which are considered the main modes of failure in composite laminates and can affect their load-carrying capacity. Therefore, previous studies attempted to enhance the ductility of these composites through using hybrid composites [15,16]. Hybrid composites are manufactured using multiple types of fibers in composite laminates and therefore further enhance the mechanical properties compared with individual reinforcement [17–19]. Thus, hybrid composites consider a logical evolution to more potential aspects, such as design freedom, cost reduction, and optimization performance [20,21]. You et al. [22] studied the tensile strengths of intra-layer hybrid composites (carbon and glass fiber composites). Their findings demonstrated that the strength of the hybrid layer composites could be improved by appropriately placing them inside the composite laminates, which enhances the mechanical performance of the hybrid composite. Hwang and Mao [23] studied the effects of combining glass and carbon fibers on the compression properties of hybrid composite laminates. Based on their results, it was found that increasing the glass fiber content led to a decrease in the compressive strength. Furthermore, Yerramalli and Waas [24] confirmed a similar result after investigating the influence of hybrid carbon−glass fiber composites on the mechanical performance of hybrid composite cylinders under compressive strength loading. However, several researchers have considered determining the baseline tensile failure strain of hybrid composites as a key issue in their studies [25–27].

Using hybrid layers (inter-ply layers) can also be considered as a promising method for protecting high-strength fibers from damage during loading [28–33]. Jesthi and Nayak [34] confirmed that the mechanical performance of hybrid composites could be improved by inter-ply rearrangement of glass and carbon-woven fabrics. Das et al. [35] and Petrucci et al. [36] observed that the mechanical performance of synthetic fiber (glass) composites could be improved by including natural fabric layers (i.e., jute, flax, and hemp). Murugan et al. [37] illustrated that a composite laminate could be reinforced by inter-plying high-modulus carbon fabric layers to achieve better performance. Because the required design strength of laminates can be obtained by including various types of fabric layers, the nominal size of the component increases, leading to an additional weight of the component.

Numerous research [38–43] demonstrated that the fibers must be aligned in a suitable direction in the ply to achieve the desired mechanical performance. This can be achieved by orienting the load almost exclusively along the fiber orientation; consequently, minimizing the shear load of the matrix. However, these studies did not consider damage failure, which is a key parameter in composite structure design. The finite element analysis (FEA) simulation technique is widely adopted in engineering applications to identify stress distributions, structural deformations, and damage failure modes. However, the published data for studying the effect of fiber orientation on the damage failures of composite laminates using both experimental and numerical methods are scarce. Thus, this research attempts to bridge this knowledge gap that was not addressed in previous studies by conducting systematic experimental tests on glass fabrics and validating them using analytical and numerical modeling. Accordingly, various laminates with fiber orientations were fabricated to evaluate the severity of visible and subsurface damage, which resulted from the change in the direction of the fibers subjected to tensile strength. In addition, Abaqus software with 2D continuum shell elements was used to simulate the tensile strength and model the modes of failure that occurred in the fiber and matrix.

2 Experimental steps

2.1 Materials and composite manufacturing

To prepare the composite laminates used in this study, the reinforcement was applied as a woven glass fabric, as shown in Fig.1, the specifications of which are listed in Tab.1. The specifications of the fabric, such as count, areal density, and thickness, were calculated according to ASTM standards D3775-02, D3776-09, and D1777-09, respectively.

In addition, the composite laminates were manufactured using Sikadur-52 resin with a resin to hardener ratio of 2:1. Four glass fabric layers were used for each laminate, and the ply configurations of the laminates were [(0°/90°)₄], [(±45°)₄], [(0°/45°)₂], [(±30°)₄], and [(0°/30°)₂]. Because a woven fabric is used, each cross-ply (i.e., 0°/90° or ±45°) implies a biaxial laminate, as illustrated in Fig.2.

The infusion vacuum process was used to create the composite laminates, whose specifications are listed in Tab.2. The laminate density was determined using the immersion method, according to BS EN ISO 1183-1 standard. Furthermore, the volume fractions of the laminates were measured using the ignition method, following the BS EN ISO 1172 standard.

2.2 Experimental test methods

2.2.1 Tensile strength test

In this research, the laminates’ tensile strength properties have been measured via tensile strength tests conducted according to the ASTM D3039M 2008 standard. The test were conducted using a universal testing machine (brand: Instron 5982) at 2 mm/min and 0.2% per second as the crosshead and strain rates, respectively. The sample dimensions were 200 mm × 20 mm and the gauge length was 50 mm. Each test was performed on three identical specimens in accordance with ASTM D30390. A video extensometer strain gauge was used to record the strain through the dots placed on the sample, as shown in Fig.3. This technique measures deformation based on the movement of attached markers and converts them into strain values.

2.2.2 Measurement of stiffness degradation

During tensile strength tests, permanent deformation can occur in composite laminate structures, which can slowly grow as small cracks in the matrix and then develop into inter-laminar failures [44,45]. Fig.4 shows the gradual loss of stiffness resulting from delamination. At the beginning of the load−unload cycles, the composite suffered from an early loss in stiffness. Subsequently, slow deterioration occurred in the composite, leading to an increased stiffness reduction. In the subsequent stages of cyclic loading, the was load increased, leading to a permanent deformation and significant reduction in stiffness. The elastic modulus of each loading cycle and hysteresis loop exhibited by the composites were calculated using the plotted line that crossed the maximum and minimum of the loop. The degradation in stiffness (i.e., damage) was measured using the following equation [46]:

(1)D=1-\frac{E_{\mathrm{i}}}{E_0},

where D, E_i, and E₀ denote the stiffness degradation, damaged elastic modulus, and undamaged elastic modulus, respectively, which occurred during the initial load cycle. The value of factor D varied between 0 and 1, which indicated to no degradation in stiffness and failure, respectively.

2.3 Analytical methods

To compare the experimental and theoretical stiffnesses of the composite laminates, an analytical method was adopted in this study. The fabric composite laminates were modeled analytically using the classic laminate theory (CLT) method. Fig.5 shows the geometries of the composite laminates.

In each lamina, which was considered a biaxial laminate consisting of two plies, the stiffness reduction of the matrix with respect to the coordinate system (xyz) was calculated.

A matrix with dimensions of 6 × 6, which comprised the terms A, B, and D, was used. These terms refer to the extensional, coupling, and bending stiffness matrices, respectively. In addition, the evaluation of these matrices in terms of lamina stiffness in the coordinate system is expressed as follows:

(2)A_{ij} ={\sum }_{k=1}^n(h_k- h_{k-1})\cdot {\left({\overline{Q}}_{ij}\right)}_k, (i=1,2,6;j=1,2,6)

(3)\begin{array}{rl}& B_{ij}=1/2\cdot {\sum }_{k=1}^n(h_k^2-h_{k-1}^2)\cdot {\left({\overline{Q}}_{ij}\right)}_k,\\ & (i=1,2,6;j=1,2,6)\end{array}

(4)\begin{array}{rl}& D_{ij}=1/3\cdot {\sum }_{k=1}^n(h_k^3-h_{k-1}^3)\cdot {\left({\overline{Q}}_{ij}\right)}_k,\\ & (i=1,2,6;j=1,2,6)\end{array}

where k is the number corresponding to the lamina k.

(5)\left[\begin{array}{c}{N}_x\\ N_y\\ N_{xy}\\ M_x\\ M_y\\ M_{xy}\end{array}\right]=\left[\begin{array}{cccccc}{A}_{11}& A_{12}& A_{16}& B_{11}& B_{12}& B_{16}\\ A_{12}& A_{22}& A_{26}& B_{12}& B_{22}& B_{26}\\ A_{16}& A_{26}& A_{66}& B_{16}& B_{26}& B_{66}\\ B_{11}& B_{12}& B_{16}& D_{11}& D_{12}& D_{16}\\ B_{12}& B_{22}& B_{26}& D_{12}& D_{22}& D_{26}\\ B_{16}& B_{26}& B_{66}& D_{16}& D_{26}& D_{66}\end{array}\right]\cdot \left[\begin{array}{c}{\epsilon }_x^0\\ {\epsilon }_y^0\\ {\gamma }_{xy}^0\\ k_x\\ k_y\\ k_{xy}\end{array}\right] ,

where N_x and N_y are the normal forces per unit length and N_{xy} is the shear force per unit length. M_x\mathrm{a}\mathrm{n}\mathrm{d}{M}_y are the bending moments per unit length and M_{xy} is the twisting moment per unit length. {\epsilon }_x^0, {\epsilon }_y^0, and {\gamma }_{xy}^0 denote midplane strains, while k_x, k_y, and k_{xy} denote curvatures. Thus, the Young’s moduli E of the composite laminates were predicted using the following equation:

(6)E=\frac{1}{h\cdot A_{11}^{\ast }},

where {[A}^{\ast }] = {[A}^{-1}] and h denotes the composite laminate thickness.

The predicted Young’s moduli of all composite laminates were calculated using MECH G-comp software. Tab.3 lists the material properties of the lamina obtained by this software.

The ultimate tensile strengths of the laminates could be determined analytically using the failure criteria. Thus, the strength can be determined based on the Tsai−Hill failure criterion as follows [48]:

(7)\frac{1}{{\sigma }_{\mathrm{c}}}=\frac{{\mathrm{c}\mathrm{o}\mathrm{s}}^4\theta }{X^2}+\left[\frac{1}{S^2}-\frac{1}{X^2}\right]{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta {\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta +\frac{{\mathrm{s}\mathrm{i}\mathrm{n}}^4\theta }{Y^2},

where X and Y denote the ultimate tensile strengths in the longitudinal and transverse directions, respectively, and S denotes the ultimate in-plane shear strength. The symbol \theta refers to orientation angle with respect to the longitudinal direction of fabric.

2.4 Simulation of tensile strength using finite element method

The ABAQUS software was employed for FEA in this study to simulate the influence of the fiber orientation angle on the mechanical properties of the glass composite laminates.

Accordingly, the laminates were modeled using an ABAQUS/CAE input file. In addition, a 3D deformable solid with continuum shell elements (SC8R) in the CAE part module was used to model the rectangular part. First, the damage failure mode of the lamina and its elastic properties were assigned based on the density by creating one lamina in the 0° direction. The corresponding properties are listed in Tab.3. Furthermore, depending on the experimental conditions, the values of the longitudinal tensile strength (X_{\mathrm{t}}) for the composite samples were obtained, while the supplier of the epoxy provided its tensile strength (Z_{\mathrm{t}}). The in-plane shear strengths (S_{12}, S_{23}, and S_{13}) of the lamina were determined using Eq. (8) [49]:

(8)\begin{array}{rl}& S_{12}=F_{\mathrm{m}\mathrm{s}}{C}_{\mathrm{v}}\left[1+(V_{\mathrm{f}}-\sqrt{V_{\mathrm{f}}})⟨1-\frac{G_{\mathrm{m}}}{G_{\mathrm{f}}}⟩\right],\\ & S_{23}=S_{13}=S_{12},\end{array}

where G_{\mathrm{m}} and G_{\mathrm{f}} are the shear moduli of the matrix and fiber, respectively, F_{\mathrm{m}\mathrm{s}} is the shear strength of the matrix, and C_{\mathrm{v}} is the coefficient of voids, which is calculated using Eq. (10):

(9)C_{\mathrm{v}}= 1-\sqrt{\frac{4V_{\mathrm{v}}}{\text{π}(1-V_{\mathrm{f}})}},

where V_{\mathrm{v}} is the volume fraction of void in the laminates.

Both compressive strengths in the longitudinal (X_{\mathrm{c}}) and transverse (Y_{\mathrm{c}}) directions and the transverse tensile strength (Y_{\mathrm{t}}) were calculated using Eqs. (11)−(15) [50]:

(10)X_{\mathrm{c}}= \frac{E_{11}{\mathit{\text{ε}}}_2^{\mathrm{T}}}{{\nu }_{12}},

(11){\mathit{\text{ε}}}_2^{\mathrm{T}}= {\mathit{\text{ε}}}_{\mathrm{m}}^{\mathrm{T}}(1-V_{\mathrm{f}}^{1/3}),

(12)Y_{\mathrm{t}}= E_{22}{\mathit{\text{ε}}}_2^{\mathrm{T}},

(13)Y_{\mathrm{c}}= E_{22}{\mathit{\text{ε}}}_2^{\mathrm{c}},

(14){\mathit{\text{ε}}}_2^{\mathrm{c}}= \frac{d}{s}x\frac{E_{\mathrm{m}}}{E_{\mathrm{f}}}+\left(1-\frac{d}{s}\right){\mathit{\text{ε}}}_{\mathrm{m}}^{\mathrm{c}},

(15)\frac{d}{s}={\left(\frac{4V_{\mathrm{f}}}{\text{π}}\right)}^{1/2},(\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{y}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{f}\mathrm{i}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{s})

where {\mathit{\text{ε}}}_2^{\mathrm{T}}, {\mathit{\text{ε}}}_{\mathrm{m}}^{\mathrm{T}} {,V}_{\mathrm{f}}, {\mathit{\text{ε}}}_2^{\mathrm{c}}, and {\mathit{\text{ε}}}_{\mathrm{m}}^{\mathrm{c}} are ultimate transverse tensile strain of lamina, ultimate tensile strain of epoxy, fiber volume fraction, ultimate compressive failure strain of lamina, and ultimate compressive failure strain of matrix, respectively. While d, s, E_{\mathrm{m}}, and E_{\mathrm{f}} are the diameter of the fibers, center-to-center spacing between the fibers, modulus of epoxy, and modulus of fibers, respectively. The value of {\mathit{\text{ε}}}_{\mathrm{m}}^{\mathrm{c}} is 0.03 for epoxy matrix [50].

The progressive damage failures in the lamina can be predicted using two-dimensional Hashin failure criteria, which include the sub-options of damage evolution and damage stabilization. The damage failures included tensile fiber failure F_{1\mathrm{t}}, compressive fiber failure F_{1\mathrm{c}}, tensile matrix failure F_{2\mathrm{t}}, and compressive matrix failure F_{2\mathrm{c}}. They are presented in the following equations:

(16)\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}:F_{1\mathrm{t}}={\left(\frac{{\sigma }_{11}}{X_{\mathrm{t}}}\right)}^2, \mathrm{i}\mathrm{f}{\sigma }_{11}\ge 0,

(17)

(18)\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{x}\mathrm{f}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{u}\mathrm{r}\mathrm{e}:F_{2\mathrm{t}}={\left(\frac{{\sigma }_{22}}{Y_{\mathrm{t}}}\right)}^2+{\left(\frac{{\tau }_{12}}{Z_{\mathrm{l}}}\right)}^2, \mathrm{i}\mathrm{f}{\sigma }_{22}> 0,

(19)

where Z_{\mathrm{l}} denotes the longitudinal shear strength. The values of \sigmaand \tau refer to the stress, which was applied on the element along various directions of composite, and shear strength, respectively. Stiffness degradation of the lamina can cause significant intralaminar propagation, which is defined as the plane stress constitutive stiffness matrix. There are three independent damage modes in the matrix with indices d_1, d_2, and d_6, within the domain [0,1], as follows:

(20)C=\frac{1}{D}\left[\begin{array}{ccc}{E}_1^0(1-d_1)& E_1^0{v}_{21}(1-d_1)& 0\\ E_1^0{v}_{21}(1-d_1)(1-d_2)& E_2^0(1-d_2)& 0\\ 0& 0& G_{12}^0(1-d_6)\end{array}\right],

(21)D=1-v_{12}{v}_{21}(1-d_1)(1 -d_2).

Based on the damage factors d_{1\mathrm{t}}, d_{1\mathrm{c}}, d_{2\mathrm{t}}, and d_{2\mathrm{c}}, the damage indices d_1, d_2, and d_6 have been derived. The initiation of delamination in the composite laminates was predicted using a quadratic nominal stress criterion. Equations (23) and (24) express the initiation of damage, including the nominal stress ratio, which reaches 1.

(22){\left[\frac{⟨{\sigma }_{\mathrm{n}}⟩}{{\sigma }_{\mathrm{n}\mathrm{c}}}\right]}^2+ {\left[\frac{{\sigma }_{\mathrm{t}}}{{\sigma }_{\mathrm{t}\mathrm{c}}}\right]}^2+{\left[\frac{{\sigma }_{\mathrm{s}}}{{\sigma }_{\mathrm{s}\mathrm{c}}}\right]}^2\ge 1,

where {\sigma }_{\mathrm{n}}, {\sigma }_{\mathrm{t}}, and {\sigma }_{\mathrm{s}} are the normal stress and two shear stresses, while {\sigma }_{\mathrm{n}\mathrm{c}}, {\sigma }_{\mathrm{t}\mathrm{c}}, and {\sigma }_{\mathrm{s}\mathrm{c}} are the peak values of the nominal stress when the deformation is either purely normal to the interface or in the first or the second shear direction, respectively. Moreover, an increase in load leads to the further progression of damage inside the composite laminates. Therefore, the power-law fracture criteria can be adapted to present the progressive damage in the cohesive zone, depending on the mixed-mode inter-laminar damage.

(23){\left[\frac{G_{\mathrm{I}}}{G_{\mathrm{I}}^{\mathrm{c}}}\right]}^{\alpha }+{\left[\frac{G_{\mathrm{I}\mathrm{I}}}{G_{\mathrm{I}\mathrm{I}}^{\mathrm{c}}}\right]}^{\beta }+{\left[\frac{G_{\mathrm{I}\mathrm{I}\mathrm{I}}}{G_{\mathrm{I}\mathrm{I}\mathrm{I}}^{\mathrm{c}}}\right]}^{\gamma }\ge 1,

where G_{\mathrm{I}}, G_{\mathrm{I}\mathrm{I}}, and G_{\mathrm{I}\mathrm{I}\mathrm{I}} are the energy release rates of modes I, II, and III, respectively. G_{\mathrm{I}}^{\mathrm{c}}, G_{\mathrm{I}\mathrm{I}}^{\mathrm{c}}, and G_{\mathrm{I}\mathrm{I}\mathrm{I}}^{\mathrm{c}} represent the critical energy release rates of modes I, II, and III, respectively. Furthermore, the factors \alpha , \beta, and \gamma are measured experimentally. Tab.4 lists the inter-laminar properties of the laminate.

Then, another similar lamina was created in a selective direction. The constant properties and orientation angles were also defined for each lamina in the CAE Property Module. In this simulation, four laminas with sequence stacking, such as [(0°/90°)₄], [(±30°)₄], [(±45°)₄], [(0°/45°)₂], and [(0°/30°)₂], were considered.

Furthermore, the cohesive zone model was used to model the inter-laminar damage failures in the composite laminates.

To ensure that the movement and rotation in any direction were fixed, an encastre boundary condition (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0) was applied to one side of the rectangular model, as illustrated in Fig.6. The velocity loading point was determined to be 0.034 mm/s in the X-direction of the rectangular model to mimic the experimental loading condition of 2 mm/min. Furthermore, a mesh with a global size of 0.0008 and linear continuum shell element in the mesh module was selected for each lamina of the composite laminates, as shown in Fig.7.

3 Results and discussion

3.1 Experimental results

Fig.8 presents the experimentally obtained stress−strain relationships of the composite samples. The mechanical properties, such as the tensile strength, modulus of elasticity, and strain to failure, are illustrated in Fig.9. The results are reported as the average values of three identical samples. Observe that the ultimate tensile strength depends on the fiber orientation. Thus, the ultimate tensile strength reached its highest value of 380 MPa for the composite with fibers oriented parallel to the longitudinal direction (0°-direction). By varying the angle of fiber orientation to 45°-direction, a significant decrease of the ultimate tensile strength of 75% was observed. This can be attributed to the fact that the composites with 0° fiber orientation possess long and continuous fibers that resist and transfer tensile loads better compared to the other fiber orientations.

Slight variations in the angle of fiber orientation, for instance 30° direction, can cause substantial weakening of the material in specific test directions. The ultimate tensile strength of the composites with 60° fiber orientation angle has showed a slight reduction of 2% compared to that of the composite with 0° fiber orientation. By mixing different fiber orientations, the ultimate tensile strength can be improved. For example, the composite with 0° and 30° fiber orientations and that with 0° and 45° fiber orientations can enhance the tensile strength by 73% and 69% compared to the composite sample with 45° fiber orientation.

Similar behavior can be identified regarding the Young’s modulus (as illustrated in Fig.9(b)). A considerable reduction in the stiffness of the laminate occurred with an increase in the fiber orientation angle (i.e., 45°), whereas the stiffness remained high in the longitudinal direction. Composites with fiber orientation angles less than 45° (i.e., 30°-direction) exhibited enhancement in the stiffness (i.e., 30%). Balancing the stiffness values can be achieved by mixing different fiber orientations in one composite sample. For instance, the composite with 0° and 60° fiber orientations and that with 0° and 45° fiber orientation have illustrated an increase in the Young’s modulus of approximately 3% and 6%, respectively, compared to the composite sample with 45° fiber orientation.

When cyclical tensile strength tests are applied, structural deformation occurs in the fiber composite. This deformation can grow slowly and develop into various failure types (e.g., small cracks in the matrix at the first load cycle induce delamination at the second load cycle). This can lead to gradual degradation in the stiffness of the composite laminates. In the first tensile loading cycle, an early loss in stiffness occurred in the composite owing to matrix cracks. Then, these cracks grow and undergo delamination and fiber fracture in the next loading cycle, leading to major stiffness degradation. Selective fiber orientations in composite laminates can be leveraged to control the stiffness reduction.

Fig.10 and Tab.5 show the stiffness degradation of the composite laminates when the tensile strength tests were applied in two cycles.

Fig.11 illustrates the damage failures of all composite laminates. As shown in Fig.11(a), the composite fracture surface was serrated and irregular owing to fiber-dominated failure. In addition, extensive fiber pull-out was observed; the lateral surfaces of these pulled-out fibers were clear from the matrix residue. The damage failure shown in Fig.11(b) depicts that the fracture surface was dominated by matrix lacerations, indicating an inter-laminar shear stress fracture. Moreover, some matrix cleavage (with irregular boundaries) was observed owing to transverse tensile fracture of the matrix.

For off-axis angles of 45°, as shown in Fig.11(c), the composite was highly anisotropic. Transverse tensile stress was the predominant fracture mode in this range, and damage failure confirmed that the fracture surface was dominated by extensive matrix cleavage. Although, composite laminates with [(±45°)₄] exhibited reduced tensile strength and Young’s modulus compared to the composite laminates with [(0°/90°)₄], these samples could sustain large strains before final failure. In addition, the stacking sequences with symmetric ply orientations at ±45° under uniaxial loading present a shear driven behavior that results in a highly nonlinear stress−strain response. The increase in strain to failure, which leads to high toughness, can be attributed to the fact that cracks initiated by fiber breakage at the cross point of the (±45°) fibers propagated via a zigzag path along the (±45°) fibers/matrix interfaces, which created a high crack propagation energy. This phenomenon was also confirmed in Refs. [52,53].

Combining fiber orientations in composite laminates can significantly influence the damage failure modes in the tensile strength tests. This is observed in Fig.11(d) and 11(e), which confirm that the dominant failures are matrix cracks with fewer fiber fractures.

3.2 Comparison between experimental and analytical results

The variations in the tensile strength and modulus of elasticity with respect to fiber orientation are shown in Fig.12 for both the experimental and analytical results. As shown in Fig.12, both the tensile strength (Fig.12(a)) and modulus of elasticity (Fig.12(b)) strongly depend on the fiber orientation angle. Thus, the stiffness and tensile strength of the composite reached their highest values when the loading was along the fiber direction. Meanwhile, these values were the lowest when the fiber direction angle was approximately 45°. The Young’s modulus and tensile strength of the composite were slightly enhanced when the fiber orientation was mixed. A comparison between the experimental and analytical results, for both the modulus of elasticity and tensile strength, showed good agreement.

3.3 Comparison between experimental and finite element analysis results

A comparison of the experimental and numerical stress−strain curves for all composite laminates is shown in Fig.13. There is a clear agreement between the model curves and experimental plots in the elastic region for all the composite laminates. However, the model results showed a lower tensile strength than the experimental findings. The most likely cause of the enhanced ductile behavior is the crimp effect, which was not included in the model calculation of the composite laminates under tensile loading.

The displacements of the composite laminates in the direction of applied load are illustrated in Fig.14. Observe that the composite with 0° fiber orientation provided higher damage failures (as observed in Fig.14(a)) in comparison with other composite laminates. This can be attributed to the higher volume fraction of fibers with higher stiffness. In contrast, the laminates with different fiber orientations, such as those with 30° and 45° orientations (as illustrated in Fig.14(b) and 14(c)), exhibited the lowest damage failures compared with the composite laminates. However, the response of the tensile load displacement of the hybrid composites, as illustrated in Fig.14(d) and Fig.14(e), showed fewer damage failures than the composite with 0° fiber orientation. Therefore, it was established that layered composite laminates with different fiber orientations would be a convenient design.

4 Conclusions

In this study, experiments were conducted to investigate the influence of fiber orientation on the mechanical performance and damage failure characteristics of glass composite laminates under tensile loading. Several composite laminates with different fiber orientations were prepared using the vacuum-assisted resin infusion technique. The properties of these laminates (i.e., tensile strength) and their damage failures were simulated via FEA using the Abaqus software. Furthermore, analytical approaches were adopted to predict the stiffness and tensile strength of the laminates. Based on the experimental, analytical, and simulation results, the following conclusions were drawn.

1) Results of tensile strength showed that composite laminate with 0° fiber orientation has exhibited the highest stiffness and strength compared to other composite laminates. However, a considerable reduction in the stiffness of these laminates can occur after they are subjected to cyclic loading.

2) Appropriately selecting the fiber orientation in composite laminates can optimize the mechanical properties and stiffness degradation (i.e., controlling damage failures). For instance, composite laminates with 30° fiber orientation have exhibited high tensile strength and low stiffness degradation.

3) The results of the analytical approaches in terms of stiffness and tensile strength have agreed well with the experimental results.

4) A simulation model was developed using the ABAQUS software, in which numerous criteria were adopted. Despite the reliability of the obtained simulation results regarding the prediction of tensile strength properties and damage failures, which are available for composite laminates, the level of accuracy between the experimental and simulation results was slightly high. This was due to the crimp, which was not included in the simulation model. In addition, the VUMAT subroutine can further enhance the computational efficiency of the model for predicting the mechanical properties of laminates.

As noted in the current research, this approach of selecting the fiber orientation of composite laminates can be effectively used to obtain a high tensile strength performance with fewer catastrophic failures.

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