Tensile mechanical behavior and failure mechanisms of multihole fiber metal laminates—Experimental characterization and numerical prediction

Abstract

This work mainly investigates the effects of the hole number and layer direction on the tensile mechanical behavior and failure mechanisms of multihole fiber metal laminates by experimental and numerical methods. With the aid of digital image correlation technique, tensile tests are implemented to obtain mechanical responses of different multihole fiber metal laminates. Subsequently, numerical simulation considering thermal residual stress is conducted to elucidate the failure modes and progressive damage evolution of multihole fiber metal laminates, which integrates the progressive damage model of composite laminates and a cohesive zone model between aluminum sheet/composite laminates. Finally, numerical predictions are found in a good agreement with experimental measurements, in terms of mechanical responses and fracture morphologies. Results demonstrate that the number of holes has negligible influence on the ultimate tensile strength, whereas affects the final failure strain of multihole fiber metal laminates evidently. With the increase of layer direction, the fracture morphology changes from evident brittle fracture to fiber pull-out and matrix damage, which indicates that the critical failure mechanism of multihole fiber metal laminates changes from tension dominated to tension–shear dominated. Additionally, the longer loading history from initial damage to final failure of composite laminates demonstrates the significance of considering progressive damage behavior in numerical simulation.

Keywords

Multihole fiber metal laminates tensile mechanical behavior failure mechanism progressive damage analysis digital image correlation technique

Introduction

As a kind of sandwich structure, fiber metal laminates (FMLs) consisting of fiber reinforced layers and metal alloy have been widely applied in many engineering structures in virtue of their light weight, excellent corrosion, and fatigue resistance as well as the impact resistance, typically in aircraft, marine structure, and auto industry.^1–3 It is worth mentioning that FMLs have been applied successfully to the fuselage skin of aircraft structures, such as Boeing 777 and Airbus A380.⁴ It is widely known that there are many inevitable holes in the surface of airplane for meeting various operating requirements, such as doors, hatches. Moreover, some multiple holes are also usually designed in structures, such as the little bolt and rivet holes, as shown in Figure 1.^5,6 Consequently, for better design and application of FMLs, the effect of multiple holes on mechanical behavior and damage mechanisms of FMLs should be investigated systematically.

To the best of our knowledge, a lot of researches have been carried out on FMLs, including low and high velocity impact,^7–9 fatigue property,^10,11 blast load,¹² and residual strength.^13,14 Based on the large amount of studies, complex damage modes can be observed from the destructive FMLs, such as plastic deformation, matrix damage, fiber fracture, interfacial delamination, inter-laminar delamination, and even metal cracking. It is worth noting that most of above researches are focused on the intact FML structures without any imperfection. However, notched FMLs are often applied in engineering structures to meet some special requirements. Therefore, it is quite necessary to investigate the notch behavior of FMLs because of the undesirable stress concentration and possible premature failure in the vicinity of those notches. In addition, the damage behavior and failure mechanisms of notched composite structure in FMLs also deserve to be investigated carefully.^15,16

In the past decades, many researches about the notch performance of FMLs under tensile loading have been implemented through experimental test, numerical simulation, and analytical method. Yeh et al.¹⁷ investigated the effects of notch size and constituent on the failure mechanisms of a high modulus FMLs experimentally. The results indicated that the notched FMLs with boron and S2-glass fibers possess excellent residual strength despite of the existing large notches. Du et al.¹⁸ researched the notch damage and failure mechanisms of thermoplastic-based FMLs under tensile loading by numerical and experimental methods. It can be concluded that the initial fiber breakage occurred after the yield of FMLs, followed by the matrix damage. Sadeghpour et al.¹⁹ studied the effect of notch shapes on the ultimate notch strength and damage modes of FMLs. Their results exhibited that the circular holes fracture appeared at a point along the longitudinal direction and the square notches fracture occurred at the corner of square along the transverse direction. Zhang et al.²⁰ characterized the effects of notch size and layer direction on the notch strength and failure mechanisms of FMLs under off-axis tensile loading by experimental and numerical methods. It can be found that the critical failure of off-axis notched FMLs was still mainly controlled by tensile loading, while the aluminum layer played a decisive role. Meanwhile, they also confirmed that the energy dissipation method can be used to research the off-axis dependence of mechanical response and damage behavior in notched GLARE.²¹ Wu et al.²² predicted the residual strength of notched FMLs through a modified point stress criterion which was verified by experimental results. In addition to the notch behavior of FMLs under axial loading, as mentioned above, the influence of layer direction on the notch strength was also investigated by many researchers. Kawai and Arai²³ developed a new multiaxial criterion to predict the off-axis tensile strength of notched FMLs. It was proved by the experimental tests that the proposed method can be used to predict the off-axis notched strength of GLARE-3 accurately and efficiently. Although many researches have been conducted on the tensile mechanical behavior of notched FMLs, it should be noted that most of these investigations were focused on single hole FMLs, and the residual tensile strength and failure mechanisms of multihole FMLs are rarely studied comprehensively.

Multihole structures are common in our daily life, and some open literatures can be found about the failure modes and residual strength of multihole structures. Feroldi and Russo²⁴ and Russo²⁵ studied the failure modes and bearing capacity of multi-bolted FRP plate which was used in the structural joints under lateral thrust. Kazemahvazi et al.²⁶ investigated the influence of the hole layout and density on the residual strength of UD-composite laminates with multiple holes under tensile loading. However, there is a scarcity of information on the mechanical behavior and residual tensile strength of multihole FMLs. Due to the particularity of materials and the complexity of structural assembly, multihole FMLs are essential in the engineering structures, especially the interconnects for the fuselage skin. Chang et al.²⁷ concluded that the multiple-site fatigue damage for multihole FMLs can lead to the increasing of crack growth rates. Similar conclusions also can be demonstrated from Wang et al.²⁸ Therefore, it is of great significance to explore the tensile mechanical responses and failure mechanisms of multihole FMLs.

In recent years, digital image correlation (DIC) technique has been a kind of relatively new and effective tool for monitoring the full-field strain and displacement on the surface of specimens. Compared to the conventional strain gauge and extensometer, DIC technique can record the strain evolution and local subtle deformation in the vicinity of each hole in real time. In virtue of these advantaged functions, DIC technique has been used in many experimental measurements.^26,29,30 Sharma and Khan³¹ used DIC technique to capture the full-field deflection and particle velocity contours of impacted FMLs. Xu et al.³² compared the final deformation response of the bolt jointed FMLs from simulation and DIC results under the quasi-static loading. However, to the best of authors’ knowledge, there is a limited attempt to reveal the damage mechanisms and failure patterns of multihole FMLs with the aid of DIC technique under tensile loading.

In the current paper, the effects of the hole number and layer direction on the residual strength and tensile mechanical behavior of multihole FMLs are investigated by experimental and numerical methods. Numerous tensile tests are implemented to obtain the stress–strain curves and ultimate strength of multihole FMLs. DIC technique is employed to trace the global variation of displacement and localized strain fields of FMLs in the process of stretching. Subsequently, a progressive damage model considering thermal residual stress (TRS) is employed to investigate the damage modes and failure mechanisms of multihole FMLs. Numerical predictions are compared with experimental measurements, in terms of stress–strain responses, ultimate tensile strength, and damage morphologies. Finally, the progressive damage evolution and energy dissipated analysis of multihole FMLs are studied based on the numerical simulation, through which the damage degree and failure sequences of FMLs at different loading stages are characterized in considerable detail.

Specimen preparation and experimental description

Specimen preparation

The symmetric FMLs are made of three layers of aluminum sheets and two layers of composite laminates, which are manufactured in a hot press machine. The corresponding thicknesses of aluminum sheet and composite laminate are 0.4 and 0.5 mm, respectively. The composite laminate is stacked with four unidirectional carbon/epoxy layers, and each layer has a thickness of 0.125 mm. The detailed cross-section distribution of FMLs is exhibited in Figure 2. It should be noted that the adhesive layers are applied to cement the aluminum sheets and composite laminates. Therefore, in order to enhance the bonding performance between aluminum sheet and composite laminates, it is necessary to conduct some treatments on the surface of aluminum sheets, which can be summarized briefly as the following: decontaminating, degreasing, deoxidizing, anodizing, cleaning and drying.³³ After these procedures, three aluminum layers and two composite laminates are bonded together with epoxy primer. Then large FML panels are cured at 135°C and 0.5 MPa in a vacuum tank for 2 h.

As shown in Figure 3, FMLs with different number of holes are manufactured to study the influence of hole numbers on mechanical behavior and failure mechanisms. A CNC machine with a diamond cutter is employed to cut different number of holes from all the standard specimens. A cooling system is employed in the machine to ensure the accuracy of notches and specimens. Figure 3(a) illustrates the particular parameters of un-notched FMLs, in which the overall length, width, gauge length, and the clamping region are 230, 25, 150, and 40 mm, respectively. Subsequently, the different number of holes is dug out from the FMLs, all of which are 4 mm in diameter. The distances of the adjacent circular holes are $w 1 =12 mm$ in the transverse direction (perpendicular to the tensile direction) and $w 2=50 mm$ in the longitudinal direction (parallel to the tensile direction), respectively, as shown in Figure 3(b) to (e). Finally, to alleviate the undesirable stress concentration, the polishing at the notch and free edge of FMLs is a necessary procedure prior to the tests.

According to the previous researches, the ductility of unidirectional composite layers under off-axis tensile loading changes evidently with the relative direction of loading axis.³⁴ Moreover, the axial modulus of composite laminates is closely related to the fiber orientation based on the classical laminate theory. Therefore, it is of great significance to research the effect of composite layer direction on the mechanical behavior of multihole FMLs. In the current study, the off-axis layer directions (20°/−70°/20°/−70°, 45°/−45°/45°/−45°) of composite laminates are selected to compare with the on-axis (0°/90°/0°/90°) configuration in multihole FMLs.

Tensile equipment and DIC technique

In the current research, a testing machine (Instron 5985, USA) with a measuring range of 150 kN is applied to conduct a series of tensile tests, in which the tensile loading is controlled by displacement mode. During the experiments, each head of specimen should be caught by a gripper which can provide a grip force parallel to the axial direction of test specimens. According to the ASTM D3039 standard,³⁵ the tensile loading is exerted on FMLs by increasing the displacement of movable gripper with a relative lower rate of 1.0 mm/min so that the deformation process and damage evolution can be captured clearly.

The DIC technique combined with a charge coupled device (CCD) camera is used to obtain the strain fields and displacement distributions during the experimental tests. The DIC technique is a kind of white light technique which can be implemented to capture the change of full-field displacement and localized strain fields on the surface of FMLs.³⁶ The basic principle of DIC is to record the surface deformation and strain of FMLs during the tensile tests by comparing the digital images before and after deformation of specimen at a specified time interval. Therefore, the digital images are particularly important for accurately calculating the deformation and strain evolution of FMLs during the quasi-static tensile tests. In the current research, a 2448 × 2050 pixels CCD camera is used to capture the digital images, and the sampling rate of this camera is set to be two images per second.

Figure 4 exhibits the tensile testing machine and layout of CCD equipment. Regarding the FML specimens, many feature points are used to represent the deformation and strain of FMLs based on the position coordinates. Therefore, the speckling patterns on the surface of FMLs need to be created before DIC experiments, especially in the vicinity of notches. Here, the black and white paints are sprayed randomly on the surface of specimens, as shown in the gauge region.

Material properties and FE-model

Material properties of FMLs

In the current research, aluminum sheets and carbon fiber reinforced composite laminates are selected to form FMLs. Aluminum alloy (2024-T3) has higher strength and heat resistance, and its material properties are exhibited in Table 1. Additionally, the isotropic hardening behavior of aluminum sheets can be described as the stress–strain relationship in Table 2. Material parameters of aluminum alloy in Tables 1 and 2 can be obtained from Yao et al.⁸ Carbon fiber reinforced composite laminates are made up of T700/3234 unidirectional carbon/epoxy prepregs at different directions. The anisotropic elastic material properties and ultimate strength of the carbon/epoxy prepregs are listed in Table 3. The properties of unidirectional carbon fiber provided by the manufacturer are given in Table 3.

Table 1.

Material properties of aluminum alloy.⁸

ρ (kg/m³)	2700	Poisson’s ratio	0.3	Fracture strain	0.15
E (GPa)	70	Yield strength (MPa)	292	Fracture energy (J/m²)	10200

Table 2.

Isotropic hardening data for 2024-T3 aluminum alloy.⁸

Yield stress (MPa)	292	300	310	312	319	322	335	342	348
Plastic strain (%)	0	0.098	0.215	0.291	0.367	0.466	0.78	0.974	1.21
	354	360	376	392	406	428
	1.468	1.65	2.481	3.49	4.82	7.18

Table 3.

Material properties of carbon/epoxy prepregs.

E₁₁ (GPa)	108	E₂₂ (GPa)	8	E₃₃ (GPa)	8
$ν_{12}$	0.32	$ν_{13}$	0.32	$ν_{23}$	0.3
G₁₂ (GPa)	4	G₁₃ (GPa)	4	G₂₃ (GPa)	3
X_t (MPa)	2100	Y_t (MPa)	25	Z_t (MPa)	50
X_c (MPa)	800	Y_c (MPa)	120	S₂₃ (MPa)	80
S₁₂ (MPa)	80	S₁₃ (MPa)	80	ρ (kg/m³)	1560

Finite element model

Based on the actual experimental conditions, the full-scale finite element models of multihole FMLs are established in ABAQUS/Explicit, which include the geometry shape, the boundary conditions, and the loading method, as illustrated in Figure 5. Discrete eight-node linear reduced integration elements (C3D8R) are adopted to simulate the aluminum sheets and composite laminates. Meanwhile, the enhanced hourglass control is selected to enhance computational accuracy. The mesh refinement around the notches is necessary to predict the damage mechanisms and characterize the fracture path accurately, while the coarser meshes are prepared for other regions. Regarding the adhesive layers between aluminum sheets and composite laminates, the discrete cohesive elements (COH3D8) are employed to predict the interfacial delamination damage, which is compressed to a thickness of 0 mm. In addition, the FML is fixed at one end, and the other end is free only in the X-direction. A reference point is coupled with all nodes of clamping surface, so that the displacement load is convenient to be applied by smooth amplitude curve to simulate the tensile loading. Through this method, the tensile loading and displacement responses at the loading end can be obtained conveniently from the reference point. Finally, the quasi-static tension simulation in ABAQUS/Explicit is implemented to predict the tensile mechanical behavior of multihole FMLs.

Progressive damage models of FMLs

Damage model of aluminum sheet

Aluminum alloy is usually regarded as an elastic–plastic material which presents the evident isotropic hardening behavior. Meanwhile, the damage initiation and evolution of aluminum alloy are also considered in the numerical model.¹⁸ In this paper, the ductile damage model in ABAQUS is employed to predict the damage initiation and evolution of aluminum sheets. The equivalent plastic strain ${\bar{ε}}_{D}^{p l}$ is used to judge the damage initiation, as shown in the following equation

w_{D} = \int \frac{d {\bar{ε}}^{p l}}{{\bar{ε}}_{D}^{p l} (η, {\dot{\bar{ε}}}^{p l})} = 1

(1)

When the damage initiation is satisfied at any material point, the damage evolution will proceed, and then the material stiffness begins to degenerate based on exponential law. At last, the related element is removed from the numerical model when the material stiffness reaches a critical value.

Damage model of carbon fiber composite material

In virtue of the user-defined material subroutine (VUMAT), the Hashin failure and Yeh delamination failure criteria are adopted to predict the damage behavior of composite laminates, and the strains of material point are used to express the failure criteria in virtue of their better continuity and smoothness than that of stresses. The damage initiation of Hashin and Yeh failure criteria are described in Table 4.

Table 4.

Hashin failure criteria and Yeh delamination failure criteria.

Fiber tensile failure^a	$R_{f t}^{2} = {(\frac{ε_{11}}{X_{T}^{ε}})}^{2} + {(\frac{ε_{12}}{S_{12}^{ε}})}^{2} + {(\frac{ε_{13}}{S_{13}^{ε}})}^{2} ε_{11} \geq 0$
Fiber compressive failure^a	$R_{f c}^{2} = {(\frac{ε_{11}}{X_{C}^{ε}})}^{2} ε_{11} \leq 0$
Matrix tensile failure^a	$R_{m t}^{2} = {(\frac{ε_{22} + ε_{33}}{Y_{T}^{ε}})}^{2} + {(\frac{1}{S_{23}^{ε}})}^{2} (ε_{23}^{2} - \frac{E_{22} E_{33}}{G_{23}^{2}} ε_{22} ε_{33}) + {(\frac{ε_{12}}{S_{12}^{ε}})}^{2} + {(\frac{ε_{13}}{S_{13}^{ε}})}^{2} (ε_{22} + ε_{33}) \geq 0$
Matrix compressive failure^a	$R_{m c}^{2} = {(\frac{E_{22} ε_{22} + E_{33} ε_{33}}{2 G_{12} S_{12}^{ε}})}^{2} + (\frac{ε_{22} + ε_{33}}{Y_{C}^{ε}}) [{(\frac{E_{22} Y_{C}^{ε}}{2 G_{12} S_{12}^{ε}})}^{2} - 1]$ $+ {(\frac{1}{S_{23}^{ε}})}^{2} (ε_{23}^{2} - \frac{E_{22} E_{33}}{G_{23}^{2}} ε_{22} ε_{33}) + {(\frac{ε_{12}}{S_{12}^{ε}})}^{2} + {(\frac{ε_{13}}{S_{13}^{ε}})}^{2} (ε_{22} + ε_{33}) \leq 0$
Yeh delamination failure^a	$R_{l d}^{2} = {(\frac{ε_{33}}{Z_{T}^{ε}})}^{2} + {(\frac{ε_{13}}{S_{13}^{ε}})}^{2} + {(\frac{ε_{23}}{S_{23}^{ε}})}^{2} (ε_{33} \geq 0)$

^aFailure factor $R_{i} (i = f t, f c, m t, m c, l d)$ is the damage threshold parameter to judge the damage initiation.

The strain strength can be calculated as the following

\begin{array}{l} X_{T}^{ε} = X_{T} / E_{11}, X_{C}^{ε} = X_{C} / E_{11} \\ Y_{T}^{ε} = Y_{T} / E_{22}, Y_{C}^{ε} = Y_{C} / E_{22}, Z_{T}^{ε} = Z_{T} / E_{33} \\ S_{12}^{ε} = S_{12} / G_{12}, S_{13}^{ε} = S_{13} / G_{13}, S_{23}^{ε} = S_{23} / G_{23} \end{array}

(2)

Once the damage initiation is met at a material point ( $R_{i} \geq 1.0$ ), the corresponding stiffness degradation in different directions ( $f t, f c$ : fiber tension and compression; $m t, m c$ : matrix tension and compression; $l d$ : inter-laminar delamination) can be obtained based on damage variable ( $0 \leq d_{i} \leq 1$ )

d_{i} = 1 - \frac{1}{R_{i}^{n}} (R_{i} \geq 1, n \geq 1; i = f t, f c, m t, m c, l d)

(3)

in which

n

is set to be 1.^37–39 Because of the irreversible energy dissipation results from material damage, the damage variable should be updated according to the previous damage state

d_{i}^{t} = \max (d_{i}^{τ}, 0) (τ \leq t; i = f t, f c, m t, m c, l d)

(4)

\begin{matrix} {\begin{array}{l} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{12} \\ γ_{23} \\ γ_{13} \end{array}} = [\begin{array}{l} \frac{1}{E_{11} (1 - ω_{1})} - \frac{ν_{12}}{E_{22}} - \frac{ν_{13}}{E_{33}} \\ - \frac{ν_{12}}{E_{22}} \frac{1}{E_{22} (1 - ω_{2})} - \frac{ν_{23}}{E_{22}} \\ - \frac{ν_{13}}{E_{33}} - \frac{ν_{23}}{E_{22}} \frac{1}{E_{33} (1 - ω_{3})} \\ \frac{1}{G_{12} α (1 - ω_{4})} \\ \frac{1}{G_{23} α (1 - ω_{5})} \\ \frac{1}{G_{13} α (1 - ω_{6})} \end{array}] {\begin{array}{l} σ_{11} \\ σ_{22} \\ σ_{33} \\ τ_{12} \\ τ_{23} \\ τ_{13} \end{array}} \end{matrix}

(5)

When material stiffness begins to degenerate, the damage parameter $ω_{i}$ ( $i = 1, \dots, 6$ ) is applied to control the constitutive relation between stress and strain, as the following equationwhere the damage parameter $ω_{i}$ can be updated based on the damage variables

\begin{array}{l} α =(1- s_{m t} d_{m t}) (1- s_{m c} d_{m c}) \\ d_{f} = \max (0, d_{f t}, d_{f c}), d_{m} = \max (0, d_{m t}, d_{m c}), \\ d_{d} = \max (0, d_{l d}) \\ ω_{1} = \max (0, d_{f}), ω_{2} = \max (0, d_{f}, d_{m}), \\ ω_{3} = \max (0, d_{f}, d_{d}) \\ ω_{4} = \max (0, d_{f}, d_{m}), ω_{5} = \max (0, d_{f}, d_{d}), \\ ω_{6} = \max (0, d_{f}, d_{d}) \end{array}

(6)

in which

α

is used to control the shear stiffness degradation resulting from matrix tension and compression damage. The matrix damage factors

S_{m t}

and

S_{m c}

are assumed to be 0.9 and 0.5, respectively.^40,41

Damage model of cohesive layers

In order to simulate the delamination damage between aluminum sheets/composite laminates interfaces, the embedded traction–separation model based on the cohesive elements is selected in ABAQUS/Explicit, in which the initiation and evolution of interfacial delamination damage can be characterized.

Figure 6 displays the relationship of damage initiation and evolution on the mixed-mode. The unshaded triangles in the two vertical coordinate planes represent the damage response under pure normal and pure shear deformation, respectively. The intermediate vertical plane indicates the damage behavior under mixed mode conditions with different mode mixes. The Benzeggagh–Kenane (B–K) fracture criterion is applied to control the damage evolution. The detailed material parameters of cohesive elements can be obtained from Sugiman et al.,⁴² as presented in Table 5.

Table 5.

Material properties of cohesive elements.

$E$ (GPa)			$t^{0}$ (MPa)			$G_{c}$ (N/mm)
$E_{n n}$	$E_{ss}$	$E_{t t}$	$t_{n}^{0}$	$t_{s}^{0}$	$t_{t}^{0}$	$G_{I c}$	$G_{II c}$	$G_{III c}$
2	0.75	0.75	65	38	38	2	3	3

$E_{n n}$ , $E_{ss}$ , $E_{t t}$ : penalty stiffness coefficients.

$t_{n}^{0}$ , $t_{s}^{0}$ , $t_{t}^{0}$ : interface strength parameters.

$G_{I c}$ , $G_{II c}$ , $G_{III c}$ : dissipated energy in normal and two shear directions.

Results and discussion

Tensile stress–strain relation and ultimate tensile strength analysis

In order to compare the tensile mechanical responses of FMLs with different number of holes, the tensile stress–strain curves are extracted from the experimental results. It should be noted that unavoidable displacement errors can be resulted from the relative sliding between the clamping fixture and FMLs as well as the slight vibration of machines. Therefore, the tensile strains are calculated according to the displacement from the DIC technique. In addition, the tensile stress is equal to the ratio of tensile loading to the gross cross-sectional area of FMLs.

In this section, the effects of numbers of holes and layer directions on the tensile stress–strain curves are investigated experimentally. For comparing the ultimate bearing capacity, the ultimate tensile strength (ultimate strength) of different specimens is listed in Table 6.

Table 6.

Comparison of ultimate tensile strength of FMLs.

FMLs	0°/90° (MPa)	20°/−70° (MPa)	45°/−45° (MPa)
No holes	654.55	509.09	407.27
Single hole	428.00	332.73	287.27
Two holes	303.91	292.73	235.45
Four holes	291.11	283.64	238.18
Six holes	287.00	274.55	225.45

FML: fiber metal laminate.

Effect of hole number

Figure 7 exhibits the mechanical responses of FMLs with different number of holes under tensile loading. The tensile stress–strain curves of multihole FMLs under different directions are displayed in Figure 7(a) to (c). Meanwhile, the ultimate tensile strength of different FMLs is displayed in Figure 7(d), which contains the tensile strength of un-notched FMLs. From Figure 7(a) to (c), it is clear that the ultimate strength of multihole FMLs has an evident decrease compared to that of single hole FML. This can be mainly attributed to the decrease of net width (the width of FMLs subtracts the width of notches) which plays an important role on the ultimate notch strength of FMLs. However, there is a negligible difference of ultimate strength between multihole FMLs due to the same net width in the transverse direction of FMLs, regardless of the layer direction. In addition, as for the same layer direction, the stiffness of multihole FMLs decreases gradually with the increase of the hole number, which is contrary to the final failure strain. This can be explained by the fact that more delamination damage can be resulted from the multiple holes in FMLs under tensile loading. Consequently, more delamination damage can be more conducive to the stress redistribution and enlargement of the deformation region of FMLs, which can finally postpone the fiber failure and delay the failure strain of FMLs. Regarding Figure 7(d), there is no doubt that the ultimate strength of un-notched FMLs is the largest as compared with that of notched ones. It can be seen clearly that the ultimate strength difference between un-notched and single hole FMLs has a significant decrease compared to that between single hole and multihole FMLs. This phenomenon is mainly because of the more stress redistribution around the more notches in multihole FMLs. Moreover, due to the lower notch sensitivity for FMLs with higher layer directions,²³ it can be found from Figure 7(d) that the ultimate strength reduction from un-notched to single hole FMLs and from single hole to multihole FMLs for 45°/−45° case is far less than that of 0°/90° case.

Effect of layer direction

As far as we know, the layer direction has a non-negligible impact on the axial stiffness of composite laminates according to the classical laminate theory. Therefore, it is necessary to investigate the effect of layer direction on the mechanical behavior of FMLs. The stress–strain curves at different layer directions are displayed in Figure 8. Combined with Figure 7(d), it can be seen clearly that the layer direction has an evident influence on the ultimate strength of un-notched and single hole FMLs, while the effect of layer direction on the ultimate strength of multihole FMLs is negligible. This phenomenon can be mainly attributed to the lower off-axis sensitivity for large notched FMLs, which is similar with the conclusion in Zhang et al.²⁰ However, with the increase of layer direction, the final failure strain of multihole FMLs increases evidently. This is mainly because of the remarkable nonlinear shear deformation resulting from the enlarged off-axis effects of composite laminates.

In addition, the curves of FMLs at 0° layer direction have a clear immediate drop, while the curves show a progressive drop tendency with an evident nonlinear characteristic for off-axis cases. This is mainly because that the catastrophic brittle fracture appears in 0° composite layers for on-axis case, while the nonlinear shear deformation resulting from the off-axis composite laminates occurs for other cases. Finally, the nonlinear shear deformation of composite laminates can lengthen the axial deformation of FMLs and lead to an evident progressive damage process. Moreover, more local plastic deformation and net section yielding of aluminum sheets as well as progressive damage accumulation of composite laminates resulting from off-axis effect also can make some contribution to the nonlinear characteristic.

Deformation and strain analysis from DIC

As mentioned above, the DIC technique is used to capture the real-time strain field on the surface of aluminum sheet. Three in-plane localized strain fields of FMLs with two holes and six holes are exhibited in Figures 9 and 10, including $ε_{x x}$ (transverse direction), $ε_{y y}$ (loading direction), and $ε_{x y}$ (in-plane shear direction). It is worth noting that the range of strain field is 15 (55) mm above and below off the center line of two (six) hole FMLs and these strain fields are all obtained by DIC technique at the final catastrophic moment. Though the accuracy of strain fields in these figures may be affected by the strain concentration in the vicinity of holes, the whole tendencies of these figures will not be influenced.

From these figures, it can be found that the maximum strain always appears around the holes, where the final fracture path is expected to begin at these strain concentration regions. It can be seen that the layer direction affects the strain concentration region of $ε_{y y}$ evidently. As shown in these figures, the strain distribution for 0°/90° case exhibits diffuse type along the loading direction, while the strip type for 20°/−70° case and the cross type for 45°/−45° case. These phenomena well demonstrate that the shear effect becomes more and more significant in multihole FMLs with off-axis angles, and the critical failure mechanism gradually becomes tension–shear dominated. In addition, it is clear that the strain fields of 20° and 45° FMLs highly concentrate in the vicinity of holes and propagate extensively along the fiber direction, which can be attributed to the matrix shear damage and slight fiber pull-out damage.

Regarding Figure 10, the strain fields change with the layer direction in six hole FMLs is similar with that in two hole FMLs, especially for the strain fields in the vicinity of holes. From the strain distribution of six hole FMLs, it can be seen clearly that there is no interaction effect of strain distribution around the holes in the tension direction due to the longer (55 mm) distance between the parallel rows of holes. This phenomenon can be used to explain the fact that the ultimate tensile strength is almost the same for different multihole FMLs. As mentioned above, DIC technique can be applied to capture the strain fields of notched FMLs effectively and reveal the failure mechanisms of FMLs with different layer directions well.

Validation of FE-model

Numerical simulation is an effective method to characterize failure mechanisms and progressive damage evolution which cannot be observed conveniently during the tensile tests. In this section, comparisons are made between the numerical simulations and experimental measurements to further explore the damage mechanisms of multihole FMLs.

Stress–strain curves and ultimate strength

As shown in Figure 11, the tensile stress–strain curves of two hole FMLs from numerical predictions and experimental measurements are compared and analyzed. Meanwhile, the numerical results with/without considering the effect of TRS are both displayed in these figures. Regarding the experimental measurements and numerical predictions without considering TRS, there is a good agreement at the initial stage, while a larger difference can be observed at the post yield stage. It is inevitable that the temperature variation from the curing temperature (135°C) to the room temperature (20°C) during the manufacture will lead to the existence of TRS in FMLs, which could weaken the tension yield load of FMLs.¹⁸ In order to consider the effect of TRS, the thermal expansion coefficient of aluminum 2024-T3 is set to be 2.2 × 10–5/°C in this paper. Regarding the numerical predictions with TRS, a better coincidence can be observed compared with the experimental measurements, especially at the post yield stage. Therefore, it can be concluded that the TRS resulting from the curing process can weaken the tension bearing capacity of multihole FMLs obviously.

Finally, the ultimate strength of all different FMLs from the experimental tests and numerical predictions is compared in Figure 12. It can be seen from the figure that numerical predictions are always slightly greater than experimental measurements due to the inevitable structure defects. On the whole, the deviations between numerical and experimental results are within 10% which can be accepted in the structure design.

As shown in Figure 13, the localized displacement distributions of FMLs with different number of holes at 0°/90° layer direction from DIC technique are compared with those from numerical predictions. The regions of displacement distributions are 30 mm above and below off the center line of FMLs, while the six hole FML shows the displacement zone about 55 mm above and below off the center line. In general, the displacement distributions from DIC technique are in a good agreement with those from numerical predictions.

In order to compare the results from experimental tests and numerical simulations intuitively, the displacement differences ( $Δ U$ ) are calculated from the maximum and minimum displacement values, as presented in Table 7. It can be seen that the deviations between experimental and numerical results are all within 10%, which well demonstrates the accuracy of numerical models. At the same layer direction, the final displacement difference increases with the rise of hole number for multihole FMLs, and the corresponding change rule also can be seen in stress–strain curves, as shown in Figure 7.

Table 7.

Comparison of displacement differences between FEA and DIC.

FMLs	0°/90°			20°/−70°			45°/−45°
FMLs	FEA (mm)	DIC (mm)	ERR (%)	FEA (mm)	DIC (mm)	ERR (%)	FEA (mm)	DIC (mm)	ERR (%)
Single hole	0.71	0.76	−6.58	1.90	2.07	−8.21	2.51	2.60	−3.46
Two holes	0.62	0.68	−8.82	1.34	1.43	−6.29	1.62	1.72	−5.81
Four holes	0.65	0.76	−14.47	1.42	1.56	−8.97	2.21	2.35	−5.96
Six holes	1.14	1.24	−8.06	2.11	2.28	−7.46	4.42	4.56	−3.07

DIC: digital image correlation; ERR: error; FEA: finite element analysis; FML: fiber metal laminate.

Final damage morphologies

The fracture paths of different FMLs are exhibited in Figure 14. The equivalent plastic strain (PEEQ) fields of aluminum surface from numerical predictions at the fracture moment are displayed. From the fracture morphologies of FMLs with on-axis angle, the smooth and brittle fracture can be observed from the fracture surface, regardless of the single hole or multihole FMLs. However, for off-axis cases, the tilted cracks resulting from off-axis composite layers always can be observed in the fracture surface. The fiber pull-out and matrix shear damage can be seen clearly in the cross-section of FMLs,⁴³ especially for the single hole FML. Additionally, the evident fiber breakage occurs in the middle of transverse holes, and the tilted cracks appear at the edge of FMLs with off-axis angles.

Regarding the fracture paths in the vicinity of holes, it is interesting that a short transverse crack rather than a tilted crack occurs at the beginning of fracture location, as shown in the red dotted box, particularly obvious for the single hole FML. The tilted crack has a distance to the edge of holes, which can be explained by the initial delamination damage and the transferred matrix shear damage. The similar phenomenon also can be observed in Zhang et al.,²⁰ which can be explained in detail from the progressive damage mechanisms in the following section.

According to the validation of FE-model, the tensile stress–strain curves, displacement distributions, and fracture morphologies from experimental and numerical results are compared and analyzed. The experimental measurements are predicted well through numerical simulations. Then, the adopted numerical models are employed to further reveal the tension failure mechanisms of multihole FMLs in the following section.

Numerical simulation analysis

In virtue of the numerical model, the final failure mechanisms and progressive damage evolution are exhibited and analyzed. Moreover, some damage mechanisms are reconfirmed by the energy dissipation analysis.

Stress distribution patterns

The stress distributions of single and six hole FMLs in the first 0° and 90° composite layers as well as the first aluminum sheet are exhibited in Figure 15. It can be concluded that the existence of holes in FMLs has an evident effect on the stress distribution patterns, regardless of the hole number. From the stress distribution pattern in the vicinity of holes, it can be seen clearly that the concentrated stress locates at the transverse region which is perpendicular to the tensile direction. Regarding the stress patterns of composite layers in six hole FMLs in Figure 15, the two adjacent holes in the transverse direction affect with each other evidently. However, the mutual stress effect among the longitudinal holes cannot be observed due to the long distance (50 mm) between the neighboring holes in the tension direction. This phenomenon can be used to explain the similar ultimate tensile strength for multihole FMLs, as shown in Figure 12. As for the Mises stress distributions in aluminum sheet, the stresses also concentrate in localized regions around the holes, which correspond to the PEEQ distributions in Figure 14.

Final damage modes of composite laminates

Because of the anisotropy of composite materials, complicated damage modes can be observed directly in composite laminates, including fiber damage, matrix damage, intra-laminar delamination in composite laminates, and inter-laminar delamination between aluminum sheet/composite laminates. However, some microscopic damage cannot be seen evidently, which can be captured in the virtue of scanning electron microscope (SEM) technique. Figure 16 displays the fracture morphologies and partial SEM images of two hole FMLs with different layer directions. With the aid of SEM technique, the fiber/matrix interfacial failure and fiber pull-out phenomenon are confirmed in the fracture surface of FMLs with off-axis angles, while the clear fiber fracture occurs in the cross-section of FML with on-axis angle.

The detailed composite material damage and inter-laminar delamination damage of two hole FMLs for different layer directions are exhibited in Figure 17 since the failure modes are similar for other FMLs (four hole FML and six hole FML). As for the 0°/90° case, it is clear that the fiber tension damage in the 0° layer and the inter-laminar delamination damage are the critical damage modes before the final fracture of FMLs. And the 90° composite layer only shows evident matrix tension damage and no fiber breakage can be observed. It can be concluded that 0° composite layer is the critical load bearing component and tension failure is the dominant failure mechanism for on-axis case. As for off-axis cases, both of the fiber and matrix damage can be observed from the different composite layers, regardless of the layer direction. In addition, an obvious direction dependence of multihole FMLs can be seen from the damage patterns. The 20° composite layer is the dominant load bearing component for 20°/−70° case. And for the 45°/−45° case, both of the 45° and −45° composite layers bear the same tensile loading.

From the matrix damage patterns of off-axis cases, it is worth noting that the evident matrix shear damage can be observed from each composite layer. It can be used to explain the tilted cracking at the edge of FMLs with off-axis angle. At the moment of fracture, clear delamination damage can be observed from the edge of holes, which can contribute to the transverse cracking in the aluminum sheets. The released energy from aluminum sheets is inherited by the adjacent composite layer. Therefore, the cracking in composite layers appears and propagates along the transverse direction until it encounters the matrix shear damage. When the matrix shear damage appears, the transverse fiber breakage is terminated, followed by a tilted cracking. Finally, the transferred shear stress from the cracked composite laminates will eventually lead to the tilted cracking in the aluminum sheets at a distance from the holes. The corresponding fracture morphologies in experimental results can be seen from Figures 14 and 16. Consequently, it can be concluded that the tension–shear failure is the dominant failure mechanism for off-axis cases.

Progressive damage analysis

As is known to all, the damage evolution of aluminum sheets and composite laminates cannot be ignored in the process of tensile test. Based on progressive damage models of aluminum sheet, composite laminates, and adhesive layers, the progressive damage analysis of multihole FMLs is conducted to further reveal the damage mechanisms and failure sequences.

The typical stress–strain curve of two hole FML for the 45°/−45° case in Figure 18 can be divided into four different stages, including initial elastic stage, transition stage, post yield stage, and descending stage. The different damage morphologies of FMLs at various stages are exhibited in Figure 19. The initial elastic stage represents the elastic deformation of aluminum sheets and composite laminates. Some slight damage in the vicinity of holes can be seen from the figure, including plastic deformation and matrix damage. It is worth noting that there is no fiber damage at the current stage. When the tension displacement increases further, the following transition stage shows evident nonlinear behavior which can mainly be attributed to the localized plasticity and yielding of aluminum sheets around the holes.⁴⁴ This can be explained by the fact that the yield strain (0.4%) of aluminum sheet is far less than the failure strain of carbon fiber. The delamination damage and matrix damage around the holes are also more serious than that at the initial stage. At the end of transition stage, it can be found that the slight fiber damage appears around the hole. Subsequently, the ever-increasing stress at the post yield stage indicates that the composite layer is the main load bearing component after the yield of aluminum sheet. The slight nonlinear at the post yield stage can be mainly attributed to the further plastic deformation of aluminum sheet, the evident progressive damage evolution of composite laminates, as well as the nonlinear shear deformation resulting from the off-axis effect.⁴⁵ At last, the final descending stage can be seen from the end of curves because of the fracture in the composite layers or aluminum sheets. The interfacial delamination damage occurs around the notches and extends through the entire FML evidently.

According to the progressive damage process mentioned above, the failure sequence of FMLs manifests as plastic deformation of aluminum sheets, followed by the matrix damage in 90° (−70°/−45°) composite layer and delamination damage in the aluminum sheet/composite laminates interfaces, then the initial fiber damage in 0° (20°/45°) composite layer, finally the aluminum sheets’ fracture and fiber breakage. Regarding the initial time of matrix and fiber damage, it can be found that there is a longer progressive damage course before the final failure of multihole FMLs, which highlights the significance of progressive damage behavior of composite laminates and aluminum sheets. Otherwise, it will greatly underestimate the ultimate tensile strength of multihole FMLs without considering the progressive damage evolution of aluminum sheet and composite laminates.

Energy dissipation analysis

As is known to all, the process of energy transfer is bound to undergo structural deformation and damage. Therefore, the energy analysis approach is usually employed to analyze mechanical behavior during many mechanical tests.^46–48 In order to better demonstrate the progressive damage mechanism and effectively distinguish the respective contribution of aluminum sheet and composite laminates, the energy dissipation curves of two hole FML with 45°/−45° layer direction are exhibited in Figure 20, including the total dissipated energy (E_{total energy}), the plastic deformation energy of aluminum sheet (E_{plastic of aluminum}), the elastic deformation energy of aluminum sheet (E_{elastic of aluminum}), and the elastic deformation energy of composite laminates (E_{elastic of composite}). From this figure, it can be seen that both of elastic deformation energies of aluminum sheets and composite laminates increase with the rise of tensile strain. However, the increasing rate of energy for aluminum sheets is clear higher than that of composite laminates at the elastic stage (strain from 0 to 0.4%), which can be explained by the fact that the volume fraction of aluminum sheets is higher than that of composite laminates in FMLs. Thus, it can also be concluded that the aluminum sheet is the main load bearing component at the elastic stage.

Regarding the transition stage (B) in stress–strain curve (0.4–0.85%), the elastic deformation energies of aluminum sheets and composite laminates increase continuously. However, the increasing rate of elastic deformation energy for aluminum sheet decreases clearly, and meanwhile, the plastic deformation energy of aluminum sheets appears and increases gradually. This phenomenon well demonstrates the fact that the transition stage in the stress–strain curves represents the localized plastic deformation and yielding of aluminum sheets around the holes. After the transition stage, the elastic deformation energy for aluminum sheet almost stops growing. The plastic deformation of aluminum sheets and the elastic deformation of composite laminates still maintain a high growth tendency. It can be concluded that the dominant load bearing component at the post yield stage is composite laminates. In general, the typical characteristics from these dissipated energy curves are almost identical with the aforementioned conclusions.

Conclusion

This article mainly investigates the effects of the hole number and layer direction on tensile mechanical responses and damage mechanisms of multihole FMLs by experimental and numerical methods. DIC technique is applied to capture the real-time displacement distributions and localized strain fields of FMLs. The cohesive zone model and progressive damage models are employed to characterize different damage modes in multihole FMLs. Finally, results from experimental tests and numerical predictions are compared and analyzed, some important conclusions can be proposed as the following:

Regarding mechanical responses, the ultimate tensile strength of different multihole FMLs is almost close due to the same net width. However, the final failure strain increases with the number of holes, which can be explained by the fact that the delamination damage gradually aggravates with the increase of the hole number, so that it enlarges the deformation region before the fracture of FMLs and postpones the final failure of FMLs.

The layer direction has a lower influence on the ultimate tensile strength of multihole FMLs due to the low off-axis sensitivity of large notched FMLs, while it has an evident effect on the final failure strain because of the existing nonlinear shear deformation.

With the increase of layer direction, the fracture morphology changes from evident brittle fracture to fiber pull-out and matrix shear damage, which indicates that the critical failure mechanism of multihole FMLs transfers from tension dominated to tension–shear dominated.

Results from DIC technique and numerical simulation indicate that the adopted numerical model can well predict the tensile mechanical responses and effectively characterize progressive damage mechanisms of multihole FMLs.

Regarding the progressive damage analysis, the failure sequence of multihole FMLs under tensile loading manifests as initial plastic deformation of aluminum sheets, followed by the matrix and delamination damage, the fiber damage, finally the fiber breakage and aluminum sheet fracture.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The present work is supported by the National Natural Science Foundation of China (Grant Nos. 51879248 and 51609089), the National Science Fund for Distinguished Young Scholars (51625902), the China Postdoctoral Science Foundation (Grant No. 2016M592338), and the Taishan Scholars Program of Shandong Province (TS201511016).

ORCID iD

Lu Yao

References

Sinmazçelik

Avcu

Bora

MÖ

, et al. A review: fibre metal laminates, background, bonding types and applied test methods. Mater Des 2011; 32: 3671–3685.

Ali

Pan

Duan

, et al. Characterization of seawater hygrothermal conditioning effects on the properties of titanium-based fiber-metal laminates for marine applications. Compos Struct 2016; 158: 199–207.

Alderliesten

Benedictus

Fiber/metal composite technology for future primary aircraft structures. J Aircr 2008; 45: 1182–1189.

Botelho

Silva

Pardini

, et al. A review on the development and properties of continuous fiber/epoxy/aluminum hybrid composites for aircraft structures. Mat Res 2016; 9: 247–256.

Hagenbeek

Van Hengel

Bosker

, et al. Static properties of fibre metal laminates. Appl Compos Mater 2003; 10: 207–222.

Van Rooijen

Sinke

De Vries

, et al. Property optimisation in fibre metal laminates. Appl Compos Mater 2004; 11: 63–76.

Jaroslaw

Barbara

Patryk

The comparison of low velocity impact resistance of aluminum/carbon and glass fiber metal laminates. Polym Compos 2014; 37: 1056–1063.

Yao

Wang

, et al. Influence of impactor shape on low-velocity impact behavior of fiber metal laminates combined numerical and experimental approaches. Thin-Walled Struct 2019; 145: 106399.

Villanueva

Cantwell

WJ.

The high velocity impact response of composite and FML-reinforced sandwich structures. Compos Sci Technol 2004; 64: 35–54.

10.

Stoll

Weidenmann

KA.

Fatigue of fiber-metal-laminates with aluminum core, CFRP face sheets and elastomer interlayers (FMEL). Int J Fatigue 2018; 107: 110–118.

11.

Yamaguchi

Okabe

Yashiro

Fatigue simulation for titanium/CFRP hybrid laminates using cohesive elements. Compos Sci Technol 2009; 69: 1968–1973.

12.

Guan

Cantwell

, et al. Low-impulse blast behaviour of fibre-metal laminates. Compos Struct 2012; 94: 954–965.

13.

Dhaliwal

Newaz

GM.

Compression after impact characteristics of carbon fiber reinforced aluminum laminates. Compos Struct 2017; 160: 1212–1224.

14.

Dadej

Bieniaś

Surowska

Residual fatigue life of carbon fibre aluminium laminates. Int J Fatigue 2017; 100: 94–104.

15.

Riccio

Di Costanzo

Di Gennaro

, et al. Intra-laminar progressive failure analysis of composite laminates with a large notch damage. Eng Fail Anal 2017; 73: 97–112.

16.

Sellitto

Riccio

Russo

, et al. Compressive behaviour of a damaged omega stiffened panel: damage detection and numerical analysis. Compos Struct 2019; 209: 300–316.

17.

Yeh

Chang

Yang

, et al. Blunt notch strength of hybrid boron/glass/aluminum fiber metal laminates. Mater Sci Eng A 2011; 528: 2164–2173.

18.

, et al. Open-hole tensile progressive damage and failure prediction of carbon fiber-reinforced PEEK–titanium laminates. Compos Part B 2016; 91: 65–74.

19.

Sadeghpour

Sadighi

Dariushi

An investigation on blunt notch behavior of fiber metal laminates containing notch with different shapes. J Reinf Plast Compos 2013; 32: 1143–1152.

20.

Zhang

Wang

Zhang

, et al. Characterizing the off-axis dependence of failure mechanism in notched fiber metal laminates. Compos Struct 2018; 185: 148–160.

21.

Zhang

Wang

Fang

, et al. Application of energy dissipation approach for notched behavior in fiber metal laminates. Compos Struct 2017; 180: 809–820.

22.

Tan

Yang

JM.

Evaluation of residual strength of notched fiber metal laminates. Mater Sci Eng A 2007; 457: 338–349.

23.

Kawai

Arai

Off-axis notched strength of fiber–metal laminates and a formula for predicting anisotropic size effect. Compos Part A 2009; 40: 1900–1910.

24.

Feroldi

Russo

Structural behavior of all-FRP beam-column plate-bolted joints. J Compos Constr 2016; 20: 04016004.

25.

Russo

On failure modes and design of multi-bolted FRP plate in structural joints. Compos Struct 2019; 218: 27–38.

26.

Kazemahvazi

Kiele

Zenkert

Tensile strength of UD-composite laminates with multiple holes. Compos Sci Technol 2010; 70: 1280–1287.

27.

Chang

Yeh

Yang

JM.

Fatigue crack growth in fibre metal laminates with multiple open holes. Fatigue Fract Eng Mater Struct 2012; 35: 93–107.

28.

Wang

Rans

Benedictus

Theoretical analysis of fatigue failure in mechanically fastened fibre metal laminate joints containing multiple cracks. Eng Fail Anal 2018; 91: 151–164.

29.

Sun

Chen

Huo

, et al. Experimental and numerical studies on indentation and perforation characteristics of honeycomb sandwich panels. Compos Struct 2018; 184: 110–124.

30.

Sun

Liu

Zheng

, et al. On fracture characteristics of adhesive joints with dissimilar materials – an experimental study using digital image correlation (DIC) technique. Compos Struct 2018; 201: 1056–1075.

31.

Sharma

Khan

SH.

Influence of metal layer distribution on the projectiles impact response of glass fiber reinforced aluminum laminates. Polym Test 2018; 70: 320–347.

32.

Zhou

Liu

, et al. Propagation of damage in bolt jointed and hybrid jointed GLARE structures subjected to the quasi-static loading. Compos Struct 2019; 218: 79–94.

33.

Yao

Sun

, et al. Investigation on impact behavior of FMLs under multiple impacts with the same total energy: experimental characterization and numerical simulation. Compos Struct 2019; 226: 111218.

34.

Sih

Chen

Huang

SL.

Fracture mechanics of plastic-fiber composites. Eng Fract Mech 1974; 6: 343–359.

35.

ASTM D3039/D3039M, Standard test method for tensile properties of polymer matrix composite materials, ASTM International, USA, 2008.

36.

Crammond

Boyd

Dulieu-Barton

JM.

Speckle pattern quality assessment for digital image correlation. Opt Lasers Eng 2013; 51: 1368–1378.

37.

Liu

Xie

, et al. The effect of impactor shape on the low-velocity impact behavior of hybrid corrugated core sandwich structures. Compos Part B 2017; 111: 315–331.

38.

Yao

Meng

, et al. Effect of structural parameters on low-velocity impact behavior of aluminum honeycomb sandwich structures with CFRP face sheets. Thin-Walled Struct 2019; 137: 411–432.

39.

, et al. Residual flexural properties of CFRP sandwich structures with aluminum honeycomb cores after low-velocity impact. Int J Mech Sci 2019; 161: 105026.

40.

Pederson

Finite element analysis of carbon fiber composite ripping using ABAQUS, Master’s thesis, Clemson University: Mechanical Engineering, USA, 2006.

41.

Liu

Liao

Jia

, et al. Finite element analysis of dynamic progressive failure of carbon fiber composite laminates under low velocity impact. Compos Struct 2016; 149: 408–422.

42.

Sugiman

Crocombe

Katnam

KB.

Investigating the static response of hybrid fibre–metal laminate doublers loaded in tension. Compos Part B 2011; 42: 1867–1884.

43.

Fakoor

Ghoreishi

SM.

Experimental and numerical investigation of progressive damage in composite laminates based on continuum damage mechanics. Polym Test 2018; 70: 533–543.

44.

De Vries

TJ.

Blunt and sharp notch behaviour of Glare laminates, Doctoral thesis, Delft University of Technology, Faculty of Aerospace Engineering, the Netherlands, 2001.

45.

Kawai

Honda

Off-axis fatigue behavior of a carbon/epoxy cross-ply laminate and predictions considering inelasticity and in situ strength of embedded plies. Int J Fatigue 2008; 30: 1743–1755.

46.

Reiner

Torres

Veidt

, et al. Experimental and numerical analysis of drop-weight low-velocity impact tests on hybrid titanium composite laminates. J Compos Mater 2016; 50: 3605–3617.

47.

Moriniere

Alderliesten

Benedictus

Low-velocity impact energy partition in GLARE. Mech Mater 2013; 66: 59–68.

48.

Moriniere

Alderliesten

Sadighi

, et al. An integrated study on the low-velocity impact response of the GLARE fibre-metal laminate. Compos Struct 2013; 100: 89–103.