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Lay-up optimisation of fibre–metal laminates panels for maximum impact absorption

This paper introduces a methodology utilising a ply-ply damage Finite Element models with Genetic algorithm optimisation procedure to investigate the effect of lay-up configuration on the impact absorption properties of fibre metal laminates (FMLs). The methodology was carried out in two steps. In the first step, a pseudo-2D model was used to explore the vast design space to identify potential optimised layup-configurations. In the second step, the optimised configurations were studied in full 3 D, with high fidelity simulations, verifying the results obtained from the optimisation process. The design variables used include thickness and material (including fibre orientation) of each ply. The results produced an optimised configuration consisting of a metallic ply on the impacted side followed by a cross-ply composite lay-up. The results also suggest that the first composite ply (second ply of the FML) should be about 3 times thicker than the other plies.

These internal damages result in the reduction of the strength and stiffness of the composite structure. For this reason, most composite structures in the aerospace applications must be designed to handle service loads even in the presence of barelyvisible impact damage (BVID) [1].
FMLs were initially developed for improved fatigue strength, studies have shown that its impact properties could be better than that of monolithic metals [2]. FMLs could be described as hybrid structures which have an alternating stacking sequence of fibre reinforced polymer-matrix composite and metal layers [3]. These structures can combine the advantageous properties of metals and composites while alleviating their disadvantages [4]. As a result, they are more durable with higher fatigue and fracture properties compared to their constituent materials [3]. This and other advantages have given it wide attention in the aerospace industry [5]. Various classes of FMLs have been developed over the years as well as its application. An example is GLARE which is currently in use for the upper fuselage of Airbus A380 and titanium-based FML wings being developed by Boeing [6].
Impact damage could be classed as one of the most important types of failure in aircraft structures. Sadighi, Alderliesten and Benedictus [7] reported that about 13% of the fuselage damages repaired are impact damages. These impact damages could occur at various times during operation and maintenance. This outlines the importance of understanding the impact properties of FMLs. Improved impact properties could lead to the development and further application of FMLs in the out warding facing components of aircraft vehicles.
The complex and large number of failure mechanism in FMLs provides a good avenue to manipulate and thus improve energy absorption properties. Research has shown that this property is dependent on four parameters which include the thickness, fibre direction, constituents and composite volume fraction [8].
Cortes [9] carried out a tensile test on FMLs and its constituent materials and showed that the properties of FMLs could be determined using the rule of mixture (ROM) which was developed by Wu et al [10]. They carried out experimental and analytical studies to determine the possibility of predicting the properties of FMLs using the volume fraction of the metal and composite components. The tensile strength, tensile modulus, compressive yield strength and compressive modulus all showed a linear relationship to the volume fraction of the metal and composite materials. However, the yield strength was noticed to behave independently to the volume fraction of the constituent materials. This showed that the ROM could not be used to predict all the properties of FMLs. Cortes [9] used ROM and experiments to investigate aluminium based FMLs. The results show that the specific absorbed energy required to perforate the laminate was dependent on the composition of the constituent materials. It was discovered that the peak impact energy for perforation occurred at a composite volume fraction of 0.6. This agreed with the findings of an analytical study carried out by Ghasemi [11]. The results also showed that the position of the metal/composite plies significantly affected the impact property. The best impact property was obtained from specimens with metallic outer plies.
Kaboglu et al. [12] carried out experiments to study the effect of the thickness of the laminate on the impact properties of FMLs. The thickness of the laminate was modified by adding more plies while maintaining the typical FML configuration. The results obtained from the experiment showed that increasing the thickness of FMLs had little to no effect on the specific absorbed energy.
Langdon et al. [13] showed that the size and shape of the damage region are dependent on the thickness of the plies. It was noticed that the damage in thicker specimens occurred in the central region of the laminate with the impacted surface exhibiting low displacements. However, the damage in thinner specimens occurred on the surface of the impacted ply. This finding indicates that the individual ply thickness affects the energy absorption properties of a FML laminate. However, the findings of Choi, Wang and Chang [14] suggest that that the individual thickness of the ply does not affect the impact resistance of the laminate. Their results showed that interlaminar failure was the major mode of dissipating low-velocity impact energy.
Further contradictory findings in literature is from Saito et al. [15], which showed that composite laminates comprised of thinner plies exhibit larger delamination areas after impact and therefore absorb higher impact energies. Compression after impact (CAI) test showed that thinner plies also exhibited a higher residual strength. Based on this, it could be assumed that FMLs comprised of thinner composite plies would experience higher delamination and as a result absorb more impact energy. This assumption was studied by Ankush et al. [16]. They carried out experiments on FML laminates with varying metallic ply thickness and constant overall laminate thickness. The results obtained from the experiments showed that increasing the thickness of the impacted metallic ply led to a reduction in deformation and matrix cracking and thus energy absorption. However, they also showed that the distribution of the metallic plies also affected the spread of delamination and subsequently the energy absorption properties.
Seyed Yaghoubi, Liu and Liaw [1] investigated the effect of stacking sequence on the impact properties of FMLs. The results showed that the unidirectional and cross-ply specimen provided the least resistance to impact. The quasi-isotropic laminates provided the best impact resistance. It was noticed that at low impact velocities, the energy was absorbed by delamination agreeing with the findings of Cortés and Cantwell [3].
Seyed Yaghoubi and Liaw [17] investigated the effect of layup configuration on the response of FMLs to impact. The results obtained showed that the cross-ply and unidirectional (0 ) specimens offered the highest resistance to the impact. This results contradicts the finding made by Seyed Yaghoubi and Liaw [1]. These contradictory results may suggest that experimental configuration such as boundary condition, impactor shape, weights and velocities all affect the response of the laminate. The interfacial strength was also seen to be dependent on the orientation of the composite ply and the deformation of the adjacent aluminium ply. The results suggested that laminates with alternating fibre directions would absorb higher impact energy.
Although some studies carried out vary in the experimental setup (for example impactor's velocity and weight) making comparison difficult, the results have shown that to improve impact energy absorption, various damage mechanisms within an FML material must be utilized to its full extent. As outlined by Alderliesten et al. [18], the sequence of the damage mechanism of an impacted FML is: 1. Plastic deformation of the metallic ply 2. Composite matrix of the subsequent composite ply cracking and delamination in the plastically deformed area 3. Fibre and metal crack in the non-impacted side (first crack) 4. Cracking of the impacted side (through crack).
The highlighted investigations on FMLs have aimed to identify which standard layering configuration produces the highest performance for impact absorption. No study exists which aim to 'optimise' the individual ply thickness and layup configuration for improvement to impact energy absorption. Carrying out an optimisation process like this would be expensive due to the high number of possible configurations to be tested.
However, this cost could be reduced using numerical models. Even so, numerical models must be capable to capture the different complex failure mechanisms of FMLs highlighted above.
Numerical studies on FMLs performed by Fan, Guan and Cantwell [19], Tsartsaris et al. [20] and Zhu and Chai [21] on FMLs subjected to low-velocity impact have used a combination of Continuum Damage Models (CDM) to simulate composite failure (Hashin Failure Criterion for composite layers and Johnson-Cook plasticity and failure model for the metallic layers) and Cohesive Zone Models (CZM) to capture delamination damage [8]. The results obtained from these numerical study were all shown to be accurate relative to experimental results with errors of as little as 5%.
This study will be focused on the effect of FRP composite and metal layer thickness and the fibre direction of the laminates on the impact properties of the FMLs. Using the numerical modelling procedures highlighted above, a systematic procedure is presented to find the optimised configuration that takes the most advantage of the various failure modes in FMLs for impact energy absorption whilst minimising the mass of the material. For this study, the authors made sure that the experimental configuration was kept consistent to minimise its effect on the laminates impact property.
This paper would be divided into three parts. Part I will focus on the optimisation procedure applied to a simplified 2D problem in-order to explore the vast design space (part of the novelty of the study). The use of the 2D model would also help in minimising the overall computational cost. In the first part of Part II, the optimised designs are applied in a full-scale 3D configuration which will cover the effect of anisotropic delamination growth behaviour. Finally, in the second part of Part II, the proposed configuration will be validated against experimental results from literature, comparing the performance of the optimised FML produced here against standard FML designs.

Numerical Model
For the numerical simulations, it was crucial to achieve a computationally efficient model for application within the optimisation framework. This is particularly challenging given the different failure and damage models implemented in the simulation. Different variations of the model were tested to determine the overall CPU-time and accuracy of the results. The 3D model required on average 5 hours to complete a simulation capturing the major failure mechanisms of FMLs. Therefore, to minimise this cost, it was decided to create a pseudo-2D model using a 3D modelling procedure. This 'strip' model, illustrated in Figure 2   were obtained from the research work carried out by [22] to ensure it was an empirical fit to the metallic behaviour. Table 1 to Table 3 Table 1 Elastic Mechanical Properties of Aluminium 7075-T6 [23] Parameter Value Young's modulus ( ) 71.7 Poisson's ratio ( ) 0.33 Mass density ( ) 2810 Table 2 Plastic Johnson-Cook Parameters of Aluminium 7075-T6 [22] Parameter Value 473 210 0.3813 Table 3 Johnson-Cook Damage Parameters of Aluminium 7075-T6 [22] Parameter Value The composite layers were modelled using the orthotropic laminate properties IM7/8552 material listed in Table 4. Failure of the composite layers was simulated using CDM with Hashin Failure Criterion with strength properties given in Table 5. The materials used for the optimisation process were selected because they are highly characterised in open literature. This allowed for increased accuracy during the initial modelling setup, calibration and validation process. Table 4 Composite IM7/8552 Elastic Properties [24] Parameter Value Young modulus, fibre direction ( ) 161 Young modulus, transverse direction ( , ) 11.38 In-plane shear modulus ( , )

Impactor
An impactor of a diameter of 25.4 was modelled as a 3D deformable solid cylinder and meshed using 8-noded continuum elements (C3D8). Similar to the beam strip, the impactor has a width of 0.8 . A rigid constraint was applied to the impactor to ensure some of the impact energy would not be dissipated by the deformation of the impactor.
The mass of the impactor was set to 0.15 by setting an equivalent density value. The initial kinetic energy of the impactor was set to 0.075 by applying an initial velocity of 10 / .

Interface Property and Mesh Size Calibration
For all interfaces not in cohesive contact, a general contact interaction property with was set to define the contact between all external surfaces. To simulate delamination, CZM was applied to each dissimilar interface in the plate. To define the cohesive contact between the plies, individual property assignments were added to the contact interaction. The cohesive contact was defined between the plies, using a surface interaction with cohesive behaviour and damage as the contact property options. The stiffness of the cohesive contact was left as its default values (infinitely stiff). The cohesive damage properties for the metal-composite and composite-composite interface are given in Table 6 and Table 7 respectively. Composite-composite interfaces of the same fibre orientation do not fail by delamination, therefore a tie constraint was added in this case.
The interface properties are mesh dependent [25] and therefore had to be calibrated for the chosen mesh element size of 0.4 used for the analysis using experimental data. During the calibration process, the values of the fracture toughness ( , , ) were kept constant as the experimentally obtained values. However, the interface strength properties ( and ) which is mesh dependent were modified in the calibration process. The metal-composite interface properties (  Following the ASTM standard, the Mode I fracture toughness ( ) calculated from the experiment was 210 ± 5 . Mode II fracture toughness properties were taken from end-notched flexure (ENF) tests performed according to ASTM D7905 standard [27] by Yasaee et. al. [28].
The interface strength ( ) property was calibrated by performing a FEM analysis of the experimental model.  The interface strength ( ) property was calibrated to match the experimental results of [28] for the element size of 0.4 . The modelling procedure follows a similar method described in section 2, replicating the ENF tests from [28]. A displacement was applied at the centre of the laminate with roller boundary conditions applied to both edges. A comparison of the force-displacement graphs for the ENF test is shown in Figure 2-4. This graph compares the calibrated FEM model with the experimental results obtained from [28]. While calibrating for the Mode II property, the properties obtained during the Mode I calibration were kept constant.
A summary of the fracture toughness and the calibrated strength parameters are given in Table 7.

Part I: Optimisation Methodology and Results
GA optimisation toolkit in MATLAB is used to carry out the optimisation of the FML structure. The algorithm works by creating a random initial population with each member matching the dimension of the function (the number of design variables). The good performing members (parents) of the initial population are mutated to create new members (children) to be tested. This process is continued until the optimal design variable is obtained or a stopping condition (example: time-limit) is met. More information on the GA toolkit provided by MATLAB can be obtained from [30,31].
The GA toolkit in MATLAB is set to find the local minimum value to an objective function. For this analysis, the GA function was set to maximise specific absorbed energy (SAE) of the panel by minimising its inverse. The objective function used by the GA algorithm was a MATLAB script created to generate a FE model in ABAQUS, submit it for analysis and extract the results from the generated ODB file. Figure 3-1 shows a flowchart of the MATLAB script used.
The design variables used to minimize the objective function include the material (including fibre orientation) and thickness for each ply. Therefore, the number of design variables is two times the total number of plies in the laminate. To reduce the overall time of the optimisation, a constraint function was included to prevent consecutive metallic plies. The effect of residual stresses in the laminate was ignored to reduce the number of design variable and optimise runtime. Although this could be included by simply constraining the design variables. It was decided to limit the restrictions of the optimiser allowing it to explore a vast design space within a reasonable computational cost. and load were also applied to laminate as shown in Error! Reference source not found.. Each ply was modelled individually as described in Section 2.
Next, the generated input file was submitted by the script to ABAQUS for analysis.

Figure 3-2 Convergence of SAE
The GA optimiser with the pseudo-2D strip model ran for a total of 3,700 iterations in approximately 720 hours. can be noticed that the optimal configuration did not exhibit the highest SAE values.
The configuration with the highest SAE was obtained at approximately 1000 iterations.
The configuration with the highest SAE is shown in Figure 3   Although counter-intuitive, this configuration was expected to generate higher SAEs due to the large delamination possibilities in the cross-ply composite layer. The results also showed that a higher number of metallic layers as in the GA-4 configuration will have detrimental effects on the SAE of the structure. Lay-up configurations which included a single metallic ply as the non-impacted ply was also analysed by the GA optimiser. This configuration produced very low energy absorption properties and subsequently very low SAE values. The lowest SAE values were obtained from laminates comprised entirely of unidirectional composite plies. configuration, the energy absorbing capability was lower than the GA-2 configuration.
For this lay-up configuration, the energy absorbed between the initial delamination and first ply failure was about half that absorbed by the GA-2 model. The GA-3 and GA-1 configuration provided a similar response to the impact. used. The results from the optimisation showed that using a thicker metallic ply allows for more energy absorption. This behaviour is similar to the results obtained by Ankush et al. [16]. The optimal configuration converged to the maximum allowed thickness for the impacted metallic ply.
As stated earlier, a tie constraint was applied to consecutive composite plies with uniform fibre direction. Therefore, in comparing the effect of the ply thickness,   To verify the different configurations proposed from the GA optimised study, the results of Part I was applied to a 3D model to provide a more realistic impact scenario. This model would also help to reduce the effects of the boundary condition on the behaviour of the laminate that resulted in configurations with thick 90 layers exhibiting higher energy absorption property than those with more alternating 0/90 layers as described by Seyed Yaghoubi and Liaw [17] and Laliberte [32].
The laminate was modelled as a square plate with 100 sides. The thickness chosen was selected from the best configuration obtained from the optimisation discussed in section 3.1. The results showed that the GA-1 configuration absorbed the least impact energy.
This contradicts the results obtained from the strip model (Figure 3-5). However, as stated earlier this was to be expected due to the small delamination area available in this configuration. Shown in Figure 4

Validation against Experimental Data
In this section, the optimised FML configuration proposed here will be validated against a standard FML configuration experimentally tested in literature. Experiments carried out by Seyed Yaghoubi [17] showed that a 3/2 cross-ply configuration offered the maximum impact resistance compared to the other configurations. The validation exercise in this paper will compare numerically the 3/2 cross-ply FML configuration describe in [1] to the GA optimised configuration (GA-2). Table 8 to Table 12 shows the material properties used to define the models. Table 8 Composite S2-Glass/FM94 Elastic Properties [29] Parameter Value

Compressive strength ( ) 90
Shear strength (in-plane), ( ) 93 Shear strength ( ) 50 0    Figure 3-7a. The overall laminate thickness of 1.93 as described in [1] was enforced. The model definitions were created using the same procedure described in section 2. However, the mass of the impactor was set to 6.14 to match the experimental procedure described in [1].

Figure 4-8 Verification models
Composite From the numerical results, the energy absorbed by the optimised configuration is shown to be 4.8% higher than that of the standard configuration. The specific absorbed energy of the optimised configuration was also 17.8% higher than the standard configuration. However, as seen from the force-displacement graph (Figure 4-9), similarly to the results shown in Figure 4-3 the impactor did not perforate the 3/2 laminate. Overall, it is shown that the presented GA optimisation procedure has produced an FML configuration with significant improvement in the SEA over standard FML configurations. The results showed that to achieve maximum specific absorbed energy, the FML laminate should be comprised of a single metallic ply on the impacted side with alternating composites plies stacked beneath it. The results showed that placing the metallic ply as the impacted ply allowed for energy absorption through the plastic deformation before triggering the other failure modes in the composite layers. In terms of the thickness of the ply, the results suggest using a thick compliant composite layer (less than 44% of overall plate thickness), directly after the metallic ply has some benefit to the overall performance. The results also showed that the fibre direction of this compliant layer played no role in the energy absorption properties of the laminate.
The composite layer that follows after the second layer should have alternating fibre direction to allow for energy absorption through delamination at dissimilar interfaces.
It was also noticed that the thickness variations of these plies offered negligible influence in the energy-absorbing properties of the FML.
Finally, a validation exercise highlighted that the optimum configuration produced exhibited up to 18% improvement in the specific energy absorption of the plate over standard FML configurations.
The optimisation portion of this study was done on a pseudo-2D strip model. It was shown that the boundary conditions of a full 3D plate have some influence on the performance, specifically on the thickness of the second compliant composite layer.
Although computationally expensive, future work may apply the same optimisation procedure directly to a full 3D model as well as exploring a wider range of thickness and fibre orientation variations of individual layers.
The modelling strategy used here captured key damage mechanisms of an FML material. However, the effect of the material properties, different metal and composite damage and failure models was not studied in this paper. As a result, improvements to both material properties and numerical modelling methods may produce more accurate results and thus could be considered in future studies.

Data Availability
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.