Numerical study on crushing damage and energy absorption of multi-cell glass fibre-reinforced composite panel: Application to the crash absorber design of tsunami lifeboat

2.1 Experimental study

The lamination process of the GFRP specimen was made using the hand lay-up method (Figure 1). This method was adopted because it is commonly employed in producing fibreglass boats. The composite layers were laminated with the chopped strand mat (mat300) and woven roving (wr400) that Asahi Fiberglass Company made. The polyester resin was determined using Yukalac 157 BQTN-EX, and Methyl Ethyl Ketone Peroxide was provided as a catalyst. The four layers of the composite specimen were defined with the variation of stacking sequence and fibre orientation angle. The fibre weight fraction is 32.8–34.2%. Furthermore, the curing process was conducted at the ambient temperature of 30°C within 2 days. The detailed specification of the specimens can be seen in Table 1.

Figure 1

The lamination process of the mechanical test specimens.

The measurement of the tensile and bending test followed the ASTM D3039 and ASTM D790-03 standards, respectively. The dimension of the bending specimen is a rectangular plate of 200 mm in length, 25 mm in width, and a thickness of 3 mm. The supporting arm length of 20 mm is located on each side of the specimen piece. The detailed tensile and bending specimen shape can be seen in Figure 2. The tensile and bending test executions were performed using a universal testing machine with a carrying load capacity of about 1,000 kN. The tension and compression rate are kept constant at 1 mm/s, controlled by the hydraulic system valve opening that drives the compressing piston. The tensile specimen length is 100 mm, with a grip length of 50 mm. Otherwise, the bending span length of the specimen is 160 mm, with a support length of 20 mm on each side. The measurement repetition is three times on each type of laminate.

Figure 2

The specimen dimension following the ASTM standard: (a) the Tensile test ASTM D3039 and (b) the bending test-ASTM D790-03.

2.2 Mechanical properties of the GFRP laminate of the crash absorber multi-cell panel

The multi-cell panel was made from the GFRP laminate composite. Therefore, the multi-cell panel structural response behaviour was determined from the mechanical properties of the adopted laminate composite. The tensile test measurement has been presented in our previous research [37]. However, the selected laminate for the multi-cell panel was merely the four layers laminate with the variation of fibre orientation angle. In the study, it has been shown that the enormous tensile strength of 110.88 MPa was performed by type 4 WRC that was reinforced with the 0° woven roving fibre (wr400) (Figure 3a). The tensile strength was increased significantly due to the fibre type replacement from mat300 to the wr400. The tensile strength improvement due to the changes in fibre type is 49.22 and 77.32% for the woven roving with 45° and 0° fibre orientation, respectively. Therefore, it is indicated that the fibre orientation angle also significantly influenced the tensile strength. The strength increment due to the changes in angle orientation from 45° to 0° is 18.83%. The measurement results indicate that the fibre orientation angle and the fibre type significantly influence the laminate tensile strength.

Figure 3

Tensile properties of the GFRP laminate: (a) tensile strength, (b) tensile Strain, and (c) tensile modulus of elasticity [37].

The tensile strain characteristic is presented in Figure 3b. The influence of the angle orientation and the type of fibre was pointedly identified. Similar to the tensile strength tendency, the woven roving type performed better strain characteristics than the others. The strain increment due to the fibre type is 41.18 and 64.71% for the woven roving laminate with 45° and 0° orientation angles, respectively. Nevertheless, theoretically, the woven roving regularly performs slighter strain behaviour than the chopped strand mat. Therefore, this irregular behaviour might occur due to the inset of mat300 on the laminate. The inserted mat300 fibre might increase the specimen elongation when resisting the tensile load. Otherwise, the positive effect of the angle orientation on the strain performance is similar to the other study [38,39]. The strain increment due to the angle orientation is 16.67%.

Regarding the tensile and strain behaviour, the modulus of elasticity can be determined from the mechanical relation of both measured properties. Figure 3c depicts the increment of modulus of elasticity due to the configuration of orientation angle and the type of fibre. This behaviour can be predicted because the tensile and strain behaviour has shown an escalating trend. The increased modulus of elasticity is 5.02 and 6% for the woven roving laminate with 45° and 0° orientation angles. Otherwise, the woven roving fibre type might increase the fibre content on the laminate. Therefore, the modulus of elasticity also can arise because of the high fibre content on the composite laminate. The positive effect of the higher fibre content on the modulus of elasticity is also presented by Kim et al. [40] and Elkazaz et al. [41].

The bending test measurement is conducted to determine the flexural mechanical behaviour, namely the bending/flexural stress, the bending moment load carrying capacity, and the flexural modulus, Figure 4. The experimental measurement shows that the most significant bending load carrying capacity was at the woven roving with 0° fibre orientation angle (4WRC), Figure 5a. This measured mechanical behaviour can be predicted correctly since the tensile strength of the 4WRC laminate is greater than the other. Otherwise, this behaviour can be explained that the bending load would generate the normal tensile stress due to the tension load on the bottom lamina. Therefore, the more significant tensile strength properties on the top and bottom lamina might support a more significant bending moment load.

Figure 4

Bending test of the laminate specimen: (a) 4CSM; (b) 4WRC45; and (c) 4WRC.

Figure 5

Flexural properties of the GFRP laminate: (a) bending moment, (b) bending stress, and (c) flexural modulus.

The maximum bending moment is used to estimate the flexural modulus of the developed lamina, and the results show that the 4 WRC lamina have the largest flexural modulus compared to the other laminates, Figure 5c. It can be seen that the lamina with the 0° orientation angle of woven roving has presented the largest flexural stiffness. This behaviour might have occurred because the woven fibre has effectively increased the carrying load capacity due to the bending load. Therefore, the maximum bending moment is significantly larger than the other laminates. Otherwise, the flexural modulus of the laminates has shown a different value from the tensile modulus. This mechanical behaviour might occur because a polymer material does not present the same deformation characteristics for tension and compression. The polymer material also presented viscous elastic behaviour during the deformation process. Therefore, the flexural modulus is required to describe the flexural rigidity of the polymer.

2.3 Material definition validation on bending test simulation

The validation of material definition is conducted through the bending test simulation. The numerical results of the bending test simulation will be compared to the experimental measurement results. The bending test was selected to validate material definition because most crash absorbers respond to the lateral load with bending deformation. Therefore, the bending test simulation is relevant to represent the mechanical response characteristics of the crash absorber.

The bending test model has been developed similarly to the previous validation procedure [42]. The FE model is created using 1,800 quadrilateral elements with 1,920 nodes. The element numbers were defined for the accurate calculation with the computational convergent. The thickness of each bending test specimen determines the element’s thickness. Furthermore, the boundary condition is a simply-supported beam with a span length following the specimen length. Multi-point constraint (MPC-RBE2) defines the concentrated load on the specimen’s midpoint. The compressive force is inserted on the independent point of the MPC. This force is distributed to the nodes with a rigid link to the independent point. The maximum compressive force and the specimen thickness are presented in Table 2. Otherwise, the FE model and the multi-point constraint definition can be seen in Figure 6.

Figure 6

The bending test model for numerical validation: (a) boundary condition and (b) multi-point constraint (MPC-RBE2) on the loading condition.

The FE model was run using the ABAQUS software with two computational algorithms. The first calculation is made using the linear perturbation static method, and the second algorithm is general static which the plasticity is considered during the numerical computation. Furthermore, the numerical results were compared to the experimental measurement. The comparison between the numerical analysis with the experimental results is presented in Figures 7–9.

Figure 7

Comparison of bending specimen deformation of 4CSM laminate type.

Figure 8

Comparison of bending specimen deformation of 4WRC45 laminate type.

Figure 9

Comparison of bending specimen deformation of 4WRC laminate type.

2.4 Description of multi-cell GFRP crash absorber for tsunami lifeboat

The tsunami lifeboat crash absorber was made using the multi-cell GFRP. The cross-section of the multi-cell is configured using the circular cell, the honeycomb cell, the square cell, and the triangular cell. All the components of the crash absorber were made using glass fibre-reinforced polyester. The multi-cell core contains a circular pipe with a diameter of 50 mm in the circular cell. The other multi-cell has sectional dimensions that are presented in Figure 10.

Figure 10

Multi-cell cross-sectional configuration of the tsunami lifeboat crash absorber: (a) circular cell core; (b) honeycomb cell core; (c) square cell core; and (d) triangular cell core.

The laminate used for this crash absorber is the laminate presented in the previous sub-chapter, namely 4CSM, 4WRC45, and 4WRC. Crash absorbers are made using a uniform type of lamination. Therefore, the number of layers, laminate thickness, stacking sequence, and orientation angle also match the type of laminate used. Furthermore, the mechanical characteristics used for numerical analysis calculations are determined using mechanical properties obtained from mechanical testing. It has been validated by comparing the results of the bending test measurements with the bending numerical analysis.

In the crash absorber, the multi-cell core only consists of an empty GFRP tube not filled with filler material. A hollow GFRP tube was chosen for the crash absorber because it focused on identifying the effect of multi-cell cross-sectional geometry design and laminate type on energy absorption performance. Based on the variation of the geometry of the multi-cell core cross-section and the type of laminate used as the crash absorber material, 12 different crash absorber design configurations will be studied for energy absorption and crushing damage performance, Table 3.

3.1 Crushing damage characteristics of the GFRP multi-cells crash absorber

The three-dimensional FE model was made to evaluate the crushing damage of the multi-cell crash absorber under the low-velocity impact. The ABAQUS explicit dynamics was adopted for collision/crash analysis between the impactor and the multi-cell crash absorber. The bending and tensile test measurement data define the GFRP multi-cell material’s mechanical properties. The impactor was determined as a rigid body with a defined mass of 4.84 tons, similar to the mass tsunami lifeboat. The initial impactor velocity of 30 knots is selected to represent the tsunami lifeboat velocity during the collision event.

The simplified FE model was adopted to define the GFRP multi-cell crash absorber. The equivalent single-ply with plasticity model is developed to represent the multi-ply laminate as a single-layer elastic laminate. The plasticity definition was formulated regarding the experimental measurement data. The equivalent single-layer adoption as a model simplification can be accepted because the tensile properties of GFRP composite with fibre orientation angles of 0° and 45° are similar on both orthogonal axes. These characteristics can be categorized as transversely isotropic. The material properties used in the simulation are presented in Table 4.

The crash absorber model mesh was defined using 86,692 nodes, 98,300 quadrilateral elements, and 1,440 triangular elements for circular cell, 54,257 nodes and 60,000 quadrilateral elements for rectangular cell, 75,158 nodes, 85,858 quadrilateral elements, and 926 triangular elements for honeycombs cell, 80,230 nodes, 90,738 quadrilateral elements, and 2,362 triangular elements for triangular cell. The mesh size of the crash absorber model was defined with a node distance of about 10–15 mm. The fine mesh size is determined according to the convergence test results that obtained 15 mm is a reasonable mesh size. However, the coarser mesh size was defined for the rigid impactor and table model. Both models are rigid structures (no deformation) which are defined as the master surface on the contact analysis between the impactor with the crash absorber (slave surface) and the crash absorber (slave surface) with the table contact surface.

The boundary condition was determined on the bottom side of the table with a clamp constraint. The initial velocity of 30 knots was defined as the impactor velocity during the collision event. The connection between the single unit cell was determined by merging nodes with the adjacent one. It is a simple joint that might be accepted because the unit cell has been joined with the same polyester resin. The gravity acceleration was not included because the simulations model was defined to represent the collision event with the constant velocity instead of the drop impactor on a particular free fall height. The FE model of the multi-cell crash absorber can be seen in Figure 11.

Figure 11

The multi-cell crash absorber FE model for the axial collision load.

Figure 12 shows the numerical model damage status of the circular cell crash absorber with the laminate type of the 4CSM, 4WRC45, and 4WRC under the low-velocity collision load. Figure 12(a) shows severe damage to the 4CSM circular crash absorber. The circular cell core appears badly damaged. Therefore, the formation of rows of circular tubes has shifted from its initial position. The top layer has been damaged and detached from the crash absorber. The sidewall components were also severely damaged. More than half of the parts had been destroyed. The severe deformation experienced by the sidewall resulted in the sidewall’s shape being different from the initial conditions. Figure 12(b) presented the damage of the 4WRC45 circular cell crash absorber. Some structural parts of the circular tube are deformed and fractured in the circular cell core. The bottom of the circular cell has shifted. It can be seen that some structural part of the circular tube is detached from the bottom plate. On the sidewall component severe damage has occurred on one side of the wall. The sidewall was shifted, separating one corner from the bottom plate.

Figure 12

Crushing damage of the circular cell crash absorber: (a) 4CSM laminate type; (b) 4WRC45 laminate type; and (c) 4WRC laminate type.

Subsequently, the 4WRC circular cell crash absorber damage is described in Figure 12(c). In the 4WRC circular cell, some top plate components are still visible, even though they have suffered severe damage. In the circular cell, severe damage is seen in the centre of the crash absorber. Although the circular cell was also severely damaged, the circular tube formation was still relatively intact compared to the circular cell damage in the 4CSM type. The damage was not too severe on the sidewall, although the lower and upper parts had fractures. The bottom plate is also detached from the sidewall and circular cell components and appears to be raised between the gaps of the circular cell components. This phenomenon can occur because the bottom plate component does not have a contact definition but is a unified component bound by nodes. When the binding node is deformed beyond the fracture strain limit, the bottom plate component is detached and can shift through the sidewall and circular cell components. Regarding the numerical results, it can be seen that the 4WRC circular cell has better crushing damage compared to the other circular cell crash absorber.

Figure 13(a)–(c) depicts the crushing damage of the honeycomb cell with various laminate types, namely the 4CSM, the 4WRC45, and the 4WRC. In Figure 13(a), severe impact damage can be identified on the honeycomb cell of the 4CSM crash absorber. The honeycomb tubes have lost their integrity due to the impact load. The top plate was severely damaged and fell out of its original position. The sidewall components were also damaged, and there was a change in shape, so the crash absorber position was distorted. Some of the walls on the sidewall components were also damaged. The bottom layer is also detached and damaged.

Figure 13

Crushing damage of the honeycomb cell crash absorber: (a) 4CSM laminate type; (b) 4WRC45 laminate type; and (c) 4WRC laminate type.

Figure 13(b) presents the crushing damage of the 4WRC45 honeycomb crash absorber. It is found that the 4WRC45 honeycomb cell has shown better damage deformation than the CSM type. Although a severe fracture was identified in the cell, the honeycomb tubes formation was not distorted. Damage to the sidewall component also does not distort the geometric shape of the component. The top plate still looks connected to the topside element in the honeycomb cell. However, at the bottom, the bottom plate appears to have been removed and entered the honeycomb cell component. This phenomenon can occur because, in the simulation model, the connection between the bottom plate component and the honeycomb cell was defined as an integral body part connected with nodes so that when this node exceeds the deformation limit, the connection is declared failed. Furthermore, the bottom plate component can pass through the honeycomb cell because it does not have a contact definition.

In Figure 13(c), it can be identified that the 4WRC honeycomb crash absorber has better damage deformation than the two others. Although the degradation is found on the wall, the sidewall component still shows an undistorted rectangular wall shape. The top plate and the honeycomb cell fracture only occurred in the central region. However, the bottom plate is severely damaged and lost its position due to the large deformation.

The crushing damage of the square cell with various laminate types, such as 4CSM, $WRC45, and 4WRC, is presented in Figure 14(a)–(c). Similar to the two other crash absorber multi-cell, the square cell with 4CSM laminate type has shown more intensive damage than the 4WRC45 and 4WRC laminate. Figure 14(a) depicts the severe damage identified on the 4CSM square cell. The crash absorber is wrecked into several parts, and large deformation has distorted the square-cell unity. It can be found that the sidewall component is tearing into several pieces and missing its structural integrity. The top and bottom plates have failed their connection with the square cell.

Figure 14

Crushing damage of the square cell crash absorber: (a) 4CSM laminate type; (b) 4WRC45 laminate type; and (c) 4WRC laminate type.

Figure 14(b) presents the crushing damage of the 4WRC45 square cell. The most severe damage was found in the centre region of the square cell. The square tube formation has been distorted and lost the unity of the multi-cell appearance. The sidewall component has severely deformed, and one of the walls is torn into two pieces. The top and bottom plates were fractured and disconnected. Otherwise, the 4WRC square cell has shown a better crushing damage condition (Figure 14(c)). Although the fracture was found on the top plate, the component was still connected to the sidewall and square cell. Some walls were tearing into several pieces. However, the square tube formation still presented a structural unity. The bottom plate failed and detached from the crash absorber body.

Finally, the crushing damage of the triangular cell crash absorber is presented with the variation of laminate type (Figure 15(a)–(c)). The 4CSM triangular cell has shown more severe damage than the other type (Figure 15(a)). Furthermore, the top and bottom plates were fractured and detached from the crash absorber body. The triangular cell was severely deformed, especially in the centre region of the crash absorber. It can be seen that the triangular tube formation was distorted. Therefore, the triangular cell components might be lost their structural integrity. Furthermore, the sidewall component has shown severe wall damage due to the exerted impact load.

Figure 15

Crushing damage of the triangular cell crash absorber: (a) 4CSM laminate type; (b) 4WRC45 laminate type; and (c) 4WRC laminate type.

Figure 15(b) illustrates the crushing damage of the 4WRC45 triangular cell. The triangular cell was seriously damaged, the triangle tube formation was distorted, and their structural unity was lost. The wall distortion can be seen on the sidewall component. All walls were fractured and torn to several pieces. Additionally, the top and bottom plates failed and disconnected from the crash absorber body.

The 45WRC triangular cell crash absorber damage was described in Figure 15(c). It can be predicted that the damage deformation of the 4WRC type is slightly better than the last previous types. The top plate has a minor fracture and is still connected with the sidewall and the triangular cell components. The triangular cell damage was identified on the bottom side of the crash absorber. The top side of the triangular tube only suffered minor fracture deformation. The damage that occurs is visible on one side of the corner on the top plate.

Regarding the crushing damage behaviour of the multi-cell crash absorber, it can be seen that the crash absorber has presented a brittle fracture. This failure characteristic is theoretically acceptable since the glass fibre-reinforced polyester polymer can be categorized as a brittle material with small plastic deformation. The results showed that the 4CSM square cell has the most severe damage due to the collision impact load. However, All 4WRC crash absorber types have presented similar fracture and damage levels. Although the damage level might represent the energy absorption capability of the crash absorber, finite element analysis should be conducted to calculate the numerical approximation of the crash absorber capability.

3.2 Effect of multi-cell cross-sectional geometry on the energy absorption performance

The effect of multi-cell cross-sectional geometry on energy absorption has been estimated from numerical analysis results on the crash absorbers with multi-cell cross-sectional design configurations such as circular cells, honeycomb cells, square cells, and triangular cells. Figure 16(a)–(c) depicts the absorbed energy characteristics of the crash absorber with the variation of multi-cell cross-section and laminate types. All the crash absorbers showed increased absorbed energy after loading the initial impact force. This phenomenon is attributed to the initial mechanical deformation response caused by the collision between the impactor and the crash absorber.

Figure 16

The effect of multi-cell cross-sectional geometry on the energy absorption performance: (a) 4CSM laminate type; (b) 4WRC45 laminate type; and (c) 4WRC laminate type.

Figure 16(a) illustrates the energy absorption performance of the 4CSM crash absorber with various cross-sectional multi-cells. The circular section presents the most significant absorbed energy. The maximum absorbed energy of the 4CSM circular cell is 21 kJ. Otherwise, the maximum absorbed energy for the other cross-section, such as square cells, honeycomb cells, and triangular cells, is 11, 18, and 19 kJ, respectively. Modifying cross-sectional geometry from the square, the honeycomb, and the triangular cell to the circular cell led to an increased absorbed energy magnitude of about 91, 17, and 11% for the 4CSM crash absorber, respectively.

In the case of the 4WRC45 crash absorber, the circular cell has presented the largest absorbed energy of 75 kJ (Figure 16(b)). The increased absorbed energy was about 121, 47, and 44% for modifying the cross-sectional of the square cells, the honeycombs cells, and the triangular cells to the circular section, respectively. Furthermore, Figure 16(c) shows the maximum absorbed energy of the 4WRC crash absorber, namely the circular, the square, the honeycomb, and the triangular cell, which are about 101, 45, 68, and 73 kJ, respectively. The increased energy absorbed by the circular cell from the square, the honeycomb, and the triangular is about 124, 49, and 38%, respectively.

Regarding the numerical results, it can be identified that the multi-cell cross-section geometry significantly influences the crash absorber’s energy absorption performance. It might be explained that the different cross-sections might generate other buckling strength characteristics. Therefore, the multi-cell cross-section shape significantly influences the crash absorber with the axial failure mechanism.

3.3 Effect of GFRP laminate type on the energy absorption

The influence of the GFRP laminate type was investigated with various laminate types, namely 4CSM, 4WRC45, and 4WRC. The same cross-sectional multi-cells are compared with different GFRP laminate types by plotting the energy absorption performance characteristics. Figure 17(a)–(d) illustrates the energy absorption characteristics of the cellular, the honeycomb, the square, and the triangular cross-section with various GFRP laminate types. All crash absorbers with different cross-sectional shapes have shown a significant difference in absorbed energy behaviour due to the changes in the laminate types. This behaviour is attributed to the mechanical properties of the crash absorber material that significantly influence the energy absorption performance.

Figure 17

The effect of laminate type on the energy absorption performance: (a) circular cell; (b) honeycomb cell; (c) square cell; and (d) triangular cell.

In the circular cross-section, the most significant absorbed energy of 101 kJ was presented by the 4WRC laminate type (Figure 17(a)). The maximum absorbed energy is 21 kJ for the 4CSM and 75 kJ for the 4WRC45 laminate type. The increment percentage of the absorbed energy from the 4CSM and the 4WRC45 laminate type to the 4WRC is about 381 and 35%. Like the cross-section shape, the laminate type also significantly influences the energy absorption performance. Figure 17(b) illustrates the honeycomb cell’s absorbed energy behaviour on various laminate types. The largest energy absorption performance of 68 kJ was shown by the honeycomb cell with 4WRC laminate type. The other laminate type has presented the maximum absorbed energy of 51 kJ for the 4WRC45 and 18 kJ for the 4CSM type. Therefore, adopting the 4WRC laminate type has shown an increment in energy absorption performance of about 33% for the 4WRC45 and 183% for the 4CSM.

Subsequently, the influence of the laminate type on the energy absorption performance of the square cell and the triangular is shown in Figure 17(c) and (d). The largest absorbed energies are 45 and 73 kJ for the square and the triangular cell. Both multi-cell crash absorbers also show that the 4WRC laminate type is superior to the other. The 4CSM showed the most considerable absorbed energy of about 11 kJ for the square cell and 19 kJ for the triangular cell. In the 4WRC45 type, the maximum absorbed energies are 34 kJ for the square cell and 52 kJ for the triangular cell. It can be seen that the energy absorption performance has increased by about 309% for the square cell and 284% for the triangular cell from the 4CSM laminate type to the 4WRC. Otherwise, the energy absorption was increased by about 32% for the 4WRC45 square cell and 40% for the 4WRC45 triangular cell to the 4WRC.

Regarding the numerical results, it is observed that the 4WRC laminate type has shown a better energy absorption performance than the two other laminate types, namely the 4CSM type and the 4WRC45 type. The 4WRC laminate type might be increased the absorbed energy by about 183–381% for the 4CSM laminate type and 32–40% for the 4WRC45 laminate type. It is indicated that the GFRP laminate type that performs a better energy absorption performance for the tsunami lifeboat crash absorber is the 4WRC.