Buckling behaviors of the impacted composite plates

1.1 Production of composite materials

The glass fiber/epoxy composite plates are manufactured from unidirectional E-glass fabrics and epoxy resin by the hand lay-up method. An epoxy resin matrix based on CY225 epoxy prepolymer and HY225 hardener is used in the production of the composite plates. The mixing ratio for resin-to-hardener in weight is 10:2. The glass/epoxy composite plates are cured in a lamination press, at a constant 0.3 MPa pressure and 120°C temperature for 2 h. Then, the composite plates are cooled down to room temperature, maintaining the pressure. The process of pressing is a better way to impregnate the glass fiber with the epoxy resin and to eliminate the air bubbles in the composites. After manufacturing process, all the specimens (130 mm long and 40 mm wide) used in the experiments are cut by water jet from the fabricated composite plates. To compare the data to be obtained from the experiment specimens, buckling length has been taken as L=100 mm in all the specimens as shown in Figure 1. Thicknesses of the composite plates with 8, 12, and 14 layers are approximately measured as 1.6, 2.4, and 2.8 mm, respectively, after the process of trimming.

Figure 1

Geometric dimensions and impact points of the specimen.

To calculate theoretically the volume fraction of the composite plate of eight layers, first, a 40×130 mm specimen was weighted and found to be 15.9 g. It is known that the weight of fibers is 11.23 g in the specimen and the rest is the weight of resin. Then, the rule of mixtures was used for the determination of the volume fractions of constituents. Finally, the fiber volume fraction of the composite plate was obtained at approximately 53%.

The mechanical properties of the composite plates are given in Table 1. The mechanical properties (E₁, E₂, v₁₂, and G₁₂) are measured by using tensile specimens manufactured according to the ASTM D3039 standard. Here, E₁ is longitudinal module, E₂ is transverse module, G₁₂ is shear module, and v₁₂ is Poisson’s ratio of composite materials. To determine the mechanical properties of unidirectional glass/epoxy composite plates under static loading conditions, [0]₈ oriented composite plates are used. Each experiment is repeated three times and the obtained average values are used.

2.1 Impact test

The impact tests are carried out by using Instron-Dynatup 9250 HV model instrumented drop weight impact testing machine. This testing machine consists of a dropping crosshead with its accessories, a pneumatic clamping fixture, a pneumatic rebound brake, and Dynatup 930-I impulse data acquisition system. Testing machine can apply an impact energy ranging from 2.6 to 826 J, with the support of a spring without adding an extra weight to the weight box. Maximum physical drop height at which weight can be dropped is 1.25 m. Similarly, the maximum impact velocity is 5 m/s. The top of the impactor has a 12.5 mm diameter hemispherical tip and the pneumatic rebound brake system prevents the repeated impact on specimens. Impulse data acquisition system records the electronic signals and converts them into the impact parameters, such as height, velocity, and energy. The total mass of the impactor is approximately 6.32 kg for all tests. The specimens are clamped with the pneumatic fixture with an impact window of 30 mm diameter and the desired impact energy is applied. Both the impact and compression test machines can be seen in Figure 2.

Figure 2

Test equipment: (A) Dynatup 9250 HV impact test (B) Instron 8801 compression test.

Specimen width has been taken as 40 mm and buckling length as 100 mm, as seen in Figure 1. The place of the impact point is changed, keeping the main dimensions of the specimen fixed, except for thickness. For this reason, the specimens are impacted at the center of the plates (IP-0) and at 15 mm (IP-1) and 30 mm (IP-2) away from the center of the plates. For each point, impact damages until vicinity of the penetration are formed in five different impact energy levels of 3, 6, 9, 12, and 15 J. They are repeated three times for each experiment to take their average value. All the experiments are carried out at room temperature of 23±1°C.

Relationships between the impact characteristics, such as impact load, deflection, contact duration, impact energy level and impact velocity, and failure mechanisms of damaged specimens are also discussed.

2.2 Buckling tests

To determine the buckling behaviors of the nonimpacted and impacted specimens at different impact points and energy levels, and having different thicknesses, Instron 8801 Servo hydraulic testing machine with 50 kN loading capacity has been used. Both ends of the specimen are clamped into the machine’s jaws, one of which is movable toward and away from the other. Axial Servo hydraulic testing machine has an adjustable crosswise head and its maximum hydraulic pressure is 207 bar. The axial compression tests are performed using displacement control with a speed of 0.3 mm/min. During the test, the load versus displacement (contraction) curve is measured and recorded automatically by test machine. The hydraulic pressure in the head of machine during buckling tests was almost 40 bar. There is not observed any damage in the surface of the specimens subjected to this pressure and slip between the specimen and machine’s jaws.

Compressive loads versus contract are plotted in Figure 3 for different impact points. Moreover, the critical buckling load (P_cr) can be determined from the same figure. The point from the left of the straight line is determined on the graphics and the value of this point on the y-axis is called the buckling load [10].

Figure 3

Variation of the force versus compressive displacement in the composite plates having different impact place (14 layers and 6 J).

3.1 Impact behaviors of composites

The load-deflection (P-d) curve is a response to the impact loading of composite plates. In addition, it gives significant information regarding the impact behaviors of plates during an impact event. It is generated from the software program when the impactor makes contact with composite specimen. For comparison, load-deflection curves of the composite plates with 12 layers are given in Figure 4 for impact energies in range of 3–15 J. As seen in the figure, each curve has an ascending section of loading, reached a maximum load value that is called a contact load, and a descending section of unloading. The ascending section of load-deflection curve occurs due to the resistance of composite to the impact loading. The descending section of load-deflection curves represents impactor rebounding from specimen surface. When the impactor makes contact with composite specimens, the loading section of load-deflection curves increases for each composite. As can be seen from the figure, by increasing impact energy, P-d curves extend larger; thus, the maximum contact load and the deflection of the composite plates increase. Because it is not allowed for penetration and perforation impact damages to take into consideration the effects of small damage shapes on the buckling behaviors, P-d curves are obtained in the closed form.

Figure 4

Impact load-deflection curve for 12 layers.

Figure 5 shows load-deflection curves of the composite plates having 8, 12, and 14 layers subjected to impact energy of 9 J. Slope in ascending section of P-d curve represents the bending stiffness of the composite plates. Although all of the composite plates with 12 layers have the same slope in increasing impact energies as seen in Figure 4, the slope for composite plates with different number of layers changes. As expected, it is shown from this figure that the bending stiffness increases with increasing number of layers in the composite plates.

Figure 5

Impact load-deflection curves of the plates subjected to 9 J.

Figure 6 depicts variations of the load and energy according to contact time in the composite plates of 12 layers. With the increasing impact energy, contact loads increase, whereas contact durations are approximately the same. Contact time changes with the change in the composite plate thickness. As the composite thickness increases, contact time decreases. In this figure, E_i, E_a, and E_e represent the impact energy, absorbed energy, and excessive energy, respectively. The absorbed energy is calculated from the area under the load deflection curve. The excessive impact energy is the difference between the impact and absorbed energies, as seen in this figure. That is, it is the energy retained in the impactor and used for rebounding of impactor from the specimen surface at the end of an impact event [18]. It is shown that absorbed energy decreases by increase in impact energy up to the vicinity of penetration threshold. However, the penetration threshold is the place where the absorbed energy becomes equal to the impact energy. In that point, there is no excessive impact energy to rebound the impactor from the specimen surface anymore.

Figure 6

Variations of load and energy curves versus contact time for 12 layers.

The impact load, deflection, and contact time are the important impact characteristics of the composite plates subjected to impact loading. During impact event, the characteristics yield the impact behaviors of the composite plates. The impact characteristics versus impact energy are plotted in Figure 7.

Figure 7

Variation of the maximum load, maximum deflection, contact time, and impact velocity versus impact energy in the composite plates of 12 layers.

This figure shows the variation of load values with impact energy in the composite plates of 12 layers. The contact load values of composites indicate a sudden increase up to 12 J. Afterwards, the load value increases with small increments until next to the penetration threshold of the composites by increasing impact energy (except for 14 layers).

The deflection values of composites increase approximately linearly as the impact energy increases until next to the penetration threshold. The damage in composites increases due to the increasing of the impact energy and so deflection increases sharply at the perforation threshold appearing after the penetration threshold. The perforation threshold can be defined as the minimum energy level at which the impactor passes through the thickness of the specimen, resulting in a permanent catastrophic damage to the specimen [3].

The contact time between the impactor and the composite plates of 12 and 14 layers versus impact energy is nearly constant at these energy levels, but it decreases for those of 8 layers. The impact velocity increases with increasing impact energy and it is the same for all the composite plates in the same impact energy.

To understand the damage mechanisms, several photographs of the damaged specimens having 8 layers, which are taken from both impact (front) surface and back surface, are shown in Figure 8 for increasing impact energy. The crack onset in resin of composites and damage can take place. As the impact energy increases, the damage area increases. As a result of this, the resistance of the composite plates decreases. Damages such as minor matrix cracking and indentation concentrate at the impact contact point of the impact surface, whereas fiber breakage starts to occur at the back surface. The fiber breakages occurring through the thickness of plates are the main cause in increasing of the deflection.

Figure 8

Damages in the impacted specimens with 8 layers.

3.2 Buckling behaviors of composites

After the impact test, to determine the buckling behavior of the specimens, compression experiments on the composite specimens impacted at the different impact points and energy levels are depicted in Figure 9. The following formal normalized variable is used at each energy level and impact point for critical buckling loads:

Figure 9

Distributions of the buckling loads versus impact energy at (A) center, (B) 15 mm, and (C) 30 mm.

The normalized critical buckling loads give a better indication of the influence of the impact damage on the buckling strength of the composite plates. As can be seen in the figure, Pcr*=1, which is the ratio of the buckling load obtained from the nonimpacted specimen itself, is a reference value for nondimensional critical buckling loads. All tests are conducted for clamped-clamped boundary conditions according to uniaxial loading.

In this figure, the distributions of the critical buckling loads versus impact energy levels are drawn for the different impact points (center IP-0, 15 mm IP-1, and 30 mm IP-2) and number of layers (8, 12, and 14 layers). The lowest critical buckling load occurs in the specimen having thin plate thickness (8 layers) and impacted about 3 J in the center point (IP-0). At impact energy of 3 J, the reductions of the buckling loads are about 13%, 66%, and 81% in plates of 14, 12, and 8 layers, respectively. The reduction may be due to the less stiff, more unstable, and liable to fail under a much lower load.

The failure in the plates occurs due to delamination, but because delamination propagation is parallel to the loading direction and less perpendicular to the loading direction, the effects of delamination on the buckling loads are very low and may even contribute until a certain delamination value, as can be seen in this figure.

The variation in the buckling load of composite plates impacted at their center point is similar to the variations of the compression, bending, or tensile strengths of the composite plates impacted at the center point in literature [6, 19, 20]. The variations in the buckling or compression after impact tests strengths are greater and reduce at the low energy levels (3 and 6 J), whereas the variations at the high energy levels (9–15 J) are approximately constant or have little increase. The composite plates buckle generally at its center for clamped-clamped boundary conditions. As the composite plates are impacted in a point away from its center, an increase in the critical buckling loads can be shown due to the fact that the buckled section moves from the center through other points (to supports).

As for the other impact points (IP-1 and IP-2), the critical buckling loads become more stable in these points. This stability increases more with increase in the number of layers. In thin plates, it is shown that the critical buckling load affects more at low energy levels (3 and 6 J), whereas the effect of the impact energy on the critical buckling loads is smaller after the low energy levels (at 9–15 J).

It is seen in Figure 9B and C that, in thicker plates (12 and 14 layers), the critical buckling load values affects some according to thin plates (8 layers) at all energy levels, except for impacted specimens in IP-0. The critical buckling loads of the thick plates, which are impacted at both IP-1 and IP-2 and low energy levels, increase even more. The loss in buckling loads decreases for the impacted specimens at IP-1 and IP-2. For example, the loss of the buckling loads for the specimens of 12 layers is approximately 1% for 3 J and IP-2. It is shown that the change in the specimens of 14 layers even gains about 15% and 11% at low impact levels. After these energy levels, the buckling load values are close to each other, as can be seen in Figure 9C.

These results are important in design because they show the impact energy levels and impact points that can be tolerated in a structure without lowering its compression strength.

All specimens are buckled at the first buckling mode. It is seen from Figure 10 that buckling damage occurs in the center axis of the nonimpacted specimen. As the energy level increases, it is clearly shown a deviation in damage failure from the center point towards the edges.

Figure 10

Damage in the composite plate after buckling.