Study on Low-Velocity Impact Behavior of Twaron® Fabric Subjected to Double-Impactor Impact from a Numerical Analysis Perspective

The drop-weight test program was performed using a 9250HV INSTRON™ Pneumatic Dynatup test system. A schematic diagram of the impact tester is shown in Fig. 1. The impactor, made from high rigid 4340 steel, has a hemispherical head of 12.7 mm standard diameter. During the impact test, the hemisphere-head-impactor was dropped from a predetermined height, which then hit the center of the test sample in between the round-clamped plates. An anti-rebound system was attached to the testing machine to prevent multiple impacts on the same specimen. The specimens were supported on a pair of pneumatically clamped rings having an internal diameter of 40 mm. The low-velocity impact tests were performed according to the ASTM standard (D7316). A minimum impact weight of about 7 kg was used for all the tests. Two impact loading and acceleration sensors were attached to the impactor. Sensors were used to measure the contact force between the impactor and specimen and the acceleration during the low-velocity impact. Based on the impact loading F(t) test, calculation of the acceleration α(t), initial velocity vi, velocity v(t), and displacement D(t) of the impactor and the absorbed energy E(t) of the specimen was possible according to equations 1–3[31] 1 v(t)=vi+∫0Tα(t)dt $$v(t)\, = \,vi\, + \,\mathop \smallint \limits_0^T \alpha (t)dt$$ 2 D(t)=∫0Tv(t)dt $$D(t)\, = \,\mathop \smallint \limits_0^T v(t)dt$$ 3 E(t)=∫0TF(t)v(t)dt $$E(t)\, = \int_0^T {F(t)v(t)dt} $$

Fig. 1.

Light weight and high strength plain-woven Twaron® CT 612, made by TEIJIN®, was used in this study. This fabric was manufactured using a plain weave of 110×110 yarns (per mm²), each of which consisting of 500 filaments. The bulk and linear density were 1440 kg/m³ and 550 dtex. 5 mm thickness plywood plates cut to 100 mm × 100 mm with a 70 mm diameter hole cut in the middle were used to sandwich and glue a fabric sample of 100 mm × 100 mm size. This effective specimen design method solves the problem that the fabric is too soft and cannot be fixed firmly. Front and side views of the specimen after impact at 10 m/s are shown in Fig. 2.

Fig. 2.

A commercial explicit nonlinear FEA code (ANSYS®-AUTODYN) was employed for FE modeling of a low-velocity drop weight impact on a Twaron®fabric. The fabric model was simulated at yarn level (meso-scale). The cross-section of the yarn was modeled as a lenticular shape, assumed as a continuous solid with the same properties as fibers. The height, width, and wavelength of the yarn cross-section were set as 0.1, 0.9, and 1.8mm, respectively, according to measurements of the real fabric by a digital microscope, from which the geometrical fabric model was deduced. The fabric model was created to be circular in shape with a diameter of 70 mm by considering the nature of clamping applied in the tests. The boundary condition of a complete fix around the fabric circumference was adopted. And a hemisphere-head-impactor with a diameter of 12.7 mm was simulated.

In addition, transversely isotropic material properties were applied to the yarn model, which were combined to create a fabric model. The material constants for the transversely isotropic aramid yarn were dominated by the longitudinal tensile modulus (E₁₁), and the transverse elastic moduli (E₂₂ and E₃₃) and shear moduli (G₁₂, G₁₃, and G₂₃) were assumed to be smaller than E₁₁, while the Poisson’s ratios were set as v₁₂ = v₁₃ = v₂₃ = 0. Although the Poisson’s ratio of the real material cannot be 0, considering that the real yarn is composed of countless fiber materials, the value of Poisson’s ratio of the yarn in simulation is determined by the characteristics of fiber movement inside the yarn. The material constants used in the FE modeling were: E₁₁ = 72.63 GPa, E₂₂ = E₃₃ = 1.13 GPa and G₁₂ = G₁₃ =G₂₃ = 1.04 GPa. Furthermore, a friction coefficient of 0.3 was designated to yarn/yarn contact, which was obtained from experiments in our previous study [32], while the friction coefficient between the impactor and yarns was designated as 0.2 [33]. Mesh sensitivity studies were carried out and results suggested that 167,860 eight-node solid brick elements meshed in the impact model were reasonable for the low-velocity impact simulation. The criterion of maximum principal strain failure determined as element erosion was considered: that is when ε ≥ ε_f, the element failed and was taken away from the model calculation, where ε_f demonstrated the yarn’s failure strain, set as 3.9%.

On the basis of the aforementioned experimental setup, impact tests of Twaron® fabric were performed at velocities between 8-16 m/s with a 2 m/s interval. At least six samples were impacted repeatedly at every designated velocity for reproducibility. From Fig. 2, it can be seen that the circular boundary of the fabric was well fixed by the plywood plates, and significant damage appeared in the fabric’s primary yarns (primary yarns in this paper refer to two groups of crossover yarns that pass through the center of the fabric, which directly contact with the impactor). Simultaneously, simulations with the same impact velocities were also performed. Correlation of simulation prediction results and mean experiment results are shown in Figure 3(a) and (b), where the gradients of the regression line are 0.9963 and 0.9988, which validate the model accuracy. In addition, Figure 3(c) demonstrates a comparison of results of the F-T curve between the experiment and simulation at an impact velocity of 10m/s and 16m/s, respectively. Approximate curves at the same impact velocity also verify the validity and success of the impact model created in this study.

Fig. 3.

Two impactors of the same type were applied to simulate the simultaneous impact of the fabric and to effectively analyze the effect of location on the impact response of the fabric. The impactors were designed with half of the diameter and mass of the real impactor. The impact model is shown in Fig.4. The impact center positions on the fabric in different impact scenarios are shown in Fig. 5. The impact locations: O, A, B, C, A₁, B₁, and C₁ were in the center of primary yarns. These points divide the central primary yarn into eight equal parts. Summarily, impact locations D, D₁, E, E₁, F, and F₁ were on a line 45° to the above central primary yarn, and impact locations D₂, E₂, and F₂ are on a line 45° to the above central primary yarn.

Fig. 4.

Fig. 5.

For instance, impact scenario IAA₁ indicates the impact event when the impact of the two impactors are in positions A and A1. Different types of 18 impact models were developed. 18 simulations of impact scenarios were performed according to IOA, IOB, IOC, IOD, IOE, and IOF, which are asymmetrical impacts with one impactor impacting the fabric center. and IAB, IAC, and IBC, which are asymmetrical impacts without an impactor impacting the fabric center. While scenarios IAA₁, IBB₁, ICC₁, IDD₁, IEE₁, IFF₁, IDD₂, IEE₂, and IFF₂ are symmetrical impacts without an impactor impacting the fabric center. Generally, an average calculation time of 64 h was the cost of a scenario using a computer with an Intel xeon^® 12 core CPU and 64G RAM configuration.

The resistance force is the reaction force applied by the fabric to the impactor, which is also a key index to judge the material’s impact resistance ability. In this study, the yarns reached their fracture limit and started to break when the maximum resistance force of each impactor was reached at a particular impact duration time. The F-T history curve was plotted to compare the influence of impact location. The impactors that impacted positions O and N were named “impactor O and impactor N,” respectively. The value range of N = A, B, C, D, E, F, A₁, B₁, C₁, D₁, E₁, F₁, D₂, E₂, and F₂. For example, in the impact scenario IOA, impact N = impactor A, representing impactor impacted position A.

3.1.1.

Asymmetrical impact scenarios

Figures 6a–6c show the F-T curve of various asymmetrical impact scenarios. Figure 6a compares impact resistance forces of impactor O in double-impactor impact scenarios with one impactor impacting the fabric center. Similar curves were observed as the impact resistance force increased to a certain level. A drastic fall was observed at this level at a certain impact duration time. However, the influence of the maximum resistance force on another impact point of the fabric, such as IOC and IOB impact scenarios, shows some volatility curves before reaching maximum resistance. Impactor O was subjected to a higher maximum impact resistance force when the other impact point was located at the line inclined at 45° to the primary yarn center, contrary to that when the impact point was located at the yarn’s primary center.

Fig. 6.

The average maximum impact resistance force of impactor O appearing in impact scenarios IOD, IOE, and IOF is 611.3N, whereas in impact scenarios IOA, IOB, and IOC it is 457.7N, which is 74.9% of the former one. There was no significant difference in the impact duration times needed to complete fracture at the fabric impact center in all impact scenarios. In addition, among the related impact scenarios, impact scenario IOD had the longest impact duration time of 0.706 ms, while impact scenario IOE had the shortest - 0.639 ms.

Figure 6(b) compares impact resistance forces of impactor N in asymmetrical double-impactor impact scenarios with one impactor impacting the fabric center. The variation in impact location has a significant effect on the impact duration time (i.e., the closer the impact point is to the fabric fixed boundary, the shorter the impact-resisting time). This effect can be attributed to the continued yarn fracture extension rate. Moreover, as the distance between the impact location and the fixed boundary decreases, the yarn fracture extension rate also decreases, reducing the fracture time (impact duration time).

The maximum resistance force showed little difference among the impact scenarios when impactor N impacted the yarns at primary center; however, it showed a large difference among the impact scenarios when impactor N impacted at the line inclined at 45° to the yarn’s primary center. And among the impact scenarios, IOD had the highest maximum impact resistance force of 650.7N, while the IOF had the lowest - about 442.3N, which is only 68.0% of the former.

Figure 6c compares the impact resistance forces of impactor N in asymmetrical double-impactor impact scenarios without the impactor impacting o the fabric center. The impact resistance force of IAB-A indicated that in impact scenario IAB, the resistance force was applied from the fabric to impactor A. Similarly, it can be seen from the figure that the closer the impact point is to the fabric fixed boundary, the shorter the impact duration time. And among all impact scenarios compared, impactor A in impact scenario IAC had the highest maximum impact resistance force of about 577.3N, while impactor B in impact scenario IBC had the lowest - about 334.1N, which is only 57.9% of the previous one.

3.1.2.

Symmetrical impact scenarios

Figure 7 shows the F-T curve of various symmetrical impact scenarios. Due to the symmetrical impact of the fabric model and the impact location, the simulated experimental results showed some similarity between the two impactor parameters, such as the resistance force and fracture time at the impact location of the fabric. As a result, only the data from one impactor were used for analysis in this study. The variation observed at the impact location significantly affected both the impact resistance force and impact duration time (i.e., the closer the impact point is to the fabric center, the longer the impact duration time).

Fig. 7.

The average maximum resistance force in impact scenarios IAA₁, IDD₁, and IDD₂ is 636.4N, while that in in scenarios IBB₁, IEE₁, and IEE₂ is 600.6N, and for ICC₁, IFF₁, and IFF₂ - 492.5N, which is only 94.4% and 77.4%, respectively, of the former one. Similarly, the average duration time in impact scenarios IAA₁, IDD₁, and IDD₂ is 0.669 ms, while that in scenarios IBB₁, IEE₁, and IEE₂ is 0.558ms, and for ICC₁, IFF₁, and IFF₂ - 0.411 ms, which is only 83.4% and 61.4% of the former one, respectively.

Failure deflection refers to the impactor deflection, which occurs at fabric failure; it is considered as one of the important indices to study the impact behavior of soft body armor. Failure deflection is proportional to fabric impact duration time. Figure 8a displays a comparison of results of the failure deflection in different asymmetrical impact scenarios, previously discussed in the above section. The short distance between the impact location and fixed boundary leads to premature yarn breakage, which results in a smaller failure deflection. Thus, in the impact scenarios with impact locations located close to a fixed boundary, the difference in failure deflection between the two impactors was significant, while in other impact scenarios, the difference was not significant. The shorter average distance between the impact location of the two impactors and the fixed boundary led to little average failure deflection (Fig.8 a).

Fig. 8.

Figure 8b shows a comparison of results of failure deflection in different symmetrical impact scenarios; the data results are taken only from a single part due to the symmetrical characteristics. The impact location plays an important role in the impactor’s failure deflection. In all the different impact scenarios, the same distance of the impact location from the fabric center results in a similar failure deflection. Similar to the above findings, the smaller the average distance between the impact location of the two impactors from the fixed boundary, the smaller the overall average failure deflection that occurs.

Moreover, during the impact event, energy absorbed by the fabric was converted into strain energy and kinetic energies derived from the stretching and movement of the yarns. This energy was converted due to transverse deflection of the fabric and inward movement of yarn material towards the impact location. Hence, some of the energies absorbed by the fabric originated from the kinetic energy loss of the impactors. Thus, the total energy absorption of fabric E can be expressed by Equation 4. 4 E=12 [ M1(V102−V1R2)+ +M2(V202−V2R2) ] $$\matrix{E \hfill & = \hfill & {{1 \over 2}[{M_1}(V{1_0}^2 - V{1_R}^2) + } \hfill \cr {} \hfill & + \hfill & {{M_2}(V{2_0}^2 - V{2_R}^2)]} \hfill \cr } $$ where M₁ and M₂ are the masses of the impactors, V1₀ and V2₀ - the initial impact velocities, and V1_R and V2_R are the residual impact velocities of the two impactors, respectively.

Figure 9 displays the energy cost of the impactors and the total energy absorption of the fabric. Data of the asymmetrical impact scenarios are shown in Fig.9a. Impactor O exhibited the best energy absorption capacity in impact scenario IOF, while it exhibited the poorest in impact scenario IOA. Due to the earlier fracture of the yarn from the impactor closer to the fixed boundary, the energy absorption of the fabric (impactor C and F) became poorer. In the double-impactor impact asymmetrical scenarios, the greater the spacing of the impactors, the greater the difference in the energy absorption capacity of the fabric to impactor O and impactor N (Fig. 9a). Generally, among all asymmetrical impact scenarios, the fabric shows the best performance in scenario IOD with a total energy absorption of 1.93J, followed by scenario IOF with 1.70J, while the poorest performance appears in scenario IBC 1.34 J, which is only 69.4% of that in scenario IOD.

Fig. 9.

Data of symmetrical impact scenarios are plotted in Fig.9b. When comparing symmetrical impact scenarios to asymmetrical impact scenarios, the data from symmetrical impact scenarios appear to be more dispersed. Similar to the above findings, impact scenarios ICC₁, IFF₁, and IFF₂ of the impactors closer to the fixed boundary resulted in a poor energy absorption capacity of the fabric. The fabric performed best in impact scenario IDD₁ with a total energy absorption of 2.20J, which is also the best performance among all asymmetrical and symmetrical scenarios, followed by scenario IAA₁ with 1.88J, while the poorest performance appears in scenario IBC with 1.26J, which is also the poorest performance among all asymmetrical and symmetrical scenarios.

The influence of variation in the impact velocity on the behaviors of fabric were investigated, and impact scenarios IDD₁ and IOC were chosen as representative of symmetric and asymmetric impact scenarios, respectively. In symmetric impact scenario IDD₁, the velocity of one of the impactors (V₁=10m/s) was constant, while that of the other impactor (V₂) varied: 10 m/s, 9 m/s, 8 m/s, and 7 m/s. In asymmetric impact scenario IOC, the velocity of impactor O (V_O=10m/s) was constant, while the velocity of impactor C (V_C) varied: 10 m/s, 9 m/s, 8 m/s, and 7 m/s, resulting in the exchange of velocity between the two impactors. The impact results are listed table 1 and table 2. Parameters such as MF, T, and ET represent the maximum resistance force, impact endurance time, and total energy absorption, respectively.

In the symmetric impact scenario, the fabric’s maximum resistance force and the fabric’s impact endurance time for impactor 1 increase with a decreasing V₂ at a constant V₁; however, the fabric’s maximum resistance force to impactor 2 and the total energy absorption decrease (Table 1). The constant V₁ of impactor 1 results in a slight increase in MF₁ and T₁, while the decreased velocity of impactor 2 results in a significant increase in T₂ but a significant decrease in MF₂. Generally, as the average impact velocity of impactors decreases, the energy absorption capacity of the fabric becomes weaker.

In the asymmetric impact scenario, MF_O, T_O, and T_C increase with the decreasing velocity of impactor C (Vc) at a constant velocity of impactor O (Vo), while MF_C decreases at the same conditions (Table 2). Conversely, MF_C and T_C initially decrease, then increase, and finally decrease with a decreasing Vo at a constant Vc, while MF_O and T_O decrease and increase, respectively. Generally, regardless of the change in velocity of either impactor, the lower the average impact velocity of impactors, the weaker the energy absorption capacity of the fabric.