The Impact Energy Dissipation Analysis of Woven Para-Aramid Fabrics

Abstract

This work investigated the propagation characteristics of impact energy along the plane of woven para-aramid fabric using the two-dimensional thin-plate spline method. To evaluate fabric deformation at different layer numbers, weights with various tip types were dropped from a specific height. We discovered the energy propagation characteristics within the fabric planes by examining shape changes in response to deformation. To further investigate energy propagation, we evaluated the bending energy of the fabrics and determined the expansion factors. Our findings show that impact energy travels through the fabric along the directions of the warp and weft strands, which are interwoven at right angles.

Introduction

The fundamental behavior of textile fibers or fabrics upon a ballistic impact has been researched in various studies. The behavior of fabric systems upon a ballistic impact has also been examined in many studies.^1–5 Because bullet–fabric interaction is a sudden and complex incident, it is impossible to predict the fabric’s ballistic performance and behavior from fiber qualities in a certain way, especially when the bullet sizes are small. Fundamentally, it is known that the speed and the mass of the fired bullet determine its energy, and a higher energy causes more deformation. Woven fabric is deformed vertically and perpendicularly to the fabric plane when exposed to a ballistic impact. The deformation is propagated outward from the impact point and is valid for a certain speed interval. As the speed increases, the bullet’s energy also increases; the bullet pierces and passes through the fabric above a certain speed.

During the ballistic impact, the high magnitude of the propagation speed of the shock wave that occurs in the ballistic plane is related to the absorption capability of the plies and is significant. More energy can be damped in systems with a high wave propagation speed. The energy in the fabric plies is distributed and damped, and some of it causes trauma and depression at the rear side of the material. While the bullet’s energy is propagated in the fabric in the lateral direction, the unpropagated energy causes trauma depth in the vertical direction. Energy distribution and damping, as a result, and the minimization of the trauma depth in the vertical direction are desired. This situation in both directions is complex and related to fiber attributes and weaving construction. In previous studies,^6–15 the ballistic performances of panels obtained from woven and unidirectional (UD) fabrics and their composites were investigated with different methods. While some of these studies,^8–10 are related to the ballistic performance of soft fabrics, some have investigated composite panels.^6,7,11–15

Many studies show how fibers dissipate the energy on the fabric or plate surfaces. Joshi et al. ¹⁶ performed a critical analysis of internal factors such as fiber properties, resin characteristics, interphase properties and composite architecture, and external factors such as projectile type, environmental conditions and impact velocity influencing the impact response of ultra-high molecular weight polyethylene (UHMWPE) fabric and composites. Okhawilai et al. ¹⁷ investigated the energy absorption capabilities of aramid fiber-reinforced poly(benzoxazine-co-urethane) composites at different urethane mass concentrations under ballistic impact. Wong et al. ¹⁸ reported increased friction between threads by modification of low-density polyethylene (LDPE) and graphene in aramid fabrics and thus increased the ballistic resistance approximately twofold. They investigated the energy absorption capacity of ballistic fabrics using the finite element (FE) method. Wang et al. ¹⁹ investigated the ballistic resistance of soft panels made from UHMWPE fabrics. This study investigated the energy absorption properties of fabrics used in different ply numbers and the damage propagation characteristics depending on the deformations on the fabric surface after impact. The studies by Wang et al. ²⁰ were carried out to simulate the energy absorption and dissipation properties of from UHMWPE fabrics under impact with FE modeling. Goda ²¹ investigated ballistic resistance and energy absorption in woven E-glass composite panels, considering different projectile nose shapes and oblique incidence angles. Within that scope, three-dimensional (3D) FE models of projectiles and the laminated target have been developed, and numerical investigations have been carried out using Abaqus Explicit solver.

Our previous studies investigated the ballistic protection levels and energy absorption capacities of aramid and UHMWPE fabrics^8,9,22 and composites^6,7,13–15 under ballistic loading with different methods. Experimental and numerical analyses have shown that the behavior of fabrics and composites under ballistic loading is quite complex and that it is impossible to characterize their energy absorption and dissipation behaviors fully. This limitation makes numerical analysis of fabrics and composites, especially under ballistic loading, difficult. This study uses a mathematical method to characterize the energy absorption and dissipation behavior of fabric layers used for ballistic purposes. For this reason, the energy propagation behavior of woven fabric along the fabric plane is critical and should be examined during the impact. This study researched woven para-aramid fabric’s propagation behavior along its plane with the two-dimensional (2D) thin-plate spline (TPS) method. With this purpose, the size of deformation that occurs after the ballistic impact will be determined, and by using the shape changes due to deformation, the fabric’s energy propagation behavior in the X and Y directions will be found. In order to find energy propagation behaviors, the fabric’s bending energy will be calculated, and expansion factors will be determined.

Materials and Method

Materials

Ballistic Fabrics

Twaron CT 710 fabric is used in this research, and the parameters of this fabric are given in Table 1.

Table 1.

Parameters of Twaron CT 710 type of fabric used in this research.

Fabric type	Count (dtex)warp/weft	Material typewarp/weft	Weave	Densities(ends andpicks/10 cm)	Fabricweight(g/m2)	Treatment	Strength (kN)dry / wet
Twaron CT 710	930/930	2040/2000	Plain	117/117	220	Scouring/water-repellenttreatment	4.45±0.15 /3.97± 0.24

Test Apparatus

The experiment setup in Figure 1 was used in the drop tests. The weights were dropped from a 1 m height to a clay ground. A pipe with a 50 mm diameter was used for guiding weights. The weights can be seen in Figure 2. All weights had a 45 mm diameter, weighed 1 kg, and had three different tip types: A, B, and C.

Figure 1.

Test apparatus used in drop tests.

Figure 2.

Weights used in drop tests (Type A has a spherical tip).

No:1 Type Roma Plastilina (clay), given in NIJ standards, was used as the clay material in this research. The clay was filled into a box, as required in the standard. The fabrics were identified by putting tapes on the front side.

Method

The mechanism shown in Figure 1 was used in the tests. Three different profiles named Type A, B, and C, shown in Figure 2, were used for drop tests. Tests were performed by dropping the weights from a 1 m height. First, the weights were dropped onto the clay without a cloth, and the resulting shape deformation was photographed from a distance. Then, the weights were dropped onto cloth layers consisting of one, two, four, six and eight layers, respectively, and once more, the resulting shape deformation was photographed from a certain distance. Due to the fabrics having equal properties in the 0- and 90-degree directions, the layer arrangements were made in 0–90 degrees in all layers. Drop tests were applied on cloth layers on a clay ground and after the tests the deformations of the cloths were considered the same as the deformation of the clay. The computation proceeded in four steps. First, landmarks were identified from photographs, and then landmark coordinates were determined.

Next, the mean landmark configurations were ascertained. In the last step, using average shapes obtained by Procrustes analysis, the deformation shape (target) was determined by dropping a TPS rotating, round-tip bullet onto the empty ground with cloth layers (source). The bending energy causing the deformation was found by a program used in MATLAB 7.0. Finally, expansion factors formed near the landmarks were calculated.

The coordinates of homologous landmarks form in two shapes. These two shapes may represent either individual specimens or the means of two sets of shapes corresponding to target landmarks. Transformation from a source shape to a target shape involves the displacement of the source landmarks to the corresponding target landmarks. ²³

We shall mainly concentrate on the essential m = 2D case, with deformations given by the bivariate function:

$$y=\phi \left(t\right)={({\phi }_1\left(t\right),{\phi }_2\left(t\right))}^T$$

(1)

Bookstein has developed a highly successful deformation approach using a pair of thin-plate splines (PTPS) for the functions ${\phi }_1(t)$ and ${\phi }_2(t)$ . We concentrate on the critical m = 2D case, the theory developed by Duchon and Meinguet. ²⁴

Consider the (2×1) landmarks t_j, j = 1,…,k, on the first figure mapped exactly into y_i; i = 1,…,k, on the second figure. We write $\phi (t_j)=({\phi }_1(t_j),{\phi }_2(t_j){)}^T$ j=1,…,k, for the 2D deformation. Consider:

$$T={[t_1{t}_2\dots t_k]}^T,Y={[y_1{y}_2\dots y_k]}^T$$

so that T and Y are both (k×2) matrices. The bivariate function gives a PTPS.

$$\phi \left(t\right)={({\phi }_1\left(t\right),{\phi }_2\left(t\right))}^T=c+\mathrm{At}+W^{T}s\left(t\right)$$

(2)

where t is (2×1), $s(t)=(\sigma (t-t_1),\dots ,\sigma (t-t_k){)}^T,$ (k×1) and

$$\sigma \left(h\right)=\left\{\begin{array}{c}\Vert h{\Vert }^2\log (\Vert h\Vert )\Vert h\Vert >0\hfill \\ \multicolumn{1}{c}{0\Vert h\Vert =0}\end{array}\right\}$$

(3)

The 2k + 6 parameters of the mapping are c(2×1), A(2×2), and W(k×2). There are 2k interpolation constraints in Equation (1), and we introduce six more constraints in order for the bending energy in Equation (8) below to be defined:

$$1_k^T=0,T^{T}W=0$$

(4)

The TPSs that satisfy Equation (4) constraints are natural TPSs. Equations (1) versus (4) can be re-written in matrix form as:

$$\left[\begin{array}{ccc}S\hfill & 1_k\hfill & T\hfill \\ \multicolumn{1}{c}{1_k^T}& 0\hfill & 0\hfill \\ \multicolumn{1}{c}{T^T}& 0\hfill & 0\hfill \end{array}\right]\left[\begin{array}{c}W\hfill \\ \multicolumn{1}{c}{c^T}\\ \multicolumn{1}{c}{A^T}\end{array}\right]=\left[\begin{array}{c}Y\hfill \\ \multicolumn{1}{c}{0}\\ \multicolumn{1}{c}{0}\end{array}\right]$$

(5)

where $(S{)}_{\mathrm{ij}}=\sigma (t_i-t_j)$ 1 _k is the k-vector of ones. The matrix is given as:

$$\mathrm{\Gamma }=\left[\begin{array}{ccc}S\hfill & 1_k\hfill & T\hfill \\ \multicolumn{1}{c}{1_k^T}& 0\hfill & 0\hfill \\ \multicolumn{1}{c}{T^T}& 0\hfill & 0\hfill \end{array}\right]$$

It is a symmetric positive definite, so the inverse exists, provided the inverse of S exists.

$$\left[\begin{array}{c}W\hfill \\ \multicolumn{1}{c}{c^T}\\ \multicolumn{1}{c}{A^T}\end{array}\right]={\mathrm{\Gamma }}^{-1}\left[\begin{array}{c}Y\hfill \\ \multicolumn{1}{c}{0}\\ \multicolumn{1}{c}{0}\end{array}\right]$$

Hence, writing the partition of Γ⁻¹ as:

$${\mathrm{\Gamma }}^{-1}=\left[\begin{array}{cc}{\mathrm{\Gamma }}^{11}\hfill & {\mathrm{\Gamma }}^{12}\hfill \\ \multicolumn{1}{c}{{\mathrm{\Gamma }}^{21}}& {\mathrm{\Gamma }}^{22}\hfill \end{array}\right]$$

where Γ ¹¹ is k×k, it follows that:

$$\begin{array}{c}\multicolumn{1}{c}{W={\mathrm{\Gamma }}^{11}Y}\\ \multicolumn{1}{c}{\left[\begin{array}{c}{c}^T\hfill \\ \multicolumn{1}{c}{A^T}\end{array}\right]=\left[\begin{array}{cc}{\hat{\beta }}_1,\hfill & {\hat{\beta }}_2\hfill \end{array}\right]={\mathrm{\Gamma }}^{21}Y}\end{array}$$

(6)

Giving the parameter values for the mapping. If S^–1 exists, then we have:

$$\begin{array}{c}{\mathrm{\Gamma }}^{11}=S^{-1}-S^{-1}Q{\left(Q^T{S}^{-1}Q\right)}^{-1}{Q}^T{S}^{-1},\hfill \\ {\mathrm{\Gamma }}^{12}={\left(Q^T{S}^{-1}Q\right)}^{-1}{Q}^T{S}^{-1}={\left({\mathrm{\Gamma }}^{21}\right)}^T,\hfill \\ {\mathrm{\Gamma }}^{22}={\left(Q^T{S}^{-1}Q\right)}^{-1}\hfill \end{array}$$

(7)

where $Q=[1_k,T]$ . The k×k matrix B_e, called the bending energy matrix, was:

$$B_e={\mathrm{\Gamma }}^{11},$$

(8)

There are constraints on the bending energy matrix:

$$1_k^T{B}_e=0,T^T{B}_e=0$$

Thus, the rank of the bending energy matrix is k – 3.

It can be proved that the transformation of Equation (5) minimizes the total bending energy of all possible interpolating functions mapping from T to Y, where the total bending energy is given by:

$$J\left(\phi \right)=\sum _{j=1}^2{\int {\int }_{R^2}{\left(\frac{{\partial }^2{\phi }_j}{\partial x^2}\right)}^2+2\left(\frac{{\partial }^2{\phi }_j}{\partial x\partial y}\right)}^2+{\left(\frac{{\partial }^2{\phi }_j}{\partial y^2}\right)}^2\mathrm{d}x\mathrm{d}y$$

(9)

As a physical model, this idealization incorporates several assumptions, such as zero energy cost for in-plane deformations. ²⁵

A simple proof is given by Maria and Dryden. ²⁶ The minimized total bending energy is given by:

$$J\left(\phi \right)=\mathrm{trace}\left(W^T\mathrm{SW}\right)=\mathrm{trace}\left(Y^T{\mathrm{\Gamma }}^{11}Y\right)$$

(10)

Hence, the minimum bending property of the TPS is highly suitable for many applications. The TPS is also popular because of the simple analytical solution. ²³

Expansion factors are computed using the Jacobian of the warp. ²⁵ For this purpose, weights were dropped first on the plain clay ground without fabrics and then on the fabric plies placed on the clay ground. The places of landmarks of deformation caused by weights dropped on the plain ground change due to the drop tests being done with fabric plies.

Results and Discussion

Drop Test and Determination of Deformation at the Impact point Along X and Y Planes

Dropping tests were repeated for every sample four times, and landmarks were marked by photographing the deformation shape that occurred on the clay. Mean shapes were constructed from the average values of the landmarks that express the shape. The deformation that occurred due to the drop tests done without fabric and with a weight with an A-type tip profile can be seen in Figure 3. Deformation shapes that occurred as a result of the drop test done with six plies of fabric and weights with C- and A-type tip profiles can be seen in Figure 4. As seen in the figures, in drop tests done with fabric, the form of the depression on clay changes. In Figure 4, the inner diameters show the diameter of the depression caused by the impact energy generated by the dropped weight, and the outer diameter shows the propagation area of the impact energy. In other words, the inner diameter shows deformation generated by the energy that fabric layers cannot dampen and that passes beyond them; the outer diameter shows the deformation formed by the energy that fabric layers absorb by propagating it in themselves. Deformation in the inner diameter is precisely circular, and the outer diameter has an elliptic cross-section, not circular. The parts in the outer diameter and the shown region where the energy intensifies are in the directions of 0° and 90°; the deformation in other directions is less. The largeness of the outer diameter shows that energy has propagated to a larger area and has been damped more. If the energy is propagated over a larger area or the outer diameter gets larger, then the inner diameter is expected to be of the same degree. Tables 2 and 3 show the changes in inner and outer diameter measurements in millimeters concerning several fabric layers and tip profiles.

Figure 3.

The deformation shape was caused by weight dropped on clay and four landmarks mark this shape.

Figure 4.

The four labeled landmarks are: (a) type-C, six-ply fabric and (b) type-A, six-ply fabric.

Table 2.

The change in radius of the depression on the impact point concerning weight tip type and number of fabric plies (mm).

Tip type	Fabric ply number
	0	1	2	4	6	8
A	27.57	26.26	21.95	21.33	22.50	22.40
B	27.46	26.13	25.26	25.21	23.59	20.02
C	23.73	22.38	22.15	22.50	22.33	21.60

Table 3.

The change in the outer radius of the depression on the impact point on the X and Y axes concerning weight tip type and number of fabric plies (mm).

Tip type	Fabric ply number
	1		2		4		6		8
	X	Y	X	Y	X	Y	X	Y	X	Y
A	31.67	32.63	32.48	34.14	33.47	37.62	38.95	39.39	39.94	38.36
B	35.72	35.20	32.34	36.73	20.80	20.66	41.05	40.52	38.67	39.15
C	38.54	43.69	39.99	44.06	46.03	49.72	42.57	48.79	46.74	58.71

When Table 2 is analyzed, the radius of the depression caused by weight with a round tip on the impact point did not show a significant change when one ply of fabric was used, but when two, four, six, and eight pieces of fabric were used, it decreased by approximately 5 mm on average. With a moderately sharp B-type weight, the radius of the depression generated on the impact point did not show a significant change with one, two, and four plies of fabric; however, it decreased significantly with six and eight plies of fabric. In the weight with a sharp tip, no significant change was observed in the radius of the depression. In this case, as the sharpness of the tip increased, the radius of the generated depression showed less decrease with an increase in the number of fabric plies, or more plies of fabric were needed to decrease the radius of the depression.

Figure 4 shows the depression formed at the impact point and the outer diameter generated by the propagated energy. The geometry of the outer diameter is not exactly circular. It has an elliptic form, and its measurements in the X and Y directions differ. Table 3 shows the outer diameter change generated on the impact point in the X and Y directions. When Table 3 is examined, it is seen that as the number of fabric plies increases, the outer diameter of the trauma at the impact point increases, meaning the energy is propagated over a broader area. When evaluated in terms of ballistic impact between the inner and outer diameters, the extension of this region means more more energy damping and decreased trauma effect.

In woven fabrics, energy dissipation and deformation are carried out through threads in the X and Y directions. Figure 4 shows this clearly. However, as the number of fabric layers increases (see Figure 4(b)), it is observed that the energy dissipation is again through the threads. This shows that increasing the number of layers creates a synergistic effect regarding energy absorption. In a quasi-isotropic multi-ply construction, the number of yarn directions representing the degree of quasi-isotropy is directly related to the ply number.

These results are compatible with similar studies in the literature.^21,27 Zhou et al. ²⁷ extensively investigated how thread directions affect energy dissipation in the face of ballistic impact. This study examined the effect of quasi-isotropic structures on the ballistic performance and mechanisms of para-aramid/epoxy composites through a validated FE model. It revealed that quasi-isotropic structures are more energy-absorbing than orthotropic structures. This healing effect is more pronounced for composites with increasing ply numbers. In the case of para-aramid/epoxy composites, increased energy absorption of at least 3.6% was produced as the structure changed from orthotropic to quasi-isotropic. This magnitude can be more pronounced and reaches 8.9% as the yarn directions increase. This improved effect is due to the contact feature of the angled plies, which contain more material for energy absorption. However, the sensitivity decreased as the yarn direction increased, resulting in a composite panel with evenly distributed yarns that did not exhibit quasi-isotropic properties. This indicates that the composite with the most yarn direction may absorb less energy. Figure 5 shows the energy dissipation stages of quasi-isotropic and orthotropic structures.

Figure 5.

Illustrations of deformation areas of woven fabric reinforced composites: (a) Orthotropic composite, (b) quasi-isotropic composite with few yarn directions, and (c) quasi-isotropic composite with massive yarn directions. ²⁷

Deformation on the impact point has specific dimensions in the X and Y directions and certain dimensions in the Z direction. This matter will be researched with the 3D TPS method.

The Determination of Bending Energy and Expansion Factors

The shape and dimensions of the deformation along the X and Y axes are determined above. The energy propagation behavior in the direction of the X and Y axes is determined with expansion factors based on this deformation. For this purpose, the differences between shape deformations obtained by drop tests are analyzed using the TPS method. Bending energies are calculated using a program written under MATLAB 7.0 software using Equation (10). The results are given in Table 4.

Table 4.

Bending energy values obtained with respect to the number of fabric plies and tip profiles.

Tip type	Fabric ply number
	1	2	4	6	8
A-type	2.966	2.936	2.934	2.932	2.932
B-type	2.919	2.956	2.942	2.999	2.923
C-type	2.901	2.903	2.901	2.916	2.908

When the data in Table 4 are analyzed, calculations yield that the shape change generated on the XY plane is made by approximately 2.9 bending energy for all tip types. The B-type tip profile provides the maximum bending energy values. However, there are obvious differences in shape deformation in the Z direction, and this subject will be researched using the 3D TPS method.

Expansion factors, which measure the expansions that occur around selected landmarks, are calculated according to the Jacobian of warps. For this purpose, the sites of landmarks of deformation caused by the weight dropped on the plain ground change for drop tests done with fabric plies. These local expansions are given in Tables 5–7. Figure 6, an example of this subject, shows the shape deformations after dropping tests with type-B weight on plain clay ground and eight plies of fabric.

Table 5.

Expansion factors for A-type tip at the landmarks shown numerically.

Fabric ply number	Y-axis		X-axis
	1. Landmark	3. Landmark	2. Landmark	4. Landmark
1	0.984	0.988	0.944	1.045
2	0.975	0.997	0.988	1.012
4	1.032	0.966	0.995	1.005
6	1.008	0.988	0.987	1.012
8	1.008	0.988	0.987	1.012

Table 6.

Expansion factors for type tip at the landmarks shown numerically.

Axis	Y-axis		X-axis
Fabric ply number	1. Landmark	3. Landmark	2. Landmark	4. Landmark
1	1.007	0.978	0.980	1.001
2	0.951	1.010	0.999	0.932
4	1.006	0.968	1.007	0.942
6	1.009	0.987	1.011	0.984
8	0.988	0.991	1.006	0.940

Table 7.

Expansion factors for C-type tip at the landmarks shown numerically.

Axis	Y-axis		X-axis
Fabric ply number	1. Landmark	3. Landmark	2. Landmark	4. Landmark
1	0.964	1.032	0.993	1.001
2	1.009	0.987	1.011	0.984
4	0.898	1.034	0.913	0.981
6	1.009	0.984	1.039	0.960
8	1.025	0.958	1.047	0.946

Figure 6.

The expansion factor option will display the area expansion factor around each landmark in yellow numbers, indicating the degree of local growth.

When Table 5 is analyzed, for the weight with the A-type tip profile, the expansion factor values around first and fourth landmarks on the deformation generated with four, six, and eight plies of fabric are larger than 1, and the expansion factors that measure the expansions on other landmarks are around 0.9. In shape deformations generated with one and two plies of fabric, expansion in the fourth landmark is larger than that for the other landmarks. These expansion factors show the fabric’s directions and amounts of energy propagation.

When Table 6 is analyzed, for the weights with a B-type tip profile, expansion factors around first and second landmarks on the shape formed by deformation with four and six plies of fabric, those on the fourth landmark on the shape generated with one ply of fabric and expansion factors on the third landmark on the shape generated with two plies of fabric are larger than 1. The expansion factors that measure the expansion on other landmarks are around 0.9.

When Table 7 is analyzed, for weight with C-type profile, expansion factors around the first and second landmarks on the shape generated with two, six, and eight plies of fabric and those around the third and fourth landmarks on the shape generated with one ply of fabric are larger than 1. Expansion factors that measure expansion on other landmarks are around 0.9.

It was established that the expansions around the first and second landmarks on the shape generated with four and six plies of fabric are almost identical for the B-type tip profile. It was observed that the shapes formed with one and two pieces of fabric for the B-type tip profile and those formed with one ply of fabric for the bullet with a sharp tip are the same around the fourth landmark.

Changes in landmarks with respect to fabric ply number and tip profile can be seen in Figures 7 and 8. When Figure 7 is analyzed, it is seen that expansion factors of the first landmark increase when six and eight pieces of fabric are used. This situation tells us that energy is propagated toward the Y-axis. The expansion factor of the second landmark of the same shape increases when eight plies of fabric are used. This means that the energy propagates in the direction of the X-axis. However, it is seen that the third landmark belongs to the Y-axis and the second landmark belongs to the X-axis, a decrease in relation to the fabric ply number. In this case, it can be said that as the fabric ply number increases, the energy propagates in the direction of the X- and Y-axes; however, on the X- and Y-axes, it does not propagate equally in 180° directions on each axis.

Figure 7.

The change in expansion factors with respect to fabric ply number.

Figure 8.

The changes in expansion factors with respect to tip type (for the X-axis, 1: type-A, 2: type-B, 3: type-C).

When Figure 8 is analyzed, it can be deduced that the expansion factors decrease as the tip forms get thinner. In this case, the fabric’s capability of propagating energy on the plane decreases in structures with sharp tips, and deformation in the Z-direction increases with the tip profile. This situation will be researched using the 3D TPS method.

As a result of the drop tests, when the deformations are examined, it is seen that energy is distributed mainly along X- and Y-axes in the 0° and ±90° directions (see Figure 4). In this case, we can say that the energy is propagated along the fabric plane in the direction of the warp and weft fibers. In this case, making the fiber orientation in the structure in ±45° directions in addition to 0° and ±90° can increase the energy’s propagation branches, and in this way, the diameter of the depression formed on the impact point, meaning the amount of energy that intensifies on a specific point, can be decreased.

The deformation that occurs after impact depends on different parameters. Here, fiber direction is the primary parameter. Energy dissipation or absorption occurs depending on the direction of the fiber. In this case, using different fiber directions to bring together fabric layers to protect against impact increases the number of directions in which the energy spreads. However, in this case, the difference in the number of fibers in each layer also reduces the synergistic effect of fibers in the same direction. These two situations negatively affect each other, and a balance must be struck between them.

Similarly, the effect of tip form on energy dissipation was observed. Figure 9, type-A, Figure 10, type B, and Figure 11 show the deformations that occurred in the tests performed with the type C tip. In these figures, a, b, c, and d show the tests performed on two, four, six, and eight-layer samples. Accordingly, in the tests performed with the type-A tip, the area where the energy spreads in the diagonal directions increases as the number of fabric layers increases. It is seen that the energy radiates in only four directions in the two-layer fabric but is radiated in a hexagonal form when an eight-layer sample is used.

Figure 9.

Geometry and schematic illustrations of the deformation obtained with the: (a) two-, (b) four-, (c) six-, and (d) eight-layer samples in the tests performed with the type-A tip.

Figure 10.

Geometry and schematic illustrations of the deformation obtained with the: (a) two-, (b) four-, (c) six-, and (d) eight-layer samples in the tests performed with the type-B tip.

Figure 11.

Geometry and schematic illustrations of the deformation obtained with the: (a) two-, (b) four-, (c) six-, and (d) eight-layer samples in the tests performed with the type-C tip.

Similarly, in the tests performed with the type-B tip, the energy radiated in only four directions in the two-layer fabric but in the octagonal geometry in the eight-layer sample. Similarly, if a type-C tip is used, the spread starts in four directions in the two-layer fabric and spreads in a polygonal geometry in the eight-layer sample. The circular section depression in the middle of all three ends becomes smaller, and its depth decreases as the number of fabric layers increases.

Similar deformation and fiber direction-dependent energy dissipation were also observed in tests performed on composite samples in our previous study. ¹¹ In these tests, it was observed that the energy dissipation directions increased depending on the fiber direction in the sample (see Figure 12). All these results are compatible with the literature. ²⁷

Figure 12.

Schematic representation of the deformation and energy dissipation directions occurring after low-speed impact in aramid plates with (a) unidirectional, (b) bidirectional, (c and d) multi-directional fiber directions. ¹¹

It is also seen that the change in the expansion factor is closely related to the sample deformation. For this reason, it is possible to use expansion factor values in modeling aramid and UHMWPE plates against impact. It can be thought that a ballistic impact causes a different deformation than a low-velocity impact. However, Figure 13 shows the deformations occurring on the sample under low-velocity and ballistic impact from this study. Accordingly, the deformations occurring under low-speed and ballistic impacts are similar. It was observed that a two-zone energy distribution occurred only with the ballistic impact. Here, the first area (blue region) is the trauma area. The second area (green region) is where the energy spreads and is entirely compatible with the data obtained in our study. Therefore, using the expansion factor values obtained under ballistic impact conditions is possible.

Figure 13.

Deformation and illustration of aramid fabrics and composite plates (b) ¹¹ under (a) low-speed and (c) ballistic impact. ⁸

Conclusion

In this study, the energy propagation behavior of para-aramid fabric plies on impact point has been researched with drop tests, and the following results have been obtained:

• The deformation area on the impact point is separated into two zones, namely, energy fabric plies pass behind, and energy absorbed by fabric plies propagating on themselves. The energy that the fabric passes to the rear side causes a deformation with a certain height and diameter, and this region is where the diameter is small and the depth is large. The deformation in this region has a circular form. The deformation in the energy’s propagation area spans a larger area with a smaller depth. This region has an elliptic shape, not exactly circular.

• With the diameter of the deformation caused by the energy passing behind decreases the increase in the number of fabric plies. As the fabric ply number increases, the diameter of the area of fabric plies propagates, and the energy also increases.

• The tip types of the weights used in drop tests also affect the deformation caused by the energy passing behind the fabric plies and the energy propagated by fabric plies. As the tip sharpness of the weights increases, the radius of the depression caused by the energy passing behind decreases with an increase in fabric ply number, or more fabric plies are needed to decrease the radius of the depression.

• Most energy propagates in the X and Y directions in the region, as displayed by the outer diameter. The largeness of the outer diameter shows that the energy propagates on a larger area and is damped more.

• Propagation of the energy in the X and Y directions is not in equal amounts, and in addition, it was observed that energy does not propagate equally in 180º directions on both X and Y axes.

• Energy is propagated in the direction of warp and weft fibers along the fabric plane. In this case, making the fiber orientation in the structure in ±45° directions in addition to 0° and ±90° can increase the energy’s propagation branches, and in this way, the diameter of the depression formed on the impact point, meaning the amount of energy that intensifies on a specific point, can be decreased.