Study on the Multi-Directional Static Friction Properties of High Performance Yarns

Yarns commonly used in bullet-proof materials: aramid 14 (Shandong Taihe New Material Co., Ltd.) and UHMWPE yarn (Hunan Zhongtai Chemical Fiber Products Co., Ltd.) were selected for this study, with a fineness of 1180 dtex and 200D, respectively, to measure the static friction coefficient of high-performance yarns.

In this experiment, the slope board method was used to measure the static friction coefficient of high-performance yarns. A total of 20 yarns were laid in parallel in a closed arrangement on a 20 mm×20 mm×20 mm square iron block to slide over a glass inclined plane, as shown in Figure 1.

Fig. 1

A self-designed device was used based on the principle of sliding over an inclined plane for yarn static friction coefficient analysis, as given in Figure 2.

Fig. 2

The basic working process is as follows: the cube iron block with a fixed bottom area was evenly covered with high-performance yarns, and the glass slope was also evenly covered with yarns. The sliding block was placed on the glass slope, and the angle “α”, which was the plane inclination angle, was changed to make the sliding block start to slide. The tangent value at the moment when the sliding block starts to slide gives the static friction coefficient “μ_s”. The test principle is shown in Figure 3.

Fig. 3

The relationship between α and μ_s is as follows. Due to the action of the block gravity G, the block produces a downward force along the inclined plane: (1) G1=G×sinα {{\rm{G}}_1} = {\rm{G}} \times \sin \alpha

Where; G - the gravity of the block [N], G₁ - the downward force along the inclined plane caused by the gravity of the block [N], α - the angle between the inclined and horizontal planes when the block begins to slide.

Gravity causes the block to produce pressure on the inclined plane, that is, the component force of gravity G₂: (2) G2=G×cosα {{\rm{G}}_2} = {\rm{G}} \times \cos \alpha

Where: G₂ is the downward force of the vertical slope caused by the gravity of the block [N].

Due to the effect of G₂, there is friction between the parallel arrangement of high-performance yarn on the surface of the block and the yarn on the inclined plane.

With the increasing angle of the inclined plane, the block begins to slide along the inclined plane, and the instantaneous friction is in balance with the downward force along the inclined plane caused by the gravity of the block; (3) G1=Fs {{\rm{G}}_1} = {{\rm{F}}_{\rm{s}}}

Where F_s is the static friction force between yarns, [N]. Equation 3 can be written as follows: (4) mgsinα=μsmgcosα mgsin\alpha = {\mu _{\rm{s}}}\,{\rm{mg}}\cos \alpha

Where m is the mass of the block, N; and μ_s is the static friction coefficient between the yarns. (5) μs=mgsinα/mgcosα=tanα {\mu _{\rm{s}}} = mgsin\alpha /\,{\rm{mg}}\cos \alpha = \tan \alpha

In order to clearly understand the multi-directional static friction coefficient μ_s of aramid and UHMWPE yarns, the included angles between the yarns were designed as follows: 0°, 15°, 30°, 45°, 60°, 75° and 90°.

Aramid yarn and UHMWPE yarn are the most common reinforcement materials in bullet-proof materials. In the process of bullet penetration, high-performance yarn will break and deviate in the yarn plane, resulting in a change in the angle between yarns. The friction between yarns significantly impacts the bullet-proof performance of materials. On this basis, the influence of the included angle between yarns on the static friction coefficient of high-performance yarn is analysed. The experimental results showed the relationship between the included angle and static friction coefficient (Figure 4).

Fig. 4

The static friction coefficient of yarn under different included angles was measured; with five repetitions of the same test, shown in Figure 4. With the increase of the included angle, the static friction coefficient of the yarn becomes smaller. The static friction coefficient changes gently when the included angle is between 15° and 90°; that is, when the included angle changes from 15° to 90°, the static friction coefficient of the yarn decreases slowly; when the included angle changes from 0° to 15°, the static friction coefficient of the yarn decreases gradually. The results show that the static friction coefficient is largest when the yarns are parallel along the axial direction, which is much higher than the static friction coefficient of the other included angles between the yarns. The main reason for this phenomenon is closely related to the yarns’ contact form and surface roughness. When two yarns are in parallel contact, the contact between them changes from point contact to line contact, and the roughness is also significantly improved. Therefore, when the included angle is 0°, the static frictional coefficient is much higher than for other included angles.

Both aramid and UHMWPE yarns show the same change trend, which indicates that the static friction coefficient of the yarn varies with a change in the included angle between yarns. The static friction coefficient is the largest when parallel friction occurs, and the smallest when vertical friction causes the included angle between yarns to be 90°. It mainly depends on the actual contact area between yarns. When the area is the largest, the number of rough peaks is the largest, and the static frictional coefficient is the largest.

The static friction coefficient of yarn at different angles presents a certain regularity, as shown in Figure 5. With an increasing included angle, the static friction coefficient shows a decreasing trend. According to the overall shape of the trend, it conforms to the exponential function form under specific conditions. Using the Origin nonlinear fitting function to fit the experimental data shows that the relationship between the static frictional coefficient μ_s of aramid and UHMWPE yarn and the yarn angle has the characteristics of a single increase in the inverse function. Therefore, the sigmoidal function is used to analyse the relationship between the static friction coefficient of aramid and UHMWPE yarn. The static friction coefficients of aramid and UHMWPE yarns are in accordance with the following functional relationship when the included angle is in the range of 0 ° to 90 °. (6) y=A1+A2−A11+10(Logx0−x)*p y = {A_1} + {{{A_2} - {A_1}} \over {1 + {{10}^{(Log{x_0} - x)*p}}}}

Fig. 5

Where A₁, A₂, logx₀ and p are the constrained sigmoidal function parameter values, and the exact parameter values of aramid and UHMWPE yarns are shown in Figure 5.

Due to the difference in the material type, spinning process, and yarn fineness, the static friction coefficient of the two kinds of yarns is very different. The results of comparing the static friction coefficient of aramid yarn and UHMWPE yarn are shown in Figure 6. At the same included angle, the static friction coefficient of aramid yarn is much higher than that of UHMWPE yarn, which is increased by more than 50%. Especially, in the case of yarn vertical friction, the static friction coefficient of aramid yarn is 63% higher than that of UHMWPE. Thus, we speculate that the bullet-proof performance of aramid woven fabric reinforced bullet-proof material is higher than that of UHMWPE bullet-proof material under the same surface density. However, the static friction coefficient of aramid yarn is less than 0.3 under vertical friction, which is far less than the requirement of 0.4. When the yarns are in parallel friction, the static frictional coefficient of aramid yarn is higher than 0.4, but in the process of bullet-proof material and bullet penetration, for the high-performance yarn in the woven fabric material it is challenging to reach the state of parallel friction. Therefore, improving the static friction coefficient of bullet-proof material and the static friction coefficient under a certain included angle can effectively enhance the bullet-proof performance of the material.

Fig. 6