Interlayer Friction Mechanism and Scale Effects in Ultra-Thin TA1 Titanium Alloy/Carbon Fiber-Reinforced Plastic Laminates

Abstract

Fiber metal laminates (FMLs) are a novel lightweight composite material, predominantly utilized in the aerospace sector for large-scale components like skin panels and fuselages. However, research on FMLs in the microsystem domain remains limited. Additionally, they are influenced by scale effects, rendering macroscopic forming theories inadequate for microforming applications. The application of ultra-thin fiber metal laminates in the microsystem field is hindered by this constraint. This paper investigates the friction performance of ultra-thin TA1 titanium alloy/carbon fiber-reinforced plastic (CFRP) laminates at the microscale. The content of the epoxy resin used is 38.0 ± 3.0%. Friction tests on ultra-thin TA1/CFRP laminates were conducted based on the Striebeck friction theory model. The effects of factors such as the weaving method, ply angle, normal force, tensile speed, and temperature on friction performance are explored in the study. Furthermore, the influences of geometric scale and grain scale on friction performance are examined. Geometric scale effects indicate that an increase in laminate width leads to an increase in the friction coefficient. Grain-scale effects demonstrate that as grain size increases, the friction coefficient also increases, attributed to reduced grain boundaries, increased twinning, and increased surface roughness of the metal. Finally, surface morphology analysis of the metal and fiber after friction tests further confirms the influence of grain size on the friction coefficient. Through detailed experimental design, result analysis and graphical representation, this paper provides a scientific basis for understanding and predicting the friction behavior of ultra-thin TA1/CFRP laminates.

1. Introduction

With the continuous advancement in high-end applications such as aerospace, the demand for product and component performance has escalated. Traditional homogeneous materials like metals struggle to meet both structural and performance requirements simultaneously. Composite materials, owing to their unique strength-to-weight ratio and superior physical properties, play a crucial role in today’s aerospace manufacturing sector. Fiber metal laminates (FMLs) represent a novel class of hybrid materials. They consist of alternating laminates of thin metal sheets and fiber-reinforced prepreg, which are subsequently cured under heat and pressure according to the prepreg’s curing curve. This distinctive structure imbues FMLs with exceptional resistance to moisture, impact, corrosion, excellent flame retardancy, high damage tolerance, and lightweight properties [1,2,3,4,5]. Additionally, optimizing laminate design can be achieved by varying the thickness of metal and prepreg, the weaving pattern of fibers in the prepreg, and the stacking angle and structure between metal and prepreg laminates [6,7,8,9,10]. As a result, FMLs find extensive applications in aerospace and automotive industries, becoming one of the primary materials for critical components like aircraft fuselages, fairings, and skins.

Microforming is a technique that directly applies plastic deformation to materials. With the increasing demand for miniature parts, the field of microforming has attracted widespread attention [11,12,13]. Micro-scale components refer to components whose overall size or a characteristic size is less than 1 mm [14]. Microforming includes two main directions: volume microforming (micro extrusion, micro forging, micro stamping, etc.) and sheet metal microforming (micro blanking, micro drawing, micro bending, etc.) [15,16,17,18]. The application prospect of plastic volume microforming is broad, and miniature parts such as screws can be manufactured using wire cutting processes [19,20]. The challenge lies in that, influenced by the scale effect, traditional macroscopic forming theories cannot be completely scaled down and applied to the microforming field [21,22,23,24]. The mechanical properties and failure mechanisms of materials in the microforming field are more complex than in the macroscopic field [25,26,27,28]. The scale effects in the microforming field can be divided into three categories: geometric scale effect (the thinness of metal parts leads to premature necking during the forming process), friction scale effect (the reduction in contact area between the material and the mold increases the coefficient of friction [29,30]), and grain-scale effect (the increase in grain size, the reduction in micro-pores on the material surface, and the decrease in tensile strength and fracture elongation rate). Due to the complex mechanisms of scale effects and the influence of multiple factors, it has become a hot topic widely studied by scholars around the world [31,32,33].

Ultra-thin titanium alloy/carbon fiber-reinforced plastic (TA1/CFRP) laminates exhibit excellent corrosion resistance, fatigue resistance, and impact resistance, making them highly promising for applications in microelectromechanical systems (MEMSs) and microsystems. Therefore, research on ultra-thin TA1/CFRP laminates is of significant importance. Chan et al. [34] investigated the grain-scale effect by selecting pure copper as the material and conducting micro-compression experiments to study the influence of grain size on material deformation, utilizing a normal distribution to simulate scattering effects. Xu et al. [35] conducted forming limit tests based on two miniaturized Holmberg and Marciniak experiments to evaluate the forming performance of metal sheets under different conditions. Both physical experiments and finite element simulations revealed significant scale effects; the forming limit curve shifted downward as the ratio of thickness to grain size decreased. Simulation results were also experimentally validated. Additionally, when the ratio of thickness to grain size was 2 or less, highly scattered ultimate strain results were observed in experiments, with strain localization tending to occur at the beginning of deformation. Wang et al. [36] studied the influence of geometric scale effects on material forming performance, investigating the rupture positions of circular dome with different depths of draw diameters. The results showed that as the die diameter feature/sample size decreased to near the grain size, the data became more dispersed. Meng et al. [37] conducted tensile tests on pure copper plates with different thicknesses and similar microstructures. Experimental results demonstrated that as the ratio of specimen thickness to grain size decreased, the flow stress, fracture stress, strain, and the number of micro-pores on the fracture surface gradually decreased.

This study investigates the interlaminar friction performance of ultra-thin TA1/CFRP laminates at the interfaces through interlaminar friction tests. Additionally, it explores the friction performance of the boundary laminate of ultra-thin TA1/CFRP laminates through interlaminar friction tests. Factors examined include the weave and fiber orientation of the prepreg, tensile speed, pre-tightening normal force, and tensile strength. The effects of prepreg structure and fiber orientation, tensile speed, pre-tensioning force, and tensile temperature on static and dynamic friction coefficients were studied. A set of friction test fixtures was designed and installed on a quasi-static tensile testing machine to explore the interlaminar friction performance of ultra-thin TA1/CFRP laminates. The influence of factors such as fiber weave pattern, ply angle, tensile speed, normal force, and test temperature on the interlaminar friction performance of laminates was investigated. Specimens were designed with various size ratios to study the effects of geometric scale effects on laminate tensile deformation behavior and interlaminar friction performance. The grain size of TA1 was altered for uniaxial tensile tests to study the influence of grain-scale effects on tensile deformation behavior, and interlaminar friction tests were conducted to investigate the effect of grain-scale effects on friction performance.

2. Friction Theory Models and Experimental Design

2.1. The Friction Theory Model

Stribeck developed a model for describing various types of frictional performance in tribology, which encompasses the interplay of sliding velocity, normal force, and lubricant viscosity. Experimental findings suggest that at lower sliding velocities, the dominance of surface roughness at the contact interface leads to higher friction coefficients (referred to as boundary lubrication). Conversely, at higher sliding velocities, the influence of fluid hydrodynamic pressure dominates the normal force, resulting in lower friction coefficients (known as fluid dynamic friction). The Stribeck curve characterizes the relationship between the friction coefficient (μ) and the Hersey number, also referred to as the Stribeck number. The Hersey number is a normalized function of viscosity (η), sliding velocity (v), and normal force (F_N). This curve offers a qualitative explanation of the impact of processing parameters such as normal force, sliding velocity, and lubricant viscosity on friction coefficients.

$$H={\displaystyle \frac{\eta \nu }{F_N}}$$

(1)

where $H$ represents the Hersey number, also known as the Stribeck number, $\eta$, $\nu$, and $F_N$ represent viscosity, velocity, and normal force.

The standard Stribeck curve illustrates three lubrication regimes based on frictional performance. The first region is primarily influenced by boundary lubrication, where the fluid film is negligible and frictional effects can be regarded as Coulomb friction. The second region corresponds to elastohydrodynamic friction, also known as mixed lubrication friction. As the lubrication film thickens, the frictional behavior gradually transitions into the third region of hydrodynamic (full-film) lubrication. In this area, the contact surfaces are completely separated by the fluid film, and the friction coefficient increases with the growing thickness of the lubrication film. Chow et al. [38] based on testing results, proposed an analytical model for assessing the frictional performance of glass–polypropylene fabric between adhesive and mold surfaces. By combining the Coulomb friction and hydrodynamic friction models, the study predicted friction coefficients suitable for numerical simulations under varying processing conditions. The research demonstrated the existence of a transitional region between these two frictional behaviors, substantiating the applicability of various experimental parameter combinations that align with the corresponding relationships of the Stribeck curve.

Due to the fact that the friction coefficient remains the same within specific surfaces having equal Hersey numbers, as per Equation (1), it is feasible to achieve identical Hersey numbers under constant viscosity by controlling the normal force and sliding velocity, consequently regulating the friction coefficient. Hence, in interactions between specific surfaces with equal Hersey numbers, the friction coefficients are expected to be equivalent. In this study, considering the clamping device encompasses two frictional surfaces—those of the top and bottom titanium alloy plates—coefficient 2 is included in the denominator of Coulomb’s law. Therefore, Formula (2) is employed for calculating the friction coefficient.

$$\mu ={\displaystyle \frac{f}{2F_N}}$$

(2)

where $\mu$ represents the friction coefficient, and $f$ represents friction.

2.2. Design of Friction Tests for Ultra-Thin TA1/CFRP Laminates

Friction tests using a DK-20 KN microcomputer-controlled electronic universal testing machine were carried out, with a maximum range of 0–20 KN, wedge tensile fixture maximum working tensile force of 20 KN, maximum range of 0–20 KN and wedge tensile fixture maximum working tensile force of 20 KN.

The metal layer was TA1 with a thickness of 0.04 mm, and the carbon fiber prepreg was GXC120-10 T/200-2/2-3 k with a thickness of 0.2 ± 0.02 mm, sourced from Composites eShop (Beijing) Technology Col., Beijing, China. To investigate the influence of the weaving method of the prepreg on frictional performance, two weave methods, namely plain weave and twill weave, were chosen for the carbon fiber prepreg in this study. Figure 1a illustrates the plain weave method of the prepreg along with cross-sectional views before and after compression, while Figure 1b depicts the twill weave method of the prepreg and its cross-sectional views before and after compression.

The schematic diagram of the friction specimens is presented in Figure 1c. These specimens consist of a 3 + 2 ply configuration of fiber metal laminates. The fixed end of the specimen is clamped by the gripping jaws of the tension machine at a distance of 20 mm, while the stretching end is held by the upper gripping jaws, also at a distance of 20 mm. To conduct interlayer friction tests [39], a specialized set of experimental fixtures was devised to apply and control the normal force. Once the mold assembly was completed, it was positioned and secured onto the tension machine, as illustrated in Figure 1d.

For the purpose of systematic documentation and categorization, a numbering system was applied to the test samples in this study. For example, “P-0–20 °C-30 N-3 mm/min” signifies a prepreg with a plain weave method, an angle of 0°, tested at a temperature of 20 °C, under a normal pressure of 30 N, and a drawing speed of 3 mm/min. Figure 1e represents the load displacement curve numbered X-0–20 °C-30 N-3 mm/min, and most of the other tests exhibit a similar trend as depicted in Figure 1e.

2.3. Friction Prediction Model

This paper investigates the influence of two friction states, dynamic and static, by different test parameters. Static friction occurs when the surfaces of the interlayer components of a composite material are in contact and have a tendency to slide relative to each other, but remain relatively stationary, i.e., the metal layer is not pulled from the fibre layer. When the metal layer and the fibre layer have undergone relative sliding, this is denoted as the dynamic friction state.

The establishment of a friction prediction model involves designing distinct experimental control groups based on varying Hersey numbers. This approach is undertaken to systematically investigate the impact of diverse parameters on friction tests conducted on ultra-thin TA1/CFRP laminates, as delineated in

Table 1. Test conditions of Hercynian number at room temperature (η₀ ≈ 10⁴ Pa·s).

Hersey Number/(m−1)	Drawing Speed/(mm/min)	Normal Force/(N)
0.556 × 10−2	1	30
1.667 × 10−2	3	30
3.333 × 10−2	6	30
5.0 × 10−2	9	30
6.0 × 10−2	9	25
7.5 × 10−2	9	20
1.0 × 10−1	3	5

.

In order to establish the suitability of the Stribeck curve in the context of this study, experiments were conducted to examine the influences of normal force and sliding velocity on the friction coefficient. Through fitting these experimental results, it was determined that the Hersey numbers governing the study of friction coefficients under ambient temperature conditions fall within the hydrodynamic lubrication regime depicted by the Stribeck curve. This regime takes on an exponential functional form and exhibits a positively sloped pattern similar to the trends observed in the experimental data, as demonstrated in Figure 2. Given the exponential correlation between the friction coefficient and Hersey number, in order to deduce a predictive equation for the friction coefficient, an assumption is made that the constant terms of the exponential function are coefficients $A$, $B$, $C$.

$$\mu =A{e}^{BH}+C$$

(3)

By employing Equation (3) and substituting the experimental relationships among static friction coefficient, dynamic friction coefficient, and Hersey number, theoretical analytical expressions for static and dynamic friction coefficients in terms of Hersey number can be derived, as represented by Equations (4) and (5). When the Hersey number is known, the theoretical analytical expressions can be utilized to predict the friction coefficients.

$$\mu =1.28592e^{19.94164H}$$

(4)

$$\mu =0.8279e^{9.976977H}$$

(5)

2.4. Scale Effects of Ultra-Thin TA1/CFRP Laminates

To explore the influence of geometric scale effects on material properties, three different scaled specimens were designed as shown in Figure 3e, with dimensions scaled proportionally in terms of gauge length and width: 150 mm and 75 mm (n = 1); 50 mm and 30 mm (n = 1/2); 15 mm and 10 mm (n = 1/3). Two types of interlaminar constraints, curing and low constraint, were employed for the laminates. Other conditions remained constant, with a tensile speed is 3 mm/min, and a testing temperature of 20 °C.

To investigate the effect of grain size scale on the performance of fiber metal laminates, thermal treatments were applied to 40 μm thick TA1 metal sheets at different temperatures, as outlined in

Table 2. TA1 heat treatment process.

Material	Heat Treatment Temperature/(℃)	Heat Treatment Process	Heating Speed/(℃/min)	Holding Time/(h)	Cooling Method
TA1	400	Vacuum heat treatment	5	1	Furnace cooling
TA1	500	Vacuum heat treatment	5	1	Furnace cooling
TA1	600	Vacuum heat treatment	5	1	Furnace cooling

. The microstructures of TA1 at various heat treatment temperatures are shown in Figure 3a–d. After the thermal treatments, TA1/CFRP laminates were prepared, and the grain sizes of TA1 and the compositions of each group of laminates are presented in

Table 3. Thickness and grain size of each laminate of TA1/CFRP laminate.

Laminated Structure	Fiber Structure/(°)	Laminate Thickness/(mm)	Heat Treatment Temperature/(℃)	Metal Grain Size/(μm)
2 + 1	0	317	Unannealed	4
2 + 1	0	317	400	5
2 + 1	0	317	500	8
2 + 1	0	317	600	10

. The grain sizes were measured using the line-intercept method.

3. Results and Discussion

3.1. Influence of Strain Rate on Friction

To investigate the influence of drawing speed on friction, experiments were conducted with a constant normal force of 30 N and a temperature of 20 °C. Two different weave methods of prepreg, namely plain weave and twill weave, were selected. Different ply angles were also considered, along with four distinct draw speeds, 1 mm/min, 3 mm/min, 6 mm/min, and 9 mm/min. The obtained results are presented in Figure 3f–h. Figure 3f–h depict the friction coefficient results for various fiber orientations and different drawing speed. Figure 3g,h illustrate the curves for static and dynamic friction coefficients, respectively. The trends indicate that for both plain weave and twill weave prepregs, regardless of the ply angle (0° or 45°), the friction coefficient increases with higher draw speeds. This observation suggests that the frictional behavior is governed by the Newtonian shear stress within the epoxy resin matrix, where shear stress increases with escalating shear rate. It is noteworthy that the friction coefficient of the twill weave prepreg is lower than that of the plain weave prepreg. Moreover, the friction coefficient of the prepreg oriented at 0° is greater than that oriented at 45°. This discrepancy can be attributed to the higher number of intersections between warp and weft yarns in the plain weave prepreg, leading to a rougher surface of the prepreg [40]. This phenomenon is depicted in Figure 3f.

Figure 3f is a schematic diagram of fiber behavior caused by friction between metal plates and fibers. At the intersections of fibers, the contact pressure is significantly higher than the average pressure, resulting in greater frictional forces and subsequently higher friction coefficients. When sliding is about to occur between the metal and fibers, the fibers rotate in the direction of tension due to the frictional forces. Comparatively, twill weave prepreg has fewer intersections between warp and weft yarns, providing better drapeability. Additionally, the rotation of fibers demands less force in the case of twill weave prepreg than plain weave prepreg due to the reduced need for rotation. As a result, plain weave prepreg requires more force to achieve fiber rotation, leading to higher frictional forces and correspondingly elevated friction coefficients. In the case of prepreg oriented at 45°, fibers in the twill weave method are more prone to rotation during the drawing process compared to the 0° oriented prepreg. Consequently, the friction coefficient is lower for the 45° oriented prepreg.

3.2. Influence of Normal Forces on Friction

To investigate the influence of normal forces on friction, experiments were conducted at a constant temperature of 20 °C using the twill weave prepreg with a ply angle of 0°. A drawing speed of 3 mm/min was employed, and four different normal forces (5 N, 10 N, 15 N, and 35 N) were considered. The obtained results are presented in Figure 4a. Figure 4a illustrates the friction force–displacement curves for the twill weave prepreg under different normal forces. Notably, the variations in interlayer friction force and displacement follow similar trends across different normal forces. An interesting observation is that as the normal force increases to 35 N, the metal undergoes necking during the drawing process without experiencing fracture. This indicates that the maximum static friction force at this point has not surpassed the tensile strength of the metal.

As shown in Figure 4b,c, the experimental results for static friction force, dynamic friction force, static friction coefficient, and dynamic friction coefficient are presented for the twill weave prepreg at 20 °C with a ply angle of 0° and a drawing speed of 3 mm/min. It can be observed that while friction force increases with higher normal forces, the friction coefficient decreases with increasing normal forces. This phenomenon arises from the interaction between the enhanced fiber prepreg and the pre-treated titanium alloy plate, where the interface exhibits higher surface roughness at lower normal forces [16]. Although higher normal forces demand greater frictional forces to separate adjacent surfaces, the woven fibers and surface asperities at the contact interface can be flattened as the normal force increases. This results in a reduction in surface roughness and consequently a decrease in the friction coefficient. This phenomenon is schematically illustrated in Figure 4d.

3.3. Influence of Temperature on Friction

To investigate the influence of temperature on friction, experiments were conducted with a constant normal force of 30 N, using the twill weave prepreg with a ply angle of 0°. A drawing speed of 3 mm/min was maintained, and seven different temperatures (20 °C, 30 °C, 40 °C, 50 °C, 60 °C, 70 °C, and 80 °C) were considered. The obtained results are presented in Figure 5.

Figure 5a present a column chart depicting the friction coefficients of the twill weave prepreg with a ply angle of 0° at different tensile temperatures, while maintaining the same drawing speed. An analysis of the results indicates significant differences in friction coefficients between room temperature and elevated temperatures. Both static and dynamic friction coefficients decrease with increasing stretching temperatures. Observing the transition from 20 °C to 30 °C, the static friction coefficient drops by a factor of 6.32, while the dynamic friction coefficient decreases by a factor of 2.35. Further temperature increases have diminishing effects on the friction coefficients. This behavior is attributed to the lower viscosity of the resin at lower temperatures. At these temperatures, the matrix flows along the 0°/90° fiber direction, making it more challenging for the fluid to extrude from the fabric. Consequently, higher forces are required to induce relative sliding between the metal and the prepreg, resulting in higher friction coefficients. As the temperature gradually increases, the resin’s viscosity also increases. This leads to a more uniform distribution of normal pressure, resembling the average pressure over the contact area. With increased resin viscosity, it becomes easier for the resin to extrude from the central region of the prepreg towards the top and bottom interfaces. This extruded resin forms a lubricating resin film at the interface, as depicted in Figure 5b. This resin film enhances lubrication and reduces the friction coefficient.

3.4. The Influence of Geometric Scale Effects on Friction

To investigate the influence of geometric scale effects on friction, a series of experiments were conducted under the conditions of a temperature of 20 °C. The material selected for these experiments was slant-weave pre-impregnated composite (CFRP), with a laminate orientation of 0°. The testing was performed using a consistent pull rate of 3 mm/min. Notably, the width of the laminate specimens was varied to explore three distinct size ratios: 10 mm, 15 mm, and 20 mm. The outcomes of these experiments are depicted in Figure 6a,b.

Figure 6a,b illustrate the static and dynamic friction coefficient curves for the slant-weave pre-impregnated composite (CFRP) with a laminate orientation of 0°, tested at a temperature of 20 °C and under a normal force of 30 N. These results are presented for various combinations of different pull rates and size ratios. Notably, the trends observed show an increase in both static and dynamic friction coefficients as the pull rate and size ratio increase. This observed phenomenon can be attributed to the widening of the laminate’s width dimension while keeping the normal force constant. With larger width dimensions, the contact area between the metal and the pre-impregnated composite increases. Additionally, the cross-intersections of the woven fibers within the laminate become more intricate, as depicted in Figure 6c. Consequently, more force is required to initiate sliding between the laminate laminates, leading to an augmented friction coefficient. For instance, at a pull rate of 3 mm/min, when the width of the laminate increases from 10 mm to 20 mm, the static friction coefficient increases by 201.5%, and the dynamic friction coefficient increases by 122%.

3.5. The Impact of Grain Size Scale Effects on Friction

In order to investigate the influence of grain size scale effects on friction, a series of experiments were conducted at a temperature of 20 °C. The chosen material for these experiments was slant-weave pre-impregnated composite (CFRP), with a laminate orientation of 0°. Specifically, four different grain sizes were selected for testing: 4 μm, 5 μm, 8 μm, and 10 μm. The obtained results are depicted in Figure 7, illustrating the variations in frictional behavior observed across these distinct grain size configurations.

Figure 7a,b illustrate the curves depicting the variation in friction force with displacement and the relationship between friction coefficient and grain size for different grain size configurations. It is evident that as the grain size increases, both the dynamic and static friction coefficients exhibit an increase. This phenomenon can be attributed to the larger grain size, which results in a reduction in grain boundaries. Consequently, it becomes more challenging for dislocations and slip to occur between laminates. Moreover, with the increase in grain size, there is a rise in the presence of twin boundaries, which absorb a portion of the energy generated by the applied load. This energy consumption contributes to an elevation in friction force, leading to a subsequent increase in friction coefficient.

Figure 8 depicts the surface topography of different grain-sized metals after friction testing. In conjunction with the analysis of fiber surface topography post-friction testing as presented in Figure 9, it is discernible that an increase in metal grain size corresponds to an elevated resin adhesion on the metal surface, while concurrently resulting in a reduction in resin adhesion on the fiber surface. This phenomenon can be attributed to the gradual augmentation of metal grain size due to heightened annealing temperatures. However, this alteration in grain size is non-uniform across the material, thereby inducing an overall escalation in metal surface roughness. This escalated surface roughness contributes to the amplification in friction coefficient. Additionally, with the escalated roughness, resin exhibits an augmented propensity to adhere to the metal surface. Consequently, as the grain size of the metal expands, a heightened resin presence is observed on the metal surface, coupled with a diminished presence on the fiber surface.

4. Conclusions

The inter-ply friction coefficient at the metal prepreg interfaces for TA1/CFRP laminates under different sliding parameters has been measured using a designed friction-test apparatus. The influenced sliding parameters were normal force, sliding velocity, temperature, geometric scale effect and grain size scale effects. The main achievements are as follows:

(1)

The way the fibers are woven in the prepreg affects the magnitude of the coefficient of friction between the laminates, with plain weave prepregs having a higher coefficient of friction due to the fact that plain weave prepregs have more interweaving points of the warp and weft yarns. The fibers in prepregs with a 45° lay-up are more easily rotated than prepregs with a 0° lay-up, resulting in a higher coefficient of friction for the 0° lay-up than for the 45° lay-up. This results in a higher coefficient of friction in the 0° direction than in the 45° direction.

(2)

Both the coefficient of static friction and the coefficient of kinetic friction increase with increasing tensile velocity, indicating that the interlaminar friction of the laminates is characterized by Newtonian shear based on the epoxy resin matrix. With other things being equal, the increase in interlaminar friction due to the increase in shear stress with the increase in tensile speed leads to an increase in the coefficient of static and dynamic friction.

(3)

With other things being equal, as the normal pressure increases, the friction increases and the coefficient of friction decreases. This is due to the fact that the interface between the prepreg and the titanium alloy plate has a high surface roughness at low normal force. Although more friction is required to pull the adjacent surfaces apart as the normal force increases, the braided fibers as well as the dimples at the contact interface can be flattened, resulting in a lower surface roughness and hence a lower coefficient of friction.

(4)

The effect of temperature on the coefficient of friction is obvious, and the coefficient of friction at room temperature has a large difference from that after warming up. With the increase in temperature, the friction coefficient decreases gradually. When the test temperature increased from 20 °C to 30 °C, the static friction coefficient decreased by 6.32 times, and the dynamic friction coefficient decreased by 2.35 times. In addition, with the increase in temperature, the effect of temperature on the coefficient of friction will decrease.

(5)

According to the selection of different Hessian numbers for the test, the relationship between Hessian number and static friction coefficient and dynamic friction coefficient was obtained. Combined with the Stribeck curve, the relationship between the static and dynamic friction coefficients and the Hessian number H was obtained by fitting the exponential function, which can be used to predict the static and dynamic friction coefficients.

(6)

The coefficient of static friction and coefficient of kinetic friction increased sequentially with the increase in stretching speed and size scale. The static friction coefficient increased by 201.5% when the geometric size was increased from n = 1 to n = 2 with the direction of 0°, the stretching speed of 3 mm/min, and the temperature of 20 °C. The coefficient of static friction increased by 201.5% and the coefficient of kinetic friction increased by 122% when the geometry was increased from n = 1 to n = 2.

(7)

The coefficient of kinetic friction and coefficient of static friction increase as the grain size increases; this is due to the fact that the grain size increases when the grain boundaries decrease, meaning that it is more difficult to produce dislocations and slips between the laminates, and as the grain size increases, the twinning increases. This is due to the fact that as the grain size increases, the grain boundaries decrease, making it more difficult to create dislocations and slip between the laminates.