Analysis of Mechanical Behavior of Different Needle Tip Shapes During Puncture of Carbon Fiber Fabric


 In the present study, the fiber-bending around the needle during the piercing process of the carbon fabric is investigated. In this regard, a mathematical model is established to investigate the bending elongation of the carbon fiber around the needle and the interaction between the carbon fiber and the needle tip. Then the mechanical behavior of the carbon fabric when moving down the tip of the steel needle is analyzed. Based on the performed analysis, a shape curve equation that satisfies the puncture needle tip is established. Furthermore, the influence of different needle tip shapes on the mechanical behavior of the carbon fiber is analyzed. The performance of the needle tip is subjected to different loads, including the puncture template, horizontal tension of the fiber to the needle tip, frictional resistance between the fiber and the needle tip, sliding force, and the bending moment. The performed analysis shows that when the shape of the needle tip assumes the form of curve 10, the downward force, horizontal tension, friction resistance, sliding force, and bending moment are minimized. Accordingly, curve 10 is proposed as the optimal shape for the needle tip. The present study is expected to provide theoretical guidance for selecting overall puncture process parameters.


Introduction
Recently, integral puncture has been proposed as an innovative processing technique in the production of weaving three-dimensional fabrics. In this technique, laminated carbon fi bers are used to produce a woven fabric and then a steel needle array is applied to puncture the fabric integrally. Then, steel needles are replaced one by one with continuous carbon fi bers to form the desired puncture fabric. Accordingly, a threedimensional carbon fi ber fabric with a special structure is obtained, which has a promising overall structure and a high fi ber volume content. Meanwhile, the produced fabric is an excellent substrate for making high-performance heat-proof and heat-insulating carbon/carbon composite materials. When the tip of the steel needle pierces the carbon fi ber fabric, a series of complex movements and effects appear in the fabric; these originate from the puncture action of the steel needle. Analyzing these movements can improve the overall puncture process, optimize the structure of the carbon fi ber fabric, and improve the puncture performance.
Studies show that during the puncture process of fabrics, pressure and friction are generated between the needle tip and the carbon fabric. Meanwhile, carbon fabric damage and needle tip damage are the main factors affecting the quality of the punctured fabric [1][2][3]. In this regard, scholars established a mechanical model of the steel needle tip in the top bending mode of the woven fabric, solved the corresponding differential equations subjected to appropriate boundary conditions, and calculated the critical pressure of the tip accordingly [4,5]. Based on the analysis of the interaction between the needle and the orthogonal laminated woven fabric, the bending elongation and elongation fracture mode of the fi ber were proposed and the structural parameters affecting the bending elongation of the fi ber were discussed in detail. Moreover, the mechanical model of the steel needle was established and the fi ber-bending and elongation mechanisms during the overall puncture process were analyzed [6][7][8][9]. In order to bend the fi ber around the needle in the overall puncture process, the puncture needle is deformed by the combination of compression and bending loads originating from the yarn tension. Under these circumstances, the needle tip may undergo displacement under the action of the tension and pierce the fabric as a result. Moreover, the wall contact damages the needle tip consequent to the action of the descending puncture template. In some cases, even the overall puncture may fail because of this phenomenon. In this regard, a mechanical model of the steel puncture needle, which is bent by the fi ber, was established [10-13]. Moreover, the effects of needle punching position and the fabric thickness on the needle resistance are studied empirically. Recently, a numerical simulation based on the concept of virtual fi ber has been proposed to establish geometric models of two-

Abstract:
In the present study, the fi ber-bending around the needle during the piercing process of the carbon fabric is investigated. In this regard, a mathematical model is established to investigate the bending elongation of the carbon fi ber around the needle and the interaction between the carbon fi ber and the needle tip. Then the mechanical behavior of the carbon fabric when moving down the tip of the steel needle is analyzed. Based on the performed analysis, a shape curve equation that satisfi es the puncture needle tip is established. Furthermore, the infl uence of different needle tip shapes on the mechanical behavior of the carbon fi ber is analyzed. The performance of the needle tip is subjected to different loads, including the puncture template, horizontal tension of the fi ber to the needle tip, frictional resistance between the fi ber and the needle tip, sliding force, and the bending moment. The performed analysis shows that when the shape of the needle tip assumes the form of curve 10, the downward force, horizontal tension, friction resistance, sliding force, and bending moment are minimized. Accordingly, curve 10 is proposed as the optimal shape for the needle tip. The present study is expected to provide theoretical guidance for selecting overall puncture process parameters.

Keywords:
Overall puncture, fi ber elongation, needle tip shape, force analysis, tip curve dimensional damaged twill fabrics and non-woven fabrics [14]. Furthermore, an explicit dynamic algorithm was proposed to simulate the needle punching process of the fabric cord using the fi nite element method [15,16]. Generally, the fi ber defl ection is analyzed to generate the virtual fi ber structure of the needled preform, calculate the effect of the needle punching process on the fi ber damage, and improve the mechanical properties of the needle-punched composite material [17,18]. In the present study, it is intended to explore the fi ber movement mode for different positions of the woven fabric. In this regard, different tip shapes and fi ber mechanical behavior are analyzed. Finally, the correlation between downforce, horizontal tension, friction resistance, sliding force, bending moment, and needle tip shape is analyzed. The main novelty of the present study lies in its consideration of the interaction between the needle and fi bers and optimization of the shape of the needle tip.

Puncture principle
The overall puncture fabric is a three-dimensional fabric that is indirectly formed using the overall puncture technology [3]. Figure 1 shows the schematic puncture process of the carbon fi ber fabric. It indicates that the puncture needle tip is subject to downward displacement under the action of the puncture template, so that the equidistant close-packed needles pass through the carbon fi ber fabric. During the overall puncture process, needles squeeze the fabric surface, while the fi bers may be squeezed, pushed, bent, and deformed; the points A and B denote the bending deformation state of the carbon fi ber fabric. Furthermore, the puncture template presses the woven carbon fabric to the bottom end of the puncture needle to prevent the rebound of the woven carbon fabric after puncturing several layers, as the point C. Figure 1 indicates that the overall puncture template should become compact enough to increase the volume content of the overall puncture formed carbon fi ber three-dimensional fabric. Meanwhile, the steel needle tip may be shifted and bent under the action of pushing and stretching loads of the fabric fi ber. In severe cases, the needle tip loses its main function and it may even break, thereby affecting the smooth implementation of the overall puncture process. Therefore, in addition to studying the bending and elongation mechanism of the fi ber in the overall puncture process, it is essential to analyze interactions between the fi ber and the needle tip. Then the corresponding mechanical model can be established to reduce the stress of the fi ber on the needle originating from the penetration of the woven carbon cloth. In this regard, optimizing the shape of the needle tip is an important research issue of the overall puncture technology.

Shape analysis of the tip
The puncture needle is composed of a steel needle shaft and a steel needle tip. The needle tip may have different shapes. In the present study, cone shaped needles made by multi-station mechanical grinding are utilized. It is worth noting that the curve of the cone surface should be set before grinding. Figure  2 presents an enlarged schematic diagram of the needle and the needle tip. Let the vertex of the needle tip be the coordinate origin O, and the direction of the needle bar is the positive direction of the y-axis. Moreover, r n and L n denote the radius of the needle shaft and the length of the needle tip, respectively.
In order to prevent complex calculations, it is essential to ensure that the shape of the needle tip is not too complicated. In this regard, a simple tip curve equation in the following form is considered: where . In the present study, 0 a is set to 0 / m n n a L r = − . Moreover, fi ve different values, including 0.5, 0.7, 1.0, 1.5, and 2.0 are considered for m. Accordingly, fi ve tip shape curves referred to as y 1 (curve 1), y 2 (curve 2), y 3 (curve 3), y 4 (curve 4), and y 5 (curve 5) are defi ned. The needle bar radius and the needle tip length are r n = 0.6 mm and L n = 10 mm [6], respectively. Different tip shapes are illustrated in Figure 3a.
When the fi ve curves in Figure 3a are subject to clockwise rotation by 180° along the line , this leads to the formation of fi ve additional curves. The corresponding tip shape curves can be expressed in the following form: (2) where m can be 0.5, 0.7, 1.0, 1.5, and 2.0, and the corresponding shape curves of the needle tip are referred to as y 6 (curve 6), y 7 (curve 7), y 8 (curve 8), y 9 (curve 9), and y 10 (curve 10), respectively. It is worth noting that y 3 = y 8 .
Studies [6] show that when the shape curve of the needle tip is y 3 , the best mechanical properties can be achieved. Therefore, other curves near the straight-line y 3 should be found for analysis. In this regard, a curve y 11 (curve 11) is considered around the straight-line. This curve can be expressed as y 11 = ax 3 + bx 2 + cx + d, and we set the two points on the curve as (x 0 , y 0 ) and (x 1 , y 1 ). This curve is subjected to the following boundary conditions: Based on these boundary conditions, parameters can be calculated as a = 95.37, b = -85, c = 0, and d = 0. Consequently, the curve equation can be expressed in the form stated below: 3 2 11 95.37 85 Now the needle tip shape curve y 12 (curve 12) can be formed around the line. Figure 4 illustrates the tip shape y 12 = f 1 (x,y),

Fiber tension between adjacent steel needles
Fiber-bending has many forms. In Figure 6, the length ⌒B 1k B 2k of the fi ber-bending around the needle between adjacent steel needles is analyzed. Figure 6a and b illustrates that fi ber elongation includes horizontal elongation and vertical elongation. The dotted line between C 2K B′ 2k in Figure 6a is the projection of ⌒C 2k B 2k on the plane in Figure 6b. The equation of the curve OR is: Similarly, the curve RO 1 can be calculated. Consequently, y 12 can be expressed in the form stated below: When L QO = 100, y 13 (curve 13) can be obtained in the same way. In this case, the curve equation can be written in the form stated below: (10) Since curve 13 along curve 3 is symmetric, y 14 (curve 14) can be obtained and the corresponding curve equation can be expressed in the form stated below: (11) Figure 3c shows the shape curves of structured steel needle tip.

Analysis of needle tip force
During the downward movement of the puncture template, the needle passing through the woven carbon fabric gradually moves from the needle tip to the needle shaft. Under the action of the needle tip cone of the steel needle, the fi bers in the woven carbon cloth produce a series of complicated changes such as displacement, pushing, bending, and elongation. Moreover, they interact with the steel needle to cause the steel needle to press down and bend. In the process of the fi ber slipping on the tip of the steel needle, 1,001 contact points of fi ber and needle tip curve are selected as the research objects, which are represented as P 0 , P 1 , P 2 , •••, P n .
where: x n = n·r n /1,000， and n = 0, 1, 2,…, 1,000. Figure 5 shows that the middle point P k is considered as an example to analyze the force of the needle tip. First, the tip of the steel needle is subjected to the horizontal tension caused by the elongation of the fi ber, which is recorded as F LK . It is worth noting that the tension F LK is decomposed into normal component force F L1K and tangential component force F L2K . The fi ber length ⌒B 1k B 2k after bending and stretching at point P k between two adjacent steel needles is mathematically expressed as the following: Eqs (14)- (17) give the four lengths of radians as ⌒B 1k B 2k . These equations are derived from the geometric correlation in Figure 6: where R 1k , R 2k, and S denote the radius of the needle tip of the contact point between the fabric and the needle tip 1, the radius of the needle tip of the contact point between the fabric and the needle tip 2, and the center distance between two adjacent holes of the puncture template, respectively.
where d h is the diameter of the hole. Further, where h is the distance from the fabric to the piercing template at any time.
According to the theory of fi ber material mechanics, the tension F Lk generated by bending and elongating fi ber is expressed as the following [6]: where E c , A z, and ε k denote the elastic modulus of the fi ber, the cross-sectional area of the carbon cloth fi ber bundle, and the fi ber elongation, respectively. Meanwhile, the elongation ε is presented as follows: Then, the fi ber normal-tension F L1k and fi ber tangential tension F L2k are obtained, which are described as the following: (20)

Downward force, frictional resistance, and sliding force
When the downward force of the carbon fi ber fabric on the needle tip at the point P k is F Nk , the normal pressure F N1k and the tangential pressure F N2k can be obtained: where ρ is the friction coeffi cient between the fi ber and the steel needle.
Then, the total frictional resistance F Z suffered by the tip of the steel needle is stated as follows: Moreover, the equation for calculating the sliding force F Hk at the intermediate point P k is expressed as follows: Then, the total sliding force F H experienced by the tip of the steel needle is: (25)  From the force analysis of the tip of the steel needle, we obtain the total bending moment M produced by the horizontal tension F Lk of the steel needle. http://www.autexrj.com/ resistance F Z corresponding to different needle tip shapes and the numerical curve of sliding force F H , respectively. Figure 12 shows the stress distribution diagram of the bending moment at different positions of the needle tip, which determines the position of the dangerous point of the needle tip section of different steel needles.

Bending moment
Moreover, Table 2 presents the sum of downward force F N , horizontal tension F L , friction force F Z , sliding force F H , and the bending moment M corresponding to different needle tip shape curves.
It is observed that the downward force, horizontal tension, friction resistance, sliding force, and bending moment at 1,001 points where the needle tip contacts the fi ber corresponding to different needle tip shape curves vary with the diameter of the needle tip. It is worth noting that the downforce, horizontal tension, friction resistance, sliding force, and bending moment values of curve 10 are lower than those of other needle tip shape curves. When the needle tip shape corresponds to curve 10, in other words when the curve equation is , the downward pressure F N of the puncture template to the needle tip and the horizontal tension F L of the fi ber to the needle tip are the lowest, which equal to121.69 N and 95.04 N, respectively. However, when the needle tip shape corresponds to curve 6, in other words when the curve equation is , the downward pressure of the puncture template on the needle

Results and discussion
In this section, from Table 1 and Eqs (12)-(26), the downward force F N , horizontal tension F L , friction force F Z , sliding force F H, and bending moment M for the abovementioned 14 different needle tip shapes are calculated.     The abovementioned data shows out of these four types, the force of the needle tip under the shape is better. The present study provides theoretical guidance for the selection of overall puncture process parameters and the selection of the needle tip shape.
In order to ensure the smooth progress of the overall puncture process and meet the displacement requirements of the needle tip without having any contact with the hole wall of the puncture template, the displacement of the needle tip is determined under the action of fiber tension. It is found that when the steel needle punctures the fabric once, the requirements of the puncture system for its displacement is met [6]. Accordingly, different parameters, including the down force of the needle tip by the puncture template, horizontal tension of the fiber to the needle tip, frictional resistance between the fiber and the needle tip, sliding force between the fiber and the needle tip, and the numerical curve of the bending moment of the needle tip under horizontal tension, are considered and analyzed in this article. Then, a comparative analysis is carried out. Based on the obtained results, quadratic curve is proposed as the optimal shape for the needle tip.

CONCLUSIONS
In the present study, based on the analysis of the principle of the puncture of the carbon fiber fabric by the needle tip and to ensure the smooth progress of the overall puncture process, 14 curve equations satisfying the shape of the puncture steel needle tip are selected. Moreover, 14 kinds of needle tips under the action of the puncture template and fiber tension are analyzed. The needle tip is subjected to the downward pressure of the puncture template, the horizontal tension of the fiber to the needle tip, the friction resistance between the fiber and the needle tip, the sliding force between the fiber and the needle tip, and the needle tip bending moment under horizontal tension. Furthermore, the fiber movement mode, mechanical model, and solving of equations of the woven fabric at different tip and the horizontal tension of the fiber to the needle tip are the highest, which are 329.14 N and 304.95 N, respectively.
Further analysis shows that when the tip shape curve corresponds to curve 10, the total friction resistance between the fiber and the tip is 109.61 N, and the total sliding force between the fiber and the steel needle is the lowest, which is 109.16 N. Moreover, when the shape curve of the steel needle tip assumes the form of curve 6, the total friction resistance between the fiber and the needle tip and the total sliding force between the fiber and the needle tip are the highest, which equal 317.38 N and 316.85 N, respectively. It is observed that when curve 10 is selected for the needle tip shape, the friction and sliding force between the fiber and the needle tip are the smallest. This indicates that when the needle tip shape is curve 10, the movement between the fiber and the needle tip is optimal among the abovementioned different needle tip shapes. Meanwhile, when the needle tip shape is curve 6, the movement between the fiber and the needle tip is the worst. Moreover, it is found that the frictional force is the same as the sliding force, which is consistent with the condition that the downward pressure of the puncture template should always be kept always uniform. Therefore, the correctness of the established mechanical model is verified.
When the needle tip shape assumes the form of curve 10, the bending moment that the needle tip can withstand is the smallest, which is 759.85 N•mm. This shows that the shape of this tip is the one that is the most optimal. When the needle tip shape corresponds to curve 1, the bending moment that the needle tip can withstand and the downward pressure of the puncture template on the needle tip are 950.72 N.mm and 139.59 N, respectively. Moreover, the horizontal tension needle tip positions are established, and different needle tip shapes and fiber mechanical behavior are analyzed.
Based on the different needle tip shape curves, force analysis and solving of equations are carried out and the numerical curves of the downward force of the needle tip subjected to the puncture template; the horizontal tension of the fiber to the needle tip; the frictional resistance between the fiber, the needle tip, and the fiber; and the sliding force between the needle tip and the bending moment of the needle tip under horizontal tension are analyzed. The analysis shows that when the shape of the needle tip curve corresponds to curve 10, the downward force, horizontal tension, friction resistance, sliding force, and bending moment are the smallest. Therefore, the shape of the needle tip is optimal when curve 10 is applied. It should be indicated that curve 1, curve 2, curve 9, and curve 12 can also be selected as the shape curve of the piercing steel needle tip in engineering applications. The proposed needle shape curves presented in this article can effectively control the tip deformation of the steel needle during the puncture process, thereby reducing the imposed damages on the carbon fiber fabric. Meanwhile, it provides a theoretical basis to improve the puncture process and optimize the fabric structure.