Three-dimensional stress analysis of textile composites: Part I. Numerical analysis

Three-dimensional stress analysis in a unit-cell of a plain-woven composite was performed by using B-spline displacement approximation. The spline approximation provides continuity of displacement and stress components within each yarn and matrix subregion. Two types of unit-cell problems with and without inter-yarn delamination were considered. A penalty function approach along with a contact surface characteristic function was used to obtain a full-field numerical solution for the frictionless contact problem between delaminated yarn surfaces.Yarn interfaces at yarn-crossover locations represent three-material wedge-type regions resulting in singular stress behavior. In the case of unit-cells with perfect bonding between the yarn interfaces, the numerical values of the inter-yarn normal stress did not exhibit trends typical for unbounded stress behavior, whereas the inter-yarn shear stress components displayed discontinuous behavior typical for numerical results in the vicinity of the stress singularity. In the presence of the delamination, both the inter-yarn normal and shear stress components exhibited unbounded behavior near the singularity. Notably, the inter-yarn normal stress showed signs of singular behavior in both cases of open and closed delaminations. Due to the stress singularity that exists at yarn-crossover locations containing three materials (yarn–yarn–matrix) interface intersections, the full-field numerical solution, even with high-order approximation functions, was not able to capture the directional nonuniqueness of the stress values in the vicinity of the singularity, and therefore calls for incorporation of the asymptotic singular stress analysis, which will be given in a follow-on paper [Sihn and Roy, International Journal of Solids and Structures (accepted for publication)].     

塑料SHPB实验中的端面摩擦效应

基于H.Meng的动摩擦实验结果,建立了一个端面动摩擦模型,以描述端面动摩擦因数随SHPB塑料试样与钢压杆接触界面间最大径向相对滑动速度的关系。在SHPB实验的数值模拟中,分别考虑了该端面动摩擦模型和以往被广泛采用的常摩擦因数模型,结果发现,选取不同的端面摩擦模型不影响通过塑料SHPB实验的数值模拟获得的转折应变率(量级为102s-1),然而当应变率超出转折应变率以上时,不同的端面摩擦模型会对塑料SHPB实验的数值模拟结果产生显著影响,使用提出的端面动摩擦模型可得到更准确的塑料SHPB实验的数值模拟结果。     

Experimental,numerical and analytical studies of abrasive wear: correlation between wear mechanisms and friction coefficient

The transport of granular material often generates severe damage. Understanding the correlation between the friction coefficient, particle geometry and wear mechanisms is of primary importance for materials undergoing abrasive wear. The aim of this study is to investigate the effect of particle geometry on wear mechanisms and the friction coefficient. Numerical and analytical simulations and experimental results have been compared. The process to be studied is the scratch made by a rigid cone with different attack angles on a 5xxx aluminium alloy (Al–Mg) flat surface. A scratch test was used and the wear mechanisms were observed for different attack angles. A numerical study with a finite element code was made in order to understand the effect of attack angle on the friction coefficient. The contact surface and the friction coefficient were also studied, and the results compared to the Bowden and Tabor model. The superposition of the numerical, analytical and experimental results showed a better correlation between the wear mechanisms and the friction coefficient. It also showed the importance of the model hypothesis used to simulate the scratch phenomenon. To cite this article: S. Mezlini et al., C. R. Mecanique 333 (2005).     

转移膜的形成对含氢碳膜超低摩擦性能的影响

含氢非晶碳膜在惰性气氛下展现了超低摩擦性能,摩擦系数可达到10~(–3)数量级.本文中通过试验设计验证了转移膜的形成是碳膜超低摩擦性能获得的必要条件.采用含氢非晶碳膜(a-C:H)与钢作为摩擦配副,球盘接触旋转运动,更换接触方式:一种是钢球与镀a-C:H薄膜的钢平板对摩,另一种是镀a-C:H薄膜钢球与钢平板对摩.保持配副材料不变,利用接触方式的差异,来改变转移膜形成的难易程度.第一种方式下,a-C:H可以转移到对偶形成均匀的转移膜,具有超低摩擦性能;在第二种方式下,a-C:H不能转移到对偶形成转移膜,摩擦系数高.而该转移膜是一种含氢的,以sp~2杂化为主的碳结构.氢能够参与钝化碳悬键,从而保证低化学作用活性,sp~2平面分子结构可以具有较低的剪切强度.因此,转移膜的形成和氢的钝化作用对a-C:H薄膜超低摩擦机理均具有重要的贡献.     

织造中碳纤维束间的摩擦磨损试验模拟

织造过程中碳纤维束的摩擦磨损会导致成型后复合材料制件的机械性能下降. 采用自制的试验装置模拟织造过程中经纬纱线间的相互作用,研究了法向负载、预加张力和摩擦速率对碳纤维束摩擦磨损行为的影响. 结果表明:碳纤维束的摩擦系数随着法向负载的增加而减小,其磨损程度随着法向负载的增加而增大,相对应的碳纤维束拉伸断裂强力也逐渐下降;碳纤维束的摩擦力和摩擦系数因实际摩擦接触面积的变化随预加张力的增加而增大;摩擦速率的增加几乎不影响碳纤维束的摩擦力和摩擦系数,但延长了其测试值达到稳定所需的周期数.      

倾斜吹吸控制下湍流边界层减阻的直接数值模拟

雷诺切应力是壁湍流高摩擦阻力的重要来源, 有理论认为可以通过壁面生成负雷诺应力(数值上为正)的方式来削弱湍流流场中雷诺应力的分布, 以此获得流动减阻. 而通过对雷诺平均运动方程的法向二次积分, 可以发现壁面生成正雷诺应力(数值上为负)对壁面摩擦阻力系数才有负贡献. 文中在湍流边界层流动的控制区域下边界设置一系列倾斜狭缝, 利用该装置通过周期性吹吸的方法产生壁面生成正(负)雷诺应力, 并采用直接数值模拟方法考察和验证上文提到的减阻理论. 文中采用的湍流边界层流动模型, 其流动雷诺数(基于外流速度及动量损失厚度)从300 发展到860. 文中通过多组数值模拟算例, 考察了射流强度和频率对壁面摩擦阻力系数的影响, 并对比了壁面生成正或负雷诺应力对流动的影响. 研究表明, 壁面生成正雷诺应力控制的减阻率能达到3.26, 而壁面生成负雷诺应力控制的减阻效果较壁面生成正雷诺应力控制的要差; 壁面生成的正雷诺应力对壁面摩擦阻力有负贡献, 而壁面生成的负雷诺应力对壁面摩擦阻力有正贡献; 通过考察控制的收支比, 发现控制方案不能获得能量净收益.      

结合面静摩擦因数分形模型的建立与仿真

提出一个确定分形维数和分形粗糙度参数(G')的分形函数,并用分形函数逼近结合面的表面粗糙度.根据分形理论和改进后的尺寸分布,推导了静摩擦因数f的解析解.数字仿真结果表明,f随量纲为一的总法向载荷(P')增加而增加.当D较小或较大时,f与(P')之间存在不同的微凸和微凹弧非线性关系,D=1.2时f与(P')的关系基本上是线性的;当D较小时,f随D增加而增加;当D较大时,f随D增加而减小;f随分形粗糙度参数(G')增加而减小,随相关系数K增加而增加,随材料特性(φ)增加而增加.     

缠绕提升钢丝绳绕入冲击摩擦特性研究

为掌握多层缠绕提升钢丝绳层与层之间滑动摩擦磨损特性,在自制缠绕式矿井提升机钢丝绳层间摩擦试验台上,以6×19热镀锌钢丝绳为研究对象,对不同载荷、滑移速度、冲击速度下钢丝绳滑动摩擦磨损规律及接触区域温升变化规律进行试验探究.研究结果表明:摩擦系数变化分为快速增长阶段、过渡阶段、稳定阶段;摩擦系数随载荷增加小幅减小,随滑移速度增大总体呈降低趋势;缠绕钢丝绳滑动摩擦温升集中于接触区域,最大温升受滑移速度影响明显,随速度增加而增大;冲击摩擦系数明显低于稳定滑动摩擦系数,最大冲击摩擦系数随冲击速度、滑移速度增大而增大,随着冲击载荷增大出现多次冲击摩擦.     

Probabilistic Analysis of the Upwind Scheme for Transport Equations

We provide a probabilistic analysis of the upwind scheme for d-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we recover recent results due to Merlet and Vovelle (Numer Math 106: 129–155, 2007) and Merlet (SIAM J Numer Anal 46(1):124–150, 2007): we prove that the scheme is of order 1/2 in L^￥([0,T],L¹(\mathbb R^d)){L^{\infty}([0,T],L^1(\mathbb R^d))} for an integrable initial datum of bounded variation and of order 1/2−ε, for all ε > 0, in L^￥([0,T] ×\mathbb R^d){L^{\infty}([0,T] \times \mathbb R^d)} for an initial datum of Lipschitz regularity. Our analysis provides a new interpretation of the numerical diffusion phenomenon.     

A mechanics-of-materials model for predicting Young’s modulus of damaged woven fabric composites involving three damage modes

An analytical model for damaged woven fabric composites is developed using the theory of advanced mechanics of materials. The analysis is based on Castigliano’s second theorem and utilizes a damaged mosaic model laminate. Three damage modes (i.e., transverse yarn cracking, interface debonding, and sliding with friction at the interface) are considered. Only one independent interfacial parameter, the friction coefficient between warp and fill yarns, is introduced in the analysis. A closed-form formula is provided for estimating effective Young’s modulus of damaged woven laminates. A parametric study of some 192 sample cases of two different composite systems (i.e., glass fiber/epoxy and ceramic fiber/ceramic) is conducted to illustrate the application and significance of the newly derived analytical model. The numerical values of the effective Young’s modulus for the special case involving only transverse yarn cracking (the first damage mode) estimated by the present mechanics-of-materials model agree fairly well with those predicted by an elasticity-based model [Int. J. Solids Struct. 38 (2001) 855]. For the general case involving all three damage modes simultaneously, the present model reveals the complex nature of Young’s modulus reduction in a quantitative manner, which differs from existing models.     

Pendulum with linear damping and variable length

The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.     

渤、黄海的底摩擦系数

利用伴随法，根据32个验潮站的水位观测资料来优化渤、黄海的底摩擦系数．所作的一系列数值模拟实验表明；利用伴随方法优化渤、黄海的底摩擦系数能够有效地减少数值模拟结果与观测结果的差异．     

Single-test determination of the friction coefficient and stress-strain curve for application in metal-forming analyses

The compression test of a ring is customarily used to determine the friction coefficient in metal-forming problems. The aim of this paper is to describe a procedure to obtain, for metals in the large deformation range, the stress-strain curve and friction coefficient through the same test. The friction coefficient is evaluated by comparing curves obtained by a finite element code with the experimental curves. The stress-strain curve is obtained by inverting an analytical solution, calculated by a lower-upper-bound approach. Good results in terms of accuracy are obtained.     

Center manifold and multivariable approximants applied to non-linear stability analysis

This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. This paper outlines the stability analysis and a procedure to reduce and simplify the non-linear system, in order to obtain limit cycle amplitudes. The center manifold approach, the multivariable approximants theory, and the alternate frequency/time domain (AFT) method are applied. Brake vibrations, and more specifically heavy trucks grabbing are concerned. The modelling introduces sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the center manifold approach, the multivariable approximants, and the AFT method are used in order to obtain equations for the limit cycle amplitudes. These methods allow the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system, as well as the contributions of non-linear terms. The goal is the validation of this procedure for a complex non-linear model by comparing results obtained by solving the full system and by using these methods. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.     

纺织复合材料预制体成形过程纤维束摩擦行为研究进展

预制体是复合材料的增强骨架,由成千上万根纤维束织造而成. 预制体中的纤维束由于织造过程中的交织运动会发生不同程度的摩擦损伤,而纤维的磨损会导致预制体力学性能损失率高达9%~12%. 因此,揭示纤维束在织造过程中的摩擦磨损机理对提升预制体力学性能具有重要意义. 本文中综述了近年来有关纤维束摩擦行为的研究进展:首先,概述纤维束-金属和纤维束-纤维束摩擦测试方法的优缺点;其次,分析得出摩擦角度、摩擦频率、预加张力和法向载荷对纤维束摩擦性能的影响机制;最后,总结纤维束摩擦磨损行为的理论分析模型. 本综述中对复合材料预制体成形工艺设计和纤维束摩擦损伤的量化分析具有指导意义.      

Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction

A high friction coefficient is first observed as a sliding between bodies commences, which is called the static friction. Then, the friction coefficient decreases approaching the lowest stationary value, which is called the kinetic friction. Thereafter, if the sliding stops for a while and then it starts again, the friction coefficient recovers and a similar behavior as that in the first sliding is reproduced. In this article the subloading-friction model with a smooth elastic–plastic sliding transition [Hashiguchi, K., Ozaki, S., Okayasu, T., 2005. Unconventional friction theory based on the subloading surface concept. Int. J. Solids Struct. 42, 1705–1727] is extended so as to describe the reduction from the static to kinetic friction and the recovery of the static friction. The reduction is formulated as the plastic softening due to the separations of the adhesions of surface asperities induced by the sliding and the recovery is formulated as the viscoplastic (creep) hardening due to the reconstructions of the adhesions of surface asperities during the elapse of time under a quite high actual contact pressure between edges of asperities.     

Experimental–Theoretical Technique for Determining the Equation-of-State Parameters for Soils

This paper considers an experimental–theoretical technique for determining pressure–strain curves and curves of yield strength versus pressure for soils based on disagreement between data of physical and numerical modeling of wave processes in a system of split Hopkinson bars with a soil sample in a holder. A convergent iterative procedure was developed to refine the equation-of-state parameters of soils obtained by the Kolsky method. The error of the technique is analyzed, the role of friction and the coefficient of sliding friction between the soil and the deformed holder.     

磨合过程中液体润滑实现超低摩擦的混合模型研究

针对球-盘滑动试验,在磨合过程中获得超低摩擦的液体润滑状态,建立耦合流体润滑、粗糙接触力学、Archard磨损方程和相关物理参数(液体黏度、表面粗糙度和磨损系数)时变函数的混合模型,研究磨合过程中液体润滑的摩擦系数演化.通过数值模拟结果可知：在磨合过程中,润滑介质等效黏度增大,形成流体动压润滑薄膜,有效隔开粗糙表面;其次在磨合过程中,新生成的表面粗糙度降低,减少粗糙峰承载比,实现超低摩擦润滑状态;最后在适当的液体黏度和提高表界面效应减少边界摩擦系数,可进一步实现液体超低摩擦润滑状态.为磨合过程宏观液体润滑性能演化所建立的混合数值模型对提高液体润滑超低摩擦设计效率具有重要价值意义.     

半金属盘式刹车材料的试验研究

通过正交试验设计和蔡氏试验机测试,得到了摩擦系数受温度、载荷和速度影响较小,磨损也较小的半金属盘式刹车材料配方,其平均摩擦系数是0.444.结果表明,在4种被研究的成分中温和的研磨剂氧化铁黑对与温度有关的摩擦系数的标准偏差影响最大,原因在于其只对冷制动起增摩作用而对热制动没有增摩作用;过多使用强的研磨剂氧化铝会导致摩擦系数和比磨损率增大,出现过恢复,并且摩擦系数随载荷增加;而过多使用混合润滑剂(石景和三硫化二锑)会减小摩擦系数和比磨损率.