橡胶楔体与刚性缺口接触的大变形分析

利用一种新的橡胶材料应变能函数，对橡胶楔体与刚性缺口接触大变形问题进行了分析。得到了接触尖点附近变形的奇异性特征，给出了奇异性指数与材料常数、橡胶楔体角度、刚性缺口角度之间的关系式。同时编制了大变形有限元程序，计算得到了与理论解一致的结论。     

橡胶楔体与刚性缺口接触大变形分析

利用Ｋｕｏｗｌｅｓ与Ｓｔｅｒｎｂｅｒｇ提出的非线性弹性大变形应变能函数,对橡胶楔体与刚性缺口接触问题进行大变形渐近分析,推导了楔体尖端场的渐近方程,得到楔体尖端附近的应力应变场及应力的奇异性指数与橡胶楔体角度、刚性缺口角度及材料常数有关的表达式;楔尖附近同一半径上应力分量为常数,同时,利用非线性有限元理论编制了大变形有限元程序,考虑楔体尖端与缺口接触边界条件,计算得到了与分析解一致的结论,当缺口角     

完整岩石拉压应力状态下的张裂破坏准则

一点的应力状态可由3个主应力$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示, 当规定主应力以压为正时, 沿最大主应力$\sigma_{1}$方向将产生收缩变形, 若中间主应力$\sigma_{2}$和最小主应力$\sigma_{3}$都远小于$\sigma_{1}$, 则沿$\sigma_{2}$和$\sigma_{3}$方向会产生横向扩张变形, 当横向扩张变形达到一定极限时, 将会在平行于$\sigma _{1}$的方向产生张裂破坏. 如何建立这种张裂破坏的强度准则目前尚缺乏研究, 最大拉应变理论(第二强度理论)有时被用来解释张裂破坏, 但最大拉应变理论难以应用于三向受力状态. 本文分别用$\varepsilon_{1}$, $\varepsilon_{2}$表示最大张应变和次大张应变, 则最大拉应变理论认为当$\varepsilon_{1}$达到单向拉伸屈服应变时, 材料将产生破坏. 而本文将根据$\varepsilon_{1}+\varepsilon_{2}$之和达到极限值$\varepsilon_u$来建立张裂破坏准则. 可以证明$\varepsilon_{1} +\varepsilon_{2}$所表示的是$\sigma_{1}$主平面的面积增长率. 当$\sigma_{3}<\sigma_{2} \ll \sigma_{1}$时, 大部分岩石都具有脆性破坏的特点, 所以可将破坏前的岩石视为满足广义胡克定律的线弹性材料, 这样用$\varepsilon_{1}$, $\varepsilon_{2}$表示的强度准则可通过$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示. 在这个过程中还可考虑岩石在拉伸和压缩时具有不同弹性参数和强度的特点, 并可通过单向拉伸和单向压缩的破坏状态来确定$\varepsilon_u$. 不管$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$是压应力, 还是拉应力, 或者$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$中有拉有压的情形, 基于$\varepsilon_{1} +\varepsilon_{2} =\varepsilon_u$都可建立相应的强度准则. 所建立的准则可以反映中间应力$\sigma_{2}$对强度的影响规律, 通过建立的强度准则还可以证明: 静水拉力能引起屈服, 而静水压力不能产生屈服; 压缩破坏能使塑性体积增大, 其结果比Mohr-Coulomb准则更能反映实际情形. 并通过拉压应力状态下的试验数据验证了所建立的强度准则, 所得理论计算结果和已有的试验数据吻合得很好. 通过提出的强度准则和圆盘劈裂的试验结果, 可获得更为可靠的岩石单轴抗拉强度.      

Asymptotic Analysis of the Nonlinear Boussinesq Problem for a Kind of Incompressible Rubber Material (Compression Case)

A half rubber space compressed by a concentrated force normal to the surface is asymptotically analyzed based on large strain elastic theory. The material domain near the singular point is divided into an expanding domain and a shrinking domain. The asymptotic equations are derived and solved individually for both domains. The solutions to expanding and shrinking domains are further assembled together so that there is only one free parameter left which can indicate the amplitude of the singular stress and strain field. Finally, the amplitude parameter of the field is determined by the given concentrated force. This revised version was published online in July 2006 with corrections to the Cover Date.     

点群10mm十次对称二维准晶中的两类接触问题

采用复变函数法探讨了在一个刚性压头作用下十次对称二维准晶材料的两类接触问题,即具有有限摩擦的接触问题以及粘结接触问题.特别地对于平底压头,获得了表征声子场和相位子场的全纯函数的显式表达式,以及在压头上的接触应力分布.结果显示,对于具有有限摩擦的接触问题,接触应力在接触区边缘具有实指数奇异性-1／2±β,其中β由准晶体的材料常数及静摩擦系数确定;而对于粘结接触问题,接触应力在接触区边缘具有振荡型奇异性-1／2±iε,其中ε由准晶体的材料常数确定.     

考虑颗粒转矩的接触网络诱发各向异性分析

颗粒材料的宏观力学行为与接触网络的组构各向异性密切相关, 根据接触点的滑动与否、转动与否和强弱力情况, 可以将颗粒间的接触系统分为不同的子接触网络. 一般而言, 不同的子接触网络在颗粒体系中的传力机制不同, 对宏观力学响应的贡献也有不同. 采用离散单元法(discrete element method, DEM)模拟了不同抗转动系数$\mu_r$下颗粒材料三轴剪切试验, 分析了剪切过程中不同子接触网络的组构张量的演变规律, 并探究了颗粒抗转动效应对子接触网络各向异性指标演变规律的影响. 研究发现: 剪切过程中转动、非转动接触的组构张量变化不是独立的, 受到颗粒间滑动与否的影响; 非滑动、强接触网络是颗粒间的主要传力结构, 非滑动接触网络的接触法向和法向接触力各向异性均随$\mu_r$的增大而增大, 其对宏观应力的贡献程度随$\mu_r$的增大而减小;强接触网络的接触法向各向异性随$\mu_r$的增大而增大, 但法向接触力各向异性随$\mu_r$的增大无明显变化, 强接触网络对宏观应力的贡献程度在不同$\mu_r$情况下均相同.      

An incompressible rubber wedge under the tension of a line load at its tip

An analysis is made of the stress distribution and the deformation pattern near the apex of an incompressible rubber wedge under the tension of a concentrated force. The asymptotic method for the tip stress field is developed. The problem is treated as a plane strain case. Finally, the FEM numerical results agree with the theoretical ones.     

铁电单晶Pb(Mg1/3Nb2/3)O3-0.32PbTiO3的实验及本构模型研究

对压力作用下沿[001]晶向极化的Pb(Mg弛豫型铁电单晶;极化旋转(相变);黏塑性模型;本构;细观力学国家自然科学基金，教育部全国优秀博士学位论文作者专项基金2006-11-06对压力作用下沿[001]晶向极化的Pb(Mg1/3Nb2/3)O3-0.32PbTiO3(PMN0.32PT)弛豫型铁电单晶的应力应变行为进行了实验研究,实验结果表明铁电单晶〈001〉晶向的应力应变行为和铁电多晶有本质的不同,是传统的电畴翻转机理所难以解释的,所提出的极化旋转(相变)模型合理地解释了实验中观察到的现象;基于提出的极化旋转(相变)模型,采用细观力学方法建立了铁电单晶的细观本构模型.在模型中采用黏塑性公式描述铁电单晶可能的8个相变系统的相变行为.为了验证模型的可靠性,用该模型模拟了铁电单晶〈001〉晶向的应力应变实验曲线.计算表明,该模型能较好地模拟铁电单晶〈001〉晶向的相变行为.     

黏弹性接触界面端附近的奇异应力场

研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.      

粒料固有各向异性的离散元模拟与细观分析

料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为$0^\circ$时, 峰值应力比和最大体积压缩应变分别提高了12.6\%和18.8\%, 其原因在于加载过程中颗粒旋转和滑动百分比更小, 内部调整时间更短、更易被剪密; 固有各向异性对颗粒法向接触力分布的影响不大, 但显著影响接触法向分布特征; 剪切过程中, $\theta$为$90^\circ$时的接触法向各向异性系数先快速减小后逐渐增大, 而$\theta$为$0^\circ$到$60^\circ$时则呈现出增大后稍有回落或趋于稳定的趋势, 且$\theta$ 愈小的试件各向异性系数增大愈快.     

基于新型裂尖杂交元的压电材料断裂力学研究

提出了一种裂尖邻域杂交元模型，将其与标准杂交应力元结合来求解压电材料裂纹尖 端的奇性电弹场和断裂参数的数值解．裂纹尖端杂交元的建立步骤为：1) 利用高次内插有限元特征法求解特征问题，得到反映裂尖奇异性电弹场状况的特 征值和特征角分布函数；2) 利用广义Hellinger-Reissner变分泛函以及特征问题的解来建立裂尖邻域杂交元模型．该 方法求解电弹场时，摒弃了传统有限元方法中裂尖奇异性场需要借助解析解的做法，也避免 了单纯有限元方法中需要在裂尖端部进行高密度单元划分．采用PZT5板中心裂纹问题 作为考核例，数值结果显示了良好的精确性．作为进一步应用，求解了含中心界面裂纹 的PZT4-PZT5两相压电材料的应力强度因子和电位移强度因子．所有的算例都考虑 了3种裂纹面电边界条件．     

Effect of friction in wedging of elastic solids

In this paper the contact problem for an elastic wedge of arbitrary angle is considered. It is assumed that the external load is applied to the medium through a rigid wedge and the coefficient of friction between the loading wedge and the elastic solid is constant. The problem is reduced to a singular integral equation of the second kind with the contact pressure as the unknown function. An effective numerical solution of the integral equation is described and the results of three examples are presented. The comparison of these results with those obtained from the frictionless wedge problem indicates that generally friction has the tendency of reducing the peak values of the stress intensity factors calculated at the wedge apex and at the end points of the contact area.This work was supported by NASA-Laugley under the Grant NGR 39-007-011 and by NSF under the Grant GK-42771X.     

Photoelastic analysis of the singular stress field in a bimaterial wedge

This paper presents an experimental investigation of the singular stress field near the vertex of a bimaterial wedge using a digital photoelastic technique. Special attention is given to the casting of bimaterial wedge specimens and analysis technique for extracting stress intensity factors from photoelastic samples. Different bimaterial wedge specimens are made of two different photoelastic materials bonded through a special casting procedure and loaded in simple tension. A new multiple-parameter method is developed to obtain the stress intensity factor reliably from the isochromatic fringe patterns and the series representation of the stress field at the vertex of the wedge. Experimental results are compared with finite element predictions, and good agreement is observed.     

混凝土一维应力层裂实验的全场DIC分析

基于74mm直径分离式Hopkinson杆(SHPB)实验平台进行了混凝土杆的一维应力层裂实验.采用超高速相机(采样频率:2 $\mu$s/frame)结合数字图像相关法(DIC),记录混凝土试件中的动态位移场实时变化情况,探讨了混凝土在拉伸断裂过程中的表面位移场及速度场演化规律.针对实验中出现的多重层裂现象,基于一维应力波传播理论,指出各个位置在发生层裂时,其最大拉应力均由透射压缩波与反射拉伸波叠加而成,各处层裂发生时均处于一维应力状态.并提出了根据层裂位置左右两点速度趋势变化判断层裂发生时刻的判据.该判据可以给出所有层裂的起裂时间,结合DIC分析直接给出了混凝土多重层裂应变.结果显示混凝土的拉伸强度具有明显的应变率效应,在30 s$^{-1}$的应变率下,其拉伸强度的动态增强因子(DIF)可以达到5.与传统的波叠加法和自由面速度回跳法相比,DIC全场分析法不受加载波形限制,可以精确给出每个层裂的位置和起裂时间,从而得到试件在高应变率加载下不同位置处的断裂应变、拉伸强度及相应应变率,提高了测量效率.      

Wedge indentation into elastic-plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.     

ANALYSIS OF MECHANICAL PROPERTIES OF CEMENT CLINKER UNDER DIFFERENT TEMPERATURES BASED ON HERTZIAN INDENTATION METHOD1)

本文通过高温球压法得到各种脆性和准脆性材料的表面压痕应力与应变之间的关系曲线。通过压痕应力-应变曲线的分析既可比较方便地确定出材料的压痕弹性模量、剪切模量和布氏硬度,又可比较不同温度下水泥熟料的变形性能。在不同温度(25 ${^\circ}\!$C$\sim $1400 ${^\circ}\!$C)处理下,球压应力松弛试验载荷松弛,在载荷峰值为100 N时,随着温度的升高,水泥熟料载荷松弛更明显。随着温度从500 ${^\circ}\!$C升高到1400 ${^\circ}\!$C,载荷松弛非常明显,尤其温度高于1200 ${^\circ}\!$C,水泥熟料样品内部的硅酸三钙(Ca$_3$SiO$_5$, 简称C3S)分解以及有部分液相的出现引起的应力松弛现象最为明显,在1275 ${^\circ}\!$C时熟料基本上已经软化,载荷急速松弛,所以认为1275 ${^\circ}\!$C为熟料的脆延转化温度。通过水泥熟料高温球压松弛试验可以确定水泥熟料在二次加热过程中的脆-延转化温度,测定熟料弹性模量和抗压强度急剧变化的温度范围。研究水泥熟料在不同温度下的力学行为和力学特性,探索提高粉磨效率的新途径,实现高温下的低能耗粉碎。     

受热载荷两相材料界面端应力场的新型有限元分析

基于一种特殊有限元特征分析方法获得两相材料界面端奇异性应力和位移场数值特征解, 据此开发了一种新型超级单元模型, 用于分析热载荷作用下两相材料界面端的应力场. 与机械载荷作用下超级单元模型的区别在于, 该模型在能量泛函中考虑了热-机耦合的影响, 将应力场分为奇异项和非奇异项, 而奇异性项又可分解为热致部分和力致部分. 模型的有效性通过了经验解和传统有限元方法的验证;模型可以避免在界面端邻域网格高度加密, 提高了计算速度, 对于分析多奇异性点应力干涉问题有重要意义.     

爆轰波在楔面上反射数值分析

应用基元反应模型和频散可控耗散格式(DCD)对氢氧爆轰波在楔面反射进行了数值模拟,计算中氢氧混合物的化学反应采用了8种组分20个反应方程式,在处理化学反应引起的刚性问题时采用了时间算子分裂的方法,模拟了爆轰波在楔面反射由马赫反射向规则反射转变的过程,得到了反射转变临界角,同时考虑了初始压力和组分的影响,并和实验及理论分析结果进行了比较,结果是令人满意的。     

Singular plastic fields in wedge indentation of pressure sensitive solids

The paper examines singular plastic fields induced near the tip of a wedge indentating a pressure sensitive solid. Plane strain conditions are assumed and material response is modelled by the small strain Drucker–Prager rigid/plastic constitutive law. A standard separation of variables solution is numerically generated for pure power-law hardening. Three possible measures of wall roughness are studied with an attempt to expose the coupling between wall friction and material pressure sensitivity. Sample calculations illustrate that stress singularity decreases with increasing friction, wedge angle and hardening exponent, but increases with pressure sensitivity. At large values of the hardening exponent, when the material is nearly perfectly plastic, effective stress contours approach the slip line limit. The concept of indentation index is introduced as a possible estimate for average indentation pressure.     

An experimental study of stress singularities at a sharp corner in a contact problem

The photoelastic method was used to investigate the nature of the local stress field at a sharp corner of a wedge that was compressed against a larger body. Planar wedge specimens made of photoelastic material were compressed against a half plane (larger body) of identical material at various load levels. Several wedge angles were studied. The nature of the singular stress field postulated by linear elastic analysis was verified and the strength of the singularity was obtained by plotting the variation of fringe order as a function of radial distance from the sharp corner on a logarithmic scale. The experimental results were found to be in good agreement with the theoretical predictions. The effect of interface friction and the effect of rounding off the sharp edge are brietly discussed.