剪切载荷作用下含损伤胶接材料界面动应力强度因子的研究

主要针对剪切载荷作用下,胶接材料接合区域界面裂纹尖端动态应力强度因子进行了分析,其中考虑了裂尖区域的损伤．通过积分变换,引入位错密度函数,奇异积分方程被简化为代数方程,并采用配点法求解;最后经过Laplace逆变换,得到动态应力强度因子的时间响应．Ⅱ型动应力强度因子随着黏弹性胶层的剪切松弛参量、弹性基底的剪切模量和Poisson比的增加而增大;随膨胀松弛参量的增加而减小．损伤屏蔽发生在裂纹扩展的起始阶段．裂纹尖端的奇异性指数(-0.5)是与材料参数、损伤程度和时间无关的,而振荡指数由黏弹性材料参数控制．     

Ⅲ型弹粘塑性/刚性界面裂纹的定常扩展裂尖场

考虑裂纹尖端的奇异性和粘性效应,建立了双材料界面扩展裂纹尖端的弹粘塑性控制方程．引入界面裂纹尖端的位移势函数和边界条件,对刚性-弹粘塑性界面Ⅲ型界面裂纹进行了数值分析,求得了界面裂纹尖端应力应变场,并讨论了界面裂纹尖端场随各影响参数的变化规律．计算结果表明,粘性效应是研究界面扩展裂纹尖端场时的一个主要因素,界面裂纹尖端为弹粘性场,其场受材料的粘性系数、Mach数和奇异性指数控制．     

弹性-应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解*

本文首先给出了一种用于描述材料软化,并存在有粘塑性的材料模型.用这种模型对反平面剪切型动态扩展状态下,裂纹尖端的弹粘塑性场进行了渐近分析,给出了弹性－应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解方程.分析结果表明,在裂纹尖端应变具有(ln(R/r))1/(n＋1)的奇异性,应力具有(ln(R/r))-n/(n＋1)的奇异性.从而本文揭示了应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近行为.     

位于两不同正交各向异性半平面间张开型界面裂纹的性能分析

利用Schmidt方法分析了位于正交各向异性材料中的张开型界面裂纹问题．经富立叶变换使问题的求解转换为求解两对对偶积分方程,其中对偶积分方程的变量为裂纹面张开位移．最终获得了应力强度因子的数值解．与以前有关界面裂纹问题的解相比,没遇到数学上难以处理的应力振荡奇异性,裂纹尖端应力场的奇异性与均匀材料中裂纹尖端应力场的奇异性相同．同时当上下半平面材料相同时,可以得到其精确解．     

不可压缩橡胶类材料平面应变缺口试件顶端的应力场

用Gao的本构关系,分析了不可压缩橡胶类材料平面应变情况下缺口试件顶端和裂纹尖端的应力场,并根据应力场的渐近方程作了数值计算,给出了应力奇异性与缺口角度的关系曲线及应力随角坐标的变化曲线.     

弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的渐近分析

建立了弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的力学模型,求得了在裂纹表面自由和裂纹面有摩擦接触两种情况下,裂纹尖端应力场分离变量形式的渐近解．求解结果表明:Ⅱ型界面裂纹问题的应力、应变具有相同的奇异性;Ⅱ型界面裂纹尖端场不存在振荡奇异性;材料的幂硬化指数n和弹性模量比对裂纹尖端应力场幂硬化蠕变性材料区有着显著的影响,而弹性区仅受幂硬化指数n的影响,当n很大时,蠕变变形占主导地位,应力场趋于稳定,不随n的变化而变化;泊松比对裂纹尖端应力场的影响不明显．     

利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

在一定的假设条件下,即不考虑界面裂纹尖端处裂纹面的相互叠入现象,研究了压电材料Ⅰ-型界面裂纹问题．利用Fourier变换使问题的求解转换为求解两对对偶积分方程．进而把裂纹表面位移差展开成Jacobi多项式形式来求解对偶积分方程．结果表明裂纹尖端应力场和电位移场的奇异性与均匀材料裂纹问题的奇异性相同．当上下半平面材料相同时,解可以退化而得到其精确解．     

求解双材料裂纹结构全域应力场的扩展边界元法

在线弹性理论中,复合材料裂纹尖端具有多重应力奇异性,常规数值方法不易求解.该文建立的扩展边界元法(XBEM)对围绕尖端区域位移函数采用自尖端径向距离r的渐近级数展开式表达,其幅值系数作为基本未知量,而尖端外部区域采用常规边界元法离散方程.两方程联立求解可获得裂纹结构完整的位移和应力场.对两相材料裂纹结构尖端的两个材料域分别采用合理的应力特征对,然后对其进行计算,通过计算结果的对比分析,表明了扩展边界元法求解两相材料裂纹结构全域应力场的准确性和有效性.     

Ⅰ型动态扩展裂纹尖端的弹粘-理想塑性场

由于材料在扩展裂纹尖端的粘性效应的存在,考虑粘性效应并假设粘性系数与塑性等效应变率的幂次成反比,对理想塑性材料中平面应变扩展裂纹尖端场进行了弹粘塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅰ型裂纹数值解的性质随各参数的变化规律．分析表明,应力和应变均具有幂奇异性,通过分析使尖端场的弹、粘、塑性可以合理匹配．对于Ⅰ型裂纹,裂尖场不含弹性卸载区．趋于极限情况时,裂纹尖端处于一种超粘性状态,并积聚了大量的能量,在各个受压应力状态下裂纹扩展．     

高速扩展平面应力裂纹尖端的理想塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下,利用Tresca屈服条件、定常运动方程及弹塑性本构方程,我们导出了高速扩展平面应力裂纹尖端的理想塑性应力场的一般解析表达式。将这些一般解析表达式用于具体裂纹,我们就得到高速扩展Ⅰ型和Ⅱ型平面应力裂纹尖端的理想塑性应力场的解析表达式。     

On corner singularities in Reissner-Mindlin's theory of elastic plates

In the framework of linear elasticity, singularities occur in domains with non-smooth boundaries. Particularly in Fracture Mechanics, the local stress field near stress concentrations is of interest. In this work, singularities at re-entrant corners or sharp notches in Reissner-Mindlin plates are studied. Therefore, an asymptotic solution of the governing system of partial differential equations is obtained by using a complex potential approach which allows for an efficient calculation of the singularity exponent λ. The effect of the notch opening angle and the boundary conditions on the singularity exponent is discussed. The results show, that it can be distinguished between singularities for symmetric and antisymmetric loading and between singularities of the bending moments and the transverse shear forces. Also, stronger singularities than the classical crack tip singularity with free crack faces are observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials

According to the linear theory of elasticity, there exists a combination of different orders of stress singularity at a V-notch tip of bonded dissimilar materials. The singularity reflects a strong stress concentration near the sharp V-notches. In this paper, a new way is proposed in order to determine the orders of singularity for two-dimensional V-notch problems. Firstly, on the basis of an asymptotic stress field in terms of radial coordinates at the V-notch tip, the governing equations of the elastic theory are transformed into an eigenvalue problem of ordinary differential equations (ODEs) with respect to the circumferential coordinate θ around the notch tip. Then the interpolating matrix method established by the first author is further developed to solve the general eigenvalue problem. Hence, the singularity orders of the V-notch problem are determined through solving the corresponding ODEs by means of the interpolating matrix method. Meanwhile, the associated eigenvectors of the displacement and stress fields near the V-notches are also obtained. These functions are essential in calculating the amplitude of the stress field described as generalized stress intensity factors of the V-notches. The present method is also available to deal with the plane V-notch problems in bonded orthotropic multi-material. Finally, numerical examples are presented to illustrate the accuracy and the effectiveness of the method.     

A closed‐form analysis of material and geometry effects on stress singularities at unsymmetric bimaterial notches

An important issue in the mechanics of adhesive bonds is the knowledge of local mechanical fields. In the present study, an asymptotic analysis of the stress fields near an unsymmetric bimaterial notch with arbitrary opening angle is performed. Using the complex potential method, the order of the singularity of the stress fields at a notch tip can be determined in closed‐form analytical manner, so that the dependency of the occurring singularity exponents on geometry and material properties can be studied systematically.     

正交异性双材料的Ⅱ型界面裂纹尖端场

通过引入含16个待定实系数和两个实应力奇异指数的应力函数,再借助边界条件,得到了两个八元非齐次线性方程组.求解该方程组,在双材料工程参数满足适当条件下,确定了两个实应力奇异指数.根据极限唯一性定理,求出了全部系数,得到了应力函数的表示式.代入相应的力学公式,推出了当特征方程组两个判别式都小于0时,每种材料的裂纹尖端应力强度因子、应力场和位移场的理论解.裂纹尖端附近的应力和位移有混合型断裂特征,但没有振荡奇异性和裂纹面相互嵌入现象作为特例,当两种正交异性材料相同时,可以推出正交异性单材料Ⅱ型断裂的应力奇异指数、应力强度因子公式、应力场、位移场表示式.     

圆形界面刚性线夹杂的反平面问题

研究了在反平面集中力和无穷远纵向剪切作用下,不同弹性材料圆形界面上有多条刚性线夹杂的问题．运用Riemann-Schwarz解析延拓技术与复势函数奇性主部分析方法,首次获得了该问题的一般解答,求出了几种典型情况的封闭解,并给出了刚性线夹杂尖端的应力场分布A·D2结果表明,在反平面加载的情况下圆形界面刚性线夹杂尖端应力具有平方根奇异性,无奇异性应力振荡;应力场与刚性线夹杂的形状,加载方式和材料性质有关．退化结果与已有的解答完全吻合．     

三维切口尖端应力应变场

本文利用双重幂级数展开法分析三维切口尖端应力应变奇异性，通过切口边界条件导出切口特征方程，进而求得不同切口内角下特征值序列解答，最后推得切口尖端应力应变场。     

反平面塑性V形切口尖端应力和位移渐近解

提出了一种确定幂硬化材料反平面V形切口尖端应力和位移渐近解的主导项和高阶项的有效方法。首先通过在弹塑性理论基本方程中引入V形切口尖端应力场和位移场的渐近级数展开,建立以应力和位移为特征函数的非线性和线性常微分方程组。然后采用插值矩阵法求解常微分方程组,可得到多阶应力特征指数和其相对应的特征函数。该方法具有通用性强、精度高等优点,可处理任意开口角度和应变硬化指数的V形切口。典型算例验证了该方法的准确性和有效性。     

断裂分析的小波数值方法

利用小波具有的良好局部化特性,用小波函数对位移场进行逼近,建立了小波数值计算格式,模拟了裂纹尖端的奇异性问题.算例求出了裂纹尖端的应力强度因子,数值结果显示出该方法具有良好的数值精度     

Analysis of the stress singularity for a bi-material V-notch by the boundary element method

A new algorithm coupling the boundary element technique with the characteristic expansion method is proposed for the computation of the singular stress field in the V-notched bi-material structure. After the stress asymptotic expansions are introduced into the linear elasticity equilibrium equations, the governing equations at the small sector dug out from the bi-material V-notch tip region are transformed into the ordinary differential eigen-equations. All the parameters in the asymptotic expansions except the combination coefficients can be achieved by solving the established eigen-equations with the interpolating matrix method. Furthermore, the conventional boundary element method is applied to modeling the remaining structure without the notch tip region. The combination coefficients in the asymptotic expansion forms can be computed by the discretized boundary integral equations. Thus, the singular stress field at the V-notch tip and the generalized stress intensity factors of the bi-material notch are successfully calculated. The accurate singular stress field obtained here is very useful in the evaluation of the fracture property and the fatigue life of the V-notched bi-material structure.