二维十次对称压电准晶含Griffith裂纹的平面问题

利用Stroh公式结合半逆解法,得到裂纹尖端附近的场解和场强度因子解,并利用权函数方法求解裂纹尖端的能量释放率.结合算例,探讨不同集中载荷作用下场强度因子和能量释放率的变化规律,并分析无限远处均匀载荷作用时裂尖附近的应力和位移,与椭圆孔以及相应的退化结果对比验证.结果表明,在裂尖附近作用集中载荷,对力强度因子以及电位移强度因子有显著影响,能量释放率是电场、声子场、相位子场、声子场-相位子场耦合效应以及电场-声子场耦合效应共同作用的结果,且应力强度因子、电位移强度因子和能量释放率共同表征了裂纹扩展过程中的应力集中以及扩展的大致方向.     

Method of lines for functionally gradient materials

The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier‘s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential equations(ODEs) defined on discrete lines with the finite difference. By solving the system of ODEs, the solutions to the problem can be obtained. An example of three-point bending was given to demonstrate the application of MOL for a crack problem in the FGM. The computational results show that the more accurate results can be obtained with less computational time and resources. The obvious difficulties of numerical method for crack problems in FGMs, such as the effect of material nonhomogeneity and the existence of high gradient stress and strain near a crack tip, can be overcome without additional consideration if this method is adopted.     

可压缩粘弹性材料Ⅰ型动态扩展裂纹尖端场

为了研究粘性效应作用下的动态扩展裂纹尖端渐近场,建立了可压缩粘弹性材料Ⅰ型动态扩展裂纹的力学模型,推导了可压缩材料Ⅰ型动态扩展裂纹的本构方程.在稳态蠕变阶段,弹性变形和粘性变形同时在裂纹尖端场中占主导地位,应力和应变具有相同的奇异量级.通过渐近分析求得了裂纹尖端应力、应变和位移分离变量形式的渐近解,并采用打靶法求得了裂纹尖端应力、应变和位移的数值结果,给出了应力、应变和位移随各种参数的变化曲线.数值计算表明,弹性可压缩变形对Ⅰ型裂纹尖端应力场影响甚微,而对应变场和位移场影响较大.裂纹尖端场主要受材料的蠕变指数n和马赫数M控制.当泊松比v=0.5时,可以退化为不可压缩粘弹性材料Ⅰ型动态扩展裂纹.     

无限长条功能梯度材料的反平面裂纹问题

研究了无限长条正交各向异性功能梯度材料在平面剪切作用下的Yoffe裂纹的动力学问题，材料的两上方向的剪切模量假定为指数模型，通过采用积分变换-积分方程方法，求得了裂纹尖端的动态应力场和动态应力强度因子，并研究了裂纹运动速度、几何尺寸、梯度参数和不均匀系数对动态应力强度因子的影响，结果表明，裂纹尖端应力具有的奇异性，裂纹的运动速度越大，应力强度因子越大；材料的模量梯度越大，应力强度因子越低；不均匀系数越大，应力强度因子越小。     

基于SBFEM计算劈拉试件裂纹尖端高阶奇异参数

比例边界有限元法是一种具有半解析性质的数值计算方法,径向位移和应力具有解析的性质,不需要特殊处理裂纹尖端,可以根据定义直接计算应力强度因子以及高阶奇异参数.为此基于比例边界有限元法计算了两种不同荷载作用下三种不同尺寸劈拉试件的奇异应力场,提取了T应力、高阶奇异参数以及应力强度因子.通过典型例题验证了SBFEM的有效性及其精度.数值计算结果表明,比例边界有限元法在计算应力强度因子、T应力和高阶奇异参数时是有效的,且具有较高的精度;联合子结构法（超单元）可以计算复杂形状问题的裂纹尖端奇异场.此外,T应力和高阶奇异参数可以作为进一步研究大体积混凝土材料和结构断裂性能的依据.     

正交异性复合材料板星形裂纹的应力分析

研究了正交异性板中星形裂纹的平面弹性问题。采用复合材料断裂复变方法,选取适当的保角映射和特殊应力函数推出了裂纹尖端附近的应力场及Ⅰ型、Ⅱ型星形裂纹应力强度因子的解析解。     

各向异性复合材料周期性Ⅰ型裂纹尖端应力分析

对各向异性复合材料板的周期性I型裂纹尖端应力场进行了力学分析.通过求解一类线性偏微分方程的边值问题,引入Westergaard应力函数,采用复变函数方法及待定系数法,给出在无穷远处受对称载荷σ作用下,周期性I型裂纹尖端的应力强度因子,推出了各向异性复合材料板周期性I型裂纹尖端附近应力场的理论计算公式.     

Stress distribution and effective stress intensity factor of a blunt crack after dislocation emission

The stress fields induced by a dislocation and its image dislocations around a narrow elliptic void are formulated. Based on the solution, the stress distribution and effective stress intensity factor of a blunt (elliptic) crack were calculated under mode I constant loading. The results show that a dislocation-free zone (DFZ) is formed after dislocation emission. There exists a second stress peak in the DFZ except a stress peak at the blunt crack tip. With an increase in the applied stress intensity factor Kla or the friction stress T, of the material, the DFZ size and the peak stress at the crack tip decrease, but the peak stress in the DFZ and the effective stress intensity factor Klf presiding at the crack tip increase. Because of dislocation shielding effects, shielding ratio Kla/Klf increases with increasing Kla, but it decreases with increasing Tf.     

热载荷作用下含裂纹功能梯度板的有限元分析

为深入理解功能梯度材料的热断裂行为,研究了热载荷作用下任意热机械属性功能梯度材料板的裂纹尖端特性.利用解析方法推导了不含裂纹功能梯度板的温度场和热应力场,根据叠加法,把热应力场转化为裂纹表面载荷,采用基于非均匀单元的有限元方法计算分析了稳态热载荷下功能梯度板的裂纹尖端特性,并针对不同材料热机械属性分布形式,考察了热应力...     

无限长条功能梯度材料自由边界反平面裂纹动力学问题

利用功能梯度材料剪切模量的指数模型,对无限长条自由边界反平面Yoffe裂纹的动力学问题进行了研究.通过积分变换求得了应力场和位移场,将混合边界值问题简化为一组对偶积分方程,并利用Copson方法对动应力强度因子进行了求解.分析了裂纹运动速度、梯度参数及裂纹长度对裂纹尖端动应力强度因子的影响.数值计算表明,动应力强度因子随着裂纹运动速度和裂纹长度的增加而增大,随着梯度参数的增加而降低.     

三相异弹模薄板界面裂缝缝端应力奇异性与应力场(英文)

研究了三相异弹模薄板界面裂缝缝端奇异性与几何边界条件和弹性常数的依赖关系 .采用原点设置在缝端的极坐标系统 ,用复势函数方法推导了缝端应力场的表达式 ,求得应力强度因子 .算例表明 ,本文的解答是正确的 ,并得到一些有意义的结论     

一类弹粘塑性材料II型扩展裂纹的尖端场

为了研究粘性效应作用下的II型扩展裂纹尖端场,假设扩展裂纹尖端的粘性系数与塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定.引入Airy应力函数,求出了裂纹尖端应力和应变场的控制方程.选取适当的特征参数,给出了边界条件,对控制方程通过双参数打靶,进行了数值计算,求得了裂纹尖端的应力应变场.分析与计算结果表明粘性效应是裂纹尖端场的一个重要因素.     

Crack initiation ahead of piled—up of dislocations emitted from a mode Ⅱ blunt crack

In situ tensile tests in a transmission electron microscope (TEM) show that dislocations emitted from a mode II crack tip will form a inverse piled-up group after equilibrium or a double piled-up group when they meet a obstruction, e.g., grain boundary or second phase. A microcrack can initiates in front of the piled-up group of dislocations. Micromechanics analysis shows that dislocations emitted from a mode II blunt crack tip can form a inverse piled-up or double piled-up group, depending upon the applied stress intensity factor K_(lla), lattice friction stress τ_ f and the distance of the obstruction from the crack tip L. The maximum normal stress in front of the double piled-up group which is located at the direction of α = -64° increases with the increase in the stress intensity K_(lla) and the obstruction site L, and the decrease in the friction stress τ_f When it increases to equate the cohesive strength, a microcrack will initiate in front of the piled-up group.     

各向异性复合材料周期性Ⅱ型裂纹尖端应力分析

对各向异性复合材料板的周期性Ⅱ型裂纹尖端应力场进行了有关的力学分析,通过求解一类线性偏微分方程的边值问题,引入Westergaard应力函数、采用复变函数方法及待定系数法,给出在无穷远处受对称载荷τ作用下,周期性Ⅱ型裂纹尖端的应力强度因子,推出了各向异性复合材料板周期性Ⅱ型裂纹尖端附近应力场的理论计算公式。     

Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics, expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack. In fact, the surface of a crack formed during the fracture is usually very irregular. So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one. Considering the irregularity of a real fracture surface or a real crack profile, the crack is taken as a fractal one, and then the real asymptotic form at the crack tip is developed by applying Griffith’s energy balance principle and fractal geometry. Through the developed asymptotic form, it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.

     

Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics, expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack. In fact, the surface of a crack formed during the fracture is usually very irregular. So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one. Considering the irregularity of a real fracture surface or a real crack profile, the crack is taken as a fractal one, and then the real asymptotic form at the crack tip is developed by applying Griffith’s energy balance principle and fractal geometry. Through the developed asymptotic form, it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.     

涂层中裂纹应力强度因子的计算及裂纹扩展

在涂层工作过程中，由于喷涂材料硬度高、抗裂性能差、喷涂工件刚性大工件表面产生应力集中，涂层很容易产生裂纹．对于含初始裂纹的喷涂材料，在拉伸载荷作用下裂纹的扩展与裂尖应力强度因子有很大的关系，根据断裂力学的基本原理，提出了利用数值模拟的方法来计算裂纹尖端的应力强度因子．并讨论了裂纹前沿网格划分对应力强度因子的影响，预测了裂纹扩展时形状的变化．     

涂层中裂纹应力强度因子的计算及裂纹扩展

在涂层工作过程中,由于喷涂材料硬度高、抗裂性能差、喷涂工件刚性大工件表面产生应力集中,涂层很容易产生裂纹.对于含初始裂纹的喷涂材料,在拉伸载荷作用下裂纹的扩展与裂尖应力强度因子有很大的关系,根据断裂力学的基本原理,提出了利用数值模拟的方法来计算裂纹尖端的应力强度因子.并讨论了裂纹前沿网格划分对应力强度因子的影响,预测了裂纹扩展时形状的变化.     

Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surfac...     

正交异性双材料反平面界面裂纹分析

研究了正交异性双材料反平面界面裂纹问题。采用复合材料断裂复变方法,构造了特殊应力函数,通过求解一类偏微分方程组边界问题,推导出界面裂纹尖端附近的应力场、位移场及应力强度因子的表达式,确定了裂纹尖端应力场的奇异性,结果现实裂尖附近应力具有r^-1/2的奇异性,但没有振荡性。