【作者】 王慧；

【导师】 张雪霞；

【作者基本信息】 太原科技大学 ， 数学， 2017， 硕士

【摘要】 随着现代科技的飞速发展,不同材料粘结组合而成的圆柱型双材料结构在很多高新领域都被越来越广泛的应用.其粘结部位传递着层与层之间的相互作用,在一定的外载荷作用下,界面端往往会出现应力集中现象.当应力集中程度过高时,材料结构的工程性能会急剧下降,甚至发生突发性开裂,因而研究圆柱型双材料界面裂纹问题有着十分重要的理论和工程意义.本文借助分离变量法和待定系数法,分别研究了受径向载荷作用下圆柱型各向同性双材料的平面界面裂纹问题和受轴向剪切力作用下的圆柱型功能梯度双材料的反平面界面裂纹问题.对于圆柱型各向同性双材料界面裂纹问题,分别通过构造位移函数和构造应力函数两种方法进行研究.首先将界面裂纹问题转换为偏微分方程组的边值问题,利用变量分离法,将设定的含待定系数的位移函数或应力函数表达成无穷级数的形式.利用待定系数法,借助边界条件,建立方程组,求解得到待定系数,从而求出偏微分方程组边值问题的解,利用位移函数或应力函数与应力、位移的关系式,计算得到级数形式的圆柱型各向同性双材料在径向应力作用下界面裂纹尖端附近的应力和位移的形式表达式.对于圆柱型功能梯度双材料界面裂纹问题,将力学问题转换为偏微分方程的边值问题,引入沿着极径方向连续变化的剪切模量,利用分离变量法和待定系数法,将偏微分方程边值问题转化为代数问题.借助边界条件和连续性条件,推导出奇异积分方程,从而得到满足偏微分方程组的解.利用位移函数与应力、位移关系式,计算得到级数形式的圆柱型功能梯度双材料在轴向剪切力作用下界面裂纹尖端附近的应力场、位移场表达式以及应力强度因子的表达式.更多还原

【Abstract】 With the rapid development of modern science and technology,the cylindrical bi-material structure bonded by different materials has been widely used in many high-tech fields.The bonding parts transmit the interaction between layer and layer,and in certain under external loading,the interface end tends to appear the stress concentration phenomenon.When the degree of stress concentration is too high,there will be a sharp drop in the engineering quality of the material structure,or even sudden destruction,therefore,the study of interface crack problems of cylindrical bi-material has important theoretical significance.Through means of variables separation method and the method of undetermined coefficients,the authors respectively studied the cylindrical isotropic bi-materials planar interface crack problem under the stress of the radial load and the cylindrical function gradient bi-material anti-plane interface crack problem under the action of axial shear force.As to the cylindrical isotropic bi-material interface crack problem,it was studied respectively by two kinds of methods which constructed the displacement function and tectonic stress function.Firstly,the authors converted the interface crack problem to boundary value problems of partial differential equations.By using the variable separation method,the stated containing of undetermined coefficients of displacement function and stress function was expressed by the form of infinite series.Using the method of undetermined coefficients,with the aid of boundary conditions to establish the system of equations,then the authors got the solution of undetermined coefficients,thus the authors obtained the solution to boundary value problems for partial differential equations,using displacement function or the relation between stress function and the stress and displacement,the formal expression of stress of the cylindrical isotropic bi-material near the interface crack tip and displacement under the effect of radial stress,with the form of the series,was calculated.For cylindrical functionally graded material interface crack problem,converting mechanical problems to partial differential equations boundary value problem,the authors introduce a continuous variation of shearmodulus in diameter direction,by using the variable separation method and the method of undetermined coefficients,converting the boundary value problems of partial differential equations into algebraic problems.With the aid of boundary conditions and continuity conditions,the singular integral equation is deduced,and the solution of partial differential equations is obtained.Using the relation between displacement function and stress and displacement equation,the authors calculated the expression of cylindrical function gradient bi-material near the interface crack tip stress field and displacement field under the action of axial shear stress and the expression of stress intensity factor.更多还原