圆柱型双材料界面裂纹问题研究

发布时间：2018-10-15 07:56

【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.
[Abstract]:With the rapid development of modern science and technology, cylindrical bimaterial structures composed of different materials are more and more widely used in many high-tech fields. The interaction between the layers is transmitted at the bonding site, and stress concentration often occurs at the interface end under a certain external load. When the stress concentration is too high, the engineering properties of the material structure will drop sharply and even break out suddenly. Therefore, it is of great theoretical and engineering significance to study the interfacial crack problem of cylindrical bimaterial. In this paper, by means of the method of separating variables and the method of undetermined coefficients, The plane interface crack problem of cylindrical isotropic bimaterials under radial loading and the anti-plane interface crack problem of cylindrical functionally graded materials subjected to axial shear force are studied respectively. The problem of interfacial crack in cylindrical isotropic bimaterials is studied by constructing displacement function and stress function respectively. Firstly, the interface crack problem is transformed into a boundary value problem of partial differential equations. By using the method of variable separation, the set displacement function or stress function table with undetermined coefficients is obtained in the form of infinite series. By using the undetermined coefficient method and the boundary conditions, the equations are set up, and the undetermined coefficients are obtained. The solution of the boundary value problem of partial differential equations is obtained, and the relationship between the displacement function or the stress function and the stress and displacement is obtained. The formal expressions of stresses and displacements near the tip of interfacial cracks of cylindrical isotropic bimaterials with series form under radial stress are obtained. For the cylindrical functionally gradient interface crack problem, the mechanical problem is transformed into the boundary value problem of partial differential equation. The shear modulus continuously varying along the polar diameter is introduced, and the separation variable method and the undetermined coefficient method are used. The boundary value problem of partial differential equation is transformed into algebraic problem. By using boundary conditions and continuity conditions, the singular integral equations are derived and the solutions satisfying the system of partial differential equations are obtained. The stress field, displacement field and stress intensity factor near the interface crack tip of cylindrical functionally graded materials with series form under axial shear force are calculated by using displacement function, stress and displacement relations.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O346.1

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