含裂纹板断裂韧度厚度效应的理论研究

从理论角度对断裂韧度厚度效应进行研究。在线弹性断裂力学与含裂纹板的二维位移场的基础上，给出分离变量型的具有待定函数的三维位移场的表达式，进而通过几何方程与物理方程获取三维应变场和三维应力场。进一步，通过虚位移原理，使用变分方法建立待定函数所应满足的支配方程与边界条件，从而确定待定函数。基于上述分析，建立一个断裂韧度与试样厚度关系的理论表达式。最后通过两种试验材料LY12CZ（L-T）与TC4（L-T）进行验证。

RESEARCH ON THICKNESS EFFECT ON CRACKED PLATE FRACTURE TOUGHNESS

Based on two-dimensional displacement field of cracked plate in the linear elastic fracture mechanics, mathematical expression with unknown function of three-dimensional displacement field are given in variable separating type. Then three-dimensional strain field and stress field are obtained. By means of equations of geometry and physics, the governing equations and boundary conditions of above unknown displacement function are formulated using variational method on the foundation of principle of virtual displacement. The displacement functions are solved by the above method. Three-dimensional effect analysis of cracked plate is conducted by the model of equivalent plane strain and equivalent plane stress sections and the theoretical formulas on the relation between fracture toughness and plate thickness are determined. Two kinds of test materials, LY12CZ(L-T)and TC4(L-T), are used to verify the theoretical equation.