紧凑拉伸试件应力强度因子的解析-变分解法以及有关系统计算结果

本文推导了在材料断裂性能测试中常见的受钉传载荷含边缘裂纹试件应力与位移的函数项级数表达式。该级数逐项满足弹性力学所有基本方程、裂纹表面边界条件与绕钉孔的合力平衡条件以及位移单值条件。通过以最小势能原理为基础的变分方程满足其余的静力边界条件,从而求解级数中的待定系数并确定应力强度因子。计算结果表明,级数收敛迅速、正确,计算节省机时,简化数据准备工作。本文还通过计算指出了目前通用的有关矩形紧凑拉伸试件应力强度因子计算公式与曲线的不准确性并且给出了正确、系统的计算曲线,同时还提供了圆形紧凑拉伸试件系统的计算结果。

Analytical -Variational Method of Solution with Relevant Systematical Computational Results about Stress Intensity Factors of Compact Tension Specimens

In this paper, series expressions with functional terms of stress and displacement components about specimens containing edge cracks and subjected to pin-loads, frequently encountered in fracture behavior tests of materials are derived. These series satisfy all of the governing equations, crack surface boundary conditions term by term. Furthermore, some additional multi-valued terms in these series are introduced to satisfy the prescribed resultant conditions of forces and single-valued conditions of displacements around pin-holes. The undetermined coefficients in the above series are solved by means of variational equations based upon principle of minimum potential energy to satisfy the remaining boundary conditions. There are only line integrals in the above variational equations, which can be transformed into linear algebraic simultaneous equations with the undetermined coefficients as unknowns. Subsequently, the stress intensity factors can be solved. The computational results show that, the series converge rapidly, and the computations are very time-saving and data manipulation can be significantly simplified. In this paper, the inaccuracies about empirical formulas and computational curves of rectangular compact tension specimens obtained by boundary collocation method, due to unappropriate simplification of boundary conditions are denoted and the correct systematical computational results of stress intensity factors about rectangular and circular compact tension specimens are carried out by means of analytical-variational method which can be applied to the edge cracked plates with arbitrary geometrical configuration.