I型裂纹应力场的精确解和近似解的比较

应力场的精确解与近似解之间存在一定的误差。用Muskhelishvili应力函数方法求出I型裂纹应力场的精确解及近似解,不仅从数据上将两种解进行比较,分析两者之间存在的误差,而且分别绘制出两种解随r和a比值变化的曲线图,从而用图形的方法对两者进行比较,最终对近似解的使用范围给出界定。通过比较可知,近似解只适用于表示裂纹尖端附近的应力场。而在工程断裂力学的实际使用中,通常也只考虑裂纹尖端附近的应力场。

Comparison of accurate and approximate values of stress fields of crack I

Certain difference exists between the accurate and the approximate values of stress fields.This paper arrives at the accurate and the approximate values of stress fields of crack I with Muskhelishvili stress function,and then analyzes the difference between them.It draws a graph to show the values' change with the ratio of r and a,on the basis of which,it compares the values again and defines the applications of the approximate values.It's held that the approximate values are only suitable for the stress fields near the crack points;and in engineering fracture mechanics,only the stress fields near the crack points need to be taken into account.