裂纹扩展阻力曲线与剩余强度关系的理论研究

Mathematical research on the relation between resistance curve of crack growth and residual strength

从断裂力学角度出发 ,给出裂纹扩展阻力曲线的数学理论表达式 ,证明KR 是裂纹扩展量Δa的函数 ,与初始裂纹长度a0 无关。同时 ,根据裂纹扩展阻力曲线的理论公式 ,得到结构剩余强度的数学表达式 ,利用该式可以获得剩余强度的准确解 ,从而方便的获取结构剩余强度图。最后 ,通过实例验证上述方法的可行性。

An mathematical expression for resistance curve of crack growth is obtained in fracture mechanics. It is verified that resistance stress intensity factor in crack propagation, K R, is only dependent on the increment, Δ a , from initial crack length to current crack length. Based on mathematical expression for crack growth resistance curve, the equation about residual strength of cracked component is obtained. Thus, by solving the equation the precise solution can be acquired and graphs of residual strength can be drawn conveniently. Some examples are given to make sure that the mathematical expression for crack growth resistance curve is effective.