I型裂纹失稳扩展的临界力学条件

本文考虑了裂纹前端塑性区的影响,首次建立了I型裂纹在平面应力和平面应变条件下失稳扩展的能量解析式,并由变分法确定了裂纹的临界尺寸。结果表明,当 或 时,裂纹失稳扩展。讨论表明,裂纹扩展能量随着裂纹尺寸的增加而呈现出先增加后减少的趋势,在临界裂纹尺寸处取得最大值；平面应力条件下裂纹扩展能量高于平面应变条件下裂纹扩展能量；临界裂纹尺寸随外加应力和裂纹张开位移的增大而减少,且平面应力条件下临界裂纹尺寸比平面应变条件下临界裂纹尺寸大。

Critical Mechanical Condition of Unstable Propagation for I Mode Crack

Considering the effect of plastic zone of crack tip, the energy solutions of unstable propagation for I model crack under plain stress and strain conditions are first obtained and the critical sizes are determined by variational method. The result shows that when or the unstable propagation occurs. Discussion shows that the crack propagation energys first increase then decrease as the crack size increases, and obtain their maximum values at critical sizes; the crack propagation energy under plain stress condition is higher than that under plain strain condition; the critical crack sizes increase as the applied stress and crack opening displacement increase, and the critical crack size under plain stress condition is higher than that under plain strain condition.