T应力对岩石裂纹扩展路径及起裂强度的影响研究

Effect of T-stress on crack growth path in rock and fracture strength

经典断裂判据在分析岩石起裂角度及强度时,往往只选择裂尖应力场展开式中的r^(1/2)奇异应力项,而将高阶的O(r^(1/2))项以及非奇异应力项(T应力)忽略,造成理论预测并不能完全吻合实际的试验结果。在充分考虑非奇异应力项对裂纹扩展影响作用的基础上,利用最大周向应力判据重新研究了岩石类材料脆性破坏的I、II及I-II复合型裂纹扩展。研究结果表明:(1)纯I型裂纹状态下,T应力为负时(压缩),裂纹的扩展是稳定的;而当T应力为正时(拉伸),只有当T2πr1/2<3K_1/8,裂纹才沿着裂纹方向扩展(经典断裂判据所预测的方向),而其他情况下裂纹的扩展将发生偏转;(2)纯II型裂纹时,不仅沿着裂纹方向的T应力影响起裂角度及强度,垂直裂纹面上的N应力也同样具有重要的影响作用;(3)对I-II型裂纹而言,修正后的最大周向应力准则与试验结果吻合良好,且正的T应力增大开裂角,而负的T应力降低开裂角。通过控制T应力的大小,可以对裂纹扩展方向加以控制,从而使得裂纹扩展偏离最危险的方向,最大地限度阻止或延缓结构整体断裂的发生。

In the classical crack-tip stress field, the singular stresses（r^1/2 term） near the crack tip are characterized by a single parameter, i.e. the stress intensity factor K. Therefore, the O（r^1/2） term and the secondary non-singular term（T-stress） are always ignored. However, the stress and strain fields around the crack tip are influenced considerably by the T-stress. In this paper, the conventional fracture growth criteria, i.e. the maximum tangential stress criterion is modified to take into account the effect of T-stress, and is used to study the fracture growth when subjected to modes I, II or mixed mode（I/II） loading. The results show that：（1） In the pure mode I loading condition, if the T-stress is negative（compression）, the crack growth is stable. However, if the T-stress is positive（tensile）, the crack grows along the crack direction only when T√2πr 〈3K/ 8, otherwise, the crack growth direction will be changed.（2） In the pure mode II loading condition, the crack growth direction and the loading capacity are influenced not only by the stresses along the fracture direction（T-stress） but also by the normal stress on the fracture.（3） For the mixed loading condition, the T-stress consideration in the fracture criteria leads to better agree with the experiments. The positive T-stress results in an increase in crack growth angle, while the negative T-stress decreases that angle. The results reveal that it is benefit to control the T-stress to change the crack growth direction, in order to avoid the most dangerous crack growth direction or stopping/slowing down the overall structural fracture.