塑性修正及相互作用对岩石裂尖塑性区影响的研究

Study on the Distribution of Crack Tip Plastic Zone of Rock Considering the Multi-Cracks Interaction and Plastic Correction

岩石内多裂纹由于相互作用的影响,其裂纹尖端塑性区分布与单裂纹有着很大不同.针对多裂纹相互作用,以对称分布的三共线裂纹为例,采用等效夹杂理论提出了裂尖应力强度因子的塑性修正方法.在此基础上,基于Drucker-Prager(D-P)强度准则推导相互作用下各裂纹尖端的塑性区边界方程,并分析了裂纹长度比值、裂纹倾角及裂纹间距对裂纹尖端塑性区分布的影响.结果表明:对裂尖应力强度因子进行塑性修正后,各裂纹尖端塑性区尺寸均增大;裂纹相互作用使得各裂纹尖端塑性区尺寸增大;随着中心裂纹与外裂纹长度比值的增加,外裂纹内外尖端塑性区尺寸受裂纹相互作用的影响逐渐加强,而中心裂纹尖端塑性区尺寸受裂纹相互作用的影响逐渐减弱;裂尖塑性区尺寸受裂纹相互作用的影响与裂纹倾角无关;同一裂纹间距下,中心裂纹尖端塑性区尺寸受相互作用的影响最强,外裂纹外尖端最弱,且随着裂纹间距的增加,裂纹相互作用的影响越来越小.

Due to the interaction of multiple cracks in the rock,the distribution of the crack tip plastic zone is very different from that of a single crack.To consider the multi-crack interaction,based on the symmetrically distributed tri-collinear cracks,a plastic correction method for the crack tip stress intensity factor using the equivalent inclusion theory has been proposed.Using the proposed method,the boundary equation of the plastic zone at each crack tip under the interaction is derived based on the Drucker-Prager(D-P)strength criterion.Moreover,the effects of crack length ratio,crack inclination and crack spacing on the distribution of the crack tip plastic zone of the crack are analyzed.The results show that,for plastic correction of the crack tip stress intensity factor,the size of the plastic zone at each crack tip increases;the interaction between the cracks increases the size of the plastic zone at each crack tip;as the ratio of the length of the central crack to the outer crack increases,the interaction of the cracks for the inner and outer tips of the size of plastic zone at outer crack are gradually improved,while the plastic zone size of the central crack tip decreases;the interaction between the cracks has nothing to do with the crack inclination;under the same crack spacing,the size of plastic at the tip of central crack is mostly affected by the interaction,and that of the outer tip of outer crack is the least.With the increase of the crack spacing,the influence of the interaction between the cracks becomes smaller and smaller.