简单剪切条件下岩石剪切带主应变轴偏转角理论研究

Theoretical study of the principal strain axis rotational angle of shear bands of rocks in simple shear

主应变轴偏转是塑性剪切变形的一种结果.同时,主应变轴偏转又会在一定程度上影响变形,从而可能对灾害孕育及发生产生某种影响.因此,正确认识主应变轴偏转角的范围及演变规律对于一些灾害的机理分析及预防可能具有重要的意义.本文在小变形条件下,基于梯度塑性理论的水平剪切带位移公式,并考虑到已有的主应变方向和主应变轴偏转角之间的联系,推导了简单剪切条件下含应变梯度岩石剪切带主应变轴偏转角公式.得到了下列结果,对于左旋剪切带,主应变轴偏转角等于剪切带倾角与45°之差;对于右旋剪切带,主应变轴偏转角等于45°与剪切带倾角之差.基于梯度塑性理论和仿射变换,制作了简单剪切条件下含应变梯度的虚拟剪切带.采用数字图像相关方法对虚拟剪切带主应变轴偏转角进行了测量,获得了虚拟剪切带中心的主应变轴偏转角随虚拟剪切带倾角的演变规律和过虚拟剪切带中心且垂直于虚拟剪切带测线上主应变轴偏转角分布,通过与理论解对比,验证了数字图像相关方法的主应变轴偏转角的正确性.

The principal strain axis rotation is a kind of results of plastic shear deformations.At the same time,the principal strain axis rotation will affect deformations to a certain extent,which may have some impacts on pregnancy and occurrence of disasters.Therefore,correctly understanding the range and evolution of the principal strain axis rotational angle may be of great significance to analyze mechanisms of disasters and to prevent them.In this paper,under small deformation of rock,the formula of the principal strain axis rotational angle of the shear band with strain gradient was derived based on the horizontal shear band displacement formula based on gradient-dependent plasticity considering the relationship between the existing principal strain direction and the principal strain axis rotational angle.The following results were obtained.For the sinistral shear band,shear band inclination minus 45°is equal to the principal strain axis rotational angle;for the dextral shear band,45°minus shear band inclination is equal to the principal strain axis rotational angle.Based on gradient-dependent plasticity and affine transformation,fictitious shear bands with strain gradient under simple shear were generated.The digital image correlation method,was used to measure principal strain axis rotational angles of fictitious shear bands.The evolution of the principal strain axis rotational angles at fictitious shear band centers with fictitious shear band inclination was obtained.The principal strain axis rotational angle measured by the digital image correlation method were validated by comparing the theoretical result with the principal strain axis rotational angle distribution at the monitored line crossing fictitious shear band centers and perpendicular to the fictitious shear band.This present paper revealed the linear relation between the principal strain axis rotational angle and the shear band inclination of rocks in simple shear in theory and provided a new way for estimating the principal strain axis rotational angles of shear bands.The theoretical study under other conditions needs to be further developed.