剪切带内部应变(率)分析及基于能量准则的失稳判据

ANALYSIS OF STRAIN AND STRAIN RATE IN SHEAR BAND AND ITS INSTABILITY BASED ON ENERGY CRITERION

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。

A theoretical analysis of localized strain and strain rate in shear band after localization occurs beyond the peak shear stress is carried out based on the strain gradient plasticity theory. The influences of the shear descending modulus, the internal length parameter of rock material, the differential stress and shear stress rate on shear localization are investigated. A theoretical (or constitutive) relation between flow shear stress and relative sliding displacement of shear band is deduced. A constitutive relation between flow shear stress rate and the relative sliding velocity of shear band is also obtained. The influences of the shear descending modulus and the internal length parameter of rock material on instability of shear band are analyzed. The direct shear test machine is simplified as a system composed of a rock specimen (i.e. shear band) and a steel block. The energy criterion is applied to the instability analysis of the system and a criterion of instability is put forward. If the shear descending modulus of rock and the equivalent length of the steel block is low or the internal length parameter of rock material and the shear stiffness of the steel block is large, then shear band can slide easily along its tangential direction, i.e., the system is prone to instability.