准脆性材料试件应变软化尺度效应理论研究

SIZE EFFECT ANALYSIS ON STRAIN SOFTENING OF QUASI-BRITTLE MATERIALS CONSIDERING STRAIN GRADIENT EFFECT

研究了由于剪切局部化而引起的试件长度的尺寸效应。基于可以考虑微结构相互作用的非局部理论,得到了非局部塑性剪应变与局部塑性剪应变及其二阶应变梯度的关系。通过获得剪切带内部的塑性剪切应变,得到了岩样轴向的平均应变与位移的理论关系。研究结果表明,这一关系具有尺寸效应。随着试件高度的增加,应力-应变曲线变陡;当试件高度非常大时,发生II类变形行为,而且,随着剪切带倾角的增加,应力-应变曲线也变陡。将理论结果与前人的试验结果进行了比较,结果表明吻合良好。

The effect of length due to shear localization is studied. Based on non-local theory considering interaction among microstructure, non-local plastic shear strain is obtained, and dependent on local plastic shear strain and its second spatial gradient. For simplicity, shear band is treated as one-dimensional problem and the closed-form solution on plastic shear strain in shear band is obtained. Then, an analytical relation between axial average strain (or displacement) and axial compressive stress is obtained, which exhibits size effect. The relation becomes steep as length is increased and class II behavior can occur as length is large. Besides, the relation also becomes steep as inclination angle of shear band increases. The presented theoretical results are compared with a few existing experimental results and the agreement is good.