摘要
研究了单轴压缩岩样应变软化阶段侧向应变与轴向应变的比值(峰后泊松比)的变化规律。岩样的塑性变形假设根源于塑性应变局部化。岩样的轴向及侧向变形被分别分为两部分:弹性变形(由虎克定律描述)及由局部化引起的塑性变形(由梯度塑性理论及几何关系确定)。应变软化阶段的轴向应变-侧向应变曲线、轴向应力-轴向应变曲线及轴向应力-侧向应变曲线都得到了实验验证。在峰值强度时,峰后泊松比等于峰前泊松比。当压缩应力降至零时,峰后泊松比达到临界值。该临界值可能比峰前泊松比大,也可能比它小。峰后泊松比还和试件尺寸有关,这与峰前泊松不同。峰后泊松比与轴向压应力之间的关系可能是一条直线,也可能是上凸的,或上凹的。这取决于岩石的本构参数(弹性模量、剪切及软化模量、剪切带宽度及峰前泊松比)、试件的结构尺寸(试件宽度及高度)及剪切带倾角之间的关系。
The ratio of lateral strains to axial strains at the strain-softening stage in uniaxial compression, which is termed as the post-peak Poisson＇s ratio, is studied analytically. It is assumed that plastic deformation stems from the localization of shear strain. After the localization is initiated at peak strength, axial and lateral strains are each decomposed into two parts. One is elastic strain described by elastic mechanics; the other is plastic part determined by gradient-dependent plasticity and geometrical relations. At the strain-softening stage, lateral strain-axial strain relation, lateral strain-axial strain relation, and axial stress-axial strain relation were verified by existing experiments. At the peak strength, the localization is just initiated and the post-peak Poisson＇s ratio is equal to the Poisson＇s ratio at the elastic stage. When compressive stress reaches zero, a critical value of the post-peak Poisson＇s ratio is achieved. Whether the critical value is greater than the Poisson＇s ratio at the elastic stage or not, the constitutive parameters of rock material, the geometrical size of the specimen and inclination angle of the shear band play an important role. It is possible for linear, upwards concave or upwards convex relations between the post-peak Poisson＇s ratio and the flow compressive stress. Generally, a post-peak Poisson＇s ratio depend on the flow compressive stress and is concerned with geometrical size. Therefore, the Poisson＇s ratio cannot be seen as a material constant, which is different from the Poisson＇s ratio at the elastic stage.
出处
《工程力学》
EI
CSCD
北大核心
2006年第4期99-103,共5页
Engineering Mechanics
基金
国家自然科学青年基金项目(50309004)
关键词
应变局部化
剪切带
轴向应变
侧向应变
峰后泊松比
单轴压缩
梯度塑性理论
strain localization
shear band
axial strain
lateral strain
post-peak Poisson＇s ratio
uniaxial compression
gradient-dependent plasticity
