摘要
基于梯度塑性理论,分析了应变软化及真实裂纹扩展阶段的局部化带的张拉位移和转角。在弹性阶段,可以由弹性理论来确定二者的关系。真实裂纹出现后,利用平衡条件、几何条件及梯度以来的应变软化本构关系,得到了真实裂纹长度与局部化带长度的关系。当真实裂纹刚出现时,局部化带长度达到最大值。在任何阶段,局部化带到中性轴的距离单调降低,局部化带的张拉位移和转角受梁深、带宽、弹模及下降模量等的影响。弹模及下降模量越大,带宽越小,则局部化带的张拉位移和转角都增加。而且,在前两个阶段,张拉位移都线性增加,但在后两个阶段,转角都非线性增加。
The tensile displacement and angle of rotation of tensile strain localized band are analyzed in strain softening stage and in real crack propagation stage based on gradient-dependent plasticity. In elastic stage, the effect of strain gradient can be neglected due to uniform elastic deformation. The relation between the displacement and the rotation is determined by classical elastic theory. After the real crack is initiated in the tensile side of the three-point bending beam, using the stress equilibrium, assumption of plane cross sections and strain softening constitutive relation dependent on strain gradient, a relation between real crack length and tensile strain localized band length is presented. When the real crack just occurs, the tensile stress in the tensile side of the beam is decreased to zero and the tensile localized band length reaches its maximum. In each stage, the distance between neutral axis and tensile strain localized zone decreases monotonously. Both the tensile displacement and angle of rotation of tensile strain localized band are influenced by depth of beam, thickness of localized band, elastic modulus and softening modulus, etc. The opening displacement and angle of rotation increase with softening modulus, elastic modulus and decreasing thickness of localized band. In addition, the tensile displacement increases linearly in elastic stage and strain softening stage. However, the angle of rotation increased nonlinearly in strain softening stage and in real crack propagating stage.
出处
《工程力学》
EI
CSCD
北大核心
2005年第1期63-68,共6页
Engineering Mechanics
基金
国家自然科学青年基金项目(50309004)
关键词
梯度依赖塑性
真实裂纹扩展
应变局部化:三点弯梁
裂纹张开位移
Bending (deformation)
Crack initiation
Crack propagation
Elastoplasticity
Gradient methods
Strain
Stress analysis
