正交各向异性圆柱体在轴压作用下的应力场

Stress Field of Orthotropic Cylinder Subjected to Axial Compression

基于材料体积不可压假设,对轴向压缩作用下圆柱试件在加载面内的环向和径向应力分布进行理论分析,计算结果表明:当试件材料本构为正交各向异性时,环向和径向应力分布为半径的幂函数形式;试件材料为横观各向同性时,环向和径向应力为半径的二次函数.在圆柱试件轴线上环向和径向应力相等,且均具有最大值;试件圆周边界上径向应力为0,环向应力具有极小值.通过最大拉伸应变破坏理论对试件环向应变进行分析,获得了产生环向拉伸破坏时的临界轴向载荷;并采用Hill-蔡强度理论对试件圆周边界上计算得到的应力参量进行描述,得到了轴压作用下圆柱试件的Hill-蔡强度理论表达式,其不仅取决于轴向应力和试件材料的基本力学性能,还与试件轴向变形的应变率及应变率随时间的变化率相关.

Based on the material volume constancy hypothesis, circumference and radial stresses of cylinder specimen were analyzed when the cylinder is loaded along the axial direction. Circumference and radial stress distribution is radius parameter power function when specimen material constitutive relation is orthotropic. The stress distribution is radius parameter quadrat- ic function for transveme isotropy material. Along the cylinder axial line, circumference and ra- dial stresses were maximum and equal to each other. In the circumference boundary surface, radial stress is zero and circumference stress value is the minimum. The max tensile circumference strain failure theory is applied to calculate critical axial loading. Circumference boundary layer failure criterion of orthotropic material cylinder is described by Hill-Tsai strength theory. The obtained strength theory is not only related to axial stress and specimen material mechanical properties, but also to specimen axial deformation strain rate and change rate of strain rate.