摘要
本文研究了材料的弹塑性性质对球体中空穴生成问题的影响,材料的弹性用一种可压超弹性材料的本构关系来描述,材料的塑性用满足材料的不可压条件和Tresca屈服条件的理想塑性材料的本构关系来描述。这类超弹性-塑性材料中可以发生空穴的生成现象,得到了在表面拉仲作用下球体中空穴生成时空穴半径与临界拉伸之间的关系式和临界拉伸。球体的变形可分为弹-塑性变形阶段和完全塑性变形阶段,球体中心首先形成塑性变形区域,并有空穴的突然生成;塑性变形区域能够快速增长,并且使球体很快进入完全塑性变形阶段;空穴在弹-塑性变形阶段迅速增长,但进入完全塑性变形阶段后增长较慢。同时给出了不同变形阶段球体中的应力分布。数值结果表明材料的塑性性质对材料中的空穴生成有明显的影响。
The effect of plasticity of material on spherical cavitation problem was studied. The constitutive relation of one of the compressible hyperelastic material is used to describe the elastic deformation of the sphere. The constitutive relation of the perfectly plastic material, which is assumed to be incompressible and satisfies the Tresca yield criterion is used to describe the plastic deformation of the sphere. Cavitation phenomenon may be found in this elastic-plastic material. Formulae between the cavity radius and the stretch were obtained. The critical stretch was given too. Deformations of the sphere include elastic-plastic deformation and full plastic deformation. The plastic deformation first appeared in the center of the sphere and the suddenly formation of cavit was found. The plastic deformation region may get a quickly increasing and so the sphere went into the full plastic deformation. The cavity may get a rapid increasing for the elastic-plastic deformation but a slower increasing for the full plastic deformation. The distributions of stresses are discussed, too. Numerical results indicate that the effect of plasticity on cavitation for the material is ver obvious.
出处
《力学季刊》
CSCD
北大核心
2003年第4期440-444,共5页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(10272069)
上海市重点学科建设资助项目
上海大学科学技术发展(214390)
关键词
超弹性-塑性材料
空穴生成
应力分布
hyperelastic-plastic material
void nucleation
distribution of stress
