平面应力Ⅰ型准静态扩展裂纹尖端场的弹粘塑性分析  

Elastic-viscoplastic Analysis of the Tip Field of a Mode Ⅰ Quasi-static Propagating Crack under Plane Stress Condition

作　　者：贾斌[1] 李加雷[2] 庞宝君[1] 王振清[2] 

机构地区：[1]哈尔滨工业大学航天工程系,哈尔滨150001 [2]哈尔滨工程大学航天与建筑工程学院,哈尔滨150001

出　　处：《机械工程学报》2011年第8期99-103,共5页Journal of Mechanical Engineering

基　　金：中国博士后科学基金资助项目(20100471059)

摘　　要：由于材料率敏感性的影响,蠕变材料中裂纹尖端场的分析更加复杂。采用弹粘塑性力学模型,并假设粘性系数为等效塑性应变率的幂函数,推导出理想弹塑性材料的一种率敏感型本构关系。通过量级匹配表明裂纹尖端场具有幂奇异性,奇异性指数由粘性系数中的幂指数唯一确定。推导出平面应力条件下准静态扩展裂纹尖端场的控制方程,并给出I型裂纹的边界条件。采用双参数打靶法,结合各材料参数的可能取值范围,对控制方程进行了数值求解,并讨论裂尖场特性随各材料参数的变化规律。结果表明当材料服从理想塑性规律时,裂纹尖端的应力场是连续的,不存在某些无粘性解中出现的不合理间断线。裂尖场应力强度由材料的粘性所控制,泊松比对于裂尖场没有影响,并且不存在弹性卸载区。The analysis of crack tip field is more complex in creeping materials because of the influence of rate-sensitivity.An elastic-viscoplastic constitutive model is adopted and a rate-sensitive constitutive relationship is derived for elastic-perfectly-plastic materials,under the assumption that the viscosity coefficient is a power function of the rate of effective plastic strain.It is obtained through dimension match that the crack tip field possesses power singularity,and the singularity exponent is uniquely determined by the power exponent in the supposed viscosity coefficient.The governing equation of quasi-static propagating crack tip field under plane stress condition is derived,and the boundary conditions are given for mode I crack.Numerical solution of governing equation is conducted by using two-parameter shooting method in combination with possible value range for each material parameter,and variations of crack tip field characters according to each material parameter are discussed.The results indicate that the stress field at crack tip is continuous when the material complies with the perfect-plastic rule,without the irrational discontinuity line that exists in some non-viscosity solutions.The stress intensity is dominated by the material viscosity and the Poisson＇s ratio has no influence on tip field.Moreover,there exists no elastic unloading zone within the tip field.

关 键 词：扩展裂纹 裂纹尖端 粘塑性 平面应力 

分 类 号：O346[理学—固体力学]