Semi-analytic stress field model of the mode-Ⅱ crack tip under finite plane strain conditions
王志强 1肖怀荣 1蔡力勋 1黄茂波1
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作者信息
1. 西南交通大学力学与航空航天学院,应用力学与结构安全四川省重点实验室,成都 610031
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摘要
针对幂律材料、有限平面应变紧凑拉伸剪切(Compact Tension and Shear,CTS)试样,基于能量密度等效方法可得到CTS试样能量密度中值点的代表性体积单元(Representative Volume Element,RVE)的等效应力解析解,以该应力解作为特征应力因子,采用表征CTS试样Ⅱ型裂纹尖端应力场的三角特殊函数,提出了描述有限平面应变幂律塑性Ⅱ型裂纹尖端应力场的半解析模型以及用于描述Ⅱ型裂纹尖端扇贝轮廓式等应力线的理论解.本文Ⅱ型裂纹裂尖场模型对平面应变CTS试样裂尖应力场的预测结果与有限元分析结果密切吻合,Ⅱ型裂纹裂尖幂律塑性应力场模型完善了弹塑性断裂力学,并对剪切型断裂安全评价有重要工程意义.
Abstract
Based on the energy density equivalent method,the equivalent stress analytical equation of the representative volume element(RVE)at the median point of energy density is obtained.For compact tension and shear(CTS)specimens under finite plane strain conditions,a semi-analytical model describing the stress field of the mode-Ⅱ crack tip and a theoretical solution describing the scallop contour isostress line of the mode-Ⅱ crack tip are proposed,with the median RVE equivalent stress solution as the characteristic stress factor and triangular special function characterizes the stress field of the mode-Ⅱ crack tip.The prediction of the new model for the CTS specimen closely agrees with the finite element analysis results.The new model enriches the elastoplastic fracture mechanics and has engineering importance for evaluating shear fracture safety.
关键词
幂律塑性/有限平面/Ⅱ型裂纹/半解析模型/应力场
Key words
power law plasticity/finite plane/mode-Ⅱ crack/semi-analytic model/stress field
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