基于能量密度等效和三维尺寸的Ⅰ型裂纹试样弹塑性问题的半解析求解

Semi-analytical Elastoplastic Solutions for Mode-Ⅰ-Crack Specimens Based on Energy Density Equivalence and Three-dimensional Sizes

Ⅰ型裂纹是工程中最常见也是最主要的裂纹类型,半个世纪以来,弹塑性断裂力学多是基于平面的Ⅰ型裂纹问题展开的。然而,对于含有限尺寸三维约束的断裂力学Ⅰ型裂纹问题,具有解析表征的三维Ⅰ型裂纹试样的J积分求解至今仍然是难题。基于能量密度等效方法,针对具有三维尺寸的Ⅰ型裂纹试样,分别提出了用于描述载荷-J积分关系和载荷-位移关系的半解析模型,模型的7个理论常数可以由有限元分析简单获得。针对6种Ⅰ型裂纹试样进行了三维有限元分析,结果表明,新模型对不同材料、不同构形、不同尺寸的受载试样预测的载荷-J积分曲线和载荷-位移曲线与有限元分析结果密切吻合,之间的比较优度均超过0.94。新模型可用于发展包括小试样试验的断裂性能非传统试验方法。

Mode-Ⅰ-crack is the main type of cracks in engineering structure components.Ⅰn the last half century,elastoplastic fracture mechanics mainly focused on plane problem of mode-Ⅰ-creak.However,for three-dimensional specimens of the ductile materials with mode-Ⅰ-crack,it is still very difficult to obtain analytical expressions for the J-integral.Based on the energy density equivalence,for mode-Ⅰ-crack specimens with three-dimensional sizes of ductile materials,two novel semi-analytical models are proposed to describe the load vs.J-integral relation and load vs.displacement relation,respectively,and the seven theoretical constants of the two model can be simply determined by three-dimensional elastoplastic finite element analysis(FEA).Three-dimensional finite element analysis for six types of mode-Ⅰ-crack specimens with different materials and different dimensional sizes were carried out.Ⅰt shows that the results predicted by the novel models for the load vs.J-integral curves and load vs.displacement curves of different types of the specimens with different materials and different sizes are closely consistent with those from FEA,and the fit goodness between the curves predicted by the model and those from FEA are greater than 0.94.The new model can be used to develop fracture performance test methods of non-traditional specimen.