基于统一强度理论的远场受拉孔洞塑性区半径解

Solutions of plastic zone radius for a borehole problem based on unified strength theory

采用统一强度理论考虑中间主应力和材料SD效应的影响,借鉴应变梯度理论对平面受拉孔洞进行弹塑性分析,得到相应塑性区半径计算公式和相关影响因素。结果表明,材料拉压强度比α值和强度参数b值对孔洞塑性区半径r0有较大影响,与b=0时相比,b=1时r0值减小了20%;当孔洞尺寸为微米量级时,考虑应变梯度理论的塑性区半径解与经典塑性解有明显差异,且孔径α和材料硬化指数m越大,孔洞塑性区半径r0越大。改变统一强度理论参数获得一系列计算结果,计算结果合理,且具有一定的统一性和实用价值。

Based on unified strength theory ,considering the intermediate principal stress and SD effect and using strain gradient theory ,the elasto-plastic analysis was carried out for a borehole problem ,and the formulas of plastic zone radius were deduced and some influence factors were analyzed . The results indicated that the tension-compression ratio αand the strength coefficient b had obvious effects on the plastic zone radius so that the value of r0 decreased by 20% when b changed from 0 to 1 ;The solution of plastic zone radius with effects of strain gradient theory showed significant difference from the classical solution when the aper-ture reached micrometers , in the meantime , the plastic region radius becomes larger as the aperture or material hardening expo-nent increases .Choosing different parameters of unified strength theory ,the solution in this paper can be simplified to some ex-isting solutions ,which has a little unity and practical value .