平面远场受拉孔洞塑性区半径应变梯度解

Strain Gradient Plasticity Solutions of Plastic Region Radius for a Borehole Problem

在应变梯度理论框架下,分别采用双剪屈服准则和Tresca屈服准则对弹塑性平面均匀受拉孔洞问题进行了分析,得到了相应塑性区半径计算公式,并与基于Mises屈服准则得到的结果进行了对比。研究发现,基于双剪屈服准则得到的解偏小,基于Tresca准则得到的解偏大,基于Mises屈服准则得到的解大小介于二者之间。此外,研究结果还表明,塑性区半径随材料硬化指数的增大而增大,且当孔洞的特征尺寸在微米量级时,基于应变梯度理论得到的结果与经典塑性解有显著差异。

In the framework of the strain gradient plasticity theory ,an analysis was conducted for the pro-blem of an elasto-plastic plane strain body containing a circular hole and subjected to uniform far field stress based on the twin-shear stress yield criterion and the Tresca yield criterion. The expressions of plastic region radius were derived and compared with that based on the Mises yield criterion. It was shown that the plastic region radius increases with the increasing material hardening exponent. The solu- tions based on the twin-shear stress yield criterion and the Tresca yield criterion are smaller and larger than that derived from the Mises yield criterion respectively. It was also indicated that the difference be-tween strain gradient solution and classical solution is significant as the borehole size on the order of mi-cron.