The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.

中文翻译：

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旋转功能梯度厚圆柱应变梯度塑性的解析解

基于应变梯度理论研究了旋转功能梯度（FG）圆柱体的弹塑性变形。控制方程是根据修改后的 von Mises 屈服准则、线性加工硬化和平面应变假设获得的。给出了所获得方程的解析解，通过该解析解可以获得圆柱体任意点的变形、应变和应力分量。在通过将获得的结果与文献中报道的结果进行比较来验证公式后，提出了一些研究来研究圆柱尺寸对内压和外压下旋转FG圆柱的应力分布和弹塑性界面半径的影响。应变梯度系数、角速度、并研究了材料的异质性常数。结果表明，增大材料的非均质常数，减小圆柱半径，可以提高材料的强度，减小弹塑性界面半径。此外，将经典理论与本研究进行了比较，并定义了两种理论导致相同结果的大小范围。