Coupling effect of strain gradient strengthening and thermal softening on the microscale plastic behavior of metallic materials

Size effects and thermal effects together determine the microscale plastic response of metallic structures in highintegrated microelectromechanical systems (MEMS) at different temperatures. To investigate the microscale plastic behavior of metallic materials at different temperatures, a thermo-mechanical coupled microscale plasticity model is developed. In the mechanical part of this model, the framework of conventional plasticity theory is maintained, and the plastic strain gradient is introduced as an internal variable to increase the tangential hardening modulus without the introduction of higher-order stress and higher-order boundary conditions. The influence of temperature on the mechanical parameters (e.g. the yield strength) is calibrated by experiment results. In the thermal part of this model, the heat generation in the plastic deformation stage is calculated by the difference between the plastic work and the hardening stored energy influenced by the plastic strain gradient. Due to the strong nonlinearity of the coupled equations, a finite element solution algorithm that combines the radial return method and the staggered solution scheme is proposed. The effectiveness of this model and its solution algorithm is verified by comparisons with the experiment results and a numerical benchmark example. Finally, taking the tensile behavior of a plate with a hole in its center as an example, the coupling effect of strain gradient strengthening and thermal softening on the microscale plastic behavior of metallic materials is investigated. The results show that the microscale plastic behavior of metallic materials at high temperatures depends on the competition between thermal softening and strain gradient strengthening. Our study provides a theoretical basis and a reliable simulation method for the design of MEMS at different temperatures