Gradient plasticity for thermo-mechanical processes in metals with length and time scales

Abstract

A thermodynamically consistent framework is developed in order to characterize the mechanical and thermal behavior of metals in small volume and on the fast transient time. In this regard, an enhanced gradient plasticity theory is coupled with the application of a micromorphic approach to the temperature variable. A physically based yield function based on the concept of thermal activation energy and the dislocation interaction mechanisms including nonlinear hardening is taken into consideration in the derivation. The effect of the material microstructural interface between two materials is also incorporated in the formulation with both temperature and rate effects. In order to accurately address the strengthening and hardening mechanisms, the theory is developed based on the decomposition of the mechanical state variables into energetic and dissipative counterparts which endowed the constitutive equations to have both energetic and dissipative gradient length scales for the bulk material and the interface. Moreover, the microstructural interaction effect in the fast transient process is addressed by incorporating two time scales into the microscopic heat equation. The numerical example of thin film on elastic substrate or a single phase bicrystal under uniform tension is addressed here. The effects of individual counterparts of the framework on the thermal and mechanical responses are investigated. The model is also compared with experimental results.

Keywords:

• nonlocal size and rate effects
• interfacial energy
• length and time scales
• gradient plasticity theory
• metal

Acknowledgements

The first author acknowledges the National Research Foundation of Korea for the funding of a World Class University project that enabled him to collaborate with Prof. Taehyo Park at Hanyang University, Seoul (Republic of Korea). He also acknowledges the support of funding from LaSPACE, Louisiana Board of Regents (LEQSF 2010-15 LaSPACE).

Notes

Notes

1. In a stable equilibrium state, the Helmholtz free energy is at minimum with respect to any isothermal small virtual variation of equilibrium state. This implied that is locally convex function of strain. However, the convexity of the internal energy with respect to entropy ensures that is a concave function of temperature. This agrees with the strictly positive values of the time scales.

2. The computation was performed with the aid of the program MATLAB.

3. The effect of different values of the time scale and the total time is investigated in Figure 8.