Effect of passivation on higher order gradient plasticity models for non-proportional loading: energetic and dissipative gradient components

Abstract

In this work, a new class of thermodynamic-based higher order gradient plasticity theory is proposed and applied to the stretch-surface passivation problem for investigating the material behaviour under the non-proportional loading condition. This paper incorporates the thermal and mechanical responses of microsystems. It addresses phenomena such as size and boundary effects and in particular microscale heat transfer in fast-transient processes. The stored energy of cold work is considered in the development of the recoverable counterpart of the free energy. The main distinction in this formulation is the presence of the dissipative higher order microstress quantity that is known to give rise to the stress jump phenomenon, which causes a controversial dispute in the field of strain gradient plasticity theory with respect to whether it is physically acceptable or not. The finite element solution for the stretch-surface passivation problem is developed and validated by comparing with three sets of small-scale experiments. Based on the validated finite element solution, the stress jump phenomenon under the stretch-surface passivation condition is investigated with the effects of the various material parameters. The evolution of the free energy and dissipation potentials is investigated at elevated temperatures. The two-dimensional simulation is also given to examine the gradient and grain boundary effect, the mesh sensitivity of the two-dimensional model and the stress jump phenomenon. Finally, some significant conclusions are presented.

Keywords:

• Higher order gradient plasticity
• passivation
• non-proportional loading
• stress jump
• energetic
• dissipative
• stored energy of cold work

Notes

1. Despite the argument of [6], there is another viewpoint to look at the stress jump phenomenon. The perspective taken in [11] is that it is premature at this moment to judge whether a formulation associated with the stress jump is physically acceptable or not, therefore, an in-depth study of dislocation mechanism and microscale experiments with non-proportional loading history is needed.

2. It should be noted that it is possible to introduce another form of the surface energy if it is convex in, .

3. One can easily obtain the flow rule for the Case II by setting ℓ_dis = 0.