Torsional response of microwires using multi-term nonlinear kinematic hardening model within strain gradient plasticity framework

The microwire torsion experiment holds significant importance in assessing the size effect at the micron and submicron scales. This paper introduces a model that examines the torsion of a microwire within a higher -order phenomenological strain gradient plasticity framework. The energetic consequences of plastic strain gradient are captured through a multi -term Chaboche-type nonlinear higher -order energetic stress evolution. This higher -order stress is linked to the formation of geometrically necessary dislocations (GNDs) and reaches saturation as effective plastic strain increases during plastic flow. The thermodynamically consistent framework demonstrates additional dissipation in the dissipation inequality. To simulate microwires, a comprehensive three-dimensional mixed finite element with displacement and plastic strain as variables is proposed. Subsequently, an axisymmetric version of the general 3D theory is derived for circular cross -sections using the micro -force balance equation, which takes into account both energetic and dissipative higher -order stress. A procedure for identifying hardening parameters from experimental torque -twist data is suggested. Comparative analysis between numerical responses and experimental observations highlights the effectiveness of saturation term(s) in the higher -order energetic stress evolution equation, as well as the influence of radiusdependent hardening parameters. The torsional behavior of a non -circular section indicates that the warping of the non -circular section diminishes with an increased strain gradient effect. Surface passivation enhances the wire's strength by preventing GNDs from escaping the surface. However, non -uniform surface passivation disrupts the symmetry of the cross-section and leads to more warping.