On the recoverable and dissipative parts of higher order stresses in strain gradient plasticity

The expressions for the free energy in two recent formulations of strain gradient plasticity are extended to include the locked-in strain energy around statistically stored dislocations. This is accomplished by using the strain dependent factor η(ep), which represents the fraction of the rate of plastic work converted into heat in accordance with the latent heat measurements from classical metal plasticity. The expressions for the plastic work in the two formulations differ by different representations of the portion of plastic work associated with the existence of plastic strain gradients and the corresponding network of geometrically necessary dislocations, while the dissipative parts of plastic work are assumed to be the same in both formulations. The expressions for the recoverable and dissipative parts of the higher order stresses, defined as the work-conjugates to plastic strain and its gradient, are then derived. It is shown that the stress and strain fields of isothermal boundary-value problems of strain gradient plasticity are independent of η, but that this factor may be of importance for non-isothermal analysis in which the dissipated plastic work acts as an internal heat source. The effects of plastic strain gradient on the plastic response of twisted hollow circular tubes made of a rigid-plastic material with different hardening properties are then evaluated and discussed.