A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

Abstract

We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

“…The higher-order energetic microscopic stresses are derived from a generalized power-law defect energy, with adjustable order-controlling index n. This form of defect energy is proposed to investigate the interaction between the form of this energy and the energetic length scale effects under proportional and non-proportional loading conditions. In spirit of multi-criterion approaches available in the literature (Forest et al, 1997(Forest et al, , 2000Forest and Sievert, 2003;Fleck et al, 2014;Panteghini et al, 2019), the dissipative microscopic stresses are derived from an uncoupled dissipation functional, which is expressed as a sum of two separate functions of first-and higher-order effective plastic strain measures. To evaluate the proposed SGCP model and to investigate the influence of its major constitutive parameters, a simplified two-dimensional (2D) version of this model was derived and implemented within the commercial finite element package Abaqus/Standard, using a User-ELment (UEL) subroutine.…”

“…To allow for more flexible control of major dissipative effects, in present work, the dissipative microscopic stresses are derived from a dissipation functional ϕ, which is postulated based on the assumption of uncoupled dissipative contributions from plastic slips and plastic slip gradients. In spirit of multi-criterion approaches available in the literature (Forest et al, 1997(Forest et al, , 2000Forest and Sievert, 2003;Panteghini et al, 2019), this functional is assumed to be divided into two independent parts: one part, which describes first-order dissipative effects, is only function of plastic slips and their rates ϕ π ; and the other part, which describes higher-order dissipative effects, depends only on gradients of plastic slips and their rates ϕ ξ . Note that similar (uncoupling) assumption was applied in the recent contribution of to describe first-and higher-order dissipative effects in the context of phenomenological strain gradient plasticity.…”

“…At the occurrence of the edges passivation, S ξ0 has only influence on the amplitude of the generated gaps but does not remove them. To the authors' knowledge, to date, there is no gap-free model in the literature including thermodynamically-consistent higher-order dissipative stresses, except for the very recent model of Panteghini et al (2019) in which dissipation is implicitly embedded within the definition of the defect energy. It should be noted that the attitude taken here is rather agnostic on the occurrence of elastic gaps in reality.…”

“…In the context of phenomenological strain gradient theories, have also proposed uncoupled formulations for the description of dissipative processes associated with first-and higher-order stresses. In the same context, the very recent model proposed by Panteghini et al (2019) can also be seen as a multi-criterion model. Indeed, several independent yield surfaces are introduced to describe the higher-order dissipation, which is considered to be independent of the first-order one.…”

Scalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects

“…To overcome limitations of conventional theories, Aifantis (1984) has proposed in a pioneering work the first gradient theory of plasticity with a single internal length scale embedded within the conventional J 2 plasticity theory. Since then, a considerable number of enhanced phenomenological and physically-based gradient theories, which are typically termed strain gradient plasticity (SGP) theories, have been developed for single-and poly-crystal structures (Gurtin et al, 2007;Hutchinson, 2012;Dahlberg and Boåsen, 2019;El-Naaman et al, 2019;Forest et al, 2018;Jebahi et al, 2020;Panteghini et al, 2019;Rys et al, 2020). In the present work, only phenomenological SGP theories are discussed.…”