Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

Abstract

Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity Nellemann, C.; Niordson, C. F. ; Nielsen, K.L. AbstractTwo rate-independent strain gradient crystal plasticity models, one new and one previously published, are compared and a numerical framework that encompasses both is developed. The model previously published is briefly outlined, while an in-depth description is given for the new, yet somewhat related, model.The difference between the two models is found in the definitions of the plastic work expended in the material and their relation to spatial gradients of plastic strains. The model predictions are highly relevant to the ongoing discussion in the literature, concerning 1) what governs the increase in the apparent yield stress due to strain gradients (also referred to as strengthening)? And 2), what is the implication of such strengthening in relation to crystalline material behavior at the micron scale? The present work characterizes material behavior, and the corresponding plastic slip evolution, by use of the finite element method.The pure shear problem of an infinite material slab is investigated, with the previously published model displaying strengthening, while the new model does not. In addition to the numerical approach an exact closed form solution, to the pure shear problem, is obtained for the new model, and it is demonstrated that the model predicts proportional straining in the entire plastic regime. Somewhat surprising it is found that the predictions for strain gradient hardening coincide for the two models.

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

“…As discussed in the introduction, in almost all existing strain gradient theories involving both first-and higher-order dissipative microscopic stresses, the evolution of the latter is described using constitutive equations based on generalized effective plastic strain measures, which imply plastic strains and their gradients in a coupled manner (e.g., Fleck and Hutchinson, 2001;Gurtin et al, 2007;Gurtin and Anand, 2009;Hutchinson, 2012;Nellemann et al, 2017Nellemann et al, , 2018. An example of these measures is:…”

“…A modified version of this model in which the higher-order stresses are assumed to be fully energetic is proposed by Hutchinson (2012) to ensure its thermodynamic consistency. The assumption of no higher-order contributions to dissipation has been used in subsequent works to develop thermodynamically-acceptable incremental models (e.g., Nellemann et al, 2017Nellemann et al, , 2018. However, the consistency of this assumption with the current understanding of dislocation physics is questioned.…”

“…Another issue related to SGP theories is how to describe the dissipative processes. In almost all existing strain gradient works, theses processes are considered to be coupled and described with the help of generalized effective plastic strain measures, which imply plastic strains and their gradients in a coupled manner (e.g., Fleck and Hutchinson, 2001;Gurtin et al, 2007;Gurtin and Anand, 2009;Hutchinson, 2012;Nellemann et al, 2017Nellemann et al, , 2018. This kind of (coupled) measures makes the issue of proposing robust and flexible dissipation formulations and the control of important dissipative effects difficult.…”

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

“…Furthermore, the difficulties in assessment of active slip systems within the crystal plasticity framework can be overcome by rate-dependent (Busso and Cailletaud, 2005) or rate-independent (Forest and Rubin, 2016;Kaiser and Menzel, 2019a) formulations. Implementation of strain gradient crystal plasticity in a finite element code is a challenging task that has been performed for example by Shu (1998); Borg et al (2008a); Yalcinkaya et al (2012); Bardella et al (2013); Nellemann et al (2017Nellemann et al ( , 2018; Panteghini and Bardella (2016) at small strains and by Niordson and Kysar (2014); Lewandowski and Stupkiewicz (2018); Ling et al (2018); Kaiser and Menzel (2019a) at finite deformations. An efficient method to implement strain gradient plasticity models is to resort to the micromorphic approach proposed by Forest (2009) at small strains and Forest (2016) at finite deformation, as demonstrated by Anand et al (2012); Brepols et al (2017) for conventional plasticity and by Cordero et al (2010); Aslan et al (2011); Ryś et al (2020) for crystal plasticity based on the dislocation density tensor.…”

A Class of Rate-Independent Lower-Order Gradient Plasticity Theories: Implementation and Application to Disc Torsion Problem

“…In previous research on gradient enhanced crystal plasticity models mostly rate dependent theories have been introduced [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ] with some exceptions such as [ 22 , 23 , 24 , 25 , 26 ]. In this study, a rate-independent crystal plasticity formulation is used, in which, slip only occurs on slip planes where the resolved shear stress value is larger than the slip resistance [ 27 ].…”