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Microstructural pattern formation in finite-deformation single-slip crystal plasticity under cyclic loading: Relaxation vs. gradient plasticity

Klusemann, Benjamin and Kochmann, Dennis M. (2014) Microstructural pattern formation in finite-deformation single-slip crystal plasticity under cyclic loading: Relaxation vs. gradient plasticity. Computer Methods in Applied Mechanics and Engineering, 278 . pp. 765-793. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20140911-085738194

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Abstract

We investigate microstructure formation and evolution during cyclic loading in rate-dependent crystal plasticity at finite strains. The non-quasiconvex free energy density in multiplicative single-slip crystal plasticity leads to fine-scale microstructure whose characteristics and resulting effective stress–strain response are studied by two independent approaches: (i) using an incremental formulation based on variational constitutive updates we approximate the quasiconvex hull by lamination, i.e. by constructing an energy-minimizing first-order laminate microstructure, and (ii) a strain-gradient plasticity model applied to a representative unit cell whose effective properties are obtained from homogenization. In the lamination model, three different formulations for updating the accumulated plastic strains are compared and discussed with a specific focus on identifying a suitable description to account for hardening due to changes of the laminate volume fractions. The gradient-plasticity model also predicts a first-order laminate microstructure to form at a comparable stress level upon microstructure initiation. However, the energy associated with the dislocation network is shown to affect the microstructure evolution, leading to considerably higher strain levels at laminate initiation and a stress overshoot. In both models, cyclic loading leads to a degeneration of the stress–strain hysteresis which ultimately experiences elastic shakedown. The amount of work hardening significantly depends on how fast the degeneration occurs. To allow for a comparison, we consider cyclic loading after pre-deformation in the gradient model which delays the degeneration of the stress–strain hysteresis. For low hardening, the two models predict differences in the stress–strain hysteresis, mainly owing to laminate migration in the gradient-plasticity model. As work hardening increases, this phenomenon is restricted and the agreement of the effective stress–strain response between the two models is excellent. Accounting for the energy stored in the domain walls leads to a delayed lamination which is in agreement with the gradient plasticity model.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.cma.2014.05.015DOIArticle
http://www.sciencedirect.com/science/article/pii/S0045782514001765PublisherArticle
ORCID:
AuthorORCID
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2014 Elsevier B.V. Received 28 January 2014; received in revised form 12 May 2014; accepted 15 May 2014 Available online 2 June 2014. Financial support for B.K. through a Feodor Lynen Research Fellowship for postdoctoral researchers from the Alexander von Humboldt-Foundation is gratefully acknowledged. We thank the anonymous reviewers for their helpful and thoughtful comments.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Alexander von Humboldt FoundationUNSPECIFIED
Subject Keywords:Microstructure; Plasticity; Finite deformation; Cyclic loading; Relaxation
Record Number:CaltechAUTHORS:20140911-085738194
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140911-085738194
Official Citation:Benjamin Klusemann, Dennis M. Kochmann, Microstructural pattern formation in finite-deformation single-slip crystal plasticity under cyclic loading: Relaxation vs. gradient plasticity, Computer Methods in Applied Mechanics and Engineering, Volume 278, 15 August 2014, Pages 765-793, ISSN 0045-7825, http://dx.doi.org/10.1016/j.cma.2014.05.015. (http://www.sciencedirect.com/science/article/pii/S0045782514001765)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49576
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Sep 2014 16:13
Last Modified:03 Oct 2019 07:15

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