Abstract
A polycrystalline plasticity model, which incorporates the contribution of deformation twinning, is proposed. For this purpose, each material point is treated as a composite material consisting of a parent constituent and multiple twin variants. In the constitutive equations, the twin volume fractions and their spatial gradients are treated as external state variables to account for the contribution of twin boundaries to free energy. The set of constitutive relations is implemented in a spectral solver, which allows solving the differential equations resulting from equilibrium and compatibility conditions. The proposed model is then used to investigate the behavior of a AZ31 magnesium alloy. For the investigated loading conditions, the mechanical behavior is controlled by the joint contribution of basal slip and tensile twinning. Also, according to the numerical results, the development of crystallographic texture, morphological texture and internal stresses is consistent with the experimental observations of the literature.
Highlights
For metallic alloys with a hexagonal close packed structure, the mechanical behavior is impacted by the competition between deformation twinning and crystallographic slip
Each material point is treated as a composite material consisting of a parent constituent and multiple twin variants
The twin volume fractions and their spatial gradients are treated as external state variables to account for the contribution of twin boundaries to free energy
Summary
For metallic alloys with a hexagonal close packed (hcp) structure, the mechanical behavior is impacted by the competition between deformation twinning and crystallographic slip. Neutron diffraction techniques have allowed investigating the evolution of this internal stress field through the evaluation of the resulting lattice strains Such techniques have been used to study load partition between twin and parent grains in magnesium (Wu et al 2008; Clausen et al 2008) and zirconium (Xu et al 2008b) alloys. Arul Kumar et al (2018) used micro-Laue X-ray diffraction techniques to estimate the stress state in the vicinity of a twin in magnesium They concluded that the formation of a twin divides the parent grain into two non-interacting domains. Since the associated constitutive models often use a pseudo-slip formulation, the morphological texture evolution resulting from the formation of twins is not always considered To circumvent these limitations, some procedures have been proposed to insert twinned domains in a polycrystalline microstructure (Ardeljan et al 2015; Cheng and Ghosh 2017). The numerical results allow discussing several aspects of deformation twinning, including twin variant selection, texture development and internal stress evolution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Theoretical, Computational and Applied Mechanics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
