Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jmps.2010.11.003
Title: Nonlocal continuum crystal plasticity with internal residual stresses
Authors: Aghababaei, R.
Joshi, S.P. 
Reddy, J.N.
Keywords: Crystal plasticity
Residual stress
Slip gradients
Strengthening and mechanisms
Issue Date: Mar-2011
Source: Aghababaei, R., Joshi, S.P., Reddy, J.N. (2011-03). Nonlocal continuum crystal plasticity with internal residual stresses. Journal of the Mechanics and Physics of Solids 59 (3) : 713-731. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jmps.2010.11.003
Abstract: We derive a three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses in crystalline materials that develop due to a non-homogeneous spatial distribution of the excess dislocation (edge and screw) density. The second-order internal stress tensor is derived using the Beltrami stress function tensor φ that is related to the Nye dislocation density tensor. The formulation is derived explicitly in a three-dimensional continuum setting for elastically isotropic materials. The internal stresses appear as additional resolved shear stresses in the crystallographic visco-plastic constitutive law for individual slip systems. Using this formulation, we investigate two boundary value problems involving single crystals under symmetric double slip. In the first problem, the response of a geometrically imperfect specimen subjected to monotonic and cyclic loading is investigated. The internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections. Such imperfections are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, etc., which may produce strong gradients in an otherwise nominally homogeneous loading condition. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. In the second example, we consider simple shear of a single crystalline lamella from a layered specimen. The lamella exhibits strengthening with decreasing thickness and increasing lattice incompatibility with shearing direction. However, as the thickness to internal length-scale ratio becomes small the strengthening saturates due to the saturation of the internal stress. Finally, we present the extension of this approach for crystalline materials exhibiting elastic anisotropy, which essentially depends on the appropriate Green function within φ. © 2010 Elsevier Ltd. All rights reserved.
Source Title: Journal of the Mechanics and Physics of Solids
URI: http://scholarbank.nus.edu.sg/handle/10635/60895
ISSN: 00225096
DOI: 10.1016/j.jmps.2010.11.003
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

8
checked on Dec 13, 2017

WEB OF SCIENCETM
Citations

7
checked on Dec 13, 2017

Page view(s)

22
checked on Dec 9, 2017

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.