Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 107, Issue -, Pages 560-579Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2017.06.008
Keywords
Homogenization; Constitutive models; Microstructure evolution; Porous materials; Crystal plasticity
Funding
- National Science Foundation [CMMI-1332965]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1332965] Funding Source: National Science Foundation
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This paper presents a homogenization-based constitutive model for the finite-strain, macroscopic response of porous viscoplastic single crystals. The model accounts explicitly for the evolution of the average lattice orientation, as well as the porosity, average shape and orientation of the voids (and their distribution), by means of appropriate microstructural variables playing the role of internal variables and serving to characterize the evolution of both the crystallographic and morphological anisotropy of the porous single crystals. The model makes use of the fully optimized second-order variational method of Ponte Castaneda (2015), together with the iterated homogenization approach of Agoras and Ponte Castaneda (2013), to characterize the instantaneous effective response of the porous single crystals with fixed values of the microstructural variables. Consistent homogenization estimates for the average strain rate and vorticity fields in the phases are then used to derive evolution equations for the associated microstructural variables. The model is 100% predictive, requiring no fitting parameters, and applies for porous viscoplastic single crystals with general crystal anisotropy and average void shape and orientation, which are subjected to general loading conditions. In Part II of this work (Song and Ponte Castaneda, 2017a), results for both the instantaneous response and the evolution of the microstructure will be presented for porous FCC and HCP single crystals under a wide range of loading conditions, and good agreement with available FEM results will be shown. (C) 2017 Elsevier Ltd. All rights reserved.
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