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Research Papers

A Crystal-Plasticity-Based Damage Model Incorporating Material Length-Scale

[+] Author and Article Information
S. Kweon

Assistant Professor
Department of Mechanical Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026
e-mail: skweon@siue.edu

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 29, 2015; final manuscript received January 1, 2016; published online February 5, 2016. Assoc. Editor: Curt Bronkhorst.

J. Eng. Mater. Technol 138(3), 031002 (Feb 05, 2016) (11 pages) Paper No: MATS-15-1245; doi: 10.1115/1.4032486 History: Received September 29, 2015; Revised January 01, 2016

A crystal-plasticity-based damage model that incorporates material length-scale through use of the slip-plane lattice incompatibility is developed with attention to the physical basis for the evolution of damage in a “bulk” shear deformation and without resort to ad hoc measures of shear deformation. To incorporate the physics of the shear damage process recently found by Kweon et al. (2010, “Experimental Characterization of Damage Processes in Aluminum AA2024-O,” ASME J. Eng. Mater. Technol., 132(3), p. 031008), the development of tensile hydrostatic stress in grains due to grain-to-grain interaction, two existing theories, crystal plasticity, and the void growth equation by Cocks and Ashby (1982, “On Creep Fracture by Void Growth,” Prog. Mater. Sci., 27(3–4), pp. 189–244) is combined to make the model in this study. The effect of the void volume increase onto the constitutive behavior is incorporated by adding the deformation gradient due to the void volume growth into a multiplicatively decomposed kinematics map. Simulations with the proposed model reveal the physics of shear and reproduce the accelerated damage in the shear deformation in lab experiments and industrial processes: the gradient of hydrostatic stress along with the development of macroscopic normal stress (hydrostatic stress) components amplifies the development of the local hydrostatic stress in grains under tensile hydrostatic stress.

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Figures

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Fig. 1

Multiplicative decomposition of deformation gradient

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Fig. 2

(a) Initial geometry with initial grain orientations displayed, (b) deformed shape of grains in ideal shear with initial grain orientations displayed, (c) hydrostatic stress in uniaxial tension at failure avg(ε¯p)=0.50, (d) hydrostatic stress in actual-process shear at failure avg(ε¯p)=0.39, (e) hydrostatic stress in ideal shear at avg(ε¯p)=0.39, and (f) hydrostatic stress in biaxial tension at failure avg(ε¯p)=0.37. Unit is megapascal.

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Fig. 3

Distribution of the damage parameter ϕ and the most damaged elements, as indicated by arrows. (a) uniaxial tension at failure avg(ε¯p)=0.50, (b) actual-process shear at failure avg(ε¯p)=0.39, (c) ideal shear at avg(ε¯p)=1.2, and (d) biaxial tension at failure avg(ε¯p)=0.37.

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Fig. 4

Evolution of the damage parameter: (a) uniaxial tension, (b) actual-process shear, (c) ideal shear, and (d) biaxial tension. Thin-dotted curves represent ± standard deviation for the average damage parameter.

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Fig. 5

Evolution of triaxiality: (a) uniaxial tension, (b) actual-process shear, (c) ideal shear, and (d) biaxial tension. Thin-dotted curves represent ± standard deviation for average triaxiality.

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Fig. 6

Fracture strain versus triaxiality. Dashed curves indicate an asymptote to all of the results (modeling and experiment) for AA2024-O. The experimental data are borrowed from Refs. [6] and [7].

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Fig. 7

Average stress without damage, i.e., ϕ=f=0 at an effective strain avg(ε¯p)=0.3

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Fig. 8

Average hardening strength of all 12 slip systems, τλα≡(k0/k1)ημλα, where λα is a scalar measure of the density of GNDs, which appear due to lattice incompatibility. Unit is megapascal. (a) Ideal shear and (b) biaxial tension.

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Fig. 9

Damage parameter ϕ distribution and the most damaged elements at the onset of fracture, i.e., ϕ=1, which is indicated by the highlights. (a) initial orientations of 125 grains represented by different colors, (b) uniaxial tension at avg(ε¯p)=0.070, (c) actual-process shear at avg(ε¯p)=0.028, and (d) ideal shear at avg(ε¯p)=0.079.

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