0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Benzerga, A. A. , and Besson, J. , 2001, “ Plastic Potentials for Anisotropic Porous Solids,” Eur. J. Mech A: Solids, 20(3), pp. 397–434. [CrossRef]
Gurson, A. L. , 1977, “ Continuum Theory of Ductile Rupture by Void Nucleation and Growth–I. Yield Criteria and Flow Rules for Porous Ductile Materials,” ASME J. Eng. Mater. Technol., 99(1), pp. 2–15. [CrossRef]
Kachanov, L. M. , 1999, “ Rupture Time Under Creep Condition,” Int. J. Fract., 97(1), pp. 11–18. [CrossRef]
Lemaitre, J. , 1985, “ A Continuous Damage Mechanics Model for Ductile Fracture,” ASME J. Eng. Mater. Technol., 107(1), pp. 83–89. [CrossRef]
Tvergaard, V. , 1981, “ Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions,” Int. J. Fract., 17(4), pp. 389–407. [CrossRef]
Kweon, S. , Beaudoin, A. J. , and McDonald, R. J. , 2010, “ Experimental Characterization of Damage Processes in Aluminum AA2024-O,” ASME J. Eng. Mater. Technol., 132(3), p. 031008. [CrossRef]
Bao, Y. , and Wierzbicki, T. , 2004, “ On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space,” Int. J. Mech. Sci., 46(1), pp. 81–98. [CrossRef]
McClintock, F. A. , Kaplan, S. M. , and Berg, C. A. , 1966, “ Ductile Fracture by Hole Growth in Shear Bands,” Int. J. Fract. Mech., 2(4), pp. 614–627.
Lode, W. , 1926, “ Versuche über den einfluβ der mittleren hauptspannug auf die flieβgrenze,” Z. Angew. Math. Mech., 5(2), pp. 142–144.
Butcher, C. , Chen, Z. , Bardelcik, A. , and Worswick, M. , 2009, “ Damage-Based Finite-Element Modeling of Tube Hydroforming,” Int. J. Fract., 155(1), pp. 55–65. [CrossRef]
Nahshon, K. , and Hutchinson, J. W. , 2008, “ Modification of the Gurson Model for Shear Failure,” Eur. J. Mech. A: Solids, 27(1), pp. 1–17. [CrossRef]
Xue, L. , 2007, “ Damage Accumulation and Fracture Initiation in Uncracked Ductile Solids Subject to Triaxial Loading,” Int. J. Solids Struct., 44(16), pp. 5163–5181. [CrossRef]
Xue, L. , 2008, “ Constitutive Modeling of Void Shearing Effect in Ductile Fracture of Porous Materials,” Eng. Fract. Mech., 75(11), pp. 3343–3366. [CrossRef]
Xue, L. , and Wierzbicki, T. , 2008, “ Ductile Fracture Initiation and Propagation Modeling Using Damage Plasticity Theory,” Eng. Fract. Mech., 75(11), pp. 3276–3293. [CrossRef]
Bammann, D. J. , and Aifantis, E. C. , 1989, “ A Damage Model for Ductile Metals,” Nucl. Eng. Des., 116(3), pp. 355–362. [CrossRef]
Ekh, M. , Lillbacka, R. , and Runesson, K. , 2004, “ A Model Framework for Anisotropic Damage Coupled to Crystal (Visco) Plasticity,” Int. J. Plast., 20(12), pp. 2143–2159. [CrossRef]
Clayton, J. D. , 2006, “ Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals,” Theor. Appl. Fract. Mech., 45(3), pp. 163–185. [CrossRef]
Potirniche, G. P. , Horstemeyer, M. F. , and Ling, X. W. , 2007, “ An Internal State Variable Damage Model in Crystal Plasticity,” Mech. Mater., 39(10), pp. 941–952. [CrossRef]
Boudifa, M. , Saanouni, K. , and Chaboche, J.-L. , 2009, “ A Micromechanical Model for Inelastic Ductile Damage Prediction in Polycrystalline Metals for Metal Forming,” Int. J. Mech. Sci., 51(6), pp. 453–464. [CrossRef]
Li, D.-F. , Davies, C. M. , Zhang, S.-Y. , Dickinson, C. , and O'Dowd, N. P. , 2013, “ The Effect of Prior Deformation on Subsequent Microplasticity and Damage Evolution in an Austenitic Stainless Steel at Elevated Temperature,” Acta Mater., 61(10), pp. 3575–3584. [CrossRef]
Luo, C. , and Chattopadhyay, A. , 2011, “ Prediction of Fatigue Crack Initial Stage Based on a Multiscale Damage Criterion,” Int. J. Fatigue, 33(3), pp. 403–413. [CrossRef]
Naderi, M. , Amiri, M. , Iyyer, N. , Kang, P. , and Phan, N. , 2015, “ Fatigue Failure Initiation Modeling in AA7075-T651 Using Microstructure-Sensitive Continuum Damage Mechanics,” J. Failure Anal. Prev., 15(5), pp. 701–710. [CrossRef]
Aslan, O. , Cordero, N. M. , Gaubert, A. , and Forest, S. , 2011, “ Micromorphic Approach to Single Crystal Plasticity and Damage,” Int. J. Eng. Sci., 49(12), pp. 1311–1325. [CrossRef]
Xu, X.-P. , and Needleman, A. , 1993, “ Void Nucleation by Inclusion Debonding in a Crystal Matrix,” Modell. Simul. Mater. Sci. Eng., 1(2), pp. 111–132. [CrossRef]
Clayton, J. D. , 2005, “ Dynamic Plasticity and Fracture in High Density Polycrystals: Constitutive Modeling and Numerical Simulation,” J. Mech. Phys. Solids, 53(2), pp. 261–301. [CrossRef]
Bieler, T. R. , Eisenlohr, P. , Roters, F. , Kumar, D. , Mason, D. E. , Crimp, M. A. , and Raabe, D. , 2009, “ The Role of Heterogeneous Deformation on Damage Nucleation at Grain Boundaries in Single Phase Metals,” Int. J. Plast., 25(9), pp. 1655–1683. [CrossRef]
Benzerga, A. A. , 2002, “ Micromechanics of Coalescence in Ductile Fracture,” J. Mech. Phys. Solids, 50(6), pp. 1331–1362. [CrossRef]
Benzerga, A. A. , Besson, J. , and Pineau, A. , 2004, “ Anisotropic Ductile Fracture Part I: Experiments,” Acta Mater., 52(15), pp. 4623–4638. [CrossRef]
Cocks, A. C. F. , and Ashby, M. F. , 1982, “ On Creep Fracture by Void Growth,” Prog. Mater. Sci., 27(3–4), pp. 189–244. [CrossRef]
Follansbee, P. S. , and Kocks, U. F. , 1988, “ A Constitutive Description of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable,” Acta Metall. Mater., 36(1), pp. 81–93. [CrossRef]
Kok, S. , Beaudoin, A. J. , and Totorelli, D. A. , 2002, “ A Polycrystal Plasticity Model Based on the Mechanical Threshold,” Int. J. Plast., 18(5–6), pp. 715–741. [CrossRef]
Clayton, J. D. , 2011, Nonlinear Mechanics of Crystals, Springer, Dordrecht, The Netherlands.
Steinmann, P. , 2015, Geometric Foundations of Continuum Mechanics, Springer, Berlin.
Marin, E. B. , and Dawson, P. R. , 1998, “ On Modeling the Elasto-Viscoplastic Response of Metals Using Polycrystal Plasticity,” Comput. Methods Appl. Mech. Eng., 165(1–4), pp. 1–21. [CrossRef]
Kweon, S. , 2012, “ Damage at Negative Triaxiality,” Eur. J. Mech. A: Solids, 31(1), pp. 203–212. [CrossRef]
Chen, S. R. , Kocks, U. , MacEwen, S. , Beaudoin, A. J. , and Stout, M. G. , 1998, “ Constitutive Modeling of a 5182 Aluminum as a Function of Strain Rate and Temperature,” Hot Deformation of Aluminum Alloys II, The Minerals, Metals & Materials Society, Warrendale, PA, pp. 205–216.
Acharya, A. , and Bassani, J. L. , 2000, “ Lattice Incompatibility and a Gradient Theory of Crystal Plasticity,” J. Mech. Phys. Solids, 48(8), pp. 1565–1595. [CrossRef]
Acharya, A. , Bassani, J. L. , and Beaudoin, A. , 2003, “ Geometrically Necessary Dislocations, Hardening, and a Simple Gradient Theory of Crystal Plasticity,” Scr. Mater., 48(2), pp. 167–172. [CrossRef]
Acharya, A. , and Beaudoin, A. J. , 2000, “ Grain-Size Effect in Viscoplastic Polycrystals at Moderate Strains,” J. Mech. Phys. Solids, 48(10), pp. 2213–2230. [CrossRef]
Beaudoin, A. J. , Acharya, A. , Chen, S. R. , Korzekwa, D. A. , and Stout, M. G. , 2000, “ Consideration of Grain-Size Effect and Kinetics in the Plastic Deformation of Metal Polycrystals,” Acta Mater., 48(13), pp. 3409–3423. [CrossRef]
Beaudoin, A. J. , and Acharya, A. , 2001, “ A Model for Rate-Dependent Flow of Metal Polycrystals Based on the Slip Plane Lattice Incompatibility,” Mater. Sci. Eng. A, 309–310, pp. 411–415. [CrossRef]
Kocks, U. F. , Tomé, C. N. , and Wenk, H.-R. , 1998, Texture and Anisotropy, Cambridge University Press, Cambridge, UK.
Estrin, Y. , and Mecking, H. , 1984, “ A Unified Phenomenological Description of Work Hardening and Creep Based on One-Parameter Models,” Acta Metall., 32(1), pp. 57–70. [CrossRef]
Mackenzie, J. , 1950, “ The Elastic Constants of a Solid Containing Spherical Holes,” Proc. Phys. Soc., London, 63(1), pp. 2–11. [CrossRef]
Steglich, D. , Brocks, W. , Heerens, J. , and Pardoen, T. , 2008, “ Anisotropic Ductile Fracture of Al 2024 Alloys,” Eng. Fract. Mech., 75(12), pp. 3692–3706. [CrossRef]
Merati, A. , 2005, “ A Study of Nucleation and Fatigue Behavior of an Aerospace Aluminum Alloy 2024-T3,” Int. J. Fatigue, 27(1), pp. 33–44. [CrossRef]
Rodrigues, E. M. , Matias, A. , Godefroid, L. B. , Bastian, F. L. , and Al-Rubaie, K. S. , 2005, “ Fatigue Crack Growth Resistance and Crack Closure Behavior in Two Aluminum Alloys for Aeronautical Applications,” Mater. Res., 8(3), pp. 287–291. [CrossRef]
Kweon, S. , 2009, “ Edge Cracking in Rolling of an Aluminum Alloy AA2024-O,” Ph.D. dissertation, University of Illinois at Urbana-Champaign, IL.
Kweon, S. , Beaudoin, A. J. , Kurath, P. , and Li, M. , 2009, “ Development of Localized Deformation in AA2024-O,” ASME J. Eng. Mater. Technol., 131(3), p. 031009. [CrossRef]
Kweon, S. , 2013, “ Investigation of Shear Damage Considering the Evolution of Anisotropy,” J. Mech. Phys. Solids, 61(12), pp. 2605–2624. [CrossRef]
Kweon, S. , 2015, “ Damage in Edge Cracking of Rolled Metal Slabs,” Mech. Res. Commun., 63, pp. 13–20. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Multiplicative decomposition of deformation gradient

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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].

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In