In the context of polycrystalline metals, the damage process analysis is generally restricted to surface of a sample containing some hundreds of grains, due to the inherent difficulties microstructural analysis. Determination of the grain size influence, misorientation and neighboring grains effect remains difficult with experimental studies. In this work, the influence of microstructural characteristics of polycrystalline metals on the evolution of the damage process under cyclic loading is investigated. On the basis of the quaternion theory, the orientation of each (crystal) grain is represented by a single angle (theta). The relative misorientation of each grain is set by the ratio of its misorientation over the average value of polycrystalline aggregate. The relative volume of grain is used as a parameter representing the grain size. The damage evolution under cyclic loading is identified using the coupling of the crystal plasticity model with the Continuum Damage Mechanics (CDM) model. The damage evolution and its distribution on polycrystalline aggregate are calculated by means of numerical homogenization over each grain. The heterogeneity distribution and damage evolution for polycrystalline metals have been analyzed. The obtained results show that neighboring grains effects are larger and may change the tendency that larger grains with great misorientation are the most damaged.
Abdul-LatifAChadliM (2007)
Modeling of the heterogeneous damage evolution at the granular scale in polycrystals under complex cyclic loadings. International Journal of Damage Mechanics16(2): 133–158.
2.
Abdul-LatifAChadliM (2010)
Determinist-probabilistic concept in modeling fatigue damage through a micromechanical approach. Journal of Engineering Materials and Technology132(1): 002–011.
3.
Abdul-LatifAMounoungaTBS (2009)
Damage deactivation modeling under multiaxial cyclic loadings for polycrystals. International Journal of Damage Mechanics18(2): 177–198.
4.
Abdul-LatifASaanouniK (1994)
Damaged anelastic behavior of FCC polycrystalline metals with micromechanical approach. International Journal of Damage Mechanics3(3): 237–259.
5.
BadreddineHLabergèreCSaanouniK (2016)
Ductile damage prediction in sheet and bulk metal forming. Comptes Rendus Mécanique344(4–5): 296–318.
6.
BadreddineHYueZMSaanouniK (2017)
Modeling of the induced plastic anisotropy fully coupled with ductile damage under finite strains. International Journal of Solids and Structures108: 49–62.
7.
BarbeFDeckerLJeulinD, et al. (2001a)
Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: FE model. International Journal of Plasticity17(4): 513–536.
8.
BarbeFForestSCailletaudG (2001b)
Intergranular and intragranular behavior of polycrystalline aggregates. Part 2: Results. International Journal of Plasticity17(4): 537–563.
9.
BarbeFQueyRMusienkoA, et al. (2009)
Three-dimensional characterization of strain localization bands in high-resolution elastoplastic polycrystals. Mechanics Research Communications36(7): 762–768.
BenzergaAALeblondJB (2010)
Ductile fracture by void growth to coalescence. Advances in Applied Mechanics44: 169–305.
12.
BettenJ (1986)
Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy. Engineering Fracture Mechanics25(5–6): 573–584.
13.
BielerTGoetzRLSemiatinSL (2005)
Anisotropic plasticity and cavity growth during upset forging of Ti–6Al–4V. Materials Science and Engineering: A405(1–2): 201–213.
14.
BielerTREisenlohrPZhangC, et al. (2014)
Grain boundaries and interfaces in slip transfer. Current Opinion in Solid State and Materials Science18(4): 212–226.
15.
BouchedjraMKanitTBoulemiaC, et al. (2018)
Determination of the RVE size for polycrystal metals to predict monotonic and cyclic elastoplastic behavior: Statistical and numerical approach with new criteria. European Journal of Mechanics – A/Solids72: 1–15.
16.
BoudifaMSaanouniKChabocheJ L (2009)
A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming. International Journal of Mechanical Sciences51(6): 453–464.
17.
BrünigMGerkeS (2011)
Simulation of damage evolution in ductile metals undergoing dynamic loading conditions. International Journal of Plasticity27(10): 1598–1617.
18.
BrünigMRicciS (2005)
Non local continuum theory of anisotropically damaged metals. International Journal of Plasticity21(7): 1346–1382.
19.
CailletaudG (1992)
A micromechanical approach to inelastic behavior of metals. International Journal of Plasticity8(1): 55–73.
20.
CanovaGRWenkHRMolinariA (1992)
Deformation modelling of multi-phase polycrystals: Case of a quartz-mica aggregate. Acta Metallurgica et Materialia40(7): 1519–1530.
21.
ChabocheJL (1978) Description thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement. Thèse université Paris VI et Publication ONERA no. 1978. 3.
22.
ChabocheJL (1992)
Damage induced anisotropy: On the difficulties associated with the active/passive unilateral condition. International Journal of Damage Mechanics1(2): 148–171.
23.
ChabocheJL (1993)
Development of continuum damage mechanics for elastics solids sustaining anisotropic and unilateral damage. International Journal of Damage Mechanics2(4): 311–329.
24.
ChabocheJLBoudifaMSaanouniK (2006)
A CDM approach of ductile damage with plastic compressibility. International Journal of Fracture137(1–4): 51–75.
25.
ChadliMAbdul-LatifA (2005)
Mesodamage evolution in polycrystals. Journal of Engineering Materials and Technology127(2): 214–221.
26.
ChoJHRollettADOhKH (2005)
Determination of a mean orientation in electron backscatter diffraction measurements. Metallurgical and Materials Transactions A36(12): 3427–3438.
27.
DeckerLJeulinD (2000)
Simulation 3D de matériaux aléatoires polycristallins. Revue de Métallurgie97(2): 271–175.
28.
DevincreBKubinLHocT (2006)
Physical analyses of crystal plasticity by DD simulations. Scripta Materialia54(5): 741–746.
29.
DiardOLeclercqSRousselierG, et al. (2002)
Distribution of normal stress at grain boundaries in multicrystals: Application to an intergranular damage modeling. Computational Materials Science25(1-2): 73–84.
30.
DiardOLeclercqSRousselierG, et al. (2005)
Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries. International Journal of Plasticity21(4): 691–722.
31.
DöbrichKMRauCKrillCE III (2004)
Quantitative characterization of the three dimensional microstructure of polycrystalline Al-Sn using X-ray micro-tomography. Metallurgical and Materials Transactions A35(7): 1953–1961.
32.
EkhMLillbackaRRunessonK (2004)
A model framework for anisotropic damage coupled to crystal (visco) plasticity. International Journal of Plasticity20(12): 2143–2159.
33.
EscobedoJPCerretaEKDennis-KollerD, et al. (2013)
Influence of boundary structure and near neighbor crystallographic orientation on the dynamic damage evolution during shock loading. Philosophical Magazine93(7): 833–846.
34.
FensinSJEscobedo-DiazJPBrandlC, et al. (2014)
Effect of loading direction on grain boundary failure under shock loading. Acta Materialia64: 113–122.
35.
FieldDPAdamsBL (1992)
Heterogeneity of intergranular damage. Metallurgical Transactions A23(9): 2515–2526.
36.
FritzenFBöhlkeTSchnackE (2009)
Periodic three-dimensional mesh generation for crystalline aggregates based on Voronoi tessellations. Computational Mechanics43(5): 701–713.
37.
GilbertEN (1962)
Random subdivisions of space into crystals. The Annals of Mathematical Statistics33(3): 958–972.
38.
GlezJCDriverJ (2001)
Orientation distribution analysis in deformed grains. Journal of Applied Crystallography34(3): 280–288.
39.
GologanuMLeblondJBPerrinG, et al. (1997)
Recent extensions of Gurson’s model for porous ductile metals. Continuum Micromechanics377: 61–130.
40.
GursonAL (1977)
Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology99(1): 2–15.
41.
HammiYHorstemeyerM F (2007)
A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence. International Journal of Plasticity23(10–11): 1641–1678.
42.
HuPLiuYZhuY, et al. (2016)
Crystal plasticity extended models based on thermal mechanism and damage functions: Application to multiscale modeling of aluminum alloy tensile behavior. International Journal of Plasticity86: 1–25.
43.
HumphreysFJBatePSHurleyPJ (2001)
Orientation averaging of electron backscattered diffraction data. Journal of Microscopy201(1): 50–58.
44.
JiangYSehitogluH (1999)
A model for rolling contact failure. Wear224(1): 38–49.
45.
KachanovM (1980)
Continuum model of medium with cracks. Journal of the Engineering Mechanics Division106(5): 1039–1051.
46.
KimJBYoonJW (2015)
Necking behavior of AA 6022-T4 based on the crystal plasticity and damage models. International Journal of Plasticity73: 3–23.
47.
LemaitreJ (1985)
A continuum damage mechanics model for ductile fracture. Journal of Engineering Materials and Technology107(1): 83–89.
48.
LemaitreJChabocheJLBenallalA, et al. (2009) Mécanique des Matériaux Solides. 3ème éd. Paris: Dunod.
49.
LemaitreJDesmoratR (2005) Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Berlin: Springer Science & Business Media.
50.
LemaitreJDesmoratRSauzayM (2000)
Anisotropic damage law of evolution. European Journal of Mechanics – A/Solids19(2): 187–208.
51.
LemaitreJDoghriI (1994)
Damage 90: A post processor for crack initiation. Computer Methods in Applied Mechanics and Engineering115(3–4): 197–232.
52.
LiebermanEJLebensohnRAMenascheDB, et al. (2016)
Microstructural effects on damage evolution in shocked copper polycrystals. Acta Materialia116: 270–280.
53.
LiuJLiJDirrasG, et al. (2018)
A three-dimensional multi-scale polycrystalline plasticity model coupled with damage for pure Ti with harmonic structure design. International Journal of Plasticity100: 192–207.
54.
LuFKangGLiuY, et al. (2013) Experimental study on uniaxial cyclic deformation of rolled 5083Al alloy plate. In: 7th ICLCF, Aachen, Germany, 9-11 September 2013.
55.
MericLPoubannePCailletaudG (1991)
Single crystal modeling for structural calculations: Part 1 – Model presentation. Journal of Engineering Materials and Technology113(1): 162–170.
56.
MengoniMPonthotJP (2015)
A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations. International Journal of Plasticity66: 46–70.
57.
MounoungaTBSAbdul-LatifARazafindramaryD (2011)
Damage induced-oriented anisotropy behavior of polycrystals under complex cyclic loadings. International Journal of Mechanical Sciences53(4): 271–280.
58.
NicolaouPDSemiatinSL (2005)
An analysis of cavity growth during open-die hot forging of Ti-6Al-4V. Metallurgical and Materials Transactions A36(6): 1567–1574.
59.
NicolasLMongaburePLe BerL, et al. (2001)
Comparison of the predictions relying on coupled/uncoupled damage-viscoplasticity models for creep test analyses. Journal of Pressure Vessel Technology123(3): 298–304.
60.
NygårdsMGudmundsonP (2002)
Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel. Computational Materials Science24(4): 513–519.
61.
OsipovNGourgues-LorenzonAFMariniB, et al. (2008)
FE modelling of bainitic steels using crystal plasticity. Philosophical Magazine88(30–32): 3757–3777.
62.
PardoenTDoghriIDelannayF (1998)
Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars. Acta Materialia46(2): 541–552.
63.
PineauABenzergaAAPardoenT (2016)
Failure of metal: Brittle and ductile fracture. Acta Materialia107: 424–483.
64.
QueyR (2014) Orientation library: A collection of routines for orientation manipulation (Version2.0.3), http://source forge. Net/projects/orilib (accessed 10 August 2020).
65.
QueyRDawsonPRBarbeF (2011)
Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing. Computer Methods in Applied Mechanics and Engineering200(17–20): 1729–1745.
66.
RousselierG (1987)
Ductile fracture models and their potential in local approach of fracture. Nuclear Engineering and Design105(1): 97–111.
67.
RowenhorstDJLewisACSpanosG (2010)
Three dimensional analysis of grain topology and interface curvature in a β-titanium alloy. Acta Materialia58(16): 5511–5519.
68.
SaanouniK (2012) Damage Mechanics in Metal Forming: Advanced Modeling and Numerical Simulation.
London:
ISTE/Wiley.
69.
SaanouniKAbdul-LatifA (1996)
Micromechanical modeling of low cycle fatigue under complex loadings – Part I. Theoretical formulation. International Journal of Plasticity12(9): 1111–1121.
70.
SaiKCailletaudGForestS (2006)
Micro-mechanical modeling of the inelastic behavior of directionally solidified materials. Mechanics of Materials38(3): 203–217.
71.
SamirE-SLeonC (2016)
Numerical investigation of grain misorientation at and close to the free surface of FCC polycrystalline metals. Computational Materials Science113: 133–142.
72.
SteglichDBrocksWHeerensJ, et al. (2008)
Anisotropic ductile fracture of Al 2024 alloys. Engineering Fracture Mechanics75(12): 3692–3706.
73.
SteglichDWafaiHBessonJ (2010a)
Interaction between anisotropic plastic deformation and damage evolution in Al 2198 sheet metal. Engineering Fracture Mechanics77(17): 3501–3518.
74.
SteglichDWafaiHBrocksW (2010b)
Anisotropic deformation and damage in aluminium2198 T8 sheets. International Journal of Damage Mechanics19(2): 131–152.
75.
TvergaardV (1982)
On localization in ductile materials containing spherical voids. International Journal of Fracture18(4): 237–252.
76.
VignjevicRDjordjevicNCampbellJ, et al. (2012a)
Modelling of dynamic damage and failure in aluminium alloys. International Journal of Impact Engineering49: 61–76.
77.
VignjevicRDjordjevicNPanovV (2012b)
Modelling of dynamic behavior of orthotropic metals including damage and failure. International Journal of Plasticity38: 47–85.
78.
VoyiadjisGZTaqieddinZNKattanPI (2009)
Theoretical formulation of a coupled elastic-plastic anisotropic damage model for concrete using the strain energy equivalence concept. International Journal of Damage Mechanics18(7): 603–638.
79.
WilkersonJ (2017)
On the micromechanics of void dynamics at extreme rate. International Journal of Plasticity95: 21–42.
80.
WongSLObstaleckiMMillerMP, et al. (2015)
Stress and deformation heterogeneity in individual grains within polycrystals subjected to fully reversed cyclic loading. Journal of the Mechanics and Physics of Solids79: 157–185.
81.
YangYZhi-QiangPXing-ZhiC, et al. (2016)
Spall behaviors of high purity copper under sweeping detonation. Materials Science and Engineering: A651: 636–645.
82.
ZhangCEnomotoMSuzukiA, et al. (2004)
Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metallurgical and Materials Transactions A35(7): 1927–1933.
83.
ZhaoZKuchnickiSRadovitzkyR, et al. (2007)
Influence of in-grain mesh resolution on the prediction of deformation textures in FCC polycrystals by crystal plasticity FEM. Acta Materialia55(7): 2361–2373.
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