A dual-time-scale finite element model is developed in this paper for simulating cyclic deformation in polycrystalline alloys. The material is characterized by crystal plasticity constitutive relations. The finite element formulation of the initial boundary-value problems with cyclic loading involves decoupling the governing equations into two sets of problems corresponding to two different time-scales. One is a long-time-scale (low-frequency) problem characterizing a cycle-averaged solution, while the other is a short-time-scale (high-frequency) problem for a remaining oscillatory portion. Cyclic averaging together with asymptotic expansion of the variables in the time domain forms the basis of the multitime-scaling. The crystal plasticity equations at the two scales are used to study cyclic deformation of a titanium alloy Ti-6Al. This model is intended to study the fatigue response of a material by simulating a large number of cycles to initiation.
FleckN. A.KangK. J.AshbyM. F.The cyclic properties of engineering materialsActa Metall. Mater., 1994, 42, 365–381.
5.
HashimotoT. M.PereiraM. S.Fatigue life studies in carbon dual-phase steelsInt. J. Fatigue, 1996, 18 (8), 529–533.
6.
ParisP. C.The fracture mechanics approach to fatigue In Fatigue - an interdisciplinary approach, 1964 (Syracuse University Press, Syracuse).
7.
MineurM.VillechaiseP.MendezJ.Influence of the crystalline texture on the fatigue behaviour of a 316L austenitic stainless steelMater. Sci. Engng, 2000, A286, 257–268.
8.
BennettV. P.McDowellD. L.Polycrystal orientation distribution effects on microslip in high cycle fatigueInt. J. Fatigue, 2003, 25, 27–29.
9.
ChuR. Q.CaiZ.LiS. X.WangZ. G.Fatigue crack initiation and propagation in α-iron polycrystalsMater. Sci. Engng, 2001, 313, 61–68.
10.
HarrenS. V.AsaroR. J.Nonuniform deformations in polycrystals and aspects of the validity of the Taylor modelJ. Mech. Phys. Solids, 1989, 37 (2), 191–232.
11.
MathurK. K.DawsonP. R.KocksU. F.On modeling anisotropy in deformation processes involving textured polycrystals with distorted grain shapeMech. Mater., 1990, 10, 183–202.
12.
KalidindiS. R.BronkhorstC. A.AnandL.On the accuracy of the Taylor assumption in polycrystalline plasticity In Anisotropy and localization of plastic deformation (Eds BoehlerJ. P.KhanA. S.), 1991, pp. 139–142 (Elsevier Science, New York).
13.
KalidindiS. R.BronkhorstC. A.AnandL.Crystallographic texture evolution in bulk deformation processing of fcc metalsJ. Mech. Phys. Solids, 1992, 40, 537–569.
14.
BeaudoinA. J.MeckingH.KocksU. F.Development of local shear bands and orientation gradients in fcc polycrystals In Simulation of materials processing; theory, methods and applications, NUMIFORM'95 (Eds ShenS. F.DawsonP.), 1995, pp. 225–230 (A. A. Balkema, Rotterdam).
15.
HasijaV.GhoshS.MillsM. J.JosephD. S.Modeling deformation and creep in Ti-6Al alloys with experimental validationActa Mater., 2003, 51, 4533–4549.
16.
DekaD.JosephD.GhoshS.MillsM. J.Crystal plasticity modeling of deformation and creep in polycrystalline Ti-6242Metall. Trans. A, 2006 (in press).
17.
VenkatramaniG.DekaD.GhoshS.Crystal plasticity based FE model for understanding microstructural effects on creep and dwell fatigue in Ti-6242Trans. ASME, J. Engng Mater. and Technol, 2006, 17A (5), 1371–1388.
18.
XieC. L.GroeberM.ButlerR.GhoshS.Computational simulations of tensile and fatigue tests of HSLA steel based on experiments. In Proceedings of SAE World Congress, 2003.
19.
XieC.GhoshS.GroeberM.Modeling cyclic deformation of HSLA steels using crystal plasticityTrans. ASME, J. Engng Mater. Technol., 2004, 126, 339–352.
20.
SinhaS.GhoshS.Modeling cyclic ratcheting based fatigue life of HSLA steels using crystal plasticity FEM simulations and experimentsInt. J. Fatigue, 2006, 28, 1690–1704.
21.
TurkmenH. S.LogeR. E.DawsonmP. R.MillerM.On the mechanical behaviour of AA 7075-T6 during cyclic loadingInt. J. Fatigue, 2003, 25, 267–281.
22.
DawsonP. R.Computational crystal plasticityInt. J. Solids Structs, 2000, 37, 115–130.
23.
YuQ.FishJ.Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loadingComput. Mechanics, 2002, 29, 199–211.
24.
OskayC.FishJ.Multiscale modeling of fatigue for ductile materialsInt. J. Multiscale Comput. Engng, 2004, 2, 1–25.
25.
BalasubramanianS.AnandL.Elastoviscoplastic constitutive equations for polycrystalline fcc materials at low homogeneous temperaturesJ. Mech. Phys. Solids, 2002, 50, 101–126.
26.
AsaroR. J.RiceJ. R.Strain localization in ductile single crystalsJ. Mech. Phys. Solids, 1977, 25, 309–338.
27.
HarderJ.Crystallographic model for the study of local deformation processes in polycrystalsInt. J. Plasticity, 1999, 15, 605–624.
28.
MorrisseyR. J.McDowellD. L.NicholasT.Microplasticity in HCF of Ti-6Al-4VInt. J. Fatigue, 2001, 23, S55-S64.
29.
MSC-MARC reference manuals, 2005 (MSC Software Corporation, Santa Ana, CA).
