Abstract
It is well known that in high cycle fatigue (HCF), macroscopically, structures undergo elastic shakedown and the stress level commonly determines the lifetime. In this domain, the fatigue phenomena is due to local plasticity at the grain scale. Therefore, some multiscale HCF multiaxial fatigue criteria were proposed, among them the well-known Dang Van criterion. This criterion supposes that in a polycrystal, some misoriented grains can undergo plastic shakedown which conducts to crack initiation. The objective of this work is to validate this assumption by conducting numerical simulations on polycrystalline aggregates. As it is necessary to estimate the stabilized state in each grain of the polycrystal, classical incremental simulations are not the best way as it will be highly time-consuming because of the size of the aggregate. In the recent years, Pommier proposed a method called Direct Cyclic Algorithm to obtain the stabilized response of a structure under cyclic periodic loading, which it is shown to be more efficient compared to an incremental analysis in such situation. However, errors can be obtained in certain case with respect to the incremental solution. In this work, a Crystal Plasticity FEM model, based on dislocation densities, was used. As a first step, an aggregate of 20 grains of AISI 316L stainless steel under strain controlled cyclic loading was studied. Precise comparisons were conducted with incremental analysis and the results show that DCA seems to be an efficient solution in order to estimate the shakedown state of polycrystalline aggregates.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
ABAQUS 6.10 (2010) Theory and user’s manual. Dassault systemes
Cailletaud G, Doquet V, Pineau A (1991) Cyclic multiaxial behaviour of an austenitic stainless steel. In: Fatigue under biaxial and multiaxial loading 12
Dang Van K, Papadopoulos IV (1999) High-cycle metal fatigue: theory to applications. CISM courses and lectures 392. Springer, Vienna
Evard P, El Bartali A, Aubin V, Rey C, Degallaix S, Kondo D (2010) Influence of boundary conditions on bi-phased polycrystal microstucture calculation. Int J Solid Struct 47(16):1979–1986
Franciosi P (1984) Etude téorique et expérimentale du comportament elastoplastique des monocrystaux métalliques se déformant par glissement. PhD thesis
Frank FC, Read WT (1950) Multiplication processes for slow moving dislocation. Phys Rev 79(4):722–723
Guilhem Y (2011) Numerical investigation of local mechanical fields in 316L steel polycrystalline aggregates under fatigue loading. PhD thesis
Huang Y (1991) A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Division of applied sciences, Harvard University, Cambridge, MA, pp 02138
Hutchinson JW (1976) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc R Soc Lond A 348
Korsunsky AM, James KE, Daymond MR (2004) Intergranular stresses in polycrystalline fatigue: diffraction measurement and self-consistent modelling. Eng Fract Mech 71:805–812
Mandel J (1965) Generalization de la theorie de la plasticité de W. T. Koiter. Int J Solids Struct 1(3):273–295
Monnet G (2009) A crystalline plasticity law for austenitic stainless steel
Mu P (2011) Study of crack initiation in low-cycle fatigue of an austenitic stainless steel. PhD thesis
Papadopoulos IV (1994) A new criterion of fatigue strength for out-of phase bending and torsion of hard metals. Int J Fatigue 16(6):377–384
Pommier B (2003) Détermination de la réponse asymptotique d’une structure anélastique sous chargement thermomécanique cyclique. PhD thesis
Quey R, Dawson PR, Barbe F (2011) Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. Comput Methods Appl Mech Eng 200:1729–1745
Schmid E, Boas W (1950) Plasticity of crystals with special reference to metals. F. A, Hughes (London)
Seghir R, Charkaluk E, Dufrénoy P, Bodelot L (2010) Thermomechanical coupling in crystalline plasticity under fatigue loading. Proc Eng 2:1155–1164
Seghir R, Bodelot L, Charkaluk E, Dufrénoy P (2011) Numerical and experimental estimation of thermochemical fields heterogeneity at grain scale of 316L stainless steel. Comput Mater Sci 53:464–473
Seghir R (2012) Experimental and numerical investigation of thermomechanical couplings and energy balance in metallic polycrystals. PhD thesis, Ecole Centrale de Lille
Simonovski I, Cizelj L (2009) The influence of grain structure size on microstructurally short crack. J Eng Gas Turbines Power 113(4)
Socie DF, et Marquis GB (2000) Multiaxial fatigue. SAE Inc Warrendale
Acknowledgements
This work is the result of the internship of Domenico Magisano at the Laboratory of Mechanics of Lille, funded by an Erasmus Placement Grant of the Lifelong Learning Programme and by a Master Grant provided by the Lille 1 University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Magisano, D., Charkaluk, E., de Saxcé, G., Kanit, T. (2018). Shakedown Within Polycrystals: A Direct Numerical Assessment. In: Barrera, O., Cocks, A., Ponter, A. (eds) Advances in Direct Methods for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-59810-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-59810-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59808-6
Online ISBN: 978-3-319-59810-9
eBook Packages: EngineeringEngineering (R0)