Stress hot spots in viscoplastic deformation of polycrystals

The viscoplastic deformation of polycrystals under uniaxial loading is investigated to determine the relationship between hot spots in stress and their location in relation to the microstructure. A 3D full-field formulation based on fast Fourier transforms for the prediction of the viscoplastic deformation of poly-crystals is used with rate-sensitive crystal plasticity. Two measured polycrystalline structures are used to instantiate the simulations, as well as a fully periodic synthetic polycrystal adapted from a simulation of grain growth. Application of (Euclidean) distance maps shows that hot spots in stress tend to occur close to grain boundaries. It is also found that low stress regions lie close to boundaries. The radial distribution function of the hot spots indicates clustering. Despite the lack of texture in the polycrystals, the hot spots are strongly concentrated in ⟨1 1 0⟩ orientations, which can account for the observed clustering. All three microstructures yield similar results despite significant differences in topology.

[1]  A. Rollett,et al.  Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms , 2011 .

[2]  D. McDowell,et al.  Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100 , 2010 .

[3]  A. Lewis,et al.  Using image-based computational modeling to study microstructure–yield correlations in metals , 2009 .

[4]  Shen J. Dillon,et al.  Relative grain boundary area and energy distributions in nickel , 2009 .

[5]  A. Constantinescu,et al.  Dissipative aspects in high cycle fatigue , 2009 .

[6]  A. Rollett,et al.  Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper , 2008 .

[7]  Krishna Rajan,et al.  Tracking correlations between mechanical response and microstructure in three-dimensional reconstructions of a commercial stainless steel , 2008 .

[8]  Somnath Ghosh,et al.  3D reconstruction and characterization of polycrystalline microstructures using a FIB-SEM system , 2006 .

[9]  E. Bringa,et al.  A viscoplastic micromechanical model for the yield strength of nanocrystalline materials , 2006 .

[10]  R. Lebensohn,et al.  Study of the antiplane deformation of linear 2-D polycrystals with different microstructures , 2005 .

[11]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[12]  Georges Cailletaud,et al.  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 , 2005 .

[13]  Yi Liu,et al.  On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations , 2004 .

[14]  Hervé Moulinec,et al.  Intraphase strain heterogeneity in nonlinear composites: a computational approach , 2003 .

[15]  D. Jeulin,et al.  Determination of the size of the representative volume element for random composites: statistical and numerical approach , 2003 .

[16]  H. Wenk,et al.  Texture and Anisotropy , 2004 .

[17]  Hervé Moulinec,et al.  A computational scheme for linear and non‐linear composites with arbitrary phase contrast , 2001 .

[18]  R. Lebensohn.  N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform , 2001 .

[19]  D. Jeulin,et al.  Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model , 2001 .

[20]  Hervé Moulinec,et al.  A Computational Method Based on Augmented Lagrangians and Fast Fourier Transforms for Composites with High Contrast , 2000 .

[21]  U. F. Kocks,et al.  Texture and Anisotropy: Preferred Orientations in Polycrystals and their Effect on Materials Properties , 1998 .

[22]  Jun-ichiro Toriwaki,et al.  New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications , 1994, Pattern Recognit..

[23]  W. Hosford.  The mechanics of crystals and textured polycrystals , 1993 .

[24]  P. S. Sahni,et al.  Computer simulation of grain growth—II. Grain size distribution, topology, and local dynamics , 1984 .

[25]  E. Arzt.  The influence of an increasing particle coordination on the densification of spherical powders , 1982 .

[26]  D. A. Aboav,et al.  The arrangement of cells in a net , 1980 .

[27]  I. Dillamore,et al.  The Mechanisms of Recrystallization in Cubic Metals with Particular Reference to Their Orientation-Dependence , 1974 .

[28]  I. Dillamore,et al.  Transition bands and recrystallization in metals , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[29]  J. D. Bernal,et al.  A Geometrical Approach to the Structure Of Liquids , 1959, Nature.