A stochastic crystal plasticity framework for deformation of micro-scale polycrystalline materials

Abstract In this paper we investigate the stochastic behavior in the mechanical response of polycrystalline materials consisting of few grains to hundreds of grains at micron size scales. We study the transition from stochastic (at small scale) to deterministic (at large scale) deformation behavior in polycrystalline samples using both simulation and nanoindentation experiments. Specifically, we develop a stochastic crystal plasticity model combining a Monte Carlo method with a polycrystal continuum dislocation dynamics model in a self-consistent viscoplasticity framework. Using this framework, we numerically calculate the mechanical properties of the polycrystal and gather randomized sampling data of the flow stress. The numerical results are compared to nanoindentation experimental data from three samples with ultra-fine grain structures manufactured via the severe plastic deformation method. The controlling mechanisms of the observed stochastic yield behavior of polycrystals are then discussed using simulations and experimental results. Our results suggest that it is the combination of stochastic plasticity at small scales (where the strength may vary from grain to grain) coupled with the effects of microstructural features such as grain size distribution and crystallite orientations that govern the uncertainty in the mechanical response of the polycrystalline materials. The extent of the uncertainty is correlated to the “effective cell size” in the sampling procedure of the simulations and experiments. The simulations and experimental results demonstrate similar quantitative behavior in terms of coefficient of variation within the same effective cell size.

[1]  D. Clarke,et al.  Size dependent hardness of silver single crystals , 1995 .

[2]  Jaafar A. El-Awady,et al.  Trapping and escape of dislocations in micro-crystals with external and internal barriers , 2011 .

[3]  Michael D. Uchic,et al.  Size-affected single-slip behavior of pure nickel microcrystals , 2005 .

[4]  A. Ngan,et al.  Specimen size and grain size effects on tensile strength of Ag microwires , 2011 .

[5]  Hussein M. Zbib,et al.  Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression , 2010 .

[6]  H. Zbib,et al.  Multiscale Modeling and Simulation of Deformation in Nanoscale Metallic Multilayered Composites , 2014 .

[7]  Huamiao Wang,et al.  Numerical Analysis of Large Strain Simple Shear and Fixed-End Torsion of HCP Polycrystals , 2010 .

[8]  Hussein M. Zbib,et al.  Stochastic dislocation dynamics for dislocation-defects interaction: A multiscale modeling approach , 2002 .

[9]  Xin Sun,et al.  Predicting plastic flow and irradiation hardening of iron single crystal with mechanism-based continuum dislocation dynamics , 2014 .

[10]  H. Zbib,et al.  Prediction of flow stress and textures of AZ31 magnesium alloy at elevated temperature , 2014 .

[11]  V. Berdichevsky.  On thermodynamics of crystal plasticity , 2006 .

[12]  Ricardo A. Lebensohn,et al.  A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys , 1993 .

[13]  B. Weiss,et al.  Size dependency of mechanical properties of high purity aluminium foils , 2010 .

[14]  Jae-il Jang,et al.  Predicting flow curves of two-phase steels from spherical nanoindentation data of constituent phases: Isostrain method vs. non-isostrain method , 2014 .

[15]  D. Tabor.  Hardness of Metals , 1937, Nature.

[16]  Frans Spaepen,et al.  The yield strength of thin copper films on Kapton , 2004 .

[17]  J. Hirth,et al.  On the strengthening effects of interfaces in multilayer fcc metallic composites , 2002 .

[18]  J. Jonas,et al.  Yield surfaces for textured polycrystals—I. Crystallographic approach , 1987 .

[19]  C. Tomé,et al.  Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet , 2010 .

[20]  Huajian Gao,et al.  Indentation size effects in crystalline materials: A law for strain gradient plasticity , 1998 .

[21]  M. Berveiller,et al.  Impact of the grain size distribution on the yield stress of heterogeneous materials , 2007 .

[22]  W. Gerberich,et al.  Microscopy and microindentation mechanics of single crystal Fe−3 wt. % Si: Part I. Atomic force microscopy of a small indentation , 1993 .

[23]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[24]  A. Ngan,et al.  Stochastic theory for jerky deformation in small crystal volumes with pre-existing dislocations , 2008 .

[25]  C. P. Frick,et al.  Strain bursts in plastically deforming molybdenum micro- and nanopillars , 2008, 0802.1843.

[26]  Masato Kawamukai,et al.  A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals , 2007 .

[27]  Guang Lin,et al.  Stochastic effects in plasticity in small volumes , 2014 .

[28]  D. Dimiduk,et al.  Sample Dimensions Influence Strength and Crystal Plasticity , 2004, Science.

[29]  Anthony G. Evans,et al.  A microbend test method for measuring the plasticity length scale , 1998 .

[30]  Ting Zhu,et al.  Temperature and strain-rate dependence of surface dislocation nucleation. , 2008, Physical review letters.

[31]  H. V. Swygenhoven,et al.  Slip-induced intergranular stress redistribution in nanocrystalline Ni , 2012 .

[32]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[33]  A. Ngan,et al.  A Monte Carlo model for the intermittent plasticity of micro-pillars , 2008 .

[34]  H. Zbib,et al.  Variation in the nanoindentation hardness of platinum , 2013 .

[35]  X. Feaugas,et al.  Microstructural size effects on mechanical properties of high purity nickel , 2011 .

[36]  A. Ngan,et al.  Transition from deterministic to stochastic deformation , 2010 .

[37]  H. Zbib,et al.  A superdislocation model for the strengthening of metal matrix composites and the initiation and propagation of shear bands , 1994 .

[38]  Horacio Dante Espinosa,et al.  Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films , 2006 .

[39]  Christopher Saldana,et al.  A study of the interactive effects of strain, strain rate and temperature in severe plastic deformation of copper , 2009 .

[40]  A. Ngan,et al.  Tensile deformation of silver micro-wires of small thickness-to-grain-size ratios , 2012 .

[41]  H. V. Swygenhoven,et al.  The stress-strain response of nanocrystalline metals: A quantized crystal plasticity approach , 2009 .

[42]  H. Zbib,et al.  Crystallographic orientation and indenter radius effects on the onset of plasticity during nanoindentation , 2012 .

[43]  D. Bahr,et al.  Plastic zone and pileup around large indentations , 1996 .

[44]  Frans Spaepen,et al.  Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers , 2000 .

[45]  D. Dimiduk,et al.  On failure of continuum plasticity theories on small scales , 2005 .

[46]  H. Zbib,et al.  A study of the hot and cold deformation of twin-roll cast magnesium alloy AZ31 , 2014 .

[47]  Motofumi Ohki,et al.  Proposal for ISO 14577 : Metallic materials : Instrumented Indentation Test for Hardness and Materials Parameters (Part 1) Test Method (3rd. Influence on Computed Young's Modulus by Different Indenter's Tip Profile and Material Property (小特集 微小部および微小部材の評価技術) , 2012 .

[48]  Ricardo A. Lebensohn,et al.  Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model , 1998 .