Plasticity of Crystals with Disordered Microstructure: Scale-dependent Fluctuations of Stress and Strain
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Plasticity of Crystals with Disordered Microstructure: Scale-dependent Fluctuations of Stress and Strain Olga Kapetanou1 and Michael Zaiser1,2 1 School of Engineering, Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH93JL, UK 2 Institute for Materials Simulation (WW8), Friedrich-Alexander-University Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762 Fürth, Germany.
ABSTRACT A generic model of bulk crystal plasticity with stochastic evolution of the local microstructure is formulated. The evolution of local fluctuations of internal stress and plastic strain, as well as the cross correlation between these variables, is investigated for different loading modes (stress control vs. displacement control) as a function of the coarse graining scale, and the spatial structure of the respective correlation functions is determined. The investigations demonstrate that, after an initial transient characterized by uncorrelated initiation of plasticity in different sample locations, nontrivial long range correlations emerge both within the strain pattern and between the internal stress and plastic strain patterns. The internal stresses, on the other hand, remain short range correlated throughout. Implications of our findings for larger-scale plasticity models are discussed. INTRODUCTION Intrinsic fluctuations of plastic deformation in crystalline solids have been studied extensively over the past decade (for overview, see [1]). These fluctuations become conspicuous in the deformation of micrometer-scale specimens where they may dominate the deformation behavior [2], but they are equally present in bulk crystals, where acoustic emission (AE) studies reveal scale-free intermittent slip avalanches in a wide class of crystalline materials [3,4]. This avalanche dynamics has been interpreted in terms of non-equilibrium critical behavior similar to a depinning transition in the dynamics of elastic manifolds moving in disordered media [1,5,6]. While temporal intermittency of plastic flow has been studied extensively both by simulation and experiment, much less attention has been devoted to the spatial organization of plastic flow. Besides the specimen size dependence of the slip avalanche statistics [7], spatial fluctuations of plastic deformation have been mainly studied in terms of the deformation-induced surface morphology of plastically deformed crystals [8,9]. These studies, as well as acoustic emission studies of the locations of AE sources [8], show long range correlations in the plastic strain patterns which manifest themselves through a nontrivial roughness exponent H>0.5 of surface profiles, or through a fractal pattern of AE source locations. Complementary questions concerning the spatial patterns of internal stresses and the correlation between internal stress and local plastic strain patterns have received comparatively
little attention. In the present investigation we present for the first time a systematic study of spatial correlations in the internal stress and plastic strain patterns, the cross c
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