Scale invariance in plastic flow of crystalline solids

From the traditional viewpoint of continuum plasticity, plastic deformation of crystalline solids is, at least in the absence of so-called plastic instabilities, envisaged as a smooth and quasi-laminar flow process. Recent theoretical and experimental investigations, however, demonstrate that crystal plasticity is characterized by large intrinsic spatio-temporal fluctuations with scale-invariant characteristics: In time, deformation proceeds through intermittent bursts with power-law size distributions; in space, deformation patterns and deformation-induced surface morphology are characterized by long-range correlations, self-similarity and/or self-affine roughness. We discuss this scale-invariant behaviour in terms of robust scaling associated with a non-equilibrium critical point (‘yielding transition’). Contents PAGE 1. Introduction 186  1.1. Continuum mechanics of crystal plasticity 187  1.2. Crystal plasticity on the dislocation level: yield stress and depinning transition 191 2. Experimental investigation of fluctuation phenomena in plastic flow 197  2.1. Acoustic emission measurements 197   2.1.1. Experimental methodology 197   2.1.2. Acoustic emission in single- and polycrystals of ice 198   2.1.3. Acoustic emission in metals and alloys 201  2.2. Deformation-induced surface patterns 202   2.2.1. Slip-line patterns 202   2.2.2. Slip-line kinematography 203   2.2.3. Surface roughening in single- and polycrystals 205  2.3. Deformation of micron-size samples 209 3. Theoretical approaches 212  3.1. Dislocation dynamics 213   3.1.1. Simulation methods 213   3.1.2. Relaxation and creep of two-dimensional dislocation systems 218   3.1.3. Stepwise deformation curves and critical behaviour at yield 220  3.2. Models of microstrain evolution 224   3.2.1. Constitutive equations 224   3.2.2. Avalanche dynamics and surface morphology evolution 227  3.3. Phase-field models 233 4. Discussion and conclusions 236  4.1. Why has it not been seen before? 237  4.2. Open questions, doubts and prospects 240 Acknowledgements 243 References 243