Statistical heterogeneity of plastic deformation: An investigation based on surface profilometry

Statistical aspects of microplasticity: experiments, discrete dislocation simulations and stochastic continuum models

“…Although the slip band heights were demonstrated to exhibit scale-free statistics, the slip band spacings were exponentially distributed, supporting the idea that slip band nucleation can be envisaged as an uncorrelated Poisson process. Using these ideas, a statistical model of the formation and evolution of slip band patterns was proposed in [23], which produced a good agreement with the overall surface morphology observed in experiments on alkali halide single crystals.…”

“…Using surface analysis methods, Schwerdtfeger et al [22,23] demonstrated that the local strains in slip bands obey the same statistics as the temporal strain increments during strain bursts, supporting the conjecture that each strain burst corresponds to the formation of a localised slip band. Although the slip band heights were demonstrated to exhibit scale-free statistics, the slip band spacings were exponentially distributed, supporting the idea that slip band nucleation can be envisaged as an uncorrelated Poisson process.…”

“…In the limit of a sufficiently small Δɛ min , the particular choice of this parameter does not affect the simulation results. For simplicity, the hardening rate Θ is assumed to be strain independent (for simulations with strain-dependent Θ, see, e.g., [23]). Thus, the stress-strain curve of each element consists of an elastic part with slope E up to a stress of σ y , followed by a random staircase of average slope Θ.…”

“…We may statistically characterise experimental deformation curves [2] and surface deformation patterns [21][22][23], and we may use advanced strain mapping and imaging techniques to gain access to the statistics of internal stress and strain fields to deduce statistical characteristics of real deformation processes and obtain information required for constructing a matching stochastic description. This strategy is, however, limited by the practical difficulties of obtaining sufficiently large statistical ensembles of experimental data as required for a reliable statistical analysis.…”

Plasticity of Crystals with Disordered Microstructure: Scale-dependent Fluctuations of Stress and Strain

“…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.…”