Spatial strain correlations, machine learning, and deformation history in crystal plasticity

Abstract

Systems far from equilibrium respond to probes in a history-dependent manner. The prediction of the system response depends on either knowing the details of that history or being able to characterize all the current system properties. In crystal plasticity, various processing routes contribute to a history dependence that may manifest itself through complex microstructural deformation features with large strain gradients. However, the complete spatial strain correlations may provide further predictive information. In this paper, we demonstrate an explicit example where spatial strain correlations can be used in a statistical manner to infer and classify prior deformation history at various strain levels. The statistical inference is provided by machine-learning (ML) techniques. As source data, we consider uniaxially compressed crystalline thin films generated by two dimensional discrete dislocation plasticity simulations, after prior compression at various levels. Crystalline thin films at the nanoscale demonstrate yield-strength size effects with very noisy mechanical responses that produce a serious challenge to learning techniques. We discuss the influence of size effects and structural uncertainty to the ability of our approach to distinguish different plasticity regimes.

Learning to Predict Crystal Plasticity at the Nanoscale: Deep Residual Networks and Size Effects in Uniaxial Compression Discrete Dislocation Simulations

“…In addition, recently developed data-driven methods have been utilized to identify initial strain deformation level of synthetic samples of small finite volumes, produced through discrete dislocation dynamics (DDD) simulations. Papanikolaou et al 13 emulated DIC using DDD, by simulating thin film uniaxial compression of samples under different states of prior deformation, and removing the average residual plastic distortion before reloading. It is worth noting that the utilized DDD model was benchmarked to minimally model size effects in small finite volumes 12 .…”

“…It is worth noting that the utilized DDD model was benchmarked to minimally model size effects in small finite volumes 12 . In 13 , two-point strain correlations at different locations were used to capture spatial features of dislocations, through their resulting strain profiles. In that work, dislocation classification was performed using Principal Component Analysis (PCA) 18 and continuous k-nearest neighbors clustering algorithms 19 .…”

“…However, the problems in existing works are either in simpler models of dislocation dynamics 20 or with less challenging limits of the model (i.e. large sample widths) 13 . Thus, it has yet to become clear how to practically, accurately and efficiently assess, using machine learning, dislocation plasticity features in realistic scenarios that can be tested experimentally.…”

Microstructural inelastic fingerprints and data-rich predictions of plasticity and damage in solids

“…where + denotes the result for a positive dislocation ( b = bx). For a dislocation pinned at an obstacle that starts gliding after the external stress increases beyond a threshold σ thr in a non-linear, but differentiable manner (so that (t) = f (t)), it is straightforward to estimate the evolution of the strain invariant I ± (r): (15) Given the simplicity of the problem, theJ operator is diagonal, thus it is straightforward to infer its properties. It is worth noting that it is non-zero only when dislocations are in motion, and it has a characteristic left-right asymmetry, with respect to the original pinning point location.…”

Effects of Rate, Size, and Prior Deformation in Microcrystal Plasticity

“…Finally, it is worth noting that the model is limited to small deformations, does not include other possible three dimensional dislocation motions and does not include boundary roughness stress effects or thermal effects on obstacles/sources (Song, Yavas, Van der Giessen andPapanikolaou 2019, Papanikolaou et al 2019).…”