Stochastic Crystal Plasticity Models with Internal Variables: Application to Slip Channel Formation in Irradiated Metals

Abstract

Stochastic crystal plasticity models are originally introduced to study slip avalanche phenomena that are ubiquitous features of the microscale plasticity of crystalline solids. Herein, a method is proposed to couple such models to the evolution of internal variables to account for microstructural hardening and softening phenomena. Specifically, strain hardening is described in terms of a Kocks–Mecking‐type dislocation density and the structural softening of irradiated metals in terms of the density of irradiation‐induced point defect agglomerates, which are cut and eliminated by moving dislocations. The interplay of both effects results in the formation of defect‐free slip channels. Critical conditions for slip channel formation are formulated, the statistical morphology of the ensuing slip channel patterns is investigated and compared with surface observations. Finally, the magnitude and nature of stress concentrations that emerge if slip channels interact with platelet‐like hard inclusions are discussed.

Prediction of creep failure time using machine learning

“…Attributes (3) and (4) are calculated by taking the sum over the individual rows and columns of the matrices shown in Fig. 1a-d, and determining the magnitude of the maximum and minimum accumulated damage along a row or column, i.e.…”

“…Local damage may accumulate even at a sub-critical loads. Accumulation of microstructural damage may be associated with the thermally activated crossing of energy barriers: examples include the accumulation of free volume as result of the thermal activation of shear transformations in amorphous materials 2,3 , or the thermally assisted removal of dislocation barriers in irradiated metals leading to microstructural slip localization and irradiation embrittlement 4 . Local damage accumulation reduces the energy barriers for future damage activation, thus promoting a tendency to localization.…”

Prediction of creep failure time using machine learning

“…and mean value Σi = Σi Γ(1 + 1/k) where Γ denotes the Gamma function. Whenever an element undergoes plastic deformation, its strength is renewed from the distribution (5). Deformation-induced damage in element i is described by a variable δ i = f ǫ eq i which is proportional to the local equivalent plastic strain.…”

“…Local damage may accumulate even at a sub-critical loads. Accumulation of microstructural damage may be associated with the thermally activated crossing of energy barriers: examples include the accumulation of free volume as result of the thermal activation of shear transformations in disordered solids [3,4], or the thermally assisted removal of dislocation barriers in irradiated metals leading to microstructural slip localization and irradiation embrittlement [5]. Local damage accumulation reduces the energy barriers for future damage activation, thus promoting a tendency to localization.…”

A stochastic solver based on the residence time algorithm for crystal plasticity models

“…However, it is often at odds physically with the observed material response [18][19][20] in which symmetry in the evolution of plastic slip can naturally break and lead to a non-homogeneous distribution of plastic shear. Accounting for symmetry-breaking modalities in the slip response has typically been done by adding external probabilistic descriptors of certain internal variables [21][22][23][24][25]. Alternatively, stochasticity can be introduced intrinsically, via the integration algorithm itself, a practice widely used for integrating differential equation systems [26][27][28][29].…”