Including Thermal Activation in Simulation Calculations of Dislocation Glide

Abstract

Our simulation method which was derived for athermal motion of flexible dislocations through obstacle arrays is extended to include thermally activated glide. The deterministic differential equations which describe the dynamics of dislocation motion get an additional stochastic term corresponding to thermal motion of atoms involved. Our approach is based on publications of Langevin, Fokker‐Planck, and Klein‐Kramers. The investigation of jerky glide reveals that there is an essential influence of the kinetic energy even in case of rather simple obstacle arrangements. Primary results of the simulations are waiting times at obstacles. Thus an activation analysis of our simulated data can be performed by Arrhenius plots in strict analogy to the procedure applied to experimental results.

Properties of dislocation lines in crystals with strong atomic-scale disorder

“…Their simulation system focused on two dimensional problems [6,7]. Hiratani and Zbib [8,9] extended the model proposed by Rönnpagel et al [6] to three-dimensional simulations and used it to simulate dislocation glide through weak obstacles which were represented by stacking fault tetrahedra (SFTs). They found that dislocation motion was obstaclecontrolled when the applied stress was below a critical resolved shear stress (CRSS), otherwise drag-controlled [8]; the dislocation line was found to exhibit a self-affine structure as manifested by non-trivial height-difference correlations of dislocation shapes [9].…”

“…Thermal effects can be considered by incorporating Langevin forces into the equations of motion [6][7][8][9]. Rönnpagel et al [6] developed a stochastic model that considers the effects of temperature in a line tension model within Brownian dynamics scheme.…”

On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

“…Then, based on the assumption of the Gaussian process, the thermal stress pulse has zero mean and no correlation [29,30] between the two difference times. This leads to the average peak height given as [9,31] …”

Multiscale Discrete Dislocation Dynamics Plasticity

“…Therefore, the DD simulation model should also account not only for deterministic effects but also for stochastic forces; leading to a model called "stochastic discrete dislocation dynamics" (SDD) . The procedure is to include the stochastic force Based on the assumption of the Gaussian process, the thermal stress pulse has zero mean and no correlation (Ronnpagel, Streit et al 1993;Raabe 1998) between any two different times.…”

“…Based on the assumption of the Gaussian process, the thermal stress pulse has zero mean and no correlation (Ronnpagel, Streit et al 1993;Raabe 1998) between any two different times.…”