Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields

Abstract

A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations. Using this model, it is shown that a nano-hydride can form in the tensile region below a dissociated edge dislocation at hydrogen concentration as low as χ 0 = 5 × 10 −5 , and its formation induces a localized hydrogen elastic shielding effect that leads to a lower stacking fault width for the edge dislocation. Additionally, the model also predicts the segregation of hydrogen at 109(13 7 0)/33.4 • symmetric tilt grain boundary dislocations. This segregation strongly alters the magnitude of the shear stresses at the grain boundary, which can subsequently alter dislocation-grain boundary interactions and dislocation slip transmissions across the grain boundary. Moreover, the model also predicts that the hydrogen concentration at a mode-I central crack tip increases with increasing external loading, higher intrinsic hydrogen concentration, and/or larger crack lengths. Finally, linearized approximate closed-form solutions for the solute concentration and the interstitial solute-induced stress field were also developed. These approximate solutions can effectively reduce the computation cost to assess the concentration and stress field in the presence of solutes. These approximate solutions are also shown to be a good approximation when the positions of interest are several nanometers away (i.e. long-ranged elastic interactions) from stress singularities (e.g. dislocation core and crack tip), for low solute concentrations, and/or at high temperatures.

Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

“…Coarse-grained approaches are often required in multiphase systems and alloys to handle simultaneously the deformation induced in the lattice, the resulting phase separations leading to Cottrell atmospheres [141][142][143], and effects on dislocation motion. The APFC model has been proved powerful in describing these effects at the mesoscale for binary systems, beyond results achieved by focusing on either atomistic or continuum length scales [144][145][146][147][148][149]. Also, it can be used to study these systems comprehensively, without focusing on concentration profiles, stress distribution around dislocations, and the force-velocity curves for defect motion separately.…”

The effect of local chemical ordering on dislocation activity in multi-principle element alloys: a three-dimensional discrete dislocation dynamics study

“…Finally, by including the effect of interstitial atoms on dislocation glide (e.g. [21]) as well as atomic diffusion, a more complete description of the dislocation activity and the mechanical behavior in real fcc alloys could be provided.…”

“…Approaches which go beyond pure metal in DDD include interstitial atoms such as hydrogen, e.g. presented in [20,21], dislocation-precipitate interaction as in [22,23], or investigate the motion of a single dislocation under stochastic forces [24]. In a phase-field dislocation dynamics model the operation of a Frank-Read (FR) source in a body-centered cubic (BCC) MPEA has been investigated, showing a significant influence of solute composition fluctuations on the FR source operation [25].…”

Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

“…Coarse-grained approaches are often required in multiphase systems and alloys to handle simultaneously the deformation induced in the lattice, the resulting phase separations leading to Cottrell atmospheres [137][138][139], and effects on dislocation motion. The APFC model has been proved powerful in describing these effects at the mesoscale for binary systems, beyond results achieved by focusing on either atomistic or continuum length scales [140][141][142][143][144][145]. Also, it can be used to study these systems comprehensively, without focusing on concentration profiles, stress distribution around dislocations, and the forcevelocity curves for defect motion separately.…”