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

Yejun Gu,Jaafar A El-Awady

doi:10.1186/s41313-020-00020-2

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 χ0=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 Σ109(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.

Highlights

Interstitial solute atoms (such as carbon (C), hydrogen (H), oxygen (O), lithium (Li), etc.) play an important role in controlling the physical and mechanical properties (e.g. yield strength (Gavriljuk et al 1998; Barrera et al 2016; Cui et al 2018), and phase composition (Schwarz and Khachaturyan 2006)) of different metals and alloys
The contour plots of the relative errors between both cases are shown in the right column of Fig. 7. These results indicate that H segregation to the Grain boundaries (GBs) dislocations is in good qualitative agreement with molecular dynamics simulation results (Chandler et al 2008)
In the crystal plasticity model developed by Castelluccio et al (2018), the flow rule can be improved by introducing a weighted average of edge and screw dislocation densities since the solute effects are dependent on the dislocation character

Summary

Introduction

Interstitial solute atoms (such as carbon (C), hydrogen (H), oxygen (O), lithium (Li), etc.) play an important role in controlling the physical and mechanical properties (e.g. yield strength (Gavriljuk et al 1998; Barrera et al 2016; Cui et al 2018), and phase composition (Schwarz and Khachaturyan 2006)) of different metals and alloys. Sofronis and Birnbaum accounted for the effect of the elastic moduli changes due to solute atoms and used iterative finite element analysis to calculate the stress field around edge dislocations under plane strain conditions (Sofronis and Birnbaum 1995). The coherency stress field induced by the solute atoms around an infinitely long edge dislocation were solved using the Papkovich-Neuber scalar potential.

Results

Conclusion