Correlation of fracture toughness with impurity components. Final contract report

摘要

This investigation was sponsored by the Los Alamos National Laboratory in an effort to understand better the phenomenon of stress assisted diffusion in cracked structures operating in corrosive environments. Work done on the extension of the existing ''Coupled Thermomechanical Diffusion'' theory to enable the prediction of diffusion of a solute species in stressed solids in the presence of cracks is presented here. Mathematical formalism is provided to support the intuitive notion that a singular solution for the concentration field can exist in crack tip neighborhoods driven by singular solutions for stresses that have been obtained within the framework of classical Linear Elastic Fracture Mechanics. It has been shown that under certain limiting assumptions, a singular solution for the concentration profile of the kind 1/(radical)r emerges from the governing equations. Both steady state and transient solutions were obtained. A numerical simulation using quarter point finite elements was carried out and the results obtained also indicated the presence of this singularity. A singular solution for the concentration profiles of diffusing species in crack tip neighborhoods was obtained by Gdoutos and Aifantis. The order of the singularity obtained in their investigation was different from that discovered in the present work as were the governing differential equations and the underlying assumptions of their model. In order to determine the reasons for the differences, a detailed study was undertaken comparing the two theories and their underlying assumptions, methodology and results. These comparisons also form part of the present work.