Equilibrium solute concentration surrounding elastically interacting precipitates
- PDF / 1,076,271 Bytes
- 11 Pages / 612 x 792 pts (letter) Page_size
- 23 Downloads / 194 Views
I.
INTRODUCTION
THE elastic
stress field associated with material defects can influence the equilibrium concentration distribution in solids. Dislocations 1'2 and interfaces 3 can redistribute solute atoms owing to the elastic interaction between the defect and the misfit strain of the individual component species. This can result in a serious degradation in the mechanical 4 and electrical5 properties of the material. Second phase particles are also observed to affect the equilibrium solute distribution in the matrix surrounding the particles. 6 Transformation strains (eigenstrains) or the stress concentration effect of particles in the presence of an applied load engender complicated stress fields that interact with solute atoms. The associated interaction energy can lower the total free energy of the system v i a a redistribution of atoms. Solubility enhancement in the vicinity of second phase particles is thought to play a significant role in the initiation and growth of voids in hydrogenated steels 7 and to influence the mechanical properties of two phase systems. 4 Implicit in any description of elastically induced solute redistribution is an understanding of the coupling between elastic and chemical effects. Several theories have been advanced recently8-1~ which address directly the role of stress on thermomechanical equilibrium in solids. A few of these theories have been used to examine dislocation-solute interactions. Relatively little work has been done, however, on isolated precipitate-solute interactions, and no effort seems to have been made in determining equilibrium solute concentrations in the vicinity of elastically interacting precipitates. Li ~~ has examined the distribution of interstitial solute atoms near isolated misfitting inclusions. A relationship between concentration (chemical potential) and strain field is obtained by introducing the concept of a partial molar strain volume. Neglecting the stress field engendered by the redistribution of atoms, knowledge of the precipitate stress field as calculated for a homogeneous matrix is then used to estimate the solubility enhancement.
WILLIAM C. JOHNSON is Assistant Professor, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213. P. W. VOORHEES is with the Metallurgy Division, National Bureau of Standards, Gaithersburg, MD 20899. Manuscript submitted July 30, 1984. METALLURGICAL TRANSACTIONS A
A major difficulty in previous treatments of elastically induced solute redistribution is that they are not self consistent to even first order in the change in concentration. The inconsistency arises in that the stress fields engendered by the concentration changes are not accounted for in determining the final state of stress in the system. The concentration induced stresses can be significant and we will show that explicit consideration of these stresses can result in substantially different concentration profiles and predictions of net solute enhancement or depletion. The purpose of this p
Data Loading...
