Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: linear and power-law strai
- PDF / 912,267 Bytes
- 10 Pages / 594 x 774 pts Page_size
- 108 Downloads / 169 Views
I. I N T R O D U C T I O N
THE plastic relaxation of the matrix surrounding a misfitting precipitate can lead to substantial decreases in the energy of the system and profound changes in the associated stress field. These changes can manifest themselves in a number of physical and mechanical properties. For example, during a solid state phase transformation plastic relaxation of the stresses, due to misfitting precipitates, may enhance the progress of the reaction by substantially reducing the strain energy of the system. Such relaxation has been observed in a number of systems including the finding of dislocation tangles surrounding Fe precipitates in a Cu matrix by Kinsman, Sprys and Asaro, ~the existence of high dislocation densities in the ferrite regions near martensite particles in dual-phase steels by Rigsbee and VanderArend 2 and in Makenas and Birnbaum's study of the accommodation effects of hydride precipitation in Nb. 3 The large changes in the stress field surrounding the precipitate may affect the diffusion process, kinetics of growth and loss of coherency. It may also play a role if the material is to be subsequently work hardened. 4~6 In a previous paper by Lee e t al, 7 hereafter referred to as Part I, the misfit energy, stress and strain fields associated with a misfitting spherical precipitate are calculated under the assumption of ideal plastic behavior in the matrix phase. A dislocation approach is also incorporated into a continuum mechanics analysis by defining an effective local yield stress. In this way, due to the dependency of dislocation nucleation on particle size, a relationship can be obtained between the size of the plastic zone and the dimensions of the particle. Most materials exhibit some type of strain-hardening behavior. Also, as more dislocations are nucleated at Y. Y. EARMME is Associate Professor, Department of Mechanical Science,Korean Advanced Institute of Scienceand Technology, Seoul, Korea. WILLIAM C. JOHNSON, formerly with Michigan TechnologicalUniversity, Houghton, MI, is now with National Bureau of Standards, Washington, D.C. 20234. J. K. LEE is Associate Professor, Michigan TechnologicalUniversity,Houghton, MI 49931. Manuscript submitted November 18, 1980. METALLURGICALTRANSACTIONSA
the precipitate-matrix interface, the more difficult it becomes to nucleate new dislocations due to the increase in back stresses. The extent of dislocation production affects the size of the plastic zone and misfit energy of the precipitate. For these reasons, the continuum mechanics approach is extended to the cases of linear-strain hardening in which complete analytical expressions are obtained for the misfit energy, stress, strain and displacement fields and to power-law hardening in which numerical techniques are employed in the determination of the above quantities. In the following development, it is assumed that the misfit is purely dilatational and that the plastic relaxation is confined entirely to the matrix phase. Such an assumption is quite reasonable since, due to the symmet
Data Loading...
