Stress and strain partition in deformation of multiphase alloys

Abstract

A new theory for the inhomogeneous deformation of multiphase alloys was proposed. The theory was based on the concept that the strain energy density of a composite body increased along the path on which the strain energy density had an extreme value. A special form of strain energy density was formulated by means of the modified rules of mixtures for stress and strain. A first order differential equation was derived from the strain energy density through variational principle or Lagrangian multiplier method. The differential equation was regarded as a general governing equation for the stress and strain partition of two phase alloys. The validity of the new theory was demonstrated by applying the governing equation to several practcal alloys. In chapter 3 the theory was applied to the plastic deformation of two spheroidized carbon steels consisted of soft ferrite matrix and rigid carbide (cementite) phase. The partitioned stresses and strains were calculated by the theory, and the in situ stress-strain curves of the ferrite matrix were obtained from them. Also, it was possible to evaluate the back stress and unrelaxed plastic incompatibility. In chapter 4 the expressions for the average elastic constants of equiaxed composites were derived from the governing equation. Then the average elastic constants of WC-Co alloys were evaluated by the expressions. All the calculated elastic constants, Young``s modulus, shear modulus, bulk modulus and Poisson``s ratio, fell-within the Hashin and Shtrikman``s upper and lower bounds. By inspecting the governing equation for plastic deformation of equiaxed two phase alloys, it was found that the governing equation described an intermediate deformation between the iso-stress condition and the iso-strain condition. The stress and strain partitions of a duplex stainless steel and a spheroidized carbon steel were also calculated by the theory, and the results were compared with each other. Aspects of the stress and strain partit...