Stress and strain partition in elastic and plastic deformation of two phase alloys

A stress and strain partition theory for two phase alloys was developed on the basis of the modified rules of mixtures. The extreme value condition of macroscopic strain energy density was found through Lagrangian multiplier method. Expressions for macroscopic elastic constants of two phase alloys were derived from the extreme value condition by assuming the strain linearity between constituent phases. Governing equation for stress and strain partition in plastic deformation was also obtained from the extreme value condition. The calculated elastic constants of WC-Co alloys fell invariably within the Hashin and Shtrikman's bounds. According to the governing equation the stress ratio between constituent phases was plotted as a function of strain increment ratio. By applying the governing equation to spheroidized carbon steel and duplex stainless steel, it was shown that the stress ratios, strain ratios, macroscopic stress-strain curves, and internal stresses could be evaluated from the in situ stress-strain curves of constituent phases.