β brass bicrystal stress-strain relations

Abstract

The stress-strain relations of three isoaxial and one nonisoaxial bicrystal whose grain boundaries are parallel to the stress axis have been studied. From one set of isoaxial bicrystals it has been possible, for a given strain, to determine the average stress$\overline \sigma _{gb}$ in the grain boundary deformation zone from the relationship$\sigma _T = \sigma _b + V_{gb} (\overline \sigma _{gb} - \sigma _b )$ where σ _T is the applied stress, σ _b is the single crystal flow stress for the given strain, andV _gb is the volume fraction of grain boundary deformation zone.$\overline \sigma _{gb}$ was determined from measured values of σ _T , σ _b , andV _gb . From these data and$\overline \sigma _{gb}$ it was possible to extrapolate to the grain boundary to obtain σ _gb , the grain boundary stress. From the nonisoaxial bicrystal series containing a hard and a soft component, it was possible to determine at a given strain the stresses in each component and therefore the stress-strain relations from the relationship$\sigma _T = \overline \sigma _H V_H + \overline \sigma _S V_S$ where$\overline \sigma _H$ and$\overline \sigma _S$ are the average stress in the hard and soft components respectively, andV _H andV _S are the corresponding volume fractions. The remaining two isoaxial bicrystal series were used to evaluate strengthening effects of bicrystal boundaries.