Three-dimensional analysis of the creep due to a viscous grain boundary phase

A three-dimensional analysis of creep due to a viscous grain boundary phase is presented where the amount of creep strain is proportional to the volume fractionf of the viscous phase. The transient response of a periodic array of rectangular grains to uniaxial deformation under conditions of either constant applied stress or constant total strain is found using a lower bound solution. The stress redistribution in pure bending due to viscoelasticity has been calculated. The short time and long time behaviour of this redistribution depends on the size ofEtf3/η0 in comparison with unity whereE andη0 are the Young's modulus and the viscosity of the boundary phase. The creep response of the periodic array caused by more general stress states is found and this result has been used to estimate the effective viscosity of an equiaxed polycrystal. The effect of the creep path upon the anisotropy is discussed.