Creep deformation due to a viscous grain boundary phase

The creep behaviour of a two-phase material composed of rigid grains embedded in a contiguous viscous matrix is analyzed, using two different models. First, in a mean field treatment, the deformation of a suitably chosen representative region (comprising a rigid spherical grain encapsulated by a viscous boundary phase) is studied. Then, in a second treatment, the deformation of a periodic array of hexagonal grains is analyzed. Both of these models predict that, for a small volume fraction ƒ of the fluid matrix phase, the overall viscosity of the two-phase composite will be inversely proportional to the cube of ƒ They also predict that the maximum possible strain occurs when the viscous fluid is squeezed out of some of the interfaces. The strain at which this occurs equals ƒ in tension and −ƒ2 in compression. Since ƒ is often larger than the failure strain in vitreous-bonded ceramics, viscous flow-controlled creep may be an important mechanism even though it is, in principle, a transient process. Finally, the asymmetric behaviour between tension and compression has been used to model the stress redistribution process which is known to occur during bend testing. The results are consistent with experimental observations of a shift in neutral axis towards the compressive face.