Spontaneous fracture of growing precipitates with large misfit strain

Abstract

Precipitates that form as a result of phase transformation are studied with regard to mechanical behaviour and initiation of internal cracks. The focus is on precipitates occupying a larger volume than the surrounding matrix. Further the study is restricted to precipitates growing by incorporating material transformed from being matrix material to the phase of the precipitate. The phase transformation is here treated as a simple homogeneous swelling. The classical solutions for expanding inclusions predict that the inclusion becomes subjected to a constant homogeneous hydrostatic compression. During the process analysed here, added transformed material progressively relieve the compressive stress in the interior of the precipitate. As the process continues the stresses change from compression to tension in both radial and tangential directions in the centre of the precipitate. Further, growth of cracks in precipitates with poor fracture mechanical properties are studied. To simplify the analysis it is assumed that the fracture toughness is insignificant. The prediction is that around a third of the precipitate will fracture. The presence of a crack only has an insignificant effect on the load exerted by the swelling precipitate on the matrix.