Phase Field Modelling of Formation and Fracture of Expanding Precipitates

It is a common belief that embedded expanding inclusions are subjected to an internal homogeneous compressive hydrostatic stress. Still, cracks that appear in precipitates that occupy a larger volume than the original material, are frequently observed. The appearance of cracks has since long been regarded as a paradox. In the present study it is shown that matrix materials that increases its volume even several percent during the precipitation process develop a tensile hydrostatic stress in the centre of the precipitate. This is the result of a complicated mechanical-chemical phase transformation process. The process is here studied using a Landau phase feld model. Before the material is transformed and incorporated in a precipitate it undergoes stretching beyond the elastic strain limit because of the presence of already expanded material. During the phase transformation, the accompanying volumetric expansion cannot be fully accommodated which instead creates an internal compressive stress and adds tension in the surrounding material. As the growth of the precipitate proceeds, a region with increasing tensile stress develops in the interior of the precipitate. This is suggested to be the most probable cause of the observed cracks. First the mechanics that lead to the tension is computed. The infuence of elastic-plastic properties is studied both for cases both with and without cracks. The growth history from microscopic to macroscopic precipitates is followed and the result is compared with observations of so called hydride blisters that are formed on surfaces of zirconium alloys in the presence of hydrogen. A common practical situation is when the zirconium is in contact with an object of lower temperature. Then the cooled spot attracts hydrogen that make the zirconium transform to a metal hydride with the shape of a blister. The simulations predicts a final size and position of the growing crack that compares well with the experimental observations.open access