Micromechanical Analysis of Void Growth in a Viscous Resin

Abstract

Void growth in a viscous resin is analyzed by using the equivalent inclusion method combined with the Mori-Tanaka theorem. In modeling, we assume that a solid-state gas-forming agent dispersed in the matrix resin a priori sublimates into a gas at the prescribed temperature and the resultant voids are formed in the matrix resin. The pressure in the void is related with both its volume and the degree of temperature in it by using the Boyle-Charles law. The coefficient of viscosity of the matrix resin is assumed to change with temperature according to the so-called W.L.F. equation. By adopting the equivalent inclusion method to the model, the dilatational strain rate in the void, and hence, the differential equation for the volume of voids with respect to the elapsed time is derived as a function of the temperature. The differential equation is solved to a forming process made up of a heating process for forming of the void, followed by a retention process under the constant temperature for the void growth, before a cooling process for bringing a stop to the void growth. Consequently, the volume of void considerably increases with decrease in the viscosity of the matrix and with increase in the retention temperature.