Efficient impact modifiers for lowering the ductile-brittle transition temperature of thermoplastic blends have been designed by modeling the stress distribution near the notch of an Izod impact test sample and the nature of stresses in spherical particle-filled polycarbonate. The model considers the inhomogeneity of a soft phase inside a relatively rigid phase, particle interaction, and the effects of thermal residual stresses imposed as a consequence of processing and differences in matrix and particle thermal coefficients of expansion. Polycarbonate blends are used as an example for the modeling. The predictions of the ductile-brittle transition temperature of blends provide guidelines for selection of impact modifier type. The model predicts that there is no further advantage in toughening by increasing the ratio of the moduli of matrix and rubber particle more than 1000. The model also predicts that the glass-rubber transition temperature, T-g, and the nature of transition (i.e., sharp or smooth transition) dominate the ductile-brittle transition temperature of blends. An energy criterion for yielding is proposed to be an improved necessary condition for the yielding of polymer instead of the Von Mises stress-yielding criterion. The energy creterion can be used to predict an optimal volume fraction of rubber particles for ductility.