We couple morphological studies of binary, immiscible blends with mechanical studies of deformation and fracture to determine the influence of the blend composition on the initiation and propagation of cracks in polymeric materials. The Cahn-Hilliard (CH) method is employed to simulate the structural evolution of the molten AB blend. We assume that the material undergoes a rapid quench to yield a solid whose microstructure is given by the CH approach. The output from these CH simulations serves as the input to a dynamic lattice spring model (LSM), a micromechanical model that consists of a three-dimensional network of springs, which connect regularly spaced mass points. Within the LSM, the A and B phases, as well as the interfacial regions, are assigned distinct spring constants, thereby allowing us to model a blend of a compliant and a stiff polymer. With the application of a tensile deformation, the heterogeneous microstructures give rise to complex local elastic fields. Using an energy-based fracture criterion, we selectively remove springs from this system and thereby simulate the initiation and propagation of cracks within the material. By varying the relative stiffness and toughness of the phases, we determine how these characteristics affect the growth of the cracks. We also consider systems where the interface between the different species is mechanically weak, and consequently, fracture occurs through the decohesion of the different polymer domains. In all the systems considered here, we find that "clustering effects", which are due to interactions between neighboring domains, play a major role in dictating where incipient fracture occurs. Through these studies, we can correlate the complex morphologies within the blend to the mechanical performance of the solid materials.