The behavior of energetic materials is significantly influenced by the density, spatial distributions, and morphologies of microstructure heterogeneities and voids. Void density can profoundly influence the shock-to-detonation transition (SDT) in polymer bonded explosives (PBX). Spatial non-uniformity of void density or void density gradients can further alter the material behavior. Five cases, two with graded void distributions from 1% to 10% and 10% to 1 % by volume along the length of the sample, and three with uniform distributions matching the lowest (1%), average (5.5%), and highest (10%) void densities are considered in this study. Three-dimensional microstructure explicit simulations are carried out. The material consists of HMX grains (~85% by volume), an Estane binder (~15%). Shock loading is applied via impact by an aluminum flyer with velocities ranging from 800 m/s to 1300 m/s (4 – 6 GPa input shock pressure). An Arrhenius reaction model is used to account for the chemical kinetics of the HMX grains. The SDT behaviors are analyzed in terms of the run distance and the time duration and shock velocity changes over the course of the SDT process. To quantify the effect of random material heterogeneities, statistically equivalent microstructure sample sets (SEMSS) containing multiple random but equivalent samples for each setting are used. The results are presented in the context of available experimental data. Different detonation behaviors are obtained from the same graded sample when impact loading is from the 1% void end and from the 10% void end. Furthermore, the graded samples show behaviors that are different from those of non-graded samples. Overall, it is shown that microstructure gradient and microstructure morphology of heterogeneity can be used to modify the SDT behaviors and achieve responses not obtainable otherwise, thereby offering a means for the design and tailoring of new energetic materials.