Effective elastic moduli of polymer bonded explosives from finite element simulations

Finite element analysis has been used successfully to estimate the effective properties of many types of composites. The prediction of effective elastic moduli of polymer-bonded explosives provides a new challenge. These particulate composites contain extremely high volume fractions of explosive particles (> 0.90). At room temperature and higher, the Young’s modulus of the particles can be 20,000 times that of the binder. Under these conditions, rigorous bounds and analytical approximations for effective elastic prope rties predict values that are orders of magnitude different from the experimental values. In this work, an approach is presented that can be used to predict three-dimensional effective elastic moduli from two-dimensional finite eleme nt simulations. The approach is validated by comparison with differential effective medium estimates and three-dimensional finite element simulations. The two-dimensional finite element approach has been used to determine the proper ties of models of polymer bonded explosives and PBX 9501 in particular, containing high volume fractions of cir cular and square particles with high modulus contrasts. Results show that estimates of effective elastic propertie s from two-dimensional finite element calculations are clos e to the values predicted by the differential effective mediu m approach for a large range of volume fractions and modulus contrasts. Two- and three-dimensional finite eleme nt estimates for volume fractions from 0.70 to 0.90 and found not to differ considerably. Simulations of models of polymer bonded explosives and PBX 9501 show that the microstructure, the amount of discretization, and the type of element used play a considerable role in determining the value predicted by finite element simulations. The effectiv e elastic moduli of PBX 9501 predicted by finite element calculations can vary from 200 MPa to 10,000 MPa depending on the microstructure and level of discretization used. The results also suggest that if a microstructure can be foun d that accurately predicts the elastic properties of PBX 9501 at a certain temperature and strain rate, then the same microstructure can be used to predict elastic properties at other temperatures and strain rates.