AbstractThe complex structure and mechanics of elastoplastic functionally graded materials (FGM) is studied from the standpoint of fractal geometry. First, upon introducing the fineness as the number of grains of either phase across the FGM, the two-phase FGM is characterized using fractals, and an interfacial fractal dimension is estimated for varying degrees of fineness. A variation in local fractal dimension is considered across or along the FGM domain, and it is characterized by Fourier series and Beta function fits. Assuming the FGM is made of locally isotropic Titanium (Ti) and Titanium Monoboride (TiB), pure shear tests are simulated using ABAQUS for fineness levels of 50, 100, and 200 under the uniform kinematic boundary condition (UKBC) and the uniform static boundary condition (USBC). The material response observed under these BCs shows high sensitivity of these systems to loading conditions. Furthermore, plastic evolution of Ti grains, assuming isotropic plastic hardening, displays a fractal, p...

A mechanisms-based fracture model applicable to a broad class of cemented aggregates and, among them, plastic-bonded explosive (PBX) composites, is presented. The model is calibrated for PBX 9502 using the available experimental data under uniaxial compression and tension gathered at various strain rates and temperatures. We show that the model correctly captures inelastic stress-strain responses prior to the load peak and it predicts the post-critical macro-fracture processes, which result from the growth and coalescence of micro-cracks. In our approach, the fracture zone is embedded into elastic matrix and effectively weakens the material's strength along the plane of the dominant fracture.