Abstract
A novel thermo-elastoplastic self-consistent homogenization model for granular materials that exhibit inter-granular plasticity is presented. The model, TEPSCA, is made possible by identifying a new inter-granular plastic Eshelby-like tensor. A micromechanical model of interfacial yielding between grains of a Mohr–Coulomb type is provided, which is relatable to the description of imperfect interfaces within the paradigm of self-consistent homogenization. The local grain constitutive laws are consistent with the description of an interphase layer comprised of local pore volume between grains, such that inelastic inter-particle displacements are directly relatable to changes in bulk porosity, i.e., dilation. The model was developed for the purpose of modeling thermally induced plasticity—the phenomenon known as thermal ratcheting or “ratchet growth”—of composites made from the high explosive triaminotrinitrobenzene (TATB). Model simulations are compared to ratchet growth measurements during cyclic thermal loading of a TATB pellet under stress-free conditions.
Highlights
Many materials can be described as granular, being comprised of distinct solid particles and often possessing some degree of inter-granular porosity
This work is concerned with analytical homogenization of bonded granular materials within the context of Self-Consistent Homogenization (SCH), which has its origin in statistical concepts of multi-scale mechanics originally elucidated by Hershey [26] and Kröner [33], generally credited to have been formalized by Hill [28,29]
Model predictions are compared to measurements by Woznick et al [65] of the ratchet growth of a pressed TATB pellet subjected to thermal cycling, demonstrating the model’s effectiveness
Summary
Many materials can be described as granular, being comprised of distinct solid particles (grains) and often possessing some degree of inter-granular porosity. The process of upscaling from the heterogeneous microscale to a homogeneous mesoscale of the material is generally called in the context of mechanics homogenization, and various specific methodologies have been proposed (cf [17,41]), falling broadly into two basic categories: direct numerical simulation of microstructure (e.g., [18,35,36,37,63]), and homogenization by analytical means, typically called micromechanical modeling or sometimes statistical mechanics (cf [13,32,44,48,52,60]). This work is concerned with analytical homogenization (micromechanical modeling) of bonded granular materials within the context of Self-Consistent Homogenization (SCH), which has its origin in statistical concepts of multi-scale mechanics originally elucidated by Hershey [26] and Kröner [33], generally credited to have been formalized by Hill [28,29]. Model predictions are compared to measurements by Woznick et al [65] of the ratchet growth of a pressed TATB pellet subjected to thermal cycling, demonstrating the model’s effectiveness
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