Quantifying power partitioning during void growth for dynamic mechanical loading in reduced form

Abstract

A study of the partitioning of external power into stress power, stored defect energy, thermal energy, and inertia during dynamic void growth is presented. An alternative form for a classical thick-walled sphere governing equation stemming from a local power balance including energetic cost of free surface creation is proposed. The importance of proper energy accounting in the context of dynamic ductile damage is discussed. An isotropic thermodynamically consistent thermomechanical dislocation density-based plasticity model is presented and compared against experimental data for high-purity BCC tantalum. This model accounts for plastic power partitioning to stored defect energy and thermal energy with evolving Taylor-Quinney coefficient. The plasticity model is used to perform a suite of thick-walled sphere calculations spanning a wide range of deformation rates and initial temperatures. Thick-walled sphere geometry and initial porosity are based on post-mortem metallographic analysis of void size and spacing in high-purity tantalum. Stress measures of interest as well as quantities provided by enforced thermodynamic consistency are evaluated across the radius of thick-walled sphere calculations as a function of strain rate and temperature. Agglomeration of the resulting 35 thick-walled sphere simulations provides a database for statistical evaluation. Analysis using information theory yields a simple reduced order functional form for the total thick-walled sphere stress power in terms of surface quantities and solid volume. Validation of the found functional form is performed for five arbitrary loading curves showing good agreement. Implications for the local power balance evolution equation are examined. Suitability of the resulting void governing equation for use in continuum-scale dynamic ductile damage models is discussed.