Modeling Dynamic Rate Dependent Pore Closure with A Range of Pore Sizes

Abstract

Previously we presented a model (which we call PORT) with rate dependent pore closing/opening, for which we assumed that all pores close/open with the same dynamics [1]. Here we upgrade PORT to take into account different dynamics as function of pore size. We represent different pore sizes by their volume (v), and we have k discrete pore sizes. We therefore call this model VK. For the i^th pore size we have n_i, i=1,k pores per unit mass. We’re not aware of information on pore size distributions of porous materials, and we assume arbitrarily that pore sizes are initially distributed with a log-normal distribution. Similar to PORT, we define quasistatic pore closure curves that depend on pore volume v, and we compute the rate of pore closure with a linear overstress equation relative to these curves. From the values of v and vdot (rate of change of v) we then compute (for each cell and for each time) the overall porosity j and its rate of change jdot. Finally, we compute Pdot and Tdot (P=pressure and T=temperature) in the same way as in PORT, using the equation of state of the porous material. To show how our VK model works, we apply it to a simple 1D problem: a 20GPa sustained pressure pulse enters a porous aluminum target. We show histories of pressure, temperature and porosity at several locations into the target. We compare these curves to the ones obtained for k=1 (which are as in PORT).