A percolation model for lifetime variability in polymeric materials under creep conditions

The authors propose a microlevel theory of damage accumulation in polymeric materials. On the basis of experimental data on submicro- and microcracks, they relate the time-dependent strength distribution in polymeric material s under applied load to the distribution of the largest cluster size in a s ite percolation lattice well below the percolation threshold rho(c). The em pty sites fraction rho in the percolation lattice is suggested to increase with a constant rate, evaluated using the model of a trigger-type molecular reaction described in the literature. Duxbury's initial study of the large st cluster size distribution is extended by Monte Carlo simulations. While the latter distribution is confirmed to be double exponential, the characte ristic largest cluster size (the distribution mode) is found to increase ex ponentially with rho within the range rho(0)<rho <rho(c), rho(0) being a co nstant, although for small rho <rho(0) the conventional logarithmic depende nce is preferable. For the considered two-dimensional square lattice rho(0) is estimated to be 0.05. A failure criterion is formulated and a constitut ive framework for the derivation of the time-dependent strength distributio n and the structural reliability is defined. The lifetime statistics for a constant enhanced load is shown to be of the Weibull type, while for low lo ads a triple-exponential distribution is suggested. Unlike the competitive theories, the proposed model predicts that the Weibull shape parameter depe nds on the applied load by a simple inverse power law with the power define d by a fractal dimension of the critical microcrack aggregate. This predict ion is confirmed based on two experimental sets of lifetime statistics, rep orted in the literature. (C) 2000 American Institute of Physics. [S0021-897 9(00)10513-4].