Creep rupture of brittle matrix composites reinforced with time dependent fibers: Scalings and Monte Carlo simulations

Abstract

This paper addresses statistical aspects of the lifetime in creep rupture of unidirectional composites having brittle matrices reinforced with brittle fibers. Time dependence enters through the fibers, which fail following a probability model due to Coleman, involving power law dependence on stress level, Weibull shape and a memory integral of the load history. The creep rupture model has many features similar to the model for composite strength of earlier work, which involves quasiperiodic cracking of the matrix, frictional sliding of fibers in fiber break zones, and fiber bridging of matrix cracks in a global load-sharing framework. No time dependence is assumed at the fiber-matrix interface, though progressive slippage does occur in time as fibers fail and load is redistributed. Starting from an “equivalent” short term strength model we identify characteristic strength and length scales which depend on strain rate and other model parameters. We are then able to identify a characteristic length for the composite for purpose of developing a scaling analysis relating parameters of strength to creep-rupture lifetime. Through Monte Carlo simulation we are able to establish key parametric relationships and distributional forms not accessible through analysis. The power law scaling that allows us to write the lifetime of a single fiber in terms of the ratio of the load level to the short term strength is preserved remarkably well in the composite, though with a different power law exponent. An interesting and unexpected result is the emergence of an asymptotic log-normal distribution for the lifetime of a composite of characteristic length in contrast to the asymptotic normal distribution for strength. We also study through analysis and simulation the size effect relating composite lifetime distribution and its median to overall composite volume.