M. Ibnabdeljalil et Sl. Phoenix, CREEP-RUPTURE OF BRITTLE-MATRIX COMPOSITES REINFORCED WITH TIME-DEPENDENT FIBERS - SCALINGS AND MONTE-CARLO SIMULATIONS, Journal of the mechanics and physics of solids, 43(6), 1995, pp. 897-931
This paper addresses statistical aspects of the lifetime in creep rupt
ure of unidirectional composites having brittle matrices reinforced wi
th brittle fibers. Time dependence enters through the fibers, which fa
il following a probability model due to Coleman, involving power law d
ependence 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 quasiper
iodic cracking of the matrix, frictional sliding of fibers in fiber br
eak zones, and fiber bridging of matrix cracks in a global load-sharin
g framework. No time dependence is assumed at the fiber-matrix interfa
ce, though progressive slippage does occur in time as fibers fail and
load is redistributed. Starting from an ''equivalent'' short term stre
ngth 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 dev
eloping a scaling analysis relating parameters of strength to creep-ru
pture lifetime. Through Monte Carlo simulation we are able to establis
h key parametric relationships and distributional forms not accessible
through analysis. The power law scaling that allows us to write the l
ifetime of a single fiber in terms of the ratio of the load level to t
he short term strength is preserved remarkably well in the composite,
though with a different power law exponent. An interesting and unexpec
ted result is the emergence of an asymptotic log-normal distribution f
or the lifetime of a composite of characteristic length in contrast to
the asymptotic normal distribution for strength. We also study throug
h analysis acid simulation the size effect relating composite lifetime
distribution and its median to overall composite volume.