  We present creep experiments on fiber composite materials. Recorded strain
rates and acoustic emission (AE) rates exhibit both a power law relaxation in
the primary creep regime and a power-law acceleration before global failure. In
particular, we observe time-to-failure power laws in the tertiary regime for
acoustic emissions over four decades in time. We also discover correlations
between some characteristics of the primary creep (exponent of the power-law
and duration) and the time to failure of the samples. This result indicates
that the tertiary regime is dependent on the relaxation and damage processes
that occur in the primary regime and suggests a method of prediction of the
time to failure based on the early time recording of the strain rate or AE
rate. We consider a simple model of representative elements, interacting via
democratic load sharing, with a large heterogeneity of strengths. Each element
consists of a non-linear dashpot in parallel with a spring. This model recovers
the experimental observations of the strain rate as a function of time.
