Relaxation creep rupture of heterogeneous material under constant strain

We focus on a system consisting of an elastic part and a damageable part in series, to study the relaxation creep rupture of a heterogeneous system subjected to a uniaxial constant strain applied instantaneously. The viscoelastic behavior of the damageable part is modeled by a fiber bundle model consisting of Kelvin-Voigt elements and global load sharing is assumed for the redistribution of load following fiber breaking in the damageable part. Analytical and numerical calculations show that the global relaxation creep rupture appears if the elastic energy stored in the elastic part exceeded the fracture energy of the damageable part. The lifetime of the system strongly depends on the values of the applied external strain and the initial stiffness ratio k between the elastic part and the damageable part. We show that a higher stiffness ratio implies a more brittle system. Prior to complete failure, relaxation creep rupture exhibits a sequence of three stages, similar to creep rupture under constant stress, and the nominal force rate presents a power law singularity with a power index -1/2 near the global rupture time.