The growth of a crack first in an elastic solid, then across an interf
ace and into an elastic-viscoplastic solid is analyzed numerically. Th
e analyses are carried out within a framework where the continuum is c
haracterized by two constitutive relations; one that relates stress an
d strain in the bulk material, the other relates the traction and sepa
ration across a specified set of cohesive surfaces. Crack initiation,
crack growth and crack arrest emerge naturally as outcomes of the impo
sed loading, without any ad hoc assumptions concerning crack growth or
crack path selection criteria. Full transient analyses are carried ou
t using two characterizations of strain rate hardening for the viscopl
astic solid; power law strain rate hardening and a combined power law-
exponential relation that gives rise to enhanced strain rate hardening
at high strain rates. Results are presented for two values of interfa
ce strength. For the higher strength interface the crack grows straigh
t through the interface into the elastic-viscoplastic solid, while for
the lower strength interface the crack deflects into the interface.