Asymptotic, plane strain near-tip fields are presented for steadily pr
opagating interface cracks between (1) a ductile solid and a rigid sub
strate, and (2) two dissimilar ductile solids. The ductile materials a
re taken to be incompressible, elastic-perfectly plastic and obey the
J2-flow theory of plasticity. It is shown that the crack-tip region ca
n be considered as being composed of two types of angular plastic sect
ors: Uniform sectors, in which stresses are constant, and nonuniform s
ectors. Solutions for the asymptotic crack-tip fields are,not unique,
and they are represented by various assemblies of the plastic sectors
that satisfy the necessary conditions. Some of the solutions are isola
ted, while others belong to one-parameter families. The crack-tip fiel
ds represented by these asymptotic solutions are fully continuous in e
ach of the two component solids, and have nonsingular strains at the c
rack tip.