  We study the growth of slip line in a plastically deforming crystal by
numerical simulation of a double-ended pile-up model with a dislocation source
at one end, and an absorbing wall at the other end. In presence of defects, the
pile-up undergoes a second order non-equilibrium phase transition as a function
of stress, which can be characterized by finite size scaling. We obtain a
complete set of critical exponents and scaling functions that describe the
spatiotemporal dynamics of the slip line. Our findings allow to reinterpret
earlier experiments on slip line kinematography as evidence of a dynamic
critical phenomenon.
