Aluminum subjected to smooth mechanical loading does not often deform in a
correspondingly smooth manner. Typically it deforms inhomogeneously through
the propagation of deformation fronts that slowly traverse the sample. The
se are called Portevin-Le Chatelier fronts; what determines their velocity
has been somewhat mysterious. We present a phenomenological theory for defo
rmation fronts that centers on a nonlocal rate dependence of the flow stres
s. In a one-dimensional idealization the equations can be solved exactly, a
nd compared directly with experiment. Many significant features of deformat
ion fronts are captured, including a well-known transition from hopping to
continuous front motion. The phenomenology's predictions are confirmed by o
ur experiments.