Dynamic ductile to brittle transition
in a one-dimensional model of viscoplasticity

J. S. Langer(1) and Alexander E. Lobkovsky(2)
(1) Physics Deprtment
(2) Institute for Theoretical Physics
Univesity of California
Santa Barbara, CA 93106

We study two closely related, non-linear models of a viscoplastic solid. These models capture essential features of a plasticly deforming solid over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. As a proof of principle we consider a problem of decohesion from the substrate of a membrane that obeys the viscoplastic constitutive equations we have constructed. We find that quite generically, when the yield stress becomes smaller than a certain than a certain threshold, the energy input required to keep a steady decohesion process going becomes a non-monotonic function of the decohesion speed. As a consequence, steady state decohesion at certain speeds becomes unstable. We believe that these results to be relevant to the understanding of the ductile to brittle transition as well as the fracture stability problems.