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

Abstract

We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow above a well defined yield stress. In this paper, we describe a first step in exploring the implications of these models for theories of fracture and related phenomena. We consider a one dimensional problem of decohesion from a substrate of a membrane that obeys the viscoplastic constitutive equations that we have constructed. We find that, quite generally, when the yield stress becomes smaller than some threshold value, the energy required for steady decohesion 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 are relevant to understanding the ductile to brittle transition as well as fracture stability.

10 pages, REVTeX, 12 postscript figures

Cited by in corpus (7)

• Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
• Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Energetic Constraints in a Minimal Theory
• Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
• Griffith cracks in the mesoscopic microcrack theory
• Rate-and-State Theory of Plastic Deformation Near a Circular Hole
• Elastic nonlinearities in a one-dimensional model of fracture
• On the geometry of a dislocated medium