From Simulation to Theory in the Physics of Deformation and Fracture
- PDF / 346,174 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 11 Downloads / 162 Views
at small applied stress, a dynamic transition to viscoplasticity above a yield stress, strain hardening, and plastic ratcheting (hysteresis). Although it has been developed specifically for amorphous systems, it may be generalized to any solid in which the processes controlling deformation are isotropically distributed and immobile. The conventional approaches to plasticity theory, such as those described in books by Lubliner 4 or Hill,5 generally (but not always) assume well-defined yield surfaces in the space of the principal stresses and make arbitrary distinctions between timedependent and time-independent formulations. These approaches seem unsatisfactory to us because they cannot, in a natural way, describe the wide range of behaviors that occur in deformable materials. For example, they cope with phenomena such as strain hardening, the transition from viscoelastic to viscoplastic behavior, and hysteresis by specifying phenomenological rules to suit particular material characteristics and histories of deformation. In our opinion, we need to construct an entirely new level of phenomenology in order to bring the theory of plastic deformation to the point where it can be usefully applied to problems like fracture.
Simulations of Noncrystalline Solids The starting point in our investigation was a MD simulation of fracture in a simple polydisperse, two-dimensional, noncrystalline Lennard-Jones solid.2 To our surprise, this oversimplified system
reproduced many of the aspects of fracture that are typically associated with much more complex materials, such as steels. Most strikingly, small changes in the interatomic potential resulted in dramatic changes in the fracture toughness. The changes in toughness were accompanied by the kinds of qualitative changes in crack-tip morphology—a propagating sharp tip versus blunting, void formation, and linkup—that characterize brittle and ductile failure (see Figure 1). We were left with a mystery: Why do such small changes in bonding lead to such dramatic changes in crack dynamics?6 In the world of computer simulation, these problems are much easier to address than in the world of experiment. We were able to change our experiments to focus on what we felt was the most salient physical process, deformation under pure shear. To reduce complications, we restricted ourselves to a two-component glass and examined bulk properties in a periodic cell in which we were able to carefully control either shear strain or shear stress as functions of time. These simulations build on previous computational investigations of deformation in amorphous metals.7–10 The limitation of MD simulations is, of course, the time scale; simulations rarely exceed even a few nanoseconds. However, such short time windows were justifiable here because we were primarily interested in dynamic fracture, where strain rates at crack tips can be this fast or faster. The simulations again revealed a rich variety of behaviors typical of real solids, specifically, reversible elastic deformation at small applied stres
Data Loading...
