Fracture at Finite Temperature: a Statistical-Thermodynamic Approach
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FRACTURE AT FINITE TEMPERATURE: A STATISTICAL-THERMODYNAMIC APPROACH ROBIN L. BLUMBERG SELINGER*, ZHEN-GANG WANG*,**,
and WILLIAM M.
GELBART* " Dept. of Chemistry, University of California, Los Angeles, California, 90024 ** Dept. of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125
ABSTRACT: We discuss both theory and simulation of fracture of ideal and almost ideal crystals at finite temperature. We propose that a solid under stress is in a metastable state, and that the onset of fracture may be characterized as the nucleation of the (stable) broken phase from the (metastable) intact phase. The role of atomic-scale defects is also discussed.
In the last several years, many researchers have investigated statistical models of fracture, including much work on network models [1] and a model of earthquake dynamics [2]. In both cases, investigators have focused on the non-equilibrium aspects of the fracture process: in network models, bonds break irreversibly at a threshold value of the local stress, while in the earthquake model, the stick-slip dynamics is dissipative. Although temperature-dependent breaking probabilities have been included in a network model of polymer systems [3], the dynamics was irreversible, and therefore the model system could not be described by an equilibrium theory. Our goal is to understand the physics of fracture at finite temperature, that is, to go beyond the Griffith (4] picture of microcrack instability and understand the role of thermal fluctuations and metastability in the onset of material failure of an ideal crystal. We propose that a solid under stress is in a metastable state, and that the onset of fracture may be characterized as the nucleation of the (stable) broken phase from the (metastable) intact phase. According to this picture, the free energy of a crystal subject to a subcritical tensile force, plotted as a function of strain, has a local minimum, corresponding to a metastable equilibrium state. As the applied force is increased, the minimum becomes shallower and eventually vanishes at a critical force f,, indicating that the crystal has reached its limit of metastability. We identify f,(T) as the (temperature-dependent) ideal strength of the crystal. Due to thermal fluctuations, the crystal may fail at an applied force below the ideal limit. Furthermore, any pre-existing defects act to lower the free energy barrier, much as a dust particle lowers the barrier to nucleation of a liquid from a supersaturated vapor. In earlier work, we illustrated this idea via a simple Ising-like bond model [5]. We now introduce a mean-field approximation to calculate directly the free energy of a twodimensional Lennard-Jones crystal under an applied tensile force, pressure and temperature. From this free energy function, we determine the crystal's ideal strength and other properties as a function of temperature.
Mat. Res. Soc. Symp. Proc. Vol. 248. @1992Materlals Research Society
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