A statistical mechanical theory of forest hardening is developed in which yielding arises as a phase transition. For simplicity, we consider the case of a single dislocation loop moving on a slip plane through randomly distributed forest dislocations, which we treat as point obstacles. The occurrence of slip at the sites occupied by these obstacles is assumed to require the expenditure of a certain amount of work commensurate with the strength of the obstacle. The case of obstacles of infinite strength is treated in detail. We show that the behavior of the dislocation loop as it sweeps the slip plane under the action of a resolved shear stress is identical to that of a lattice gas, or, equivalently, to that of the two-dimensional spin-1/2 Ising model. In particular, there exists a critical temperature Tc below which the system exhibits a yield point, i.e., the slip strain increases sharply when the applied resolved shear stress attains a critical value. Above the critical temperature the yield point disappears and the slip strain depends continuously on the applied stress. The critical exponents, which describe the behavior of the system near the critical temperature, coincide with those of the two-dimensional spin-1/2 Ising model.
Skip Nav Destination
Article navigation
June 1999
Research-Article
Plastic Yielding as a Phase Transition
M. Ortiz
M. Ortiz
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125
Search for other works by this author on:
M. Ortiz
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125
J. Appl. Mech. Jun 1999, 66(2): 289-298 (9 pages)
Published Online: October 25, 1999
Article history
Received:
August 14, 1998
Revised:
November 20, 1998
Citation
Ortiz, M. (October 25, 1999). "Plastic Yielding as a Phase Transition." ASME. J. Appl. Mech. June 1999; 66(2): 289–298. https://doi.org/10.1115/1.2791048
Download citation file:
Get Email Alerts
Related Articles
A Thermodynamical Theory of Plastic Spin and Internal Stress With Dislocation Density Tensor
J. Eng. Mater. Technol (April,1999)
Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity
J. Appl. Mech (September,1983)
On the Effect of Anisotropy and Inertia on Shear Banding: Instability of Biaxial Stretching
Appl. Mech. Rev (March,1992)
Phenomenological Theories of Elastoplasticity and Strain Localization at High Strain Rates
Appl. Mech. Rev (March,1992)
Related Proceedings Papers
Related Chapters
Verifying of a Network Cryptographic Protocol Using the Model Checking Tools
International Conference on Software Technology and Engineering (ICSTE 2012)
The Direct Contribution of Spin-Down Compression for Rotochemical Deviations in Stars Containing Mixed- Phase Matter
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
Sznajd Social Model on Weighted Network with Improved Rules
International Conference on Advanced Computer Theory and Engineering (ICACTE 2009)