A phenomenological constitutive law is developed for the deformation of polycrystalline ferroelastic materials. The model is framed within a thermodynamic setting common to internal variable plasticity. The two significant inputs to this model are a switching (yield) surface, and a hardening potential. To maintain simplicity, the shape of the switching surface is assumed to be spherical in a modified deviatoric stress space. In order to ascertain the functional form of the hardening potential, micromechanical self-consistent simulations of multiple single crystals, with tetragonal crystal structure, embedded in an effective polycrystalline matrix, are performed for differing loading paths in remanent (plastic) strain space. As a result of the asymmetry in the tension versus compression behavior of these materials, it is shown that pure shear loading does not result in pure shear straining. This feature of the material behavior is demonstrated with the self-consistent simulations and predicted by the phenomenological constitutive law. Ultimately, the phenomenological theory is able to capture the complex constitutive behavior of ferroelastic materials predicted by the micromechanical model.
On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 29, 2002; final revision, Dec. 10, 2002. Associate Editor: H. Gao. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Landis, C. M. (August 25, 2003). "On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials ." ASME. J. Appl. Mech. July 2003; 70(4): 470–478. https://doi.org/10.1115/1.1600472
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