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TECHNICAL PAPERS

On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials

[+] Author and Article Information
C. M. Landis

Department of Mechanical Engineering and Materials Science, MS 321, Rice University, P.O. Box 1892, Houston, TX 77251e-mail: landis@rice.edu

J. Appl. Mech 70(4), 470-478 (Aug 25, 2003) (9 pages) doi:10.1115/1.1600472 History: Received July 29, 2002; Revised December 10, 2002; Online August 25, 2003
Copyright © 2003 by ASME
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References

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Landis,  C. M., and McMeeking,  R. M., 1999, “A Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting Asymptotic Crack Tip Solution,” J. Intell. Mater. Syst. Struct., 10, pp. 155–163.
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Figures

Grahic Jump Location
(a) The three possible orientations of tetragonal variants within a single crystal. Different variants within a single crystal will be separated by a domain wall or twin boundary. (b) The uniaxial stress-strain response of a model single crystal loaded along any of the 〈100〉 directions. Notice the asymmetry in tension versus compression.
Grahic Jump Location
Self-consistent computations of the deformation behavior of the ferroelastic material for different proportional remanent straining paths. The stresses are normalized by the critical resolved shear stress required to cause switching and the effective remanent strains are normalized by the tensile saturation strain of a single crystal. Note that J3e/J2e=−1,0,1 represents axisymmetric contraction, pure shear remanent strain, and axisymmetric extension, respectively. The inset is an expanded view of the region cut off from the larger plots. Note the lack of tension-compression asymmetry for small strains, but the significant asymmetry of the saturation strains.
Grahic Jump Location
Self-consistent computations of the uniaxial compression deformation behavior of the ferroelastic material for different levels of the dimensionless ratio με00. Note that the saturation strain for each test is the same but the shape of the stress-strain curve differs.
Grahic Jump Location
The effective saturation strain level as a function of the remanent strain invariant ratio J3e/J2e. Note that J3e/J2e=−1,0,1 represents axisymmetric contraction, pure shear remanent strain, and axisymmetric extension respectively. This figure illustrates the anisotropic nature of the material in response to tension versus compression.
Grahic Jump Location
A comparison of the phenomenological theory to the self-consistent calculations for different proportional stressing paths. The stresses and strains are now normalized by the parameters of the phenomenological model. Note that the ratio σe/39sijsjkski/2=−1,0,1 represents axisymmetric compression, pure shear stressing, and axisymmetric tension, respectively. Notice that even the stress path with significant compression results in an ultimate remanent strain state with significant extension. Of course, the tensile strain is not aligned with the compressive stress in this situation.

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