We study the equilibrium stress field in an annulus composed of a material that admits stress-induced displacive phase transformation that preserves volume. A standard example is the austenite to martensite transformation in shape memory alloys. Attention is restricted to isothermal and axisymmetric load increase. The constitutive model follows a standard formulation appropriate for small strains and incorporates a single internal variable (the martensite phase fraction). A plane-stress boundary value problem is analyzed so as to determine the partitioning of the annulus into regions of (pure) austenite, (pure) martensite, and austenite/martensite mixture. Structure maps are presented, giving concise descriptions of the phase partitioning as the loads increase.
Axisymmetric Plane Stress States of an Annulus Subject to Displacive Shear Transformation
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 Applied Mechanics Division, July 8, 2003; final revision, August 16, 2004. Associate Editor: K. Ravi-Chandar. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, 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 in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Chi , Y., Pence , T. J., and Tsai, H. (February 1, 2005). "Axisymmetric Plane Stress States of an Annulus Subject to Displacive Shear Transformation ." ASME. J. Appl. Mech. January 2005; 72(1): 44–53. https://doi.org/10.1115/1.1828062
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