Axisymmetric Plane Stress States of an Annulus Subject to Displacive Shear Transformation

[+] Author and Article Information
Yuwei Chi, Thomas J. Pence, Hungyu Tsai

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

J. Appl. Mech 72(1), 44-53 (Feb 01, 2005) (10 pages) doi:10.1115/1.1828062 History: Received July 08, 2003; Revised August 16, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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Grahic Jump Location
(a) Typical one-dimensional stress-strain curve for T>Af. (b) Temperature dependence of threshold stresses σsFTfFTsRT and σfRT.
Grahic Jump Location
Generic phase distribution within the shape memory alloy annulus. The inner ring M (ri≤r≤rM) consists of martensite. The outer ring A (rA≤r≤ro) consists of austenite. The intermediate ring C (rM<r<rA) consists of an austenite/martensite mixture.
Grahic Jump Location
Martensite phase fraction as a function of effective stress for T>Af
Grahic Jump Location
Typical stress distributions (normalized by σs) for a plate with M phase distribution [σ(r)≥σf]. Here E=50 GPa,σf=4σs=300 MPa,ro/ri=2 and (pi,po)=(1,5)σs. Solid lines represent the case of α=0.05. For comparison, stresses for an elastic solution (α=0) under the same boundary conditions are plotted as dashed lines.
Grahic Jump Location
The FML (fully martensitic loop) and FAL (fully austenitic loop) for E=50 GPa, α=0.05, σf=4σs=300 MPa and ro/ri=2. Thrusts inside the smaller ellipse (FAL) produce a fully austenitic plate, while thrusts outside the bigger loop (FML) produce a fully martensitic plate.
Grahic Jump Location
FMLs for various σf values. Here E=50 GPa, α=0.05, σs=75 MPa and ro/ri=2. The smallest loop is the common FAL, and the other curves are FMLs, each marked with corresponding value of σfs.
Grahic Jump Location
Structure map (type I) for ro/ri=2. Here E=50 GPa, α=0.05 and σf=4σs=300 MPa. Note that there is no ACM region. Thrust pair (pi,po)=(5,0.5)σs, marked as a dot, produces a CM phase distribution. The resulting stresses are shown in Fig. 10.
Grahic Jump Location
Structure map (type II) for ro/ri=5. Here E=50 GPa, α=0.05 and σf=4σs=300 MPa. All six types of phase distributions are present. Thrust pair (pi,po)=(5,0.5)σs, marked as a dot, produces a ACM phase distribution. The resulting stresses are shown in Fig. 11.
Grahic Jump Location
Structure map for the special value ro/ri=3.58. Lower values produce type I structure maps, while higher values produces type II. Here E=50 GPa, α=0.05 and σf=4σs=300 MPa. There is no ACM region, and ADL contacts MEL at two points. One of the two points (shown as a dot) represents (pi,po)=(3.565,0.995)σs, producing a C phase distribution with σ(ri)=σf and σ(ro)=σs. The resulting stresses are shown in Fig. 12.
Grahic Jump Location
Stresses (normalized by σs) for a CM phase distribution. Here E=50 GPa, α=0.05, σf=4σs=300 MPa,ro/ri=2 and (pi,po)=(5,0.5)σs. An elastic solution (α=0) is shown for comparison (dashed lines).
Grahic Jump Location
Stresses (normalized by σs) for a ACM phase distribution. Here E=50 GPa, α=0.05, σf=4σs=300 MPa,ro/ri=5 and (pi,po)=(5,0.5)σs. An elastic solution (α=0) is shown for comparison (dashed lines).
Grahic Jump Location
Stresses (normalized by σs) for a special C phase distribution with rM=ri and rA=ro, for E=50 GPa, α=0.05, σf=4σs=300 MPa,ro/ri=3.58 and (pi,po)=(3.565,0.995)σs. An elastic solution (α=0) is shown for comparison (dashed lines).




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