Finite-Strain Elastic-Plastic Circular Shear in Materials with Isotropic Hardening

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Abstract

This study presents an analytical solution to the problem of azimuthal shear in a hollow circular cylinder, isotropic and incompressible, the elastic properties of which are described by the Mooney – Rivlin model, and the plastic properties by the Tresca model with arbitrary monotonic hardening. Both elastic and plastic deformations are assumed to be finite. Sufficient conditions for the existence of the presented solution are given.

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About the authors

G. M. Sevastyanov

Institute of Mechanical Science and Metallurgy, KhFRC FEB RAS

Author for correspondence.
Email: akela.86@mail.ru
Russian Federation, Komsomolsk-on-Amur

A. S. Begun

Institute of Mechanical Science and Metallurgy, KhFRC FEB RAS

Email: ustinova@iacp.dvo.ru
Russian Federation, Komsomolsk-on-Amur

A. A. Burenin

Institute of Mechanical Science and Metallurgy, KhFRC FEB RAS

Email: burenin@iacp.dvo.ru
Russian Federation, Komsomolsk-on-Amur

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Supplementary files

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2. Fig. 1. Circular shear under plane strain conditions.

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3. Fig. 2. Elastic-plastic deformation.

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4. Fig. 3. Curvature of initially radially oriented material fibers after circular shear (rotation angle in degrees). The symbol “■” denotes the position of the elastic-plastic boundary.

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5. Fig. 4. Relationship between the tangential stress on the outer surface of the specimen and the angle of rotation (in radians). The radian value corresponds to the complete transition of the specimen to the plastic state.

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6. Fig. 5. Propagation of elastic-plastic boundary (rotation angle in radians).

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7. Fig. 6. Distribution of the accumulated plastic strain along the cross-section of the specimen: 1 - , 2 - , 3 - , 4 - , 5 - , 6 - , 7 - (rotation angle in radians).

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8. Fig. 7. Evolution of the accumulated plastic strain on the boundary surfaces (rotation angle in radians). The radian value corresponds to the complete transition of the specimen into the plastic state.

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