Principal Direction Paths in Tension‐Torsion Test at Finite Strain
Publication: Journal of Engineering Mechanics
Volume 116, Issue 5
Abstract
General equations are presented for the determination of principal direction paths of each of the Lagrangian strain ellipsoid, Eulerian strain ellipsoid, strain rate, and Cauchy stress for uniform finite deformation of thin‐walled tubes in combined tension and torsion. Specific paths are evaluated from experimental results for nonproportional loading of tubes of annealed copper (Bell and Khan 1980) and mild steel (Bell 1983a). It is found that the principal directions of Cauchy stress are not correlated with either of the strain ellipsoids, but that Cauchy stress and Eulerian strain rate are very nearly coaxial throughout the moderate finite‐deformation range of the experiments.
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References
1.
Al‐Gadhib, A. H. (1989). “A comparative analysis and assessment of different macroscopic plasticity theories as applied to the tension‐torsion test of thin‐walled tubes at finite strain,” thesis presented to North Carolina State University, at Raleigh, N.C., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Barsch, G. R., and Chang, Z. P. (1967). “Adiabatic, isothermal, and intermediate derivatives of the elastic constants for cubic symmetry, II: Numerical results for 25 materials.” Physica Status Solidi, 19, 139–151.
3.
Bell, J. F. (1973). The experimental foundations of solid mechanics, handbuch der physik, VIa/1, Springer‐Verlag, Berlin.
4.
Bell, J. F. (1979). “A physical basis for continuum theories of finite strain plasticity: Part I.” Archive for Rational Mech. and Analysis, 70, 319–338.
5.
Bell, J. F. (1983a). “Finite plastic strain in annealed mild steel during proportional and non‐proportional loading.” Int. J. Solids Structures, 16, 683–693.
6.
Bell, J. F. (1983b). “Continuum plasticity at finite strain for stress paths of arbitrary composition and direction.” Arch. Rational Mech. Anal., 84, 139–170.
7.
Bell, J. F. (1985). “Contemporary perspectives in finite strain plasticity.” Int. J. Plasticity, 1, 3–27.
8.
Bell, J. F. (1988). “Plane stress, plane strain, and pure shear at large finite strain.” Int. J. Plasticity, 4, 127–148.
9.
Bell, J. F., and Khan, A. S. (1980). “Finite plastic strain in annealed copper during non‐proportional loading.” Int. J. Solids Structures, 16, 683–693.
10.
Havner, K. S. (1973). “On the mechanics of crystalline solids.” J. Mech. Phys. Solids, 21, 383–394.
11.
Hill, R. (1950). The mathematical theory of plasticity. Oxford University Press, London, England.
12.
Khan, A. S., and Parikh, Y. (1986). “Large deformation in polycrystallme copper under combined tension‐torsion, loading, unloading, and reloading or reverse loading: A study of two incremental theories of plasticity.” Int. J. Plasticity, 2, 379–392.
13.
McMeeking, R. M. (1982). “The finite strain tension‐torsion test of a thin‐walled tube of elastic‐plastic material.” Int. J. Solids Structures, 18, 199–204.
14.
Mittal, R. K. (1971). “Biaxial loading of aluminum and a generalization of the parabolic law.” J. Materials, 6, 67–81.
15.
Moon, H. (1975). “An experimental study of incremental response functions in the totally plastic region.” Acta Mechanica, 23, 49–63.
16.
Taylor, G. I., and Quinney, H. (1931). “The plastic deformation of metals.” Phil. Trans. Royal Soc. London, London, England, A230, 323–362.
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Copyright © 1990 ASCE.
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Published online: May 1, 1990
Published in print: May 1990
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