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IssuesArchive of Issues2005-2pp.104-112

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K. F. Komkov, "The calculation of the Lode parameters when processing the results of experiments," Mech. Solids. 40 (2), 104-112 (2005)
Year 2005 Volume 40 Number 2 Pages 104-112
Title The calculation of the Lode parameters when processing the results of experiments
Author(s) K. F. Komkov (Moscow)
Abstract The difference between the Lode parameters for the stresses and strains is an important indicator of the dependence of the material properties on the type of the stress state. Investigations of this problem lead to contradictory conclusions primarily because information on the strains, which cannot be measured in the experiment, is incomplete.

In the present paper, it is shown that the accuracy of the calculation of the parameters can be improved significantly on the basis of the analysis of the analysis of nonlinear tensor equations.

This analysis indicates that the Lode parameter for the stresses is greater than the corresponding parameter for the strains for all kinds of the stress state, apart from the boundary states, namely, the generalized tension or the corresponding compression, in which these parameters are equal. In addition, it is shown that the value of the difference between these parameters is approximately two times the tangent of the deviator similarity phase introduced by V. V. Novozhilov as a generalized characteristic of the strain properties of materials.

A method for reconstructing the Lode diagrams on the basis of the results of experiments with tubular samples is proposed. The analysis of experimental data confirmed the hypothesis proposed earlier that, in the case of plastic deformation, the change of the shape is occurring so that the shear compliance in the principal shear stress directions is characterized in the general case by three different values. This indicates the strain anisotropy which manifests itself primarily by the non-similarity of the stress and strain deviators.
References
1.  V. Prager, Metal Hardening in a Complex Stress State [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1948.
2.  V. V. Novozhilov, "On the stress-strain relation in a nonlinearly elastic medium," PMM [J. Applied Mathematics and Mechanics], Vol. 15, No. 2, pp. 183-194, 1951.
3.  K. F. Komkov, "On the appliction of nonlinear tensor equations in mechanics of solids," Prikl. Mekhanika, Vol. 27, No. 7, pp. 36-41, 1991.
4.  A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow, 1980.
5.  V. Lode, "Effect of the mean principal stress on the yield of metals," In Theory of Plasticity, Izd-vo Inostr. Lit-ry, Moscow, 1948.
6.  E. Davis, "Stress growth with the variation of strains and the stress-strain characteristic in the plastic region for copper in a complex stress state," In Theory of Plasticity, Izd-vo Inostr. Lit-ry, Moscow, 1948.
7.  A. M. Zhukov, "Complex loading in the theory of plasticity for isotropic metals," Izv. AN SSSR. OTN, No. 8, pp. 81-92, 1955.
8.  O. G. Rybakina and Ya. S. Sidorin, "Experimental investigation of plastic loosening of metals," Inzh. Zh. MTT, No. 1, pp. 120-124, 1966.
Received 02 February 2004
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