Effective Stress and Effective Strain in Relation to Stress Theories of Plasticity

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Abstract
The correlation of experimental data and the proper description of the state and history of deformation of work‐hardening materials has received much attention. An often desired objective is the plotting of a variable involving stress alone, a so‐called effective stress, against a variable depending on the instantaneous strain or the history of strain, effective strain. Quantities such as maximum or octahedral shearing stress and strain or better an integrated effective strain increment have been employed. Also, simple effective stress definitions have been given for anisotropic as well as isotropic metals by Dorn, by Jackson, Smith, Lankford, and by previous investigators. It is shown that the stress‐strain relations of a recent theory of plasticity provide a very convenient means of defining and studying effective stress and effective strain. The strong theoretical and practical limitations of such concepts are indicated and the calculation of specific plastic work is discussed for both isotropic and anisotropic metals. One of the major objectives of the paper is to stimulate critical experimental examination of as yet unproved assumptions in the theory of plasticity and in the correlation of experimental data.

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