Summary
The mathematical expressions for the stress strain relations of metals in uniaxial loading, which have been proposed by Ludwik and Hollomon and find a more general application now, are discussed. It is elucidated that these empirical formulae cannot agree with the essential behaviour of a metal during uniform straining.
The existence of one and the same stress-strain relation for uniform uniaxial tension and compression, the fundamental stress-strain relation, is emphasized. It is shown that a mathematical expression of this relation can be derived along purely theoretical lines, which essentially agrees with the experimentally determined stress-strain relation.
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References
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Palm, J.H. Stress-strain relations for uniaxial loading. Appl. Sci. Res. 1, 198–214 (1949). https://doi.org/10.1007/BF02120327
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DOI: https://doi.org/10.1007/BF02120327