Computation of Tensile Strain-Hardening Exponents through the Power-Law Relationship

Abstract

Abstract Many metals flow in the region of uniform plastic deformation following a power-law relationship, which states that true stress is proportional to true-plastic strain raised to the power n. The exponent n, known as the tensile strain-hardening exponent, can be determined from a tension test through appropriate transformations of stress-strain data and least-squares fitting of a straight line. Procedures for the computation of n have been standardized by ASTM International and ISO. Current ASTM and ISO standards differ, most notably, in the type of strain used in calculations. The ASTM procedure permits the use of true strain (true-elastic strain plus true-plastic strain), when true-elastic strain represents less than 10 % of total strain. On the other hand, the ISO version stipulates the subtraction of true-elastic strain from true strain, using a formula whose derivation is not publicly available. In this work, we revisit the expressions that enable the transformation of engineering stress-strain data to true-stress and true-plastic-strain values. Using eight tension-test curves from several materials, obtained through ASCII files publicly available at the website of the National Physical Laboratory of the United Kingdom, we compare n-values obtained via three definitions of strain: (i) true strain, (ii) conventional definition of true-plastic strain, and (iii) true-plastic strain according to the ISO formula. In addition, we investigate the dependency of the results on the strain range over which n-values are calculated. To evaluate strain-range dependency, which arises when metals do not closely follow the power-law relationship, we analyze the effect of strain intervals of increasing length and study the variation of n-values when the range of interest is divided into subintervals. To improve the approximation given by the power-law relationship over the region under analysis, we propose an alternative formulation in which the strength coefficient and the strain-hardening exponent are functions of true-plastic strain.