Inversion of Ramberg-Osgood equation and description of hysteresis loops

The Ramberg-Osgood equation has been approximately inverted. Four orders of approximations providing progressively more accurate inversions are considered. The second order inversion is used to develop closed-form relations for stress in terms of strain and for cyclic stress in terms of cyclic strain. Explicit relations between the cyclic-strength coefficient and the cyclic strain-hardening exponent and between the cyclic strain-hardening exponent and the elastic modulus are developed. Application to nine different engineering metals shows that the proposed approximate inversion provides a powerful tool for describing stress-strain relations. Examples of hysteresis loops for a number of strain time-histories are presented. Also, it is shown that augmenting the strain time-history with fictitious strain segments to close all the hysteresis loops yields the same stress-strain relation as that obtained through the rain-flow counting method. (C) 2002 Elsevier Science Ltd. All rights reserved.