Full-Range Moment–Curvature Relationships for Beams Made of Low-Hardening Aluminium Alloys

Aluminium alloys are characterised by a rounded stress-strain relationship, with no sharply defined yield point. For example, aluminium alloy grades 6061-T6, 6082-T6, and 7075-T6 exhibit low-hardening response, which is close to linear elastic-linear plastic hardening characteristics. Commonly, the behaviour of aluminium alloys is described by Ramberg-Osgood (RO) one-dimensional constitutive relationship in the format of strain in terms of stress. In the case of low-hardening response, an alternative Richard-Abbott (RA) relationship of stress as a function of strain can be used. Both relations are analytically irreversible, but the RA is more appropriate for use in slender beams theory. In the present study, we use the latter function to derive moment as an explicit function of curvature for the sectional relation of beams. Since the obtained relation is expressed via special functions, we also propose its close approximation, which is more useful for practical purposes. It is uncomplicated and reasonably accurate compared to available models. The predictive capabilities of the new moment-curvature models developed in this article are verified with experimental results available in the literature for beams tested under four-point and three-point bending. In the case of four-point beams, predictions show very good agreement with experiments, while for three-point bending of beams, higher discrepancies are observed.