A simple approach to the description of multiaxial cyclic stress-strain relationship

The multiaxial cyclic stress-strain relationship under both proportional and nonproportional loading was studied according to the characteristic of the stress-strain on the critical plane and the research results of multiaxial critical plane principle. The multiaxial cyclic stress-strain model under proportional loading is first derived based on the uniaxial cyclic stress-strain relationship. The normal strain excursion between adjacent turning points of the maximum strain and the maximum shear strain amplitude on the critical plane are then combined as an equivalent strain amplitude by von Mises criterion to replace the equivalent strain amplitude of the proportional loading, which takes account of the effect of additional hardening due to nonproportional loading. As this result shows, a simple multiaxial cyclic stress-strain relationship is obtained for nonproportional loading. The experiments under the tension-torsion proportional and nonproportional cyclic loading were conducted to verify the multiaxial cyclic stress-strain model proposed in this paper. The prediction has a good correction with the experimental results.