The transformation ratchetting of super-elastic NiTi shape memory alloy was observed by the uniaxial stress-controlled cyclic tests [Kang, G.Z., Kan, Q.H., Qian, L.M., Liu, Y.J, 2009a. Ratchetting deformation of super-elastic and shape memory NiTi Alloys. Mech. Mater. 41, 139-153]. It is concluded that the NiTi alloy presents apparent ratchetting behaviour, and the ratchetting is collectively caused by the cyclic accumulation of residual inducedmartensite and the transformation-induced plastic deformation (i.e., namely transformation ratchetting). Based on the experimental results, a cyclic constitutive model was constructed in the framework of generalized plasticity [Lubliner, J., Auricchio, F., 1996. Generalized plasticity and shape memory alloys. Int. J. Solids Struct. 33, 991-1003] to describe the transformation ratchetting of super-elastic NiTi alloy. The proposed model simultaneously accounts for the evolutions of residual induced-martensite and transformation-induced plastic strain during the stress-controlled cyclic loading by introducing an internal variable zc, i.e., cumulated induced-martensite volume fraction. The dependence of transformation ratchetting on the applied stress levels and the phase transformation hardening behaviour of the NiTi alloy are also considered in the developed model. The anisotropic phase transformation behaviours of the alloy presented in the tension and compression cases are described by employing a Drucker-Prager-typed transformation surface. It is shown that the simulated results of transformation ratchetting obtained by the proposed model are in good agreement with the corresponding experiments, since the typical features of transformation ratchetting are reasonably captured by the proposed model.

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steelwere observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258-268]. Based on the obtained experimental results, the evolution features ofwhole-life ratcheting behavior and low-cycle fatigue (LCF) damage of thematerial were discussed first. Then, in the frameworkof unifiedvisco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive modelwas proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zeromean stress. In the proposedmodel, the damagewas divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since themaximumapplied stresses inmost of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225-240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulatedwhole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.

The ratchetting deformation of super-elastic NiTi alloy was first observed by uniaxial stress-controlled cyclic tests, and the dependence of ratchetting upon the applied stress and loading type was discussed. The evolutions of responded peak/valley strain, nominal elastic modulus and transformation stress, as well as dissipation energy of the alloy during the stress-controlled cyclic loading were investigated. It is shown that the super-elastic NiTi alloy presents significant "transformation ratchetting" which is mainly caused by the cyclic accumulation of remained martensite due to the incomplete reverse transformation from the stress-induced martensite to original austenite, and the transformation ratchetting and its evolution depend greatly upon the applied stress ampl itude, mean stress and loading chart. For comparison, the ratchetting deformation of shape-memory NiTi alloy and its dependence upon the loading condition were also observed. It is seen that the ratchetting deformation of shape-memory NiTi alloy under the stress-controlled cyclic loading differs greatly from that of super-elastic NiTi alloy, since no reversible transformation from the austenite to the stress-induced martensite occurs in the shape-memory NiTi alloy during the stress-controlled cyclic loading at room temperature. It means that no transformation ratchetting occurs in the shape-memory NiTi alloy, and the ratchetting deformation of the alloy occurred during the asymmetrical stress-controlled cyclic loading is mainly caused by the cyclic accumulation of visco-plastic deformation of re-oriented martensite, which is similar to the ratchetting deformation of ordinary metals. For both the super-elastic and shape-memory NiTi alloys, a nearly stable stress-strain response with small dissipation energy occurs after certain cycles. Some significant conclusions are obtained, which are useful to establish a constitutive model describing the ratchetting deformation of the NiTi alloys.