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Fatigue failure, ratcheting behaviour and influence of pre‐fatigue on fatigue behaviour were investigated under uniaxial cyclic loading for CK45 steel at room temperature. The fatigue life was recorded for various stress ratios, and then, three mean stress models were considered. The Walker model showed an acceptable accuracy in comparison with Smith–Watson–Topper and Park et al. models. The ratcheting strains were measured for various loading conditions in order to evaluate the impact of mean stress, stress amplitude and stress ratio on ratcheting behaviour. The experimental results showed that the ratcheting strain increased with increasing mean stress, stress amplitude and stress ratio. In addition, the results of the post‐ratcheting‐fatigue tests showed that although the fatigue life decreased with increasing pre‐ratcheting strain (the ratcheting strain that is accumulated in pre‐fatigue), the loading condition that pre‐fatigue experiments were conducted has a significant effect on subsequent fatigue behaviour.

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This study develops a new phenomenological constitutive model to capture the unique evolving cyclic elastoplastic behaviours of hexagonal close-packed (HCP) sheet metals. This new constitutive model is developed by adopting the concepts of multiple-yield surface approaches. Four phenomenological deformation modes, including Monotonic Compression (MC), Monotonic Tension (MT), Reverse Compression (RC), and Reverse Tension (RT), are considered to represent the hardening evolution of the materials, including the twining/untwining behaviours. Reference flow stress equations are introduced, and a Cazacu-Barlat 2004 (CB2004) type yield surface is employed to each deformation mode. In addition, the RT hardening parameters are defined as functions of plastic pre-strains to mitigate the interpolation error caused by parameter determination processes of existing models. For validation, the calculated stress–strain curves of AZ31B magnesium alloy are compared with experimental curves available from literature. Moreover, to show the accuracy of the proposed analytical model, the reproduced stress–strain curves are compared with those of an existing model—the modified homogeneous anisotropic hardening (HAH) model. The obtained results show that the new constitutive model can successfully reproduce experimental Tension–Compression-Tension (TCT) and Compression-Tension–Compression (CTC) stress–strain curves of HCP sheet metals with considerably less percentage errors.

Stainless steels (SUS) and dual-phase (DP) steels have tension-compression asymmetry (TCA) in mechanical responses to full loading cycles. This phenomenon can significantly influence sheet metal forming of such metals, however, it is difficult to describe this behaviour analytically. In this research, a novel analytical method for asymmetric elastic-plastic pure bending using the Cazacu–Barlat 2004 asymmetric yield function is proposed. It only uses material parameters in tension along with an asymmetry coefficient related to the yield function. Bending operations of SUS304 and DP980 are investigated as two case studies. In the pure bending for both SUS304 and DP980, moment–curvature diagrams are analytically obtained. Furthermore, linear and nonlinear springback behaviours of SUS304 are analytically investigated. Moreover, using the analytical model as a user-defined material, a numerical model is developed for both steels under pure bending. In the V-bending case of SUS304 with and without TCA effects, the springback behaviours of the material are investigated numerically. In addition, considering friction effects, the analytical method is further modified for predicting springback behaviours in the V-bending of 16 types of SUS304 with various strengths are determined. All the analytical and numerical results have good agreement with those experimental results from literature for validation.