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• The maximum principal strain critical plane is more effective under both IP and OP loading. • FS model and KBM-P model can be applied to both IP and OP loading in a general form. • MLCF life prediction model based on newly defined α N f and α are established. Non-proportional multiaxial low-cycle fatigue (MLCF) tests were performed on CP-Ti at different multiaxial strain ratios. The optical microscopy observations and life prediction models verified that the critical plane of CP-Ti was the maximum principal strain plane and that it was effective under non-proportional loading. A non-proportional life coefficient and strain energy density coefficient are proposed. Typical MLCF life prediction models, such as the ESN, FS, KBM, and KBM-P models, are discussed under non-proportional loading. Finally, by associating the newly defined non-proportional life coefficient with the non-proportional hardening factor, two comprehensive non-proportional MLCF life prediction models are established, which have higher accuracies than those of previous models. [ABSTRACT FROM AUTHOR]

• For CP-Ti, the threshold value for ratcheting strain accumulation of the axial stress amplitude is closer to 287 MPa. • Rate Surface Ratio is proposed to represent the difference in velocity during ratcheting accumulation. • The brand-new KBM-PH model with mean stress correction is the best overall among all models. Asymmetrical multiaxial fatigue tests were performed. A new quantification parameter is proposed to represent the difference in velocity during ratcheting accumulation. Although the stress–strain response under asymmetric loading is similar to that under symmetric loading, substantial deteriorations of life are observed. The threshold value for ratcheting strain accumulation of axial stress amplitude is closer to 287 MPa. The brand-new stress parameters-based KBM-PH model with mean stress correction is the best overall among a series of models based on strain and stress parameters with or without mean strain and stress corrections with the best accuracy and ease of use. [ABSTRACT FROM AUTHOR]