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Multiaxial low cycle fatigue tests under non‐proportional stress (NPSS) controlled mode were performed on commercial pure titanium (CP‐Ti). Strain responses of axial and torsional channels under highly applied stress amplitudes show an initial hardening phenomenon. Non‐proportional hardening coefficient of CP‐Ti is independent of the controlled mode. The critical plane of CP‐Ti under NPSS controlled mode is aligned with the maximum principal stress plane proved by optical microscopy observation. Optimized FSM model and KBM‐PM model with mean axial and torsional strain are established. These models are further integrated into equations related to multiaxial stress ratio with high accuracy of life prediction for CP‐Ti under NPSS controlled mode. Highlights: Non‐proportional hardening coefficient of CP‐Ti is independent of the controlled mode.The critical plane of CP‐Ti is aligned with the maximum principal stress plane.Energy and optimized critical plane model with mean strain are established. [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]