The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

基于Miner法则的线性疲劳寿命预测模型已被广泛应用于恒定振幅单轴和多轴载荷下的疲劳寿命预测。考虑到裂纹形成和扩展的物理意义，提出了基于Miner法则和临界面法的等幅载荷下多轴等效线性疲劳寿命预测模型。这种方法的本质是，由临界面上的剪切应变和法向应变组成的等效应变替代了单轴非线性疲劳损伤模型的相关参数。应力/应变的主轴在非比例载荷下旋转。同时，材料和滑移系统的微观结构发生变化，从而导致额外的硬化效果。用循环屈服应力与静态屈服应力之比表示材料的循环硬化能力，并考虑了相差和加载条件对非比例硬化效应的影响。使用等效染色方法，最大剪切染色幅度模型，CXH模型和等效和/或非比例载荷下的等效多轴衬砌模型来预测多轴疲劳寿命。在多轴疲劳实验中使用了四种材料（Q235B钢，钛合金TC4，Haynes 188和Mod.9Cr-1Mo钢）的光滑且有缺口的疲劳试样来验证所提出的模型。将这些材料的预测结果与测试结果进行了比较，结果表明，这四个模型在按比例加载的情况下都能取得良好的效果，但是所提出的模型在非比例负荷下的性能优于其他三个模型。同时，还验证了所提出的增强因子可以反映相差和材料特性对附加硬化的影响。