In this study, based on the nominal stress method and the influence of stress gradient on fatigue life, a fatigue life prediction method combined with the Weibull distribution is proposed. Firstly, the strain energy density is defined as the damage parameter to determine the location of the critical plane. Then, the equivalent stress function is established by extracting the equivalent stress of the specific path on the critical plane, which is used to establish the modified nominal stress method by combining with the stress gradient factor. Secondly, the Weibull distribution is combined to establish a new fatigue life prediction model of the notched specimens under different failure probabilities. The accuracy of the model is verified with three materials, then the prediction life of the proposed model is compared with that of the SWT model, the FS model and the Manson-Coffin equation. The results show that the accuracy of the proposed model is higher than the other three models. Finally, the reliability of the proposed model is evaluated by the lower confidence limit (LCL) estimation and interval estimation to explore the feasibility of this method. In addition, the P-S-N curves under different failure probabilities are established to guide actual projects.

本研究基于名义应力法和应力梯度对疲劳寿命的影响，提出了一种结合威布尔分布的疲劳寿命预测方法。首先，将应变能密度定义为损伤参数，以确定临界面的位置。然后，通过提取关键平面上特定路径的等效应力建立等效应力函数，用于结合应力梯度因子建立修正的名义应力法。其次，结合 Weibull 分布，建立了缺口试件在不同失效概率下的疲劳寿命预测新模型。用三种材料验证模型的准确性，然后将所提出模型的预测寿命与SWT模型的预测寿命进行比较，FS 模型和 Manson-Coffin 方程。结果表明，所提模型的准确率高于其他三种模型。最后，通过置信下限（LCL）估计和区间估计对所提模型的可靠性进行评估，以探讨该方法的可行性。除此之外建立不同失效概率下的P- SN曲线，指导实际工程。