The present paper describes a probabilistic framework to predict the fatigue life and failure mode under various thermo-mechanical loading conditions. Specifically, inclusion- and matrix-driven competing failure modes are examined within nickel-based superalloys. The critical accumulated plastic strain energy density (APSED) is employed as a unified metric to predict fatigue crack initiation in metals, which is favorable due to the usage of a single unknown parameter and its capability to predict failure across loading conditions and failure modes. In this research, we characterize the temperature-dependent variation of the critical APSED using a Bayesian inference framework and predict the competing failure modes in a coarse grain variant of RR1000 with varying strain range and temperature. The critical APSED appears to decrease along a vertically reflected sigmoidal curve with increasing temperature. Further, (a) the prediction of a failure mode, (b) failure mode associated with the minimum life, and (c) the change in the location associated with the matrix-driven failure mode with increasing temperature and decreasing strain range are consistent with the experimentally observed trends in RR1000, as well as other Nickel-based superalloys, documented in the literature. Finally, for each simulated loading condition, the uncertainty in the fatigue life is quantified as a prediction interval computed based on a \(95\%\) confidence level of the critical APSED and the computed APSED from simulations. The overall framework provides a promising step towards microstructural-based fatigue life determination of components and enables a location-specific lifing approach.

本文描述了一种概率框架，可预测各种热机械载荷条件下的疲劳寿命和失效模式。具体而言，在镍基高温合金中检查了夹杂物和基体驱动的竞争失效模式。临界累积塑性应变能密度（APSED）被用作预测金属中疲劳裂纹萌生的统一指标，这是有利的，这是由于使用了单个未知参数及其在整个载荷条件和失效模式下预测失效的能力。在这项研究中，我们使用贝叶斯推断框架表征了关键APSED的温度依赖性变化，并预测了应变范围和温度变化的RR1000粗晶粒变体中的竞争失效模式。随着温度的升高，临界APSED似乎沿着垂直反射的S形曲线减小。此外，（a）失效模式的预测，（b）与最小寿命相关的失效模式，以及（c）与矩阵驱动的失效模式相关的位置随温度升高和应变范围减小的变化与在实验中观察到的RR1000以及其他镍基高温合金的趋势已在文献中记录。最后，对于每个模拟载荷条件，疲劳寿命的不确定性被量化为基于 （c）随着温度升高和应变范围减小，与矩阵驱动的失效模式相关的位置变化与文献中所记录的RR1000以及其他镍基高温合金的实验趋势一致。最后，对于每个模拟载荷条件，疲劳寿命的不确定性被量化为基于 （c）随着温度升高和应变范围减小，与矩阵驱动的失效模式相关的位置变化与文献中所记录的RR1000以及其他镍基高温合金的实验趋势一致。最后，对于每个模拟载荷条件，疲劳寿命的不确定性被量化为基于临界APSED的置信度为（95 \％\），并且通过模拟计算得出的APSED。总体框架为确定基于微结构的组件的疲劳寿命提供了一个有希望的步骤，并实现了针对特定地点的生活方式。