Rolling bearing elements develop structural changes during rolling contact fatigue (RCF) along with the non-proportional stress histories, evolved residual stresses and extensive work hardening. Considerable work has been reported in the past few decades to model bearing material hardening response under RCF; however, they are mainly based on torsion testing or uniaxial compression testing data. An effort has been made here to model the RCF loading on a standard AISI 52100 bearing steel with the help of a 3D Finite Element Model (FEM) which employs a semi-empirical approach to mimic the material hardening response evolved during cyclic loadings. Standard bearing balls were tested in a rotary tribometer where pure rolling cycles were simulated in a 4-ball configuration. The localised material properties were derived from post-experimental subsurface analysis with the help of nanoindentation in conjunction with the expanding cavity model. These constitutive properties were used as input cyclic hardening parameters for FEM. Simulation results have revealed that the simplistic power-law hardening model based on monotonic compression test underpredicts the residual generation, whereas the semi-empirical approach employed in current study corroborated well with the experimental findings from current research work as well as literature cited. The presence of high compressive residual stresses, evolved over millions of RCF cycles, showed a significant reduction of maximum Mises stress, predicting significant improvement in fatigue life. Moreover, the predicted evolved flow stresses are comparable with the progression of subsurface structural changes and be extended to develop numerical models for microstructural alterations.

Graphic Abstract

中文翻译：

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用于演化材料响应和残余应力估算的滚动接触疲劳的3D有限元模型

滚动轴承元件在滚动接触疲劳（RCF）期间会产生结构变化，并伴随着非比例应力历史，产生的残余应力和广泛的工作硬化。在过去的几十年中，已经报道了许多工作来模拟RCF下轴承材料的硬化反应。但是，它们主要基于扭转测试或单轴压缩测试数据。此处已努力借助3D有限元模型（FEM）对标准AISI 52100轴承钢上的RCF载荷进行建模，该模型采用半经验方法来模拟循环载荷过程中产生的材料硬化响应。标准轴承球在旋转摩擦计中进行了测试，其中纯滚动循环以4球配置进行了模拟。局部材料的特性是在纳米压痕的帮助下，结合膨胀腔模型，从实验后的地下分析中得出的。这些本构特性用作FEM的输入循环硬化参数。仿真结果表明，基于单调压缩测试的简单幂律强化模型无法预测残差的产生，而本研究中采用的半经验方法与当前研究工作和所引用文献的实验结果相吻合。在数百万个RCF循环中演变而来的高压缩残余应力的存在表明最大Mises应力显着降低，预示着疲劳寿命的显着改善。此外，

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