Prediction of the endurance limit in the high and very high cycle loading range (102−1010) is an important problem in aircraft engine construction and high-speed rail transport. It involves the development of models and their experimental verification taking into account damage evolution stages and fatigue crack growth in a damaged medium. A damage evolution model that takes into account the kinetics of defects and microplasticity effects was proposed. The model was used to study the process of fatigue failure of an AlMg2.5 structural alloy. The model parameters were identified and verified using experimental data on static, dynamic, and fatigue loading, as well as tests at various temperatures. The numerical results were used to construct the Wohler curve, which was found to agree well with experimental data in the range of high cycle fatigue. The duality effect of the S-N curve was described. A computational experiment was performed to study the effect of dynamic loading on the fatigue strength. It was found that the fatigue limit depends weakly on the preliminary dynamic strain, which was confirmed by experimental data. Various mathematical packages and numerical methods for solving the constructed system of differential equations were compared. The Adams method and its modifications were shown to be optimal for the numerical integration of the problem under consideration. Wolfram Mathematica was found to be a preferred software package for numerical solution. The convergence of the numerical solution was investigated.

中文翻译：

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AlMg2.5合金高周疲劳和甚高周疲劳失效过程的数学建模

预测高循环和极高循环载荷范围（102-1010）的耐久极限是飞机发动机制造和高速铁路运输中的一个重要问题。它涉及模型的开发及其实验验证，同时考虑到损坏介质中的损伤演化阶段和疲劳裂纹扩展。提出了一种考虑缺陷动力学和微塑性效应的损伤演化模型。该模型用于研究一种AlMg2.5结构合金的疲劳失效过程。使用静态、动态和疲劳载荷的实验数据以及不同温度下的测试，确定和验证模型参数。数值结果用于构建 Wohler 曲线，发现该曲线与高周疲劳范围内的实验数据非常吻合。描述了 SN 曲线的对偶效应。进行了计算实验以研究动态载荷对疲劳强度的影响。发现疲劳极限弱依赖于初步动态应变，这已被实验数据证实。比较了求解所构造的微分方程组的各种数学包和数值方法。Adams 方法及其修改被证明对于所考虑问题的数值积分是最佳的。Wolfram Mathematica 被发现是用于数值求解的首选软件包。研究了数值解的收敛性。发现疲劳极限弱依赖于初步动态应变，这已被实验数据证实。比较了求解所构造的微分方程组的各种数学包和数值方法。Adams 方法及其修改被证明对于所考虑问题的数值积分是最佳的。Wolfram Mathematica 被发现是用于数值求解的首选软件包。研究了数值解的收敛性。发现疲劳极限弱依赖于初步动态应变，这已被实验数据证实。比较了求解所构造的微分方程组的各种数学包和数值方法。Adams 方法及其修改被证明对于所考虑问题的数值积分是最佳的。Wolfram Mathematica 被发现是用于数值求解的首选软件包。研究了数值解的收敛性。Adams 方法及其修改被证明对于所考虑问题的数值积分是最佳的。Wolfram Mathematica 被发现是用于数值求解的首选软件包。研究了数值解的收敛性。Adams 方法及其修改被证明对于所考虑问题的数值积分是最佳的。Wolfram Mathematica 被发现是用于数值求解的首选软件包。研究了数值解的收敛性。