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The problem of high and very high fatigue at various program loading processes arises in power equipment components, product pipelines, blades, and disks of turbopump units of aircraft and rocket engines and other systems, so the elaboration of a mathematical apparatus and algorithms for the durability are relevant. Analysis of experimental data and physical mechanisms of fatigue leads to the need to consider the fracture as a multi-scale random process of brittle and viscous failures. For the brittle failure probability at symmetric block loading with of a finite number of different amplitudes and cycles, the system of recurrent constitutive relations at each level using the Hilbert–Schmidt integral operator is presented. An algorithm for the material functions on the basis of standard fatigue tests at axial loading and taking into account the results of physical studies of brittle cracks are given. The results of calculations for 0.25% carbon steel at loads of two or three blocks with different amplitudes and cycle numbers, for 45 steel with different stress amplitude distributions and titanium alloy TC21 at loads, each block of which consists of two amplitudes of different cycle numbers, are discussed. For all materials, the model well describes the fatigue curve of macrofailure at symmetrical loading. The scope of presented model for program loadings is determined. The model describes the fatigue curve of macrofailure in the range of numbers \(N_{f} \ge 10^{6}\) cycles and program loadings, in which the maximum stress values do not exceed the endurance more than 30%.

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On the Regularities of the Material Brittle Failure at Different Scale-Structural Levels Under Variable Amplitudes of Uniaxial Loading

  • 章节

  • 发表日期：

    2025年

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  • Eleonora B. Zavoychinskaya,
  • Georgii E. Lavrikov

摘要

The problem of high and very high fatigue at various program loading processes arises in power equipment components, product pipelines, blades, and disks of turbopump units of aircraft and rocket engines and other systems, so the elaboration of a mathematical apparatus and algorithms for the durability are relevant. Analysis of experimental data and physical mechanisms of fatigue leads to the need to consider the fracture as a multi-scale random process of brittle and viscous failures. For the brittle failure probability at symmetric block loading with of a finite number of different amplitudes and cycles, the system of recurrent constitutive relations at each level using the Hilbert–Schmidt integral operator is presented. An algorithm for the material functions on the basis of standard fatigue tests at axial loading and taking into account the results of physical studies of brittle cracks are given. The results of calculations for 0.25% carbon steel at loads of two or three blocks with different amplitudes and cycle numbers, for 45 steel with different stress amplitude distributions and titanium alloy TC21 at loads, each block of which consists of two amplitudes of different cycle numbers, are discussed. For all materials, the model well describes the fatigue curve of macrofailure at symmetrical loading. The scope of presented model for program loadings is determined. The model describes the fatigue curve of macrofailure in the range of numbers \(N_{f} \ge 10^{6}\) cycles and program loadings, in which the maximum stress values do not exceed the endurance more than 30%.