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Macha, E. (1989) Generalization of Fatigue Fracture Criteria for Multiaxial Sinusoidal Loadings in the Range of Random Loadings. In: Brown, M.W. and Miller, K.J., Eds., Biaxial and Multiaxial Fatigue, EGF 3, Mechanical Engineering Publications, London, 425-436.
https://www.gruppofrattura.it/ocs/index.php/ICMFF/ICBMFF2/paper/viewFile/11748/11218

has been cited by the following article:

• TITLE: Effect of Stress Gradient on Fatigue Life Estimation (Statistical Approach Criteria: Variance Method)

  AUTHORS: Mbaiyelkom Esdras, Abakar Malgnan, Ngargueudedjim Kimtangar, Kenmeugne Bienvenu

  KEYWORDS: Biaxial Fatigue, Fracture Plane Direction, Critical Plane, Stress Gradient and Equivalent Stress Variance, Fatigue Life

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.16 No.9, September 10, 2026

  ABSTRACT: This article begins with the general formulation of the fatigue criterion based on a statistical approach, followed by the consideration of the stress gradient, which has been recognized as a beneficial effect on the material’s fatigue performance. The use of these models to predict the lifespan of a component subjected to random multiaxial loading is also discussed. The experimental data from biaxial fatigue tests allowed us to evaluate the effectiveness of each model. In summary, analyzes were conducted to better represent the influence of the stress gradient. For mechanical design, we recommend using the model that takes into account the stress gradient.