Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue Development of a new simple energy method for life prediction in multiaxial fatigue C. Braccesi, G. Morettini ⁎ , F. Cianetti, M. Palmieri University of Perugia, Department of Industrial Engineering, Via. G. Duranti 1/A-4, 06125 Perugia, Italy ARTICLE INFO Keywords: Multiaxial fatigue method Fatigue life prediction Energy multiaxial method Damage criteria Energy density criteria ABSTRACT In this paper, a new, simple Damage Energy Criterium for life prediction in multiaxial fatigue, developed in the frequency domain, is described and verified. The first aim of this paper is to demonstrate that through a correct use of the energetic approach, developed in the frequency domain, it is possible to achieve an accurate result. The proposed theoretical procedure finds its conceptual foundation in the fact that the energy criterion cannot be directly applied to usual stress state in the time domain; however, with a simple passage it is possible to ac- curately reduce a multiaxial stress state to an equivalent uniaxial one. For this reason, this work will be char- acterized by analytical content and by substantial mathematical demonstrations. At the end, in order to verify the method and consolidate the general procedure, some experimental tests are used to corroborate the validity of this criterion. This proposal shows drastically simpler technique than any other proposed in current literature. 1. Introduction Multiaxial fatigue is a topic of great interest for industry and aca- demic world. Therefore, the fatigue design of structural components is actually subject to considerable attention. In the scientific community, there is no universally accepted criteria regarding the methodology for the study of such a problem, although it is worth mentioning that in recent years, several methods have been presented in the literature. It is possible to classify these methods into different categories depending on the parameters and the approach with which the phenomenon is analysed. The first significant distinction stems from dividing the cri- teria into two categories: Safe/Unsafe Criteria and Damage Criteria. The first category determines whether the component, subjected to a multiaxial stress state, is resistant or not. To better analyse these criteria, it is useful to refer to their graphic interpretation. Indeed, each of these [1–3] defines one or more failure straight lines that split the plain, on which the loading path can be drawn, in a safety and unsafety domain [4]. A loading path that remains into bounding failure lines is expected to have infinite life while any path that extends outside the damage line will have fatigue failures. With this type of approach, only a safety factor for fatigue limit can be evaluated. Morel [5] was the first who tried to apply this approach to the damage evaluation concept. With his work, he tried to formulate a method to evaluate the damage. Through the second category, (Damage Criteria), it is possible to evaluate the damage caused by load time history as well as the damage contribution of a part of the stress signal. To this day, most multiaxial fatigue criteria fall under this category. Within the Damage Criteria it is possible to make a further distinction based on the approach with which the damage is calculated: the Geometric Approach and the Energetic Approach. The Geometric approach is also known as “Critical Plane” approach, which has been evolving since Findley [6] first proposed his critical plane-based criterion in 1959. This approach is based on the experi- mental observation that fatigue cracks initiate and grow on a certain material plane. Only stress and/or strain components acting on the critical plane are responsible for fatigue failure of the material. The chosen geometric reference system, and then of the critical plane, can happen either a priori or by iteration, using the maximization of some stress and/or strain parameters. According to Matake [7] the critical plane orientation equals the maximum shear stress amplitude, whereas according to Tao [8], it equals the maximum shear strain. For the other [9–14] this particular parameter could vary. The Critical Plane Damage criteria require calculation times which depend on the number of physical planes investigated during the fatigue limit estimation. It is clear that the fatigue limit is correlated to the micro-structure of the material [15] and thus to its geometry; however, the Energy Da- mage criteria are based on the assumption that it is possible to analyse the damage fatigue phenomenon using another parameter, the energy density, which is independent on the geometric reference system of choice. Energy density thus represents the only parameter necessary for the estimation of fatigue limit of metallic structural components subject to a multiaxial stress state. https://doi.org/10.1016/j.ijfatigue.2018.03.003 Received 27 November 2017; Received in revised form 2 March 2018; Accepted 3 March 2018 ⁎ Corresponding author. E-mail addresses: claudio.braccesi@unipg.it (C. Braccesi), morettinigiulia@gmail.com (G. Morettini). International Journal of Fatigue 112 (2018) 1–8 Available online 07 March 2018 0142-1123/ © 2018 Published by Elsevier Ltd. T