PSI - Issue 57

SEVEDE Théo et al. / Procedia Structural Integrity 57 (2024) 335–342 SEVEDE Théo/ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Fatigue is a crucial component in the dimensioning of materials and structures, yet it is still the recurrent cause in in service failure. Internal defects can be the onset of crack initiation and propagation and lead to the fracture of the structure [7] under uniaxial or multiaxial loadings [6]. Since the phenomenon was first identified in the late 19th century, numerous studies have been carried out to better characterize it and determine the fatigue properties of materials. However, this phenomenon dependents on numerous parameters, making dimensioning methods ever more precise. The fatigue properties of a metallic materialdepend on its microstructure, the loading to which it is subjected, its obtaining process and the effects of the environment in which it is used. The large number of these parameters leads to a probabilistic nature of the phenomenon leads to wide variations in the number of cycles to failure. There are three fatigue domains, corresponding to different service lives: Low Cycle Fatigue (LCF), is concerned with lifetimes of the order of 10 4 to 10 5 cycles. These are generally loadings whose maximum value is close to or even greater than the material's yield stress, High Cycle Fatigue (HCF) whose range extends from 10 5 to 10 7 cycles, with loads below the material's macroscopic yield strength and Very High Cycle Fatigue (VHCF) or Gigacyclic fatigue, extending up to 10 10 /10 11 cycles. Current fatigue design criteria on metallic alloys assume an asymptotic form of the fatigue curve. That means a material can withstand infinite number of cycles while the loading amplitude remains lower than its intrinsic fatigue limit, generally defined at 10 7 cycles. However, some mechanicalsystems show failures when they are subjected to much higher number of cycles than 10 7 , mainly due to low-amplitude vibrations. For example, certain parts of turbojet engines or ship propulsion lines can undergo between 10 8 and 10 10 cycles during service. Furthermore, in practice, it has been observed that fatigue fractures still occur beyond 10 7 cycles, or at stresses amplitudes below the fatigue limit [1]. In such cases, the adoption of conventional fatigue design criteria presents a risk for the system safety and its integrity. The evaluation of the resistance of the materials in VHCF fatigue domain is therefore essential for the dimensioning of these parts [8]. Over the last century, fatigue studies have mainly focused on LCF and HCF domains, i.e. up to 10 7 cycles, due to cost and time constraints. These constraints are mainly attributed to the limitations of conventionaltest systems, since for a machine loading at a frequency of 10Hz, reaching 10 9 cycles would take more than 3 years. As a result, many machines have been developed to achieve higher load frequencies. The characterization of VHCF domain was facilitated by the development of 20kHz piezoelectric actuators in the early 1950s. This type of machine has become the standard for all VHCF fatigue testing facilities, enabling 10 9 cycles to be completed in just 14 hours. When a sample is subjected to cyclic loading, a self-heating phenomenon is observed, characterized by a rise in its temperature. This phenomenon has its origins in the dissipative mechanisms that develop within the material at microscopic scale. Research studies have succeeded in developing a method for deriving materialfatigue assessment from its thermal signature. This method reduces the time and cost required to characterize the fatigue limit of materials and has been validated on numerous materials for HCF fatigue. A two scales probabilistic model to describe the self heating phenomenon on one hand, and on the other hand establish a n approach to predict the fatigue curves for a given fracture probability has been proposed in [3] and [9]. Generally, for isotropic materials, homogenous approach is assumed. The temperature is measured using thermocouple fixed in the central part of the sample subjected to a constant stress amplitude [2]. This is so called 0D approach. However, in the VHCF domain, a few studies have sought to interpret this thermal signature. In this case and given the boundary conditions of ultrasonic testing machine, the stress amplitude takes a hyperbolic cosine shape alongthe specimen length. Assuming a one-dimension (1D) form of the stress amplitude for an axisymmetric sample geometry, this requires to adopt a 1D approach analysis for the thermal source distribution. The aim of this article is therefore to propose a method of analysis for determining the thermal source field from temperature elevation measurements under tension-compression loadings at 20kHz. This study represents a first step toward the fatigue study using the self-heating method. Future work will concentrate on implementing the multiscale probabilistic model to predict the fatigue curves of the material.