13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Finite element modeling of the coupling between thermal dissipation and fish-eye crack growth in very high cycle fatigue regime Laurent Gallimard*, Hoang Quan Nguyen, Claude Bathias Laboratoire Energétique, Mécanique, Electromagnétisme, Université Paris Ouest Nanterre-La Défense, 50 rue de Sèvres - 92410 Ville d'Avray – France. * Corresponding author: laurent.gallimard@u-paris10.fr Abstract The aim of the paper is to model the thermal dissipation associated to a fish-eye crack growth during an ultrasonic fatigue testing. We use a Paris-Hertzberg crack growth model to simulate the evolution of the crack and a perfectly elastic-plastic constitutive law to model the plastic dissipation per cycle. A finite element analysis is used to compute the evolution of the temperature field during the crack propagation. Numerical results are presented and they agree well with experimental results. Keywords: very high fatigue cycle, ultrasonic testing, finite element modeling, crack growth, thermal dissipation 1. Introduction The considerable attention given, in the past ten years, to fatigue fracture of metallic material in very high cycle regime, is mainly due to the increasing use of engineering materials in applications with service lives reaching up to 1010 load cycles. It has been shown that very high cycles fatigue (VHCF) failures of steels are characterized by a fracture which does not occurs on the surface but rather internally in the material, especially in high strength steels [1-3], and leads to the so-called fish-eye. Ultrasonic fatigue testing is a powerful tool for evaluating VHCF properties as 109 cycles can be completed in a day [4]. During an ultrasonic fatigue testing, the crack propagation in the tested specimen leads to an important cyclic plastic dissipation. One way of assessing this dissipated energy, and thus the crack propagation, is to use an infrared camera to measure the temperature increase during the test since part of this dissipation will occur as heat [5]. As far we know few studies have been devoted to the numerical computation of the temperature field associated with the propagation of a fatigue crack during VHCF failure [6,7]. In this presentation, we study numerically the temperature field associated with the propagation of a fatigue crack in a very high cycle fatigue regime during ultrasonic fatigue testing. The crack propagation is modeled by a classical Paris-Hertzberg crack growth law, and the plastic dissipation per cycle is determined by 3D-elastic plastic finite element modeling of stationary mode I crack under constant amplitude loading. A fraction of this plastic dissipation is converted heat and used as a mobile thermal source to compute the temperature field evolution. The first part of the presentation is devoted to the Finite Element modeling of the problem to be solved: The fatigue crack law is described, as well as the thermal dissipation model and the computation of the computation of the plastic energy dissipation. The second part of the presentation is devoted to the numerical results: The proposed model is compared with experimental results and the distribution of the plastic dissipation around the crack is computed.
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