Elsevier

International Journal of Fatigue

Volume 47, February 2013, Pages 31-43
International Journal of Fatigue

Fretting fatigue crack growth simulation based on a combined experimental and XFEM strategy

https://doi.org/10.1016/j.ijfatigue.2012.07.007Get rights and content

Abstract

A combined experimental and numerical study is presented in order to predict fretting crack propagation. It rests on 2D and 3D fretting tests, with carefully controlled loading conditions leading to cracking as the main material response, the extraction of 2D and 3D crack geometry from post-mortem cross-sections, a three-dimensional X-FEM model based on a three field weak formulation accounting for 3D non-planar frictional crack and the level set formalism authorising a direct use of actual reconstructed crack shape, the stress intensity factors quantification, a mixed mode Paris law identification and finally the crack growth simulation. The 2D fretting tests are numerically simulated. The mixed mode crack growth law identified is then used to simulate the fretting crack growth. A very good agreement with experimental results is obtained. Then 3D fretting tests are simulated and the crack fronts are compared with actual ones.

Highlights

Fretting fatigue is studied using a combined experimental and numerical methodology. ► Actual crack shapes are used as input data for the computation. ► An X-FEM frictional fatigue crack model is used to compute stress intensity factors. ► A Paris crack growth law is proposed. ► Crack growth is predicted in an excellent agreement with experimental results.

Introduction

Fretting has long been recognized as a source of wear and premature fatigue failure within mechanical parts. Fretting damage may occur whenever a junction between contacting parts is subjected to cyclic sliding micromotions, whose characteristic amplitudes are much less than the size of the contact. Numerous studies have shown that wear and cracking processes may coexist within the same contact [1], [2], that the main damage mechanism is dependent on the contact conditions and their evolution at the two-body interface versus time [3], [1], [2], [4], [5]. Cracks initiate at a very early stage and most of the component life is determined by the crack propagation that may lead up to failure. This illustrates the importance of predicting fretting crack initiation and propagation. An extensive literature is centered on this problematic. Numerous difficulties are encountered:

  • Experimentally, the inability to localize, identify and monitor the nucleation and growth of cracks within the contact interface and hence the great lack of information regarding the crack shape evolution versus the number of cycles is certainly a factor impeding the development of reliable fretting models. Different routes have emerged to get a better and deeper understanding of fretting crack initiation and propagation. For experiments dealing with opaque materials, crack shapes are usually reconstructed from observations performed on post-mortem metallographic cross-sections [6], [7]. In the last years, some attempts have been carried out to follow continuously the crack propagation using X-ray tomography. The latter is a very attractive technique which enables the visualisation of internal features in a sample. Being a non-destructive technique, it also enables, in principle, in situ visualisation of damage during loading and provides therefore the chronology of damage initiation and growth [8], [9]. Fretting crack characterisation is not feasible under load. Buffière et al. [10] have in that context, first conducted fretting tests in order to initiate at least a small fretting crack in the slip zone of the fretting scar, before the fretting pre-cracked specimen was loaded and cycled using an in situ uniaxial fatigue testing machine during scans. For transparent materials, the selection of appropriate brittle glassy polymers offers the possibility of performing a continuous in situ visualization of the crack development processes within the loaded contact zone [6], [11], [12].

  • Numerically, the simulation of 3D fretting cracks is also complicated by the contradictory constraints that must be met to successfully address this problem. The first one is that the problem is strongly multi-scale. The different scales involved – i.e. those of the structure, of the crack, and of possible localized non-linearities like confined plasticity or frictional contact – differ by several orders of magnitude and an arbitrary finite element mesh of a given structure is usually not designed to account for a crack. Fretting cracks are submitted to severe multi-axial non-proportional stress fields and experienced complex frictional mixed mode sequences at their interface. An accurate description and solution of the frictional contact between the crack faces is thus an essential pre-requisite. Then, the effects of multiaxial non-proportional mixed mode on the crack propagation require dealing with two issues, the crack path determination and the crack growth rate quantification.

A methodology coupling experimental and modelling is proposed here in order to predict crack initiation and propagation. The outline of the paper is as follows. In Section 2, the materials, experimental devices and the fretting test methodology are presented. Loading conditions leading to partial slip conditions throughout the fretting tests being determined as well as the friction coefficient value at the sliding transition, the tests are run and the crack profiles are measured for 2D and 3D tests versus the number of cycles. The numerical procedure, is presented in Section 3, includes the cylinder/plane contact solution for the experimental loading conditions, a frictional fatigue crack model using innovative techniques, such as the eXtended Finite Element Method (X-FeM) to compute the stress intensity factors (SIF) under experimental fretting conditions. A mixed mode Paris crack growth law is then identified from the coupling of experimental results, crack lengths and orientations at different number of cycles and the computation of the SIF for cracks corresponding to the extracted actual profiles. Finally, introducing multiaxial fatigue criteria, the crack growth prediction is performed for a given fretting test using the identified Paris law. The predicted crack path is compared to the corresponding experimental one, and leads to a very good agreement. Finally, 3D numerical simulations corresponding to 3D sphere/plane fretting tests are carried out. 3D non-planar frictional cracks whose shapes were extracted from the reconstructed crack surfaces are described with levels sets are considered. The energy release rate G and the stress intensity factors in mode I, II and III are computed along the crack fronts. The numerical results outline that the SIFs are non-uniform along the crack front and that their distribution vary versus the number of cycles, leading to a better understanding of local varying kinetics and offering a comprehensive understanding of the propagation along a 3D crack front.

Section snippets

Material and contact parameters

Two types of contact have been investigated, 2D cylinder on flat and 3D sphere on flat configurations. The material used for the plane specimen is a steel alloy 35 NCD16 with a specified heat treatment. The mechanical and fatigue properties are listed in Table 1. The cylindrical and spherical counter bodies are made of heat treated steel 100 C6 (see Table 2) with a controlled roughness (Ra = 0.4 μm).

Loading conditions and cracking as main damage response

The first goal of the test campaign is to determine the loading conditions leading to partial slip

X-FEM

The numerical crack growth simulation is a large research topic which involves the understanding and the modelling of numerous local phenomena like confined plasticity or interfacial frictional contact. These non-linearities impact directly the propagation rate and path of the cracks. Contact with friction between the crack faces notably occurs in contact fatigue problems, characterized by frictional contacting mechanical parts submitted to alternative small micromotions. These time-dependent,

Fretting crack growth law identification and crack propagation simulation for the cylinder/plane configuration

The experimental analysis and the numerical tools are gathered to get a deeper understanding of the cracking phenomena and to obtain a first mixed mode crack growth law. The experimental data, including sample geometry and mechanical properties, loading conditions, crack profile estimations from post-processing of the metallographic cross-sections, are used as input data for the numerical tools dealing with two-body fretting contact solution, X-FEM simulation of the fretting test accounting for

3D sphere/plane tests

The next step consists of dealing with 3D non-planar fretting cracks and carry out the analysis of their behaviour and the computation of the stress intensity factors along the crack fronts. The integrated experimental and numerical strategy is followed. The sphere on flat fretting test data (P = 5000 N, Q = 1300 N, R = 200 mm, μt = 0.9, σs = 140 MPa) and the crack profiles extracted from the metallographic cross-sections are used as input data for the numerical simulations. The sphere/plane contact is

Conclusion

The experimental analysis and numerical tools based on X-FEM are gathered to get a deeper understanding of the cracking phenomena and to obtain a first mixed mode crack growth law. 2D and 3D fretting tests have been performed using original experimental set-up carefully controlled and monitored under partial slip conditions to get cracking as the material response. A systematic and rigorous post test methodology has been adopted to get crack data versus the fatigue life. Metallographic

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      experimental tests available in the literature [42] and carried out on AISI 1034 steel under cylindrical contact are presented in Sub-Section 2.1; experimental tests available in the literature [43] and carried out on 35NCD16 steel alloy under cylindrical contact are presented in Sub-Section 2.2; experimental tests available in the literature [43] and carried out on 35NCD16 steel alloy under spherical contact are presented in Sub-Section 2.3.

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