Coupling between direct cyclic methods in structural computation and dissipative full-field measurements: a strategy for a fast determination of crack initiation map in fretting-fatigue. – FAST 3D

The objective of FAST FM is to better understanding and modelling damage under cyclic contact stress with high stress gradients like imposed by fretting stressing. To reach this one, we define the following subtasks:
1. Development of a method for a rapid determination of the fretting map based on original experimental devices and two quantitative full-field measurement techniques: infrared thermography and image correlation. Methods of rapid determination of fatigue limit from self-heating measurements will be generalized.
2. Determination of inelastic thermomechanical laws suitable for the fretting specificities. These latter will be identified from kinematic and thermal experimental fields.
3. Development of alternative numerical strategies to drastically reduce the computation time in structural analysis. These latter will permit to take into account fretting in engineering design. In this case, a Direct Cyclic Method is the best solution.

- a method for a rapid determination of the fretting map,
- inelastic thermomechanical laws suitable for the fretting specificities,
- numerical strategies to drastically reduce the computation time in structural analysis (Direct Cyclic Method).

Develop experimental and numerical method at the grain size.
Develop a method to estimate heat souces during a fretting test.

Articles :
1. Berthel B., Moustafa A.-R., Charkaluk E., and Fouvry S., 2014, “Crack nucleation threshold under fretting loading by a thermal method,” Tribol. Int., 76, pp. 35–44.
2. Alquezar, M., Arrieta, V., Flandi, L., Constantinescu, A., Maitournam, M., and Wackers, P. Computational. fretting-fatigue maps for different plasticity models. Fat.Fract.Eng.Mat.Stru., 37(4):446–461, 201, dx.doi.org/10.1111/ffe.12130.

Conferences :
1. Berthel B., and Fouvry S., 2013, “Crack nucleation threshold obtained by thermal method,” 7th International Symposium on Fretting Fatigue - ISFF7, Oxford, UK.
2. Berthel B., and Fouvry S., 2013, “Crack Nucleation Threshold Under Fretting Loading by a Thermal Method,” SEM 2013 Annual Conference, Lombard, USA.
3. Berthel B., Moustafa A. R., and Fouvry S., 2013, “CRACK THRESHOLD CONDITIONS UNDER FRETTING LOADING BY THERMAL ANALYSIS,” PhotoMechanics 2013, Montpellier, France.
4. Moustafa A.-R., Berthel B., Charkaluk E., and Fouvry S., 2014, “Experimental study by full field measurement techniques of the stress gradients effect under fretting, fretting-fatigue and notch fatigue,” International Conference on Fatigue Damage of Structural Materials X, Hyannis, USA.
5. Moustafa A. R., Berthel B., Charkaluk E., and Fouvry S., 2014, “Experimental study by full field measurement techniques of the stress gradients effect under fretting, fretting-fatigue and notch fatigue,” QIRT 2014, Bordeaux, France.
6. Moustafa A. R., Berthel B., Fouvry S., and Charkaluk E., 2013, “Détermination par analyse thermique des seuils d’amorçage des fissures sous chargement de Fretting,” Congrès Français de Mécanique 2013, Bordeaux, France.

Fatigue loadings on real structure are generally a combination of cyclic and static stress gradients. Stress gradients can have a strong influence on components lifetime subjected to multiaxial fatigue loadings. This is the reason why the objectives of this project are: (i) the development of a fast method to determine crack nucleation conditions (ii) the proposition of suitable thermomechanical constitutive laws (iii) the development of numerical strategies to drastically reduce computation time.
In this way, the fretting loading is probably the case introducing the strongest gradients in the structures. Therefore we focus on this type of loadings but results coming from this project will be more general and can be extended to the case of cyclic loadings with stress gradients.
Fretting loadings cause damages which decrease highly the lifetime of industrial systems. All industrial domains are concerned: transport, energy... This phenomenon is characterized by very small sliding amplitudes significantly smaller than the contact size. Under partial slip conditions, part of the contact zone remains stuck and the damage is mainly characterized by initiation of cracks. To describe the different fretting-fatigue damages, a synthetic form of a fretting-fatigue mapping is used. This map defines three damage domains depending on loading parameters: the no cracks nucleated, the safe crack arrest and the ultimate failure domain. Experimentally, these latter are obtained by destructive methods which are time and material consuming and give scattered results.
Cracks initiation is directly linked to the plastic response of the material. The aim of FAST 3D is to develop an experimental method based on the dissipative response of the material under fretting loadings coupled with a numerical strategy. The final objectives are a better understanding of fretting mechanisms and the development of an alternative computational method.
From a mechanical point of view, in order to describe the plastic behaviour of a material under cyclic loadings, elastic shakedown, plastic shakedown and ratcheting phenomena have to be taken into account. However, it is generally not the case in conventional modelling approaches. From a computational point of view, conventional methods by incremental finite elements are very time consuming due to the stress gradient (mesh size) and the number of cycles to reach the asymptotic response of the material. Then, fretting phenomenon is also generally not taken into account in structural analysis.
The objective of FAST 3D is a better understanding and modelling of the damage under cyclic contact stresses with high stress gradients like imposed by fretting loadings. To reach this one, we define the following tasks:
1. Development of a method for a fast determination of the fretting map based on original experimental devices and two quantitative full-field measurement techniques: infrared thermography and digital image correlation.
2. Determination of inelastic thermomechanical constitutive laws suitable for the fretting specificities. These latter will be identified from kinematic and thermal experimental fields.
3. Development of alternative numerical strategies to drastically reduce the computation time in structural analysis. These latter will permit to take into account fretting in engineering design. In this case, a Direct Cyclic Method is the best solution.
The three partners involved in FAST 3D (LML, LMS and LTDS) provide the know-how and the complementary experimental and numerical devices to achieve this objective. All researchers involved in this project have worked on crack initiation mechanisms in fretting and/or fatigue and the majority on a thermomechanical approach based on the concepts of elastic and plastic shakedown.
Our approach is a fundamental one and this is the reason why we submit it to the call for proposals Blanc 2010, but the results of this research will obviously have industrial applications.