In recent years the number of applications in which structural components such as railway wheel sets or roller bearings of automobiles are cyclically loaded up to a very high number of loading cycles (far beyond 10 million cycles) has risen continually due to the need for increased economic efficiency. In turn, to guarantee the safety of human, machine and environment the exploration of the deformation behavior during very high cycle fatigue (VHCF) is of particular importance.
In an interdisciplinary project cooperation funded by Deutsche Forschungsgemeinschaft (DFG) the cyclic deformation behavior of austenitic stainless steels under VHCF loading conditions is investigated. In this context, the working group of material science and testing (Universität Siegen, Prof. H.-J. Christ, LINK) and the working group of mechanics of materials and failure analysis (TU Dresden, Prof. M. Zimmermann) are concentrating on experimental characterization, while the working group of applied technical mechanics (Universität Siegen, Prof. C.-P. Fritzen) focuses on modeling and simulation.
Austenitic stainless steels (Cr-Ni-steels) are the most commonly used stainless steels and combine excellent ductility, formability and corrosion resistance. Experimental observations revealed that during VHCF-loading the austenitic alloys undergo localization of plastic deformation in so-called shear bands and a deformation-induced phase transformation from the ductile γ-austenite into the harder α'-martensite phase. The investigation based on the resonant behavior showed, that the material exhibits a distinctly transient behavior during VHCF.
Experimental studies represent the basic approach in the field of material science. But, due to various measurement restrictions, experimental observations often cannot describe the deformation process to the last detail. Therefore, it is useful to supplement experimental investigations by modelling and simulation of the respective microstructural changes in order to achieve a more profound understanding.
For that purpose a certain modeling and simulation strategy is carried out, as illustrated in Fig. 1. By means of experimental data taken form scanning electron microscope (SEM) in combination with the electron backscattered diffraction (EBSD)-technique, two-dimensional (2-D) microstructures consisting of several grains are represented using the 2-D boundary element method. Plastic deformation within the microstructure is considered by a mechanism-based approach. Specific mechanisms of cyclic plastic deformation in shear bands and deformation-induced martensitic phase transformation - as documented by experimental results and based on well-known model approaches - are defined and implemented into the model. Since the plastic deformation depends amongst others on the initial sample temperature, the effect of a moderate increase of temperature is reflected in the model.
Fig. 1 Modeling and simulation strategy and comparison to experimental observations
The fatigue loading is applied by a quasi-static approach in which the external loading is sampled and for each sample an elastostatic simulation is carried out. During each sample the mechanisms of plastic deformation are incorporated into the simulation by iteratively adjusting the microstructure and its boundary conditions. Simulation results are directly compared to the observed deformation evolution on the real specimen surfaces (I in Fig. 1). Additionally, the cyclic transient behavior of the material during fatigue is compared on the basis of the resonant behavior (II in Fig. 1). For that purpose, resonant frequencies are monitored during fatigue tests and simulated hysteresis loops are evaluated by means of a damping model.
Good agreement of results confirms the model assumptions and allows for assigning certain deformation mechanisms to the specific change of transient resonant behavior. The latter is also very fruitful for structural health monitoring (SHM) techniques, because it allows the estimation of the actual health state of structures only by measuring vibration data during operation (ultimate SHM Level: Prognosis of remaining lifetime). Finally, a more profound understanding of the VHCF deformation behavior of austenitic stainless steels is provided.
The authors gratefully acknowledge financial support of this study by Deutsche Forschungsgemeinschaft (DFG) in the framework of the priority program Life∞ (SPP 1466).
Journal publications:
P.-M. Hilgendorff, A. Grigorescu, M. Zimmermann, C.-P. Fritzen and H.-J. Christ: 'Simulation of irreversible damage accumulation in the very high cycle fatigue (VHCF) regime using the boundary element method', Mater. Sci. Eng. A, 2013, 575, 169-176, LINK.
P.-M. Hilgendorff, A. Grigorescu, M. Zimmermann, C.-P. Fritzen and H.-J. Christ: 'Numerical investigation of the influence of shear band localization on the resonant behavior in the VHCF regime', Theor. Appl. Mech. Lett., 2014, 4, LINK.
P.-M. Hilgendorff, A. Grigorescu, M. Zimmermann, C.-P. Fritzen and H.-J. Christ: 'Simulation of deformation-induced martensite formation and its influence on the resonant behavior in the very high cycle fatigue (VHCF) regime', Proc. Mat. Sci., 2014, 3, 1135-1142, LINK.
P. M. Hilgendorff, A. Grigorescu, M. Zimmermann, C. P. Fritzen and H. J. Christ: 'Simulation of the interaction of plastic deformation in shear bands with deformation-induced martensitic phase transformation in the VHCF regime', Key Eng. Mat., 2015, 664, 314-325, LINK.
P.-M. Hilgendorff, A. Grigorescu, M. Zimmermann, C.-P. Fritzen and H.-J. Christ: 'Cyclic deformation behavior of austenitic Cr-Ni-steels in the VHCF regime: Part II - microstructure-sensitive simulation', Int. J. Fatigue, 2016, 93, 261–271, LINK.
P.-M. Hilgendorff, A. Grigorescu, M. Zimmermann, C.-P. Fritzen and H.-J. Christ: 'Modeling and simulation of temperature-dependent cyclic plastic deformation of austenitic stainless steels at the VHCF limit', Structural Integrity Procedia, 2016, 2, 1156-1163, LINK.
Further journal publications by Grigorescu et al., which focus on the experimental characterization as part of this research project, can be found in the publication list of the working group of material science and testing (Universität Siegen, Prof. H.-J. Christ), LINK.
Conferences:
DGM-Arbeitskreis Mikrostrukturmechanik, Siegen, Germany, March 2012, Presentation.
23rd Colloquium on Fatigue Mechanisms, Futuroscope, Poitiers, France, April 2012, Presentation.
Materials Science and Engineering Conference, Darmstadt, Germany, September 2012, Poster.
DPG-Frühjahrstagung, Regensburg, Germany, March 2013, Presentation.
GAMM-Tagung, Novi Sad, Serbia, March 2013, Presentation.
13th International Conference on Fracture, Beijing, China, June 2013, Presentation.
DGM-Arbeitskreis Mikrostrukturmechanik, Osnabrück, Germany, June 2013, Presentation.
GAMM-Tagung, Erlangen-Nürnberg, Germany, March 2014, Presentation.
20th European Conference on Fracture, Trondheim, Norway, June 2014, Presentation.
Materials Science and Engineering Conference, Darmstadt, Germany, September 2014, Poster.
6th International Conference on Very High Cycle Fatigue, Chengdu, China, October 2014, Presentation.
DGM-Arbeitskreis Mikrostrukturmechanik, Kassel, Germany, February 2014, Presentation.
9th European Solid Mechanics Conference, Madrid, Spain, July 2015, Presentation.
21th European Conference on Fracture, Catania, Italy, June 2016, Presentation.
Materials Science and Engineering Conference, Darmstadt, Germany, September 2016, Presentation.
DGM-Arbeitskreis Mikrostrukturmechanik, Aachen, Germany, November 2016, Presentation.
Awards:
Best Paper Award for Young Researchers at the 13th International Conference on Fracture, Beijing, China, June 2013, LINK.
