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Über dieses Buch

This book represents the final reports of the scientific projects funded within the DFG-SPP1466 and, hence, provides the reader with the possibility to familiarize with the leading edge of VHCF research. It draws a balance on the existing knowledge and its enhancement by the joint research action of the priority program. Three different material classes are dealt with: structural metallic materials, long-fiber-reinforced polymers and materials used in micro-electro-mechanical systems. The project topics address the development of suitable experimental techniques for high-frequency testing and damage monitoring, the characterization of damage mechanisms and damage evolution, the development of mechanism-based models and the transfer of the obtained knowledge and understanding into engineering regulations and applications.

Inhaltsverzeichnis

Frontmatter

Fatigue of low alloyed carbon steels in the HCF/VHCF-regimes

Abstract
The fatigue behaviour and damage evolution in body centered cubic low alloyed steels in the high cycle and very high cycle fatigue regimes (HCF/VHCF) were in focus of this work. For this purpose, the steels C15E, C45E and C60E, with different ferritic-pearlitic microstructures were investigated. Due to the different carbon contents the ratio of ferrite to pearlite decreased from C15E to C60E. C15E mainly consist of ferrite grains. The ferrite grains deform plastically under cyclic loading. With decreasing stress amplitudes plastic deformation becomes more and more localized in particular ferrite grains. During further cyclic loading plastic deformation accumulates in those grains and finally leads to crack initiation and fatigue failure. The accumulation of irreversible plastic deformation in the ferrite grains and the strength of microstructural barriers in the vicinity of the plastically deformed grains are mainly determining the total fatigue life. In order to assess quantitatively the contribution of irreversible plastic deformation a new method was developed. By determining the dissipated energy per fatigue cycle, which was derived from the power input of the ultrasonic fatigue machine, it is possible to account for the amount of irreversibility during one loading pulse. Based on these results a prediction of the fatigue life can be made at a very early stage of the fatigue experiment. It also allows distinguishing very early whether the specimen will become a runout or if it will fail at a given amplitude. It also turned out that the interaction of localized plastic deformation with microstructural barriers in the direct vicinity is the key for understanding the occurrence of late fatigue failure. If specimens showed macroscopic crack growth and fatigue failure, critical cracks always initiated at interfaces. On the other hand, runout specimens showed some crack nuclei, but they were not able to overcome the next microstructural barrier.
In addition to the ferritic-pearlitic condition C15E was also investigated in a quenched state. This significant different microstructure changes the deformation behaviour and the sites of crack initiation from grain boundaries to the grain interior. Special interest was also laid on the influence of test frequency on the fatigue behaviour and crack initiation. Thus, tests were done using the ultrasonic fatigue technique which operates at 20 kHz and conventionally resonance fatigue machines which operate at 110 Hz. Based on the well-known Hart formula for strain rate sensitivity under monotonic load, a new relation was derived there from to quantify the strain rate dependence in cyclic experiments.
J. Bach, M. Göken, Heinz-Werner Höppel

Atomic-scale modeling of elementary processes during the fatigue of metallic materials: from crack initiation to crack-microstructure interactions

Abstract
It is well known that the fatigue of metallic materials is governed by the accumulation of plastic slip, which ultimately leads to the initiation and propagation of cracks. Whether a material exhibits an infinite fatigue life or not is therefore determined by the complex interplay between plastic deformation processes, the formation of small crack nuclei and the direct and indirect interactions of cracks with the surrounding microstructure. It is this complex interplay with the microstructure that makes predictive modeling of fatigue in metals such an arduous task, even though the first empirical expressions for the fatigue life have been developed more than hundred years ago. For this reason, most macroscale material models for large-scale computer simulations are still directly parameterized through costly fatigue experiments instead of considering microstructural information and lower-scale deformation mechanisms. The focus of this work is therefore to investigate the fundamental mechanisms that are of relevance to metal fatigue: crack nucleation by slip accumulation at grain boundaries (GBs), crack propagation along GBs, dislocation-crack interactions, and the influence of crack front curvature, which is especially important as long as the cracks are very small. Studying the direct defect-defect interactions characteristic for these processes require atomic-scale resolution. Atomistic modeling methods, such as molecular dynamics (MD) simulations, are therefore ideally suited for their close and detailed investigation. Since atomistic simulations come with their own challenges in terms of limited time and length scale, it is important to note that the present work is intended to lay the foundations for the future developments of predictive, mechanism-based and microstructure-sensitive material models for large-scale fatigue simulations, rather than being by itself quantitatively predictive. Instead, we present several qualitative and semi-quantitative observations, which should also hold true in real materials. I.e., that dislocation pile ups are more critical for crack nucleation at GBs than homogeneously distributed dislocations and vacancies; that furthermore, the fracture behavior and toughness is markedly influenced by (i) crystal orientations, (ii) GB structures, (iii) pre-existing dislocations, and (iv) crack front curvature. Finally, future directions for atomistic modeling of fatigue damage are presented.
J. Möller, Erik Bitzek

Fatigue behaviour of austenitic stainless steels in the VHCF regime

Abstract
The focus of this work lies on the investigation of the fatigue properties of austenitic Cr-Ni steels in the HCF and VHCF regime. This class of steels is characterized by low stacking fault energies which determine the main characteristics of deformation mechanisms (dislocation gliding, phase transformation). Three austenitic stainless steels, having distinct stacking fault energies and correspondingly distinct stabilities of the austenitic phase, were used in this study (304L, 316L and 904L). Other factors that influence the propensity of the materials for α’ martensite formation were also considered (e. g. temperature, strain rate/frequency). The metastable austenitic stainless steel 304L shows a very pronounced transient behaviour and a true durability without failure beyond 106 cycles. A comprehensive description of the microstructural changes governing the cyclic deformation is presented. The 316L steel has higher stacking fault energy and its cyclic deformation is much less pronounced. The plastic shear is more localized and the topography investigations show the formation of deep intrusions where microcracks can be initiated. The propagation of such microcracks however is impeded by the α’ martensite formed within the slip bands. The fatigue tests using different frequencies show higher fatigue strength for samples tested at 20 kHz compared to those tested at 140 Hz. This can be explained by the dependency of the plastic strain amplitude on the strain rate which was experimentally demonstrated in this study. The highly stable steel 904L exhibits a decrease in fatigue strength in the VHCF regime with failures up to 5.5∙108 cycles. Microcracks initiate from twin boundaries with extremely few signs of plasticity and grow very inhomogeneously due to the strong barrier effect of neighboring grains. The effect of predeformation on the HCF and VHCF properties was also investigated in the case of the metastable grade 304L. The amount of the α’ martensite phase obtained by means of monotonic predeformation was deliberately adjusted in order to influence the fatigue properties of the material. The results show that the initial martensite content should be kept below 30 vol-% in order to obtain optimal HCF and VHCF properties. For very high martensite contents (e.g. 60 vol-%) internal cracks are initiated and the fatigue life is strongly determined by the local stress and the geometry of the crack initiating inclusions.
A. Grigorescu, P.-M. Hilgendorff, Martina Zimmermann, Claus-Peter Fritzen, Hans-Jürgen Christ

Simulation of the VHCF deformation of austenitic stainless steels and its effect on the resonant behaviour

Abstract
In the context of a project cooperation – consisting of an experimental part (see previous article of this book) and a modelling and simulation part – the characterisation of the cyclic deformation behaviour of austenitic stainless steels during very high cycle fatigue (VHCF) was carried out. Experimental observations indicated clear differences between the VHCF deformation behaviour of a metastable and a stable austenitic stainless steel. In order to provide a more profound knowledge about the individual deformation mechanisms, the experimental study was extended by modelling and simulation. Two-dimensional microstructures consisting of several grains were represented using the boundary element method and plastic deformation within the microstructure was 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 – were defined and implemented into the simulation. 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. Simulation results were directly compared with the observed deformation evolution on the real specimen surfaces and a comparison based on the transient resonant behaviour of the specimens and of the modelled microstructures was carried out. Good agreement of results confirms the model assumptions and allowed for assigning certain deformation mechanisms to the specific change of transient resonant behaviour. Finally, a more profound understanding of the VHCF deformation behaviour of both austenitic stainless steels is provided.
P.-M. Hilgendorff, A. C. Grigorescu, Martina Zimmermann, Claus-Peter Fritzen, Hans-Jürgen Christ

Slip band formation and crack initiation during very high cycle fatigue of duplex stainless steel – Part 1: Mechanical testing and microstructural investigations

Abstract
To investigate 3D effects during the very high cycle fatigue behaviour of two-phase materials, tailored small-sized specimens of duplex (DSS) and super duplex stainless steel (SDSS) were tested by means of ultrasonic testing in ambient air, corrosive atmosphere and under vacuum conditions in situ within a scanning electron microscope. Selected experiments were carried out in combination with high-energy synchrotron diffraction). In general, fatigue damage manifests itself by preferential slip band formation in the softer fcc austenite phase as it was observed in situ by using a thermo-camera with microscopic resolution. Heat dissipation due to localized plasticity becomes visible as hot-spots offering the possibility for predict the onset of fatigue damage at an early state of VHCF life. Crack initiation is observed transgranular and intergranular at austenite/ferrite phase boundaries where slip band impingement results in local stress concentration. Slip band cracking within the austenite grains was observed in the case of the SDSS, while in the case of DSS, the crack starts in the bcc ferrite phase. A corrosive atmosphere promotes slip band cracking, leading to a strong tendency to micro cleavage and eventually to a drastic decrease in VHCF life. During crack propagation, the grain and phase boundaries act as microstructural obstacles, their strength is depending on the crystallographic misorientation relationship between adjacent grains. This is the key factor for limiting the fatigue life of duplex stainless steels and can be altered, e.g., by strengthening the fcc austenite by alloying with nitrogen or by spinodal decomposition of the bcc ferrite during 475°C treatment.
T. Waurischk, M. Söker, A. Giertler, N. Schönhoff, M. Galster, B. Dönges, Hans-Jürgen Christ, Ulrich Krupp

Fatigue mechanism and its modeling of an austenitic-ferritic duplex stainless steel under HCF and VHCF loading conditions

Abstract
By means of high frequency (about 20 kHz) fatigue testing techniques, the fatigue behavior of an austenitic-ferritic duplex stainless steel was experimentally investigated up to one billion load cycles. Additional fatigue tests were performed by means of conventional fatigue testing techniques at 30 Hz in order to characterize the influence of the strain rate on the obtained fatigue data. The fatigue lives are shifted to higher numbers of load cycles with increasing testing frequency or strain rates, whereas the fatigue limit and the mechanisms of fatigue crack initiation are not affected. The present study documents, that at low loading amplitudes and very high numbers of loading cycles fatigue damage in form of slip bands predominantly occurs in the softer austenitic phase, whereas crack initiation takes place at intersection points between austenite slip traces and phase boundaries in neighboring ferritic grains. Some of these fatigue cracks are able to grow further – others are not. The stress distribution on the grain scale and crystallographic misorientations at grain or phase boundaries may inhibit the ongoing of fatigue damage in form of crack propagation, leading to a real fatigue damage despite the presence of short fatigue cracks. The experimentally identified mechanisms of fatigue crack nucleation and short fatigue crack propagation were implemented into crystal plasticity finite element simulations by applying a fatigue damage parameter, which was derived from traditional mechanism based fatigue models. When a material specific threshold value is achieved, damage manifests itself by a loss of stiffness of the respective finite elements. Furthermore, anisotropic elasticity as well as first and second order residual stresses due to the manufacturing process of the investigated material were considered. The simulation results were verified by means of a comparison with real observed fatigue cracks. The current investigation clearly shows the relevance of the consideration of 3D-grain-shapes and residual stresses for the accuracy of the simulation results, which are the basis for a fatigue life assessment concept.
B. Dönges, Claus-Peter Fritzen, Hans-Jürgen Christ

Influence of different loading stresses on the peak shape of X-ray rocking curves of an austenitic-ferritic duplex stainless steel during VHCF

Abstract
The behavior of X-ray rocking curves of an austenitic-ferritic duplex stainless steel is investigated in this study. Flat samples were fatigued with different load amplitudes to certain fatigue cycles with an ultrasonic testing device. After each load amplitude X-ray diffraction scans were performed and the rocking curves were compared to the rocking curves of the unfatigued state. These measurements were performed at the synchrotron light source DELTA at beamline BL10. Due to the grain structure of the duplex stainless steel it is possible to perform a single grain analysis even if several grains are illuminated at one time. Each grain whose lattice planes have the right orientation to the incoming beam and the detector, gives a single Bragg reflection on the detector. Different grains have different orientations and so the reflections are arranged on Debye-Scherrer-Rings and it is nearly impossible for two grains to have exactly the same orientations. The reflections can then be indexed as Austenite or Ferrite reflections. The rocking curves are compared for each grain after different loading amplitudes, so the development of one grain can be seen. Possible changes of the rocking curves are broadening, splitting, change in position and intensity and also the integrated intensity. All these changes are discussed in this study and examples are given. Not only Austenite grains are affected even ferrite grains are, but not as much as Austenite is. Changes of rocking curves are explained by formation of slip bands, changes of small angle grain boundaries or initiation and propagation of cracks.
A. K. Hüsecken, B. Dönges, M. Söker, K. Istomin, Ulrich Krupp, Hans-Jürgen Christ, Ullrich Pietsch

Three-dimensional characterization of duplex stainless steel by means of synchrotron radiation X-ray diffraction imaging techniques

Abstract
The combined use of X-ray diffraction contrast tomography (DCT) and X-ray phase imaging techniques like phase contrast tomography and holotomography enable non-destructive characterization of the three dimensional grain and phase microstructure in austenitic-ferritic duplex stainless steel. Phase contrast tomography highlights discontinuities of the refractive index inside a material and is therefore ideally suited for imaging fatigue cracks and phase boundaries. The acquisition of phase images at multiple propagation distances allows for the two-step procedure of phase retrieval and tomographic reconstruction of the refractive index via holotomography. Combined with appropriate regularization and segmentation techniques, this technique provides the sensitivity to discriminate the minute difference in electron density between the austenitic and ferritic constituent phases of duplex steel. X-ray diffraction contrast tomography on the other hand exploits X-ray Bragg diffraction signals of the individual crystallites and yields three-dimensional grain orientation maps for each of the constituent phases (austenite and ferrite). Merging the results of both imaging modalities, the fidelity of the inter-phase boundaries (derived from X-ray holotomography) can be used to enhance the spatial fidelity of the 3D grain orientation maps produced by DCT. We have combined this microstructure characterization scheme with time lapse observations of a propagating fatigue crack by means of repeated phase contrast tomography inspection during an interrupted fatigue test. Access to the crack growth history and the crystallographic microstructure allow for qualitative analysis of fatigue crack – microstructure interactions and provides valuable input for refinement and benchmarking of image based crystal plasticity finite element calculations.
Wolfgang Ludwig, M. Syha, N. Vigano, B. Dönges, A. Giertler

Very high cycle fatigue crack initiation: investigation of fatigue mechanisms and threshold values for 100Cr6

Abstract
High-strength steels do not show a classical fatigue limit and failure still occurs far beyond 107 cycles. The fatigue properties in this very high cycle fatigue (VHCF) region are strongly affected by non-metallic inclusions inside the material. The mechanisms responsible for this late failure are not fully understood until now. In the scope of this work the mechanisms of VHCF failure and the connected threshold values are observed in detail. Ultrasonic tension-compression fatigue tests (R = -1) with the high-strength steel 100Cr6 (AISI 52100) were carried out until an ultimate number of cycles of 109. Some additional tests were also performed with artificial surface defects in air and vacuum for comparison. Single step fatigue tests, crack propagation tests and very high cycle stress increase tests are performed to understand the fatigue behaviour for very high cycle failure. By the combination of these tests a threshold for the VHCF by fine granular area (FGA) formation at inclusions can be derived. The results of mechanical testing are completed by investigating the inclusion distribution in tested specimen and the evaluation of harmless inclusions. Comprehensive fracture mechanical investigation for the performed tests enabled the determination of a VHCF threshold value. Microstructural analyses of the crack origin with focused ion beam imaging, transmission electron microscopy and atom probe tomography are used to investigate microstructure after fatigue failure in detail. Thereby the VHCF mechanisms leading to crack initiation are revealed. Finally by combination of fatigue results and microstructural investigations a new model for VHCF crack initiation in high-strength steels is proposed.
D. Spriestersbach, P. Grad, A. Brodyanski, J. Lösch, M. Kopnarski, Eberhard Kerscher

Evaluation of multiple-flaw failure of bearing steel 52100 of different heats in the VHCF regime and mathematical determination of single-flaw behaviour

Abstract
Caused by different factors, the interest in extended fatigue life of components is increasing. Therefore, the demand for additional knowledge about the fatigue behaviour in the VHCF regime grows. In the case of high strength steels, fatigue tests mostly reveal that multiple failure mechanisms occur. However, the common statistical analysis of constant amplitude tests generates summarized multiple-flaw S-N curves, which neglect the differentiation between the type of failure origin, e.g. oxides or sulphides as non-metallic inclusions. To improve the fatigue life of materials it is essential to determine single-flaw S-N curves for the assessment of the harmfulness of each failure type. It has to be taken into account that some mechanisms occur rarely because they are covered by others. Furthermore, it has to be considered that the probability of the occurrence of different failure types depends not only on the stress amplitude but also on the applied mean stress. In this investigation specimens made of different heats of the bearing steel 52100 were tested uniaxially at two stress ratios up to 2·109 load cycles. The tests exhibited crack initiation at different types of inclusions and at the surface depending on the chemical composition of the heat and the applied mean stress. A mathematical procedure for the determination of single-flaw S-N curves from multiple-flaw test results derived from the adaption of the competing risks theory is presented.
Klaus Burkart, B. Clausen, H.-W. Zoch

Influence of near-surface stress gradients and strength effect on the very high cycle fatigue behavior of 42CrMo4 Steel

Abstract
The present study investigates the effect of tempering temperature, residual stresses and me-chanical induced stress gradients on the fatigue properties / resistance up to 109 cycles. Uni-axial tension-compression tests (50 Hz, 1 kHz and R = -1) were performed on specimens made of 42CrMo4 (AISI 4140) at room temperature. At first smooth specimens, which were tempered at six different temperatures to produce a wide range of ultimate tensile strength were tested to clarify the strength effect. With the decrease in tempering temperature the sensitivity of subsurface crack initiation at inner defects increases. The study indicated that for high-strength heat treatment conditions (Rm > 1400 MPa) the difference between the fatigue strength at 106 and 109 increases with increasing tensile strength. A functional relationship between these two fatigue strength was found and verified experimental. It seems that the stress intensity factor K which arises as a function of local loading conditions at inner stress-raisers depends on the yielding /hardening properties of the material around them. Based on K and ODA-size a lifetime prediction for crack initiation at inner defects was developed as a function of tempering temperature. In a second step residual stresses with different penetration depth were induced by macro- and micro-peening processes on smooth and notched (Kt = 1.23, 1.41 and 1.94) specimen. As a result of work-hardening and compressive residual stresses near the surface change the place of crack initiation from the surface of smooth and notched untreated specimen to subsurface for shot-peened treated specimen in the regime of high-stress amplitudes. The test results of notched/shot-peened specimen indicated that the depth-effect of residual stresses has a significant influence on the location of subsurface crack initiation. The stability of the residual stresses during cyclic loading in the VHCF regime was determined by interrupting the fatigue tests after a defined number of cycles.
M. Korn, T. Rohm, Karl-Heinz Lang

Fatigue behavior of X10CrNiMoV12-2-2 under the influence of mean loads and stress concentration factors in the very high cycle fatigue regime

Abstract
In this study the fatigue behavior of X10CrNiMoV12-2-2 has been investigated for different stress concentration factors (1.00 < αk < 2.42) and load ratios from R = -1 to R = 0.7 up to 2∙109 load cycles at room temperature. The tests were performed under axial loading using ultrasonic fatigue testing setups of the type BOKU Vienna and a system developed at the Institute of Materials Science and Engineering (WKK) of TU Kaiserslautern. For cylindrical samples and specimens with low stress concentration factor (αk = 1.09) the S-N-curves show a flat slope with no significant decrease of the fatigue strength in the VHCF-regime. A transition of crack initiation from surface to volume cracks starting at oxide inclusions of the type AlCaO or AlCaMgO can be observed at about 1∙107 load cycles for load ratios from R = -1 up to 0.5. The maximum number of load cycles where sample failure occurs increases with increasing load ratio. For R = 0.5 fatigue fractures occur even beyond 2∙109 load cycles. Murakami`s widely accepted √area-approach [1] shows a good correlation for a wide range of R-values over four decades of the fatigue life. Fracture surfaces for internal crack initiation show the typical fish-eye structure around the inclusion. A fine granular area can only be observed for a load ratio of R = -1. The mechanism by Grad et al. [2] can describe the FGA formation. FGAs could not be observed for higher load ratios. For specimens with high stress concentration factor (αk = 2.42) the maximum number of load cycles where fracture occurs is about 1∙106 load cycles which means no VHCF-failure can be observed. In this case, cracks are always initiated at small machining induced surface defects. In the HCF-regime the S-N-curve shows a steeper slope which is typical for notched samples.
F. Ritz, T. Beck, S. Kovacs

Experimental and numerical investigations on crack initiation and crack growth under constant and variable amplitude loadings in the VHCF regime

Abstract
For a fatigue strength assessment of safety-relevant components subjected to a very high number of cycles, it has to be considered that the fatigue limit is decreased and the crack initiation site is changed. Because the investigations in this field are mainly limited to constant amplitude loadings without mean stresses, within this research project experimental, numerical and analytical investigations are focused on the influences of variable amplitude loadings on the crack initiation site, the crack growth and the lifetime for a high-strength steel. Therefore, experiments with different repeated two-step loadings as well as standardized load-time-histories have been performed, which have different amounts of small amplitudes beneath the experimentally determined fatigue strength of the investigated material. In addition to the experimental results, complex elastic-plastic finite element simulations have been performed in order to investigate the influence of the mean stresses on the crack closure behaviour. Moreover, the experimental results are used to evaluate different analytical approaches for calculating fatigue lifetimes.
Manuela Sander, C. Stäcker, T. Müller

Influence of ceramic particles and fibre reinforcement in metal-matrix-composites on the VHCF behaviour. Part I: Experimental investigations of fatigue and damage behaviour

Abstract
High performance materials can be exposed to high frequency cyclic loading conditions during technical operation. In particular, small strains operating in the very high cycle fatigue (VHCF)-regime lead to accumulative damage. Thus, appropriate local deformation on discontinuities such as porosities, inclusions, and secondary phase reinforcements lead to crack initiation and to final fatal fracture. Concurrently, quite high requirements with regard to high number of cycles are demanded for many applications. Because of the desire for high strength at low density, fibre or particulate aluminium matrix composites (Al-MMCs) were developed. Fields of application of these light-weight, but expensive materials, are e.g. in the automobile industry (e.g. engine blocks, cylinder heads, brakes). The fatigue behaviour of Al-MMCs reinforced by alumina particles (15 vol. % Al2O3) or short fibres (20 vol. % Saffil) was extensively studied in earlier work in the low cycle fatigue (LCF) and high cycle fatigue (HCF) range. Therefore, present studies are focused on investigations in the very high cycle fatigue (VHCF) regime at stress amplitudes equal to or lower than 140 MPa to reach fatigue life of about 1010 cycles. All experiments were carried out using an ultrasonic fatigue testing device under symmetric loading conditions (R = – 1). Fatigue tests were complemented by in situ thermographic measurements to record the temperature of the whole specimen and to find “hot spots” indicating changes in microstructure and, therefore, the initiation or growth of cracks. Moreover, the resonant frequency as well as a nonlinearity parameter were evaluated to determine the initiation of damage. For a better understanding of the damage mechanism (matrix decohesion, matrix failure or failure of reinforcements) all fractured surfaces were investigated by scanning electron microscopy. The combination of these methods contributes to a better understanding of underlying mechanisms of damage in aluminium matrix composites.
A. Illgen, M. Baaske, Felix Ballani, Anja Weidner, H. Biermann

Influence of ceramic particles and fibre reinforcement in metal matrix composites on the VHCF behaviour. Part II: Stochastic modelling and statistical inference

Abstract
We present a comprehensive stochastic model for the very high cycle fatigue (VHCF) behaviour of metal matrix composites which are reinforced by a system of either ceramic particles or short fibres. The stochastic modelling includes first that of the random spatial arrangement of the reinforcements since naturally the latter build potential sources for crack initiation under VHCF loading. Then, based on general principles like the weakest-link concept and damage accumulation as well as on empirical laws known from the literature a stochastic model for the random fatigue lifetime of a specimen with given arrangement of the reinforcements is developed. The comparison of simulated data from the model with the so far available experimental data indicates that the model covers the typical VHCF behaviour of the experimentally investigated specimens.
M. Baaske, A. Illgen, Anja Weidner, H. Biermann, Felix Ballani

Development of a fatigue life prediction concept in the very high cycle fatigue range based on covariate microstructural features

Abstract
In the present work the dependence between the size and space distribution of defects relating to the material quality as well as the size and location of failure initiation defects in fatigue specimens correlating with their fatigue lives in the VHCF-range was investigated. The investigations were made for two reference materials, a nickel-based superalloy Nimonic 80A and a metastable austenitic stainless steel AISI 304 (1.4301) with a high deformation-induced martensite volume fraction. The effect of typical damage-relevant defects for the investigated materials was modeled by corresponding failure-relevant parameters. The stress concentration at crack initiating twin boundaries as well as regular grain boundaries in Nimonic 80A was quantified using a misorientation factor by Blochwitz et al. [1] and a developed crack initiation parameter. The effect of size and location of extrinsic defects in 1.4301 representing the type-II-materials was estimated by means of a stress intensity factor with consideration of the local stress at defects. The investigation of the distribution of failure-relevant parameters in the single specimens showed that crack initiation predominately takes place at defects with the maximum values of the defined parameter. Applying the findings of the fatigue test results generated in the framework of this project, the observed dependence between the failure-relevant parameters and corresponding number of cycles until failure or crack initiation was modeled.
The analysis and statistical modeling of the defined damage-relevant defects was carried out on the basis of metallographic investigations of the reference materials in the as-received condition. Using the extreme value statistics (EVS) the size and (if necessary) space distributions of the larger values of defined damage-relevant defects were modeled for metallographic samples. These models were used in order to evaluate the value of failure-relevant parameters in fatigue specimens and corresponding fatigue lives. The good agreement of experimental and modeling results as well as the likely application of the method on other alloys are discussed in the paper.
A. Kolyshkin, E. Kaufmann, M. Zimmermann, H.-J. Christ

Experimental investigation of damage detection and crack initiation up to the very high cycle fatigue regime

Abstract
Materials in many modern small-scale applications are under complex cyclic stress states and undergo up to 109 cycles. Fatigue mechanisms limit their lifetime and lead to failure. There-fore, the Very High Cycle Fatigue (VHCF) regime needs to be studied. This project investi-gates the fatigue mechanisms and crack initiation of fcc materials such as nickel, aluminum and copper, and bcc materials such as 17-4PH on a small-scale in the VHCF regime by means of innovative fatigue experimentation. Firstly, the development and implementation of a novel custom-built resonant fatigue setup showed that the resonant frequency of bending micro-samples changes with increasing cycle number due to the accumulating fatigue dam-age. Then, additional insights on early damage formation have been explored. Mechanisms, prior to crack initiation, such as slip band formation at a state where it appears in only a few grains, have been observed. Cyclic hardening, vacancy formation and oxidation formation may be considered as possible explanations for early fatigue mechanisms. In addition, the new experimental setup can be used to define parameters needed for crack initiation models. Finally, these crack initiation processes have been experimentally examined for pure alumi-num and pure copper.
M. Buck, T. Straub, Christoph Eberl

Discrete dislocation dynamics study of dislocation microstructure during cyclic loading

Abstract
The role of loading conditions, grain morphology and crystallographic orientation on the dislocation microstructure evolution in fcc metals under high frequency cyclic loading is studied by three-dimensional discrete dislocation dynamics simulations. The formation of characteristic dislocation structures, e.g. prismatic loops, dipolar structures and debris clusters is analyzed based on a graph analysis of the dislocation network. The type of defects formed is found to be independent of the loading amplitude. Very early stages of structure formation are only observed for larger amplitudes. Furthermore, a threshold in loading amplitude has to be reached to increase the rate of defect formation and dislocation density. Also, the grain morphology has a major impact on dislocation multiplication, comparing grains with a shape of a cube or a truncated dodecahedron. Surface grains generally show more pronounced irreversibility, due to the asymmetry for dislocation motion. The free surface acts as dislocation sink, thus causing increased irreversibility. The overall mechanical response can be characterized by an effective lower stiffness for larger strain amplitudes, as a strong anelastic behavior is observed.
T. El-Achkar, Daniel Weygand

Investigation of the infinite life of fibre-reinforced plastics using X-ray refraction topography for the in-situ, non-destructive evaluation of micro-structural degradation processes during cyclic fatigue loading

Abstract
The described investigation of carbon-fibre-reinforced plastics (CFRP) documents that damage evolution can be observed by means of X-ray refractography [1]. Comparative investigations with synchrotron technique on CFRP and grey-scale analysis on glass fibre-rein-forced-plastics (GFRP) confirm these results. Moreover it was found that the fracture mechanical properties of the matrix system influence damage nucleation and propagation in the laminate during static and fatigue loads. Single-step fatigue tests were carried out on laminates with RIM135 and LY556 matrix systems made from non-crimped fabric (NCF) or twill weave in different fibre orientations. The damage to the LY556 laminates was characterized by laminate cracks growing rapidly over the whole specimen width, whereas the damage on the RIM135 laminates was characterized by an earlier onset of micro-cracking followed by laminate cracks. The specimens were fatigued up to 108 (very high cycle fatigue (VHCF) regime) load cycles. S-N-curves of damage initiation were drawn and boundaries were identified for endurance within the VHCF regime. A phenomenology based model focusing on matrix stress was applied to reproduce the first inter-fibre failure (IFF) under static and fatigue loads.
A. Müller, Volker Trappe, S. Hickmann, H.-P. Ortwein

Very high cycle fatigue of carbon fiber reinforced polyphenylene sulfide at ultrasonic frequencies

Abstract
Carbon fiber reinforced polymers (CFRP) are increasingly used for high performance applications such as aircraft structures which are often subjected higher than 108 loading cycles during their operation time. To utilize the full mechanical performance of CFRP for light-weight applications, the very high cycle fatigue (VHCF) behavior has to be well understood. In this project the VHCF behavior of a carbon fiber twill 2/2 fabric reinforced polyphenylene sulfide (CF-PPS) was analyzed systematically up to 109 cycles for the first time. To realize these investigations in an economic reasonable time period a novel ultrasonic fatigue testing facility for CFRP was developed. This facility works with cyclic three-point bending at a frequency of 20 kHz. Lifetime-oriented investigations showed a significant decrease of the bearable stress amplitudes in the range between 106 and 109 cycles. 3D-Scanning-Laser vibrometry was applied to analyze high frequency oscillations and cyclic strain amplitudes. Based on light optical microscopy and SEM investigations as well as computed tomography scans the fatigue damage mechanisms in the VHCF regime were characterized in detail. New damage mechanisms compared to the state of the art in CFRP fatigue were not observed so far.
Frank Balle, D. Backe

Acoustics based assessment of a composite material under very high cycle fatigue loading

Abstract
Carbon fibre reinforced polymers are increasingly used for high performance applications, especially in aerospace because of their excellent strength and stiffness. CFRP structures with a request of lifetimes of 30 years and more have still to be designed seemingly very conservative for long endurance (‘infinite life’) because their Very High Cycle Fatigue behaviour is not known in detail so far. The objective of the project being reported and performed within the scope of SPP 1466 has been the characterization of the fatigue behaviour of CFRP by means of non-destructive testing techniques under 3-point bending loads at cycle numbers beyond 108 cycles and hence in the VHCF regime. Therefore, an ultrasonic testing facility for bending fatigue tests operating at a frequency of 20 kHz developed at the Institute of Materials Science and Engineering at the University of Kaiserslautern was used to get these VHCF experiments realized within reasonable period of time. The fatigue damage processes were characterized by different analytic means to understand the failure mechanisms in CFRP. During the fatigue experiments, the vibration spectra of the specimens and their sound irradiation were recorded by means of a laser vibrometer and a microphone. The time domain signals have been used to characterize the 3-point bending fatigue behaviour and as input parameters for the simulation of damage progression. Phenomena observed from those signals have been interpreted by some supporting validations based on ultrasonic techniques and measurements by means of computed tomography applied offline before fatigue, during load-free interruptions and finally after failure.
This paper looks into the aspect on how damage incubators in composite materials and structures including matrix fracture, delamination, fibre-matrix debonding, fibre fracture and any progression of those damage incubators can be detected by taking advantage of the material’s inherit mechanical properties. To explain and understand the effect of the non-linear behaviour observed a 2D-FEM model using COMSOL with the presence of delamination damage has been generated which induced breathing of the delaminations under the fatigue load applied with higher harmonic eigenfrequencies transforming in dependence of delamination sizes and locations within the specimen considered.
R. S. Venkat, P. Starke, Christian Boller

Methodology for the high-frequency testing of fiber-reinforced plastics

Abstract
Nowadays, composite materials are used in many structural applications. In order to achieve maximum reliability and safety, it is necessary to perform fatigue tests that cover load cases ranging from short and intense lives to long-lasting lives with low stresses. The latter case leads to a high number of load cycles up to the very high cycle fatigue regime. Conservative testing methods use testing frequencies below 10 Hz to avoid specimen heating or strainrate-related effects in the material. This results in long testing times and, given the number of specimens required, very long test periods. The only way to shorten these testing times is to raise the testing frequency by a significant factor. Positively driven test machines such as standard servohydraulic test rigs, however, have a limited testing frequency. To improve this, the testing approach must be shifted from the positively driven concept towards a resonantly driven concept. The specimen then becomes a part of the load-generating system and the entire test rig uses its own mass inertia rather than suppressing it. Following this approach, a dual-mass oscillator is presented in order to demonstrate the working principle. This principle is then validated against an analytic model of the oscillator. The control circuit, which tracks the resonant frequency of the oscillator and maintains a constant stress amplitude in the specimen, is also discussed, followed by the presentation of the working principle of this nested controller and its ability to measure data over the fatigue life of the specimen. The study is then concluded with the results of the fatigue test.
P. Lorsch, M. Sinapius, Peter Wierach

Very high cycle fatigue testing and behavior of GFRP cross- and angle-ply laminates

Abstract
Compared to low cycle and high cycle fatigue of fiber-reinforced composites, the very high cycle fatigue behavior has only been explored in part. Underlying reasons are time consumption and the variety of difficulties of high-frequency testing. Therefore, a special high frequency bending test rig providing reasonable testing times and online damage monitoring has been developed within the DFG priority program 1466. Comprehensive test series have been conducted investigating the VHCF of two GFRP laminates, a cross-ply and an angle-ply lay-up. Several load levels have been applied to investigate the effect of stress amplitude. Whereas both laminates show a characteristic HCF behavior at higher load levels, damage initiation and progression are delayed at lower loads. Differences in VHCF and HCF damage behavior are revealed. As neither cracking nor delamination is found at lower loads, the existence of initiation thresholds and a fatigue limit is discussed. In fact, angle-ply specimens tested at low load levels do not fail within 1.5∙108cycles. A deeper understanding of the experimental results is achieved by additional modelling. Firstly, stiffness degradation is simulated by means of a 2D representative laminate element including cracking and delamination. Secondly, a statistical approach by Berthelot is adopted to analyze the role of weak areas. For the first time, a comprehensive investigation of VHCF of FRP including both fatigue life investigation and damage growth characterization is presented.
T. J. Adam, Peter Horst

A physically based fatigue damage model for simulating three-dimensional stress states in composites under very high cycle fatigue loading

Abstract
Over the years, various models have been developed to predict the fatigue behavior in fibre reinforced plastics. Recently, a new fatigue damage model (FDM) was developed. The FDM relates the energy dissipated in the quasi-static case to the energy dissipated under a cyclic loading. The model is based on evolution laws for fatigue based degradation and is more physically oriented than most models as it has an energy based methodology and takes into account Puck’s failure modes for the degradation of strength and stiffness. Since it is based on a macro-mechanical analysis scale and uses a block wise loading approach, the FDM can be applied to arbitrary structures and consideration of a large number of cycles is also possible with this model. Moreover, phenomena such as stress redistribution and sequence effects occurring under fatigue conditions can also be analyzed. Originally, the FDM was based on a two-dimensional (2D) formulation and implemented within layer-based shell elements. In the present work, an extended version of the FDM is presented. The extended version comprises a three-dimensional (3D) formulation and a finite element implementation based on solid elements. The extended FDM is used for numerical simulations of the very high cycle fatigue behavior of laminates for specific reference cases such as four-point bending based cyclic loading. Results obtained from the original FDM (2D FDM) and the present work (3D FDM) are compared and in a final step compared with the results obtained from experiments in a four-point bending test.
H. Madhusoodanan, E. Jansen, Raimund Rolfes

Investigation of the fatigue behaviour of carbon fibre reinforced plastics due to micro-damage and effects of the micro-damage on the ply strengths in the very high cycle fatigue regime

Abstract
The investigations discussed in this section treat the micromechanical fatigue mechanisms in transversally loaded unidirectional plies of carbon fibre reinforced epoxy and their interaction with the strength properties of the respective ply. The damage process initiated by the formation of matrix and interface cracks and filament failures has been determined by non-destructive acoustic emission measurements. In order to extract physically interpretable results a novel clustering methodology has been developed and implemented. Results show a dependency of the damage onset on temperature and strain rate. The micromechanical damage process is further investigated using a novel transverse single fibre specimen concept and micromechanical numerical calculations. It can be shown that the inelastic properties of the resin have a significant impact on the damage onset and evolution. Findings of the static and micromechanical investigations agree well with the experimental fatigue results. AE measurements and the determination of residual strength of the fatigue loaded ply show that micromechanical damage occurs very late in the fatigue life of UD plies under swelling transverse loads. It could be observed that transverse preloading may even increase the longitudinal compressive strength of the material, but transverse strengths are not significantly influenced by the preloading. Based on the findings from the single fibre tests, from the recorded damage evolution and the interaction of the cyclic preloading with the strength properties of the material it is concluded that the fatigue process of transversely loaded CFRP plies is dominated by the viscous properties of the matrix material.
Christian Hopmann, J. Marder

Damage initiation and failure mechanisms of carbon nanoparticle modified CFRP up to very high cycle fatigue-loading

Abstract
The influence of different carbon nanoparticles like multi-walled carbon nanotubes and few layered graphene on the damage initiation and failure mechanisms of carbon fibre reinforced plastic (CFRP) under static and fatigue loading up to the very high cycle fatigue regime is investigated. Quasi-static mechanical properties of cross-ply laminates are not affected by the nanoparticle modification but an improvement of fatigue life and change in dominating damage mechanism due to the nanoparticle modification can be achieved. Fracture toughness tests with CFRP in mode I and mode II show an influence of the orientation of the particles with regard to the crack growth direction and on the surface roughness. Hence, the toughness increases. Fractography analysis by scanning electron microscopy (SEM) reveals increased plastic deformation with a rougher fracture surface and thus higher energy absorption due to the nanoparticles. Nanoparticles act as crack initiators and consume fracture energy. Different energy dissipation mechanisms at the nanoparticles, depending on their structure, are discussed.
J. Kosmann, C. Leopold, K. Schulte, Bodo Fiedler

Characterisation and modelling of the inter-fibre cracking behaviour of CFRP up to very high cycles

Abstract
A freely vibrating test stand for experiments with carbon fibre reinforced (CFRP) cross-ply specimens loaded in pure bending, is presented and used for fatigue testing. The developed test stand does not generate out-of-plane shear forces within the specimens, thus minimises specimen heating and enables testing at high frequencies above 100 Hz.
The fatigue results of unmodified and carbon nano tube (CNT) modified specimens are used in conjunction with static four-point bending experiments to study the microcracking behaviour of transverse plies. The well-known failure mechanisms inter fibre cracking and delamination have been observed throughout fatigue experiments, whereas no delaminations were detected in static experiments. Furthermore, considerable weak area cracking was encountered in static as well as fatigue testing.
Based on the experimental findings, a modelling approach, considering static as well as fatigue microcracking is proposed. It is based on the calculation of the strain energy release rate for crack formation in terms of finite element analysis. The modelling approach is compared to experimental data, showing good agreement.
G. Just, I. Koch, Maik Gude
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