Harald Zenner

On the fatigue limit of ductile metals under complex multiaxial loading

Abstract The classical strength hypotheses are not applicable for the calculation of the fatigue limit under multiaxial loading with changing directions of the principal stresses. Hitherto, two groups of concepts have been proposed, the critical plane approach and the integral approach. In the present paper it is shown that with the integral approach, in particular the Shear Stress Intensity Hypothesis SIH, a good estimation can be achieved with complex periodical loads. This is verified using the results of 179 test series with ferritic and ferritic perlitic steel with a range of the tensile strength of R m =400–1600 MPa. References will be given to further hypotheses and developments.

Betriebsfestigkeit in Germany — an overview ☆

Abstract The German word “Betriebsfestigkeit” can be translated into English with several terms. The best expression seems to be structural durability or structural integrity. This article gives a brief description of the efforts taken especially by the German automotive industry and its cooperating research institutes to improve the accuracy of life time prediction and to optimise the proof-out by usage of experimental and numerical procedures. The advantages of standardised load–time histories (SLHs) for the user particularly in the pre design stage are shown and an overview of the existing SLHs is given. At the end of the article some aspects of practical applications of “Betriebsfestigkeit” in the German automotive industry are presented.

Cyclic material behaviour of magnesium die castings and extrusions

Abstract An increasing number of components are designed by using the local strain concept. This concept is commonly used for many different materials. The question is, can the local concept be used for components made of magnesium alloys? Therefore the material behaviour must be described and the material properties need to be adequate. The main topic of the present investigations is the verification of the Masing and memory behaviours. These two material properties are necessary for the component design by the local strain concept. Therefore the cyclic deformation behaviour is investigated in strain controlled tension compression tests. The magnesium die casting alloys AZ91 and AE42 and the magnesium extrusions AZ31 and AZ80 are tested. The magnesium die castings show approximately Masing behaviour, but the hysteresis of magnesium differs from the hysteresis of steel. All investigated magnesium alloys show the material memory M2. The magnesium extrusions show a totally different behaviour in tension and in compression. The hysteresis in experiments differs from the calculated hysteresis for the cyclic stress–strain curve. The Masing behaviour cannot be observed because of the strong anisotropic behaviour in tension and in compression direction. The calculation by the local strain concept cannot be used for the investigated magnesium extrusions without modifications because the hysteresis in tensile and in compression direction is very asymmetric. The cyclic stress–strain curve of the extrusions can only be described approximately by the Ramberg–Osgood equation.

Fatigue limit of ductile metals under multiaxial loading

Abstract The further-developed Shear Stress Intensity Hypothesis (SIH) is presented for the calculation of the fatigue limit of ductile materials under multiaxial loading. The fatigue limit behaviour for different cases of multiaxial loading is analysed with SEH and experimental results, especially with the effect of mean stresses, phase difference, frequency difference, and wave form. In a statistical evaluation, the further-developed SIH provides a good agreement with the experimental results.

Present limitations in the assessment of components under multiaxial service loading This keynote has been published also in the Proceedings of the 7 th Inter- national Conference on Biaxial/Multiaxial Fatigue and Fracture (7 th ICBMFF)

Abstract This paper is focused on a research project supported by the German automotive industry and international software producers. Six multiaxially loaded components were tested under random multiaxial service loading conditions and evaluated by different algorithms. The results reveal a large scatter of calculated fatigue lives which are, in most cases, on the unsafe side. The contradictory unsatisfactory results are determined by the complex interaction of the multiaxial stress state with cumulative damage. Therefore, in the case of safety critical components, experimental structural durability tests must be carried out.

Mikrorissentstehung und Mikrorisswachstum in Aluminiumlegierungen bei zyklischer Beanspruchung – Werkstoffliche Untersuchung und Simulation

In this paper a model designed to simulate the growth of microcracks under the influence of cyclic loading is presented. Considering fatigue crack growth microstructural barriers as well as the state of stress play an essential role. The polycristalline metal was modelled as an aggregate of hexagonal grains with each of the grains showing a different crystallographic orientation. The crack growth is initially dominated by shear stresses leading to microstructurally short cracks (stage I). As the tip of the microcrack approaches a grain boundary the crack growth rate decreases. The transition from stage I to stage II crack growth is also considered in the model as the crack reaches a specific length and continues to grow under the influence of normal stresses (physically short cracks). The model is applied to tubular specimens of the aluminum alloy AlMgSil which are subjected to tension and torsion as well as to combined tension-torsion loading cycles. In terms of the microcrack distribution as a function of their orientation the simulated crack growth behaviour reveals a close match with the experimental results.

Ein verbessertes Verfahren zur Lebensdauerabschätzung mittels linearer Schadensakkumulation

Kurzfassung Ermüdungsfestigkeitsnachweise von Bauteilen werden häufig nach dem Nennspannungskonzept bzw. dem örtlichen Spannungskonzept geführt. Einen zentralen Punkt dieser Konzepte bildet die lineare Schadensakkumulation nach Palmgren und Miner (Miner-Regel). Statistische Auswertungen zeigen, dass die Lebensdauerabschätzung nach der linearen Schadensakkumulation im Mittel auf der unsicheren Seite liegt und eine höhere Treffsicherheit wünschenswert ist. Durch die Anwendung effektiver Schadenssummen kann die mittlere Lebensdauerüberschätzung korrigiert werden. Im Einzelfall kann es dennoch zu größeren Abweichungen zwischen Rechnung und Versuch kommen. Zur Verbesserung der Lebensdauerabschätzung mittels linearer Schadensakkumulation werden zwei Lebensdauerkorrekturverfahren vorgestellt. Die Anpassung der rechnerischen Gaßnerlinie an Versuchsergebnisse erfolgt in Abhängigkeit von der Kollektivform und der Wöhlerlinienneigung durch einen Lebensdauerkorrekturexponenten anstatt einer (multiplikativen) konstanten effektiven Schadenssumme. Neben der höheren Treffsicherheit wird der Übergang der Gaßnerlinie in die Wöhlerlinie für Rechteckkollektive sichergestellt.

Multiaxial fatigue – methods, hypotheses and applications

Abstract The present overview covers the fundamentals of multiaxial loading and the state of the art of the theoretical assessment of fatigue strength.

Multiaxial loading and fatigue lifetime in LCF Comparison with simulation results

Abstract Generally, most machine parts are loaded with a combination of different variable forces and moments. This often causes a state of multiaxial stress in the fatigue critical areas of the parts. In most cases, a nonproportional cyclic multiaxial state of stress occurs. Compared to the in-phase loading, a multiaxial loading with a phase difference of 90° between the stress components and a load ratio of γa/∊a = 1.33 (τa/σa ≈ 0.5) between tension/compression and torsion lead to a significant influence on the fatigue lifetime. The reason is the changing direction and ratio of the principal stresses during one cycle. The present research results for constant and variable amplitudes indicate that a phase difference of 90° causes a decreased lifetime compared with proportional loading under strain controlled tests with different ductile materials AlMgSi1 and SAE 1015, while the experimental analysis with magnesium die casting alloy AZ 91 reveals an increase of fatigue life compared with the in-phase loading. The lifetime prediction with a new concept on the basis of microcrack growth is compared with the experimental results.

Abschätzung von zyklischen Werkstoffkennwerten

Kurzfassung Bei der Untersuchung von Stahlfeinblechen wurde ein Näherungsverfahren entwickelt, bei dem das bestehende Kennwertesystem ersetzt und die Neigung der plastischen und elastischen Gerade im Manson-Coffin-Diagramm nicht mehr als konstant angenommen wird. Die „Method of Variable Slopes (MVS)“ benötigt zur Bestimmung der zyklischen Kennwerte lediglich die Zugfestigkeit und den Elastizitätsmodul des Werkstoffes sowie den Vergleichsumformgrad, wenn eine Blechumformung vorliegt. Die Übertragung dieser Methodik auf das „Uniform Material Law (UML)“ führt zu einer Verbesserung der Abschätzung zyklischer Kennwerte von Werkstoffen und Halbzeugen der Datensammlung „Materials Data for Cyclic Loading“ von Boller, Seeger und Bäumel.