A general model for stress‐life fatigue prediction

From several factors that influence the fatigue behaviour of a particular material, the stress ratio or mean stress and the stress concentration factor are of great importance for the structural calculation. Since most components and structural members contain notches that could be sites of fatigue crack initiation, fatigue data from specimens with different forms of notches have to be collected. The collection of such data at various stress ratios or mean stresses is not economic and time‐consuming. Based on the Walker equivalent stress model, a general fatigue life model is presented and tested with 2024‐T3 fatigue data, available in the literature. The Walker model considered only the effect of stress ratio or mean stress on the fatigue behaviour. On the other hand, in the proposed model, the combined effect of mean stress and stress concentration factor on fatigue behaviour is demonstrated. The statistical analysis indicates that the presented model is very efficient to interpolate the fatigue life successfully, thereby reducing both time and cost.     

A practical stress analysis for predicting fatigue limit of metal with axisymmetric complex surface

In order to predict the fatigue limit of a specimen with an axisymmetric complex surface, a practical method to estimate a stress concentration factor (SCF) of its surface was proposed. The roughness is coarse-grained by removing high frequency components and approximated with a parallel row of a local notch and innumerable average notches. Then, the notches are each approximated with the elliptical holes in the infinite plate, and the SCF is calculated approximately by superposing the elastic solutions of the holes. Moreover, FEM analyses were carried out on the various notch models which consist of the local notch and innumerable average notches to examine the application limit of the present method. Then, the validity of the application limit was examined by using the real roughness and the infinite parallel row of the various notches, and it was shown that the present method was available for the real roughness.     

On the development of fatigue failure maps for titanium matrix composites

The purpose of the present article is to demonstrate how fatigue failure maps can be constructed for fiber-reinforced titanium alloys. The maps are constructed using a combination of micromechanical models and experimental measurements of fatigue cracking and fracture. The maps are used to identify the regimes in which various failure mechanisms dominate. Moreover, they provide information about the fatigue life and the critical amount of crack extension at failure. Examples of such maps for a well-characterized titanium matrix composite are presented and used to illustrate the sensitivity of fatigue life and critical crack extension to both the applied stress and the length of pre-existing cracks or notches.     

Verhalten gekerbter Biegeproben aus der Aluminiumlegierung AA7075 im Kurzzeitermüdungsbereich

Prediction on Fatigue Life of Notched Specimens under Cyclic Bending Loading Pulsating 3P‐bending fatigue tests are conducted on edge‐notched specimens of AA7075. Measurements of electrical potential drop across notches were used to determine the number of cycles up to crack initiation. Cyclic material data determined from strain–controlled constant amplitude loading are use in FE‐analyses to the determination time functions of the local stresses and strains at the notch root using non‐linear material model according to Chaboche and Lemaitre. Using these FE computations, the fatigue life is predicted by the equivalent strain approach of the “ASME Boiler and Pressure Vessel Code” and compared with the results of the plastic strain energy approach. It is found that both approaches lead to relatively good predictions.     

Analysis on the Rupture Failure of Railway Cross Rails

In this paper the failure of two railway cross rails that ruptured during a simulation test under alternating load was investigated. The railway cross rails were made of alloy steel. Visual inspection found that the macrofracture surfaces of the ruptured rails were very flat without macroscopic plastic deformation, and there were conchoidal structures on the fractures that were covered with corrosion products. These are the typical macrofracture characteristics of corrosion fatigue cracking. Tensile and impact tests showed that the mechanical properties of the steel plates met the proper specifications. Optical microscopy found the microstructure of the steel also qualified. Macrofracture analysis revealed that the two ruptures originated at the transitional line from flat plane to camber area on the outer surface of the steel plates. Microfracture observations showed that there were some machining notches near the rupture origins. It was concluded that there was localized stress concentration near the transitional line that was caused by machining notches or the transition structure from the flat plane to camber or by both. The localized stress concentration induced the initiation of a fatigue crack under alternating load, which propagated by corrosion fatigue under alternating load in a humid atmosphere.     

A methodology for the fatigue design of notched castings in gray cast iron

Fatigue failures of machine components remain a topic of relevant importance in the industrial world. They usually occur from geometrical features such as holes, notches, corners and grooves, whose actual influence is not well estimated in the design phase. Cast parts made in gray cast iron are typical examples of components difficult to design in fatigue because they are simultaneously characterized by complex geometries and microstructure. In this contribution the issue is discussed starting from the failure analysis of a cyclically pressurized hydraulic component. The work consists of an experimental procedure, i.e. the fatigue characterization of the material on specimens extracted from cast parts, and of a numerical design activity, i.e. the prediction of life time according to the critical distance method [Taylor D. Crack modelling: a technique for the fatigue design of components. Engng Fail Anal 1996;3(2):129-36]. The implication is that cracks and localized damage begin to appear in the microstructure of gray cast iron at sharp notches from the first cycles of loading. In order to obtain a correct prediction, the fatigue design should adopt fracture mechanics arguments to determine non-propagating conditions.     

Fatigue of welded hybrid‐joints

Only for steels up to grade S690QL the well‐known fact is confirmed that the fatigue strength of welded joints is independent of the material. For higher strength steels a remarkable reduction of the fatigue strength is found. Some advice is given for designers in which situations the one or the other of the various approaches for the assessment of the fatigue strength of welds could be applied. In complex, real situations even the highly sophisticated effective notch stress approach might loose its applicability. A new alternative approach is proposed for these situations. It is based on stresses in real notches and an example is presented for the familiar case of a start‐stop position.     

Beeinflussung des Dauerschwingverhaltens gekerbter Proben durch unterschiedlichen Verschleißzustand der zur Kerbherstellung verwendeten Werkzeuge

Influence on the fatigue behavior of notched specimens by different wear and tear of the tools used for producing the notches . In fatigue-specimens of × 5 CrNi 18 9 and Ck 45 notches had been produced by sharp and blunt tools. The fatigue strength of this specimens from austenitic steeel was smaller when the notches had been produced by sharp and blunt tools. The fatigue strength of this specimens from austenitic steeel was smaller when the notches had been produced by sharp tools. Specimens of ferritic steel on the contrary had a greater fatigue strength, when the notches had been produced by blunt tools. Statistical methods had been used for planning and evaluation of the tests. Therefore appear differences in the strength reduction factor ß_k between in conventional manner determined statements and the here calculated ones.     

Local deformation at micro‐notches and crack initiation in an intermetallic γ‐TiAl‐alloy

The relation is studied between crack initiation from micro‐notches in a fully lamellar intermetallic γ‐TiAl alloy and the local strain field. These micro‐notches were introduced using femtosecond‐laser ablation and had dimensions below the average colony size. The specimen under investigation was then subjected to fatigue loading. Continuous monitoring using a travelling optical microscope allowed detecting microcracks at an early stage. Prior to fatigue loading, a sustained load was applied and the local strain field was determined using digital image correlation. This was supplemented by a Finite Element analysis of the notches and their neighbourhood. It was found that a crack was initiated from a notch causing high normal strains in lamella direction, whereas no crack was initiated from notches with high shear strains.     

Fatigue behaviour of laser repairing welded joints

This paper presents a fatigue study in Nd-YAG laser surface repairing welded joints in specimens of two base materials used in mould production. The tests were carried out in a servo-hydraulic machine in tension, under constant amplitude loading, with two stress ratios R = 0 and R = 0.4. Welded specimens were prepared with U notches and filled with laser welding deposits. The fatigue results are presented in the form of S–N curves obtained in welded and non-welded conditions. Complementary measurements of hardness and residual stresses profiles were carried out along the surface of laser welded specimens to understand the observed fatigue behaviour. The melted material was the weaker region, with lower values of hardness and higher tensile residual stresses, presenting also a high number of defects that are potential failure sites. The presence of such defects can explain the relatively poor fatigue strength of the laser repairing joints in comparison to base materials.     

Ermüdungsrißwachstum in Kerben

Fatigue Crack Growth in Notches Nowadays it is wellknown that an important part of the fatigue life time, usually differenciated in crack initiation and crack growth, is often controlled by fatigue crack growth of cracks in notches. An elastic-plastic on the J-integral based crack growth model considering the crack opening and closure phenomenon will be described to determine crack growth of cracks in notches between crack initiation and failure. Experimental results and finite element analysis were used to verify the developed model.     

The theory of critical distances and fatigue from notches in aluminium 6061

Fatigue failure of metal components containing notches, cracks and other defects has been an active research topic for many years because of its important practical and theoretical implications. Recently, Taylor and his colleagues have re‐visited this topic and proposed the theory of critical distance (TCD), which summarizes the early work by Neuber, Peterson and others in a unifying theory and predicts fatigue fracture with the use of a critical distance, L_o. In this paper, an experimental and numerical study of the fatigue of notched and un‐notched 6061 aluminium alloys is used to verify the TCD and some of the limitations of the TCD are discussed on this basis.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

On the Frost–Dugdale plot for non‐propagating cracks

The Frost–Dugdale plot is re‐examined and the subject of the non‐propagation of fatigue cracks is updated to emphasize that fatigue crack closure is the principal factor responsible for the non‐propagation of fatigue cracks which originate at notches. The limitations of the original Frost–Dugdale plot with respect to notch depth are also discussed.     

The effect of anodising on the fatigue performance of self-tapping aluminium screws

Self-tapping aluminium screws are an innovative joining technology for the assembly of lightweight components in industrial scale. It has been established in the past that porous anodic oxide coatings in many cases reduce the fatigue strength of specimens without notches. In the present work, the fatigue behaviour of notched specimens, i.e. self-tapping screws made from aluminium alloys EN AW-6056, 6082 (both in a conventional state and in a fine-grained state produced by equal channel angular pressing – ECAP) and 7068 with and without oxide coatings is examined. The coatings are produced by hard anodising and are necessary for the thread-forming process during assembly. While the coatings do not affect the static tensile strength, they reduce the fatigue strength for the specimens of the 6056 and the 6082 alloy. For the 7068 alloy a slight increase in fatigue strength is discovered on a low load horizon. The scatter of endured fatigue cycles until fracture of specimens is generally reduced by the anodic oxide coatings.     

A simple approximate expression for finite life fatigue behaviour in the presence of ‘crack‐like’ or ‘blunt’ notches

In this note, we explore the possibility of simple extensions of the heuristic El Haddad formula for finite life, as an approximate expression valid for crack‐like notches, and of the ‘Luká? and Klesnil’ equation for blunt notches. The key starting point is to assume, in analogy to the Basquin power‐law SN curve for the fatigue life of the uncracked (plain) specimen, a power law for the ‘finite life’intrinsic El Haddad crack size. The approach has similarities with what recently proposed by Susmel and Taylor as a Critical Distance Method for Medium‐Cycle Fatigue regime. Reasonable agreement is found with the fatigue data of Susmel and Taylor for notches, and in particular the error seems smaller in finite life than for infinite life, where these equations are already used. In these respects, the present proposal can be considered as a simple empirical unified approach for rapid assessment of the notch effect under finite life.     

Analyse der Wirkung von Kerben,Mittel‐ und Eigenspannungen auf die Schwingfestigkeit des hochumgeformten Werkstoffbereichs von Spaltprofilen

Analysis of the effect of notches, mean and residual stresses on the fatigue strength of severely deformed material areas of linear flow split profiles The results of fatigue experiments on specimens extracted from the highly deformed area of linear flow split profiles are presented. The Focus is on the effect of mean stresses and notches, which is influenced by the previous forming process. The residual stress state inside a component as well as inside specimens is described. By numerical analyses considering residual stresses their effect on fatigue life can be analysed. Using Weibulls Weakest‐Link Appoach parameters, which were derived by testing smooth specimen are transferred to notched ones.     

Review of the fatigue strength of welded joints based on the notch stress intensity factor and SED approaches

Several approaches exist for the fatigue strength assessment of welded joints. In addition to the traditional nominal stress approach, various approaches were developed using a local stress as fatigue parameter. In recent times, the N-SIF based approaches using the notch stress intensity at the weld toe or root have been developed. Based on this, the more practical strain energy density (SED) and the Peak Stress approaches were proposed. This paper reviews the proposed design S–N curves of the N-SIF and SED approaches questioning in particular the consideration of misalignment effects, which should be included on the load side of local approaches in order to consider them individually in different types of welded joints. A re-analysis of fatigue tests evaluated for the effective notch stress approach leads to slight changes of the design S–N curves and of the radius of the control volume used for averaging the SED at the notches. Further, on purpose fatigue tests of artificially notched specimens show that the fatigue assessment using a single-point fatigue parameter might be problematic because the crack propagation phase, being part of the fatigue life, is strongly affected by the stress distribution along the crack path that may vary considerably between different geometries and loading cases.     

Fatigue strength of a clutch pedal made of reprocessed short glass fibre reinforced polyamide

The fatigue behaviour of a clutch pedal made of reprocessed short glass fibre reinforced polyamide 6,6 was experimentally investigated and results were compared with tests on the same part made of virgin material. The study concentrated on the differences between the fatigue behaviour of injection moulded parts and standard specimens made of the same reprocessed reinforced polyamide. The different types of loading than in standard specimens resulted into a different fatigue mechanism. Moreover the presence of sharp notches transformed the diffused damage observed in plain specimens into the formation of cracks at few critical locations. This investigation also allowed to evidence that in real parts the role of fibre shortening due to reprocessing is more pronounced because of the more complex shape of the mould cavity, causing a higher degree of fibre breakage during injection moulding, due to the longer and more tortuous path followed by the melt polymer filling the mould cavity. The use of reground material also caused the appearance of defects in pedals, i.e. voids, which diminished the fatigue strength. Nevertheless, the use of a 100% reprocessed material still ensured a high degree of safety and allowed for obtaining parts fully complying with safety specifications.