Fatigue strength of rolled JIS SM50A beams

The fatigue strength of rolled beams with stiffeners welded to the web was examined. The state of residual stress in these beams was varied by different cooling and straightening processes. Parallel series of tests were carried out both on plate specimens with corner-notches, simulating the edge notches in the beam-flange tip, and on fillet welded specimens. These test results were analysed using the fracture mechanics concepts of stable crack growth. A new fracture mechanics model for cracks originating from notches is proposed. This is based on the concept that the cyclic plastic zone size at the root of a notch determines the equivalent size of the notch as a fatigue crack. With this model, the severity of notches as well as their size can be taken into account to describe the initial flaw conditions. With the initial crack size estimated, a theoretical crack-growth equation was derived from the fatigue test data of rolled beams and notched plates. The analysing method together with the derived relationship was applied for the evaluation of the fatigue strength of welded beams and transverse fillet welds. The effect of residual stresses on fatigue behavior of these beams and plate specimens was also estimated by assuming an additional effect of the maximum stress on the theoretical crack-growth equation.     

Vorhersage der Schwingfestigkeit von Schweißverbindungen auf der Basis des statistischen Größeneinflusses

Prediction of the fatigue strength of welded joints based on the statistical size effect With increasing length of welding seams the fatigue strength decreases. This effect is confirmed in fatigue tests on butt joints and cruciform joints. The influence of the length of the welding seam on the fatigue strength depends on the scatter of the parameters describing the geometry of the welding seam. The theory of the statistical size effect worked well in fitting and predicting the test results. The fatigue strength of welded joints is well predicted, if no other influences like e. g. residual stresses change the fatigue strength. Additionally a method for the calculation of crack propagation is proposed, which takes in account angular and linear misalignement as well as local changes of the geometry of the welding seam.     

Fatigue strength of carbon steel specimens having an extremely shallow notch

In order to elucidate how the principal dimensions of a notch as small as grains affect the fatigue strength of carbon steel, rotating bending fatigue tests were carried out on annealed 0.45% C steel specimens having an extremely small artificial notch whose depth is either 5 or 10μm. The fatigue processes at notched parts were observed successively.In these extremely shallow notches, the parameter controlling fatigue limits for fracture σ_w was the notch depth, independently of notch sharpness. On the other hand, the crack initiation limits in the notches σ_W1 were determined by a single K_tσ_W1 — χ relation obtained from the tests on ordinary notches, where K_t is the stress concentration factor and χ is the stress gradient at the notch root.These results were studied on the basis of the characteristics of crack initiation process, the stress intensity variations at the crack tip and the stress distribution near the notch root.     

Fatigue Strength Assessment of Laser Beam Welded Joints Made of AA7075 and Magnetic Pulse Welded Joints Made of AA7075 and 3D-Printed AlSi10Mg

The use of 7000 aluminum alloys has an important role in future lightweight structures in the field of mobility due to the low density and high strength. However, these alloys can only be fusion welded to a limited extent because welding defects can rarely be prevented. For this reason, investigations are carried out to identify the most suitable welding parameters for two processes: laser beam and magnetic pulse welding. Herein, laser beam welding is successfully used to manufacture a roll-formed and longitudinally welded pipe made of AA7075 and joined by magnetic pulse welding with a 3D-printed lug-tube made of AlSi10Mg. The fatigue strength of these pipe joints and of laser beam welded butt joint specimens is determined using load-controlled fatigue tests. For the characterization of the specimens, cross sections are prepared and examined metallographically, which reflect the local weld seam geometry in the joining area. A fatigue assessment is made using linear-elastic approaches. The reference radius concept is applied to map the influence of geometric notches on the fatigue strength, assuming linear-elastic stress–strain behavior. It is shown that the recommended notch stress fatigue class FAT 178 (von Mises stress) can be applied for a safe and reliable fatigue assessment.     

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.     

A stress-based method to predict lifetime under multiaxial fatigue loadings

This paper extends to low/medium‐cycle fatigue a stress‐based method recently proposed by the same authors for high‐cycle multiaxial fatigue assessments. By considering the plane of maximum shear stress amplitude coincident with the microcrack initiation plane, the method requires the calculation both of the maximum shear stress amplitude and the maximum normal stress relative to the same plane. Multiaxial fatigue life estimates are made by means of bi‐parametric modified Wöhler curves, which take into account the mean stress effect, the influence of the out‐of‐phase angle and the presence of notches by using a generalization to multiaxial fatigue of the fatigue strength reduction factor K_f. Approximately 700 experimental data taken from the literature are used to demonstrate that the method is a useful tool to summarize fatigue strength data of both smooth and notched components, subjected to either in‐phase or out‐of‐phase loads. Finally, a simple practical rule for the calculation of the multiaxial fatigue strength reduction factor is proposed.     

NON-DAMAGING NOTCHES IN FATIGUE*

The fact that very small notches (cavities, holes, scratches, etc.) have no effect on the fatigue limit of metallic materials is well known. This paper presents both a qualitative explanation for the existence of non-damaging notches and a quantitative derivation of their critical sizes. The condition for a notch (characterized by the stress concentration factor K_t and the notch root radius ρ) to be non-damaging in a metallic material (characterized by a critical crack size l₀) is (K²_t? 1)ρ≤ 4.5 l₀. The critical crack size can be expressed with good approximation in terms of the threshold stress intensity for fatigue crack growth and the plain fatigue limit. Therefore the above relation can be applied for an engineering evaluation of non-damaging notches. Test results obtained for copper and a pressure vessel steel demonstrate the applicability of the proposed method.     

Fatigue limit evaluation of notches,small cracks and defects: an engineering approach

In this paper, the average stress method for the fatigue limit evaluation of stress raising geometrical features is revised and extended. In particular, an analytical close‐form approach was used and the linear elastic stress equations were modified by taking into account the effect of nominal stress on the local stress distribution. Hence, the average tangential stress was correctly evaluated over a distance of 2a₀, where a₀ was El Haddad's short crack constant, for long and small notches as well as for crack‐like notches. When this model is applied to a wide range of geometrical features subjected to mode I fatigue loading, the classical shape of the curves of the Kitagawa–Takahashi diagram was obtained for changes in crack‐like notch size. Similarly, notch sensitivity was estimated by reducing the notch tip radius. The accuracy of the proposed method in predicting fatigue limits was then checked by using experimental data taken from the literature and generated on testing specimens weakened by rounded and sharp notches as well as by small artificial defects.     

NOTCHED FATIGUE BEHAVIOUR OF TWO COLD ROLLED STEELS

Abstract— A SAE1010 plain carbon steel and a SAE945X HSLA steel were cold rolled to various thickness reductions. Centre notched specimens were tested under stress control at a stress ratio of—1. The effect of loading direction on the fatigue strength was examined. The notched specimen fatigue strength was only slightly increased by cold rolling, since two opposing factors: the smooth specimen fatigue strength and the notch sensitivity, were increased by cold rolling. The notched specimen fatigue strength in the transverse direction was approximately the same as that in the longitudinal direction. An empirical equation and equations derived from fracture mechanics and Neuber's rule were applied to predict the fatigue notch factor for the sharp and blunt notch geometries examined. A reasonable agreement between the predictions and the experimental results was observed for the sharp notches. For the blunt notches, the predicted fatigue notch factors were conservative.     

High‐strength steel wires containing corrosion pits: stress analysis and critical distance based fatigue life estimation

The present paper deals with the problem of assessing the fatigue lifetime of high‐strength steel wires containing corrosion pits, with this investigation being based on a large number of experimental data selected from the technical literature. To evaluate the stress concentration phenomena characterising corroded metallic wires, according to the state‐of‐the‐art knowledge, pits were modelled either as semi‐ellipsoidal cavities or as hemispherical notches. The stress concentration factors, K_t, associated with these simplified pit geometries were calculated numerically by solving numerous three‐dimensional FE models. Subsequently, the K_t values being determined according to this standard numerical procedure were post‐processed systematically to derive simple analytical solutions suitable for estimating, in situations of engineering interest, the stress concentration factors associated with pitting corrosion. Finally, after making some assumptions to derive the necessary fatigue properties, the Theory of Critical Distances was used in the form of the Point Method and the Line Method to reanalyse the literature data being collected. This systematic validation exercise allowed us to prove that the Theory of Critical Distances is successful also in assessing the fatigue lifetime of high‐strength metallic cables containing corrosion pits, with the obtained estimates falling within an error factor of 3. Therefore, as far as wires weakened by corrosion pits are concerned, it was demonstrated that the Theory of Critical Distances can be used to post‐process the local linear‐elastic stress fields when they are not only determined numerically but also estimated by using those standard analytical solutions which are strictly valid solely for conventional notches.     

Fatigue behavior of friction stir welded Al–Mg–Sc alloy

The effect of Friction Stir Welding on the fatigue behavior of Al–Mg–Sc alloy has been studied. To reveal the influence of the welding parameters, different travel speeds of the welding tool have been used to provide weld seams with varying microstructural features. Crack initiation as well as crack propagation behavior under fatigue loading has been investigated with respect to the local microstructure at the crack initiation sites and along the crack path. Fatigue cracks were mostly initiated around the stir zone and the adjacent thermo-mechanical affected zone independent from hardness distributions in the weld seams. In some specimens, defect-like feature was observed at the crack origins, which shortened the fatigue lives. It has been found that while the effect of the tool travel speed on the fatigue lifetime seems to be little, the varying and complex local microstructure in the weld seam basically affects both the crack initiation sites and the crack propagation paths.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Residual stresses analysis of ND-YAG laser welded joints

Laser deposit welding based on modern ND-YAG lasers is a new mould repair process with advantages relatively to the traditional methods (micro-plasma and TIG methods), namely deposition of small volumes of the filler material without distortion. Residual stresses play a major role on the fatigue and thermal–mechanical fatigue behaviour of welds. This paper presents the experimental results and numerical predictions of the residual stresses in joints manufactured with two hot-working tool steels: X.40.CrMoV.5.1 and 40.CrMnNiMo.8.6.4, in the laser-deposited layer and in the heat-affected zone. Welded specimens were prepared with U notches and filled with ND-YAG laser welding deposits. Trough-depth residual stresses evaluation after laser deposit welding were performed in order to analyse the influence of the residual stress state on fatigue behaviour of mould steels. Both X-ray diffraction sin²γ method (XRD) and incremental hole-drilling technique (IHD) were used in residual stress measurement. Numerical predictions of the residual stress distributions were obtained for several values of the technologic parameters, compared with experimental results and discussed based on the assumptions stated.     

Werkstoffauswahl für schlagartig und zyklisch belastete metallische Bauteile

Material Selection for Impact and Fatigue Loading The structural durability of components is dominated mainly by the geometry, i.e. notches. Compared with the impact resistance of forged components from ductile materials high impact values can be realized by an appropriate shaping also using less ductile cast materials. Creep deformations can be suppressed in presence of notches. The strength level of the base material remains for stress concentrations above K_t = 2.5 and for the welded state without influence on the fatigue behaviour. If sharp notches cannot be avoided by a new design, benefits from high‐strength materials can be taken only in connection with surface treatments which introduce high compressive residual stresses. Principally, advantages from high‐strength materials can be gained for unwelded components only by reduction of the stress‐concentration and in case of welded joints by smoothening or removal of the weld notches and in case of spot welds by transferring of the failure location outside of the nugget.     

Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects

The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of r_ref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW).On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length.     

Mean stress and plasticity effect prediction on notch fatigue and crack growth threshold,combining the theory of critical distances and multiaxial fatigue criteria

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σ_fl,R = ?1/σ_YS, such as 7075‐T6 (σ_fl,R = ?1/σ_YS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σ_fl,R = ?1/σ_YS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD.     

Generalised Neuber concept of fictitious notch rounding

The microsupport effect at sharp notches subjected to high-cycle fatigue can be described according to Neuber by averaging the maximum notch stress in a small material volume (microsupport length ρ^*) at the notch root (radius ρ). The averaged stress may be expressed by the maximum stress of a corresponding notch of an enlarged, fictitious radius, ρ_f = ρ + sρ^*, where s is the microsupport factor. The status of Neuber’s concept within his general theory of notch stresses is reviewed, followed by more recent theoretical and application-relevant developments. The theoretical developments refer to the notch angle dependency of the support factor, to its value for pointed versus rounded notches and to in-plane shear loading with out-of-bisector crack propagation. The application developments refer to the fatigue assessment of welded joints.     

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.     

Fatigue life prediction for stainless steel welded plate CCT geometry based on Lawrence''s local-stress approach

In the present study, the effect of welding process and procedure on fatigue crack initiation from notches and fatigue crack propagation in AISI 304L stainless steel welds was experimentally investigated. Full penetration, double-vee butt welds have been fabricated and CCT type specimens were used. Lawrence's local-stress approach (a two-stage model) is used to predict the fatigue life. The notch-root stress method was applied to calculate the fatigue crack initiation life, while the fatigue crack propagation life was estimated using fracture mechanics concepts. The fatigue notch factor is calculated using Lawrence's approach. Constant amplitude fatigue tests with stress ratio, R=0 were carried out using 100 kN servo-hydraulic DARTEC universal testing machine with a frequency of 30 Hz. The predicted lives were compared with the experimental values. A good agreement has been reached. It is found that the weld procedure has a stronger effect on lives to initiation than on propagation lives.