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The classical Palmgren-Miner (PM) rule, despite clearly approximation, is commonly applied for the case of variable amplitude loading, and to date, there is no simple alternative. In the literature, previous authors have commented that the PMhypothesis is based on an exponential fatigue crack growth law, ie, when da-dN is proportional to the crack size a, the case that includes also Paris law for m = 2, in particular. This is because they applied it by updating the damage estimate during the crack growth. It is here shown that applying PM to the "initial" and nominal (Stress vs Number of cycles) curve of a cracked structure results exactly in the integration of the simple Paris power law equation and more in general to any crack law in the form da-dN = HΔ-han. This leads to an interesting new interpretation of PM rule. Indeed, the fact that PM rule is often considered to be quite inaccurate pertains more to the general case when propagation cannot be simplified to this form (like when there are distinct initiation and propagation phases), rather than in long crack propagation. Indeed, results from well-known round-robin experiments under spectrum loading confirm that even using modified Paris laws for crack propagation, the results of the "noninteraction" models, neglecting retardation and other crack closure or plasticity effects due to overloads, are quite satisfactory, and these correspond indeed very closely to applying PM, at least when geometrical factors can be neglected. The use of generalized exponential crack growth, even in the context of spectrum loading, seems to imply the PM rule applies. Therefore, this seems closely related to the so-called lead crack fatigue lifing framework. The connection means however that the same sort of accuracy is expected from PM rule and from assuming exponential crack growth for the entire lifetime. [ABSTRACT FROM AUTHOR]

The aim of the present work is to investigate the influence of different stress concentration factors (1.09, 1.31, and 2.42) and several R-values on the fatigue behaviour of martensitic steel X10CrNiMoV12-2-2 up to 2 · 109 load cycles at ambient temperature. The tests were performed using an ultrasonic fatigue testing system developed at the authors' institute. The S-N curves of specimens with the lowest investigated stress concentration factor of 1.09 show for both R = −1 and R = 0.5 a flat slope with transition from surface to volume crack initiation at about 1-2 · 107 load cycles. The maximum number of load cycles where fracture occurs increases with increasing R-value. The √area approach by Murakami describes lifetime behaviour within about 4 decades of lifetime and a wide range of load ratios. In case of internal crack initiation at R = −1, the fracture surface contains a fine granular area (FGA) around the inclusion within the typical 'fish-eye' fracture. With increasing notch factor, the fatigue strength up to 2 · 109 load cycles decreases and the slope of the S-N curve becomes steeper in the low cycle fatigue and high cycle fatigue regime, especially for α k = 2.42. In this case, damage at internal defects is suppressed and fatigue cracks are generally initiated at the notch root. [ABSTRACT FROM AUTHOR]

Das Fließstreifenmodell ist ein verbreitetes Hilfsmittel zur Berechnung der zyklischen Rissspitzenöffnungsverschiebung und des Ermüdungsrisswachstums von Strukturen unter isothermer zyklischer Belastung. Im Zuge einer Modellerweiterung kommt das rheologische Masing-Modell zum Einsatz, das aus parallel geschalteten Reihenschaltungen von Feder und Reibelement besteht. Indem den Reibelementen unterschiedliche Fließspannungen zugeordnet werden, kann mit dem Masing-Modell die zyklische Spannungs-Dehnungs-Kurve des Werkstoffs beschrieben werden. Anstelle einer konstanten Fließspannung werden diese verschiedenen Fließspannungen zufällig den einzelnen Elementen, in die die Riss-Ligament-Linie im Fließstreifenmodell unterteilt ist, zugewiesen. Neben einer besseren Modellierung des mechanischen Materialverhaltens ist auf diese Weise die Berücksichtigung mikrostruktureller Aspekte des Ermüdungsrisswachstums möglich, wenn auf die Werte der Fließspannungen im Bereich des frühen mikrostrukturellen Risswachstums Einfluss genommen wird. Zur Untersuchung thermomechanischer Ermüdung werden die Fließspannungen in Abhängigkeit von der Temperatur formuliert. The strip-yield model is a common tool to calculate the cyclic crack tip opening displacement and the fatigue crack growth life of structures in case of isothermal fatigue loading. As part of an extension of the model the rheological Masing model consisting of spring-slider elements connected in parallel is used to describe the material's stress-strain curve. For this purpose, different yield stresses are allocated to the numerous sliding frictional elements. Instead of the usually applied constant yield stress, these different yield stresses are assigned to the elements into which the crack ligament line is divided. Afterwards, these elements are randomly arranged along the crack ligament line. Besides an improved modelling of the mechanical material behavior the consideration of microstructural aspects of fatigue crack growth becomes possible by influencing the values of the yield stresses near the crack initiation site. [ABSTRACT FROM AUTHOR]

The paper investigates the fatigue strength of laser stake-welded T-joints subjected to reversed bending. The fatigue tests are carried out with the load ratio, R ≈ −0.8. The experimental data is firstly analysed using the nominal stress approach and then by the J-integral as the local fatigue strength parameter in the finite element (FE) assessment. The nominal stress approach demonstrated that the fatigue strength of the investigated T-joints is lower than encountered for any other steel joint under reversed tensile loading. The results also showed that the fatigue strength of this joint under the load ratio R ≈ −0.8 increases with respect to R = 0 bending by 22.6% in the case of the nominal stress approach and 13% in the case of the J-integral approach. However, the slopes of the fatigue resistance curves for different load ratios appear very similar, suggesting that the load ratio has an insignificant influence to the slope. In contrast to the similar slopes, the scatter indexes were different. The nominal stress approach shows that the scatter index is 3.4 times larger for R ≈ −0.8 than R = 0 bending. The J-integral approach showed that the scatter index for R ≈ −0.8 is only 67% larger than in the R = 0 case because the weld geometry is modelled in the FE analysis. [ABSTRACT FROM AUTHOR]

Welded assemblies are commonly used in the shipbuilding industry. Because of the combination of stress concentration and cyclic loading, welded joints could be a critical area for fatigue damage. Thus, knowing stress and strain histories at the critical points of the structure is necessary, particularly when a confined plasticity occurs, to determine the fatigue life of welded assemblies. To avoid time-consuming nonlinear finite element analyses (FEA), simplified estimation methods of the elastic-plastic strain/stress can be used. In a previous work, an approach to estimate stress state at critical points was developed and employed in the case of double-notched specimens. The present paper focuses on welded joints in order to validate this strategy with the aim to estimate the fatigue crack initiation life of T-joints. To go further, a parametric approach has been adopted to take into account the local geometries of welded joints and to determine the constraint operator without any FEA. The results predicted by this approach are compared with experimental fatigue results. [ABSTRACT FROM AUTHOR]

ABSTRACT The article presents two-stage fatigue life evaluation of a stiffened aluminium aircraft fuselage panel, subject to ground-air-ground pressure cycles, with a bulging circumferential crack and a broken stringer. As a worst-case scenario, it is assumed that double cracks start at the edge of a rivet hole both in the skin and in the stringer simultaneously. In the first stage, fatigue crack growth analysis is performed until the stringer is completely broken with the crack on the fuselage skin propagating. After the stringer is completely broken, the effect of bulging crack on the fatigue life of the panel is investigated utilizing the stress intensity factors determined by the three-dimensional finite element analyses of the fuselage panel with the broken stringer. It is concluded that bulging of the skin due to the internal pressure can have significant effect on the stress intensity factor, resulting in fast crack propagation after the stringer is completely broken. [ABSTRACT FROM AUTHOR]

ABSTRACT Experimental analyses on the structural response caused by local fatigue damage accumulation in welded details are accomplished to perform failure process and nonlinear effect analysis at different structural levels. The experiment is carried out by using welded compact tension (CT) specimens and a scaled truss specimen, and all of them have a notch at the weld toe to facilitate damage initiation. Cyclic loads are applied to those specimens to generate accumulative fatigue damage, respectively. The process of fatigue accumulation including initiation and propagation of fatigue cracks in the welded detail and resultant structural responses of CT specimens and the truss are measured with integration of multiple testing techniques. Multi-scale experimental results show that microscopic-/mesoscopic-concentrated strain and extension of plastic zone in the vicinity of notch tip are both affected significantly by the fatigue damage accumulation and present appreciable nonlinear behaviour; however, the macroscopic response such as the frequency and stiffness parameters of the welded truss specimen are less sensitive to the low-level fatigue damage. It is concluded that the fatigue failure of the welded truss is a multi-scale progressive process due to fatigue damage trans-scale evolving, in which the local meso-damage firstly affects local strain of plastic zone in the vicinity of the notch tip, and then fatigue damage evolving from meso- to macro-scale affects nonlinear responses of the damaged components; lastly, the fatigue failure could be expected as the results of the propagation of macroscopic fatigue cracks. [ABSTRACT FROM AUTHOR]

ABSTRACT It is a traditional that the fatigue crack growth behavior is sensitive to microstructure in threshold regime, while it is sensitive to R-ratio in Paris regime. Fatigue test is carried out for welded joints of a Q345 steel where the compact tension specimens with 3.8 and 12.5 mm thickness are used, and comparisons of fatigue crack growth behavior between base metal and a few different locations in the welded joint are considered in Paris regime. Welding residual stresses are removed by heat treatment to focus the study on the microstructural effect. It is shown that fatigue crack growth rate (FCGR) in the base metal is not sensitive to R-ratio, but the FCGR increases in the overheated zone, the fusion zone and the weld metal zone with R-ratio increasing. To the low R-ratio, FCGR in the three zones is smaller than that in the base metal, but they approximate the same with base metal under the high R-ratio. The mechanism of fatigue crack growth is analyzed through crack path in microstructures and SEM fractograph. The coarse-grained ferrite in the base metal is of benefit to relaxation of the average stress at the crack tip, and the fatigue crack growth predicts branching and deflection within above different locations in the welded joint. These tortuous crack paths with crack branching and deflection will promote crack closure as well as crack-tip stress shielding and then resulted in higher crack growth resistance. [ABSTRACT FROM AUTHOR]

A technique to in-situ measure the displacements in the vicinity of the crack tip during fatigue crack propagation has been developed. High-resolution images of the crack tip were taken continuously throughout the fatigue load cycles with a scanning electron microscope (SEM), and an image analysis program was used to determine the displacements at different positions with respect to the crack tip. The displacements were then used to determine crack shapes and compliance curves. The measured crack shapes show a general √ r dependence versus the distance to the crack tip. However, close to the crack tip the crack shape is clearly affected by plastic deformation, even in cases when small scale yielding prevails. The compliance curve measurements close to the crack tip can be used to determine the global stress level when the crack surfaces are separated, so that the exact opening and closure stresses can be determined. [ABSTRACT FROM AUTHOR]

A paste comprising fine alumina particles was applied on surfaces of steel plate specimens and a welded joint specimen, and the effects of the paste on restraint and visual detection of fatigue crack growth were experimentally investigated by performing fatigue tests with in situ observations by a harge oupled evice (CCD) microscope and through various kinds of fractographic observations and elemental analyses using an scanning electron microscope (SEM) and an electron probe microanalyser (EPMA). As a result, the crack growth rate in the plate specimen was drastically retarded by the wedge effect of the alumina particles, and a 311% increase in failure life was produced on an average. The restraint of crack opening displacement (COD) value by the wedge materials was estimated by elastic finite element (FE) analyses, and the results were compared with the experimental data. Similar crack growth restraint effects were also observed on the welded joint specimen, producing a 117% increase in failure life. In the fatigue tests of the specimens on which the alumina paste was applied, a remarkable black colour developed in the white alumina paste along the paths of crack propagation, facilitating the visual detection of the cracks. An analysis using an X-ray diffractometer showed that the black matter in the paste consists of fine debris derived from the base metal. [ABSTRACT FROM AUTHOR]

During use, a component or a structure is exposed to variable amplitude loading, which influences the lifetime. Within the scope of this work, systematic investigations of different loading situations are carried out by means of experimental studies (part I) as well as analytical and numerical studies (part II). The experimental investigations show that overloads lead to retardation effects, which are influenced by several factors, e.g. the overload ratio, baseline-level loading, number of overloads or the fraction of mixed mode. In a high–low–high block loading, both retarded and accelerated crack growth can be obtained, which is also influenced, e.g. by the block loading ratio and the length of the block. Moreover, experimental studies have been performed with load spectra, like FELIX/28, CARLOS vertical and WISPER. They have been applied in original form as well as in counted and reconstructed sequences. [ABSTRACT FROM AUTHOR]

In part I, the effects of variable amplitude loadings on the fatigue crack growths were illustrated by means of experimental results. Within the scope of part II, systematic analytical and numerical investigations are presented. Using different analytical concepts it can be shown that the lifetime depends both on the concept used and on the loading sequence. Also, the influence of the parameters that must be fitted by experimental data for all analytical prediction models has been investigated. By means of detailed elastic–plastic finite element simulations it becomes obvious that not only the crack opening caused by large plastic deformations subsequent to overloads and block loadings, but also the stress field in the ligament is an indicator for the retardation effect. If the σy-stresses both at maximum and minimum loading are identical with the σy-stress distribution of an appropriate constant amplitude (CA) loading, one can assume that the interaction effect is annihilated. [ABSTRACT FROM AUTHOR]

The paper presents the results of fatigue crack growth on low-alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one-sided sharp notch were used. The tests were performed under the stress ratios R=−1, −0.5 and 0. The test results were described by the Δ J-integral range and compared with the Δ K stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the Δ J-integral range. [ABSTRACT FROM AUTHOR]

This paper examines fatigue crack paths in coarse-grained magnesium alloys. Visualization of the microstructure by etching and continuous crack monitoring with a microscope provide evidence of the crack-grain interaction at different fatigue crack growth regimes. Near-threshold fatigue crack growth promotes the development of rough surfaces by the activation of single slip mechanisms and crack deflection. TheR-ratio effect on near-threshold results is discussed in the light of the partial crack-closure model. The role of grain boundaries and grain-to-grain crack deflections on fatigue crack growth rates is discussed. [ABSTRACT FROM AUTHOR]

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress-strain curve was used in the energy balance. The near crack tip elastic-plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested. [ABSTRACT FROM AUTHOR]

The behaviour of fatigue growth and cyclic tip deformation of long cracks due to two successive single overloads was investigated both experimentally and numerically. The results show the effect of the ratio of the second and first overloads, and the crack increment between the two overloads. The contributions of both crack tip blunting and residual stress fields were separated and accommodated in a previously developed crack tip deformation parameter, which was utilized to predict the resulting fatigue crack growth behaviour. The following trends were experimentally observed. Should the ratio of the second and first overloads not be less than one, fatigue crack growth rates followed the predictions based on the second overload. Otherwise, either of the following two situations resulted: (1) when the two overloads were closely applied, the second overload caused an initial acceleration in growth rates followed by a behaviour controlled by the first overload; (2) when the second overload was applied after the crack growth had reached its minimum rate due to the first overload, more retardation in growth rate was observed. Based on the model developed in the paper, it is possible to enhance the retardation effect of an overload if this overload is preceded by another overload. This enhancement depends on the ratio of the two overloads and the crack increment between them. [ABSTRACT FROM AUTHOR]

The effect of the load ratio, R, on fatigue crack growth behaviour is analysed on the basis of the recently proposed inelastic discrete asperities model. A wide range of load ratios, both positive and negative, are examined. Particular emphasis is placed on compressive excursions, i.e. negative R loadings. The inelastic discrete asperities model is a micro-mechanical analysis based on the plastic crushing of a single asperity (or multiple asperities) located on the crack face close to the crack tip and under dominantly plane strain conditions. Experimental data have indicated that the primary crack face contacts which obstruct closure are immediately adjacent to the crack tip, although segments of the crack face more distant from the crack tip are not neglected. However, the more distant asperities are a part of the past crack advance history which does not influence current behaviour. By use of this model, it is shown that the effect of the load ratio can be adequately predicted once some baseline information on mechanical material properties and surface roughness is provided. The model also provides useful trend information and explains many of the observed phenomena, e.g. the ‘saturation’ of the compressive underload effects. For a constant applied nominal stress intensity factor range, ΔKnom , it is shown that the effective stress intensity factor range, ΔKeff , initially decreases as the positive R decreases (corresponding to the increasing influence of closure), reaches a minimum around R = 0, and then starts increasing with negative R (corresponding to the plastic crushing of the asperities which reduces closure), eventually reaching a saturation level below ΔKnom . Conversely, for an assumption of a constant ΔKeff , the applied ΔKnom increases as the positive load ratio decreases, reaching a maximum around... [ABSTRACT FROM AUTHOR]