Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

FE‐Festwalzsimulation und Dauerfestigkeitsberechnung festgewalzter Bauteile mit Konzepten der Schwingbruchmechanik

FE‐Simulation of Fillet Rolling and Fatigue life Calculation based on Fracture Mechanics Concepts Fillet rolling is a method which significantly improves the fatigue strength of members. Residual stresses induced in the surface layer during the fillet rolling process are able to retard or prevent crack propagation. For fatigue strength prediction of fillet rolled notched members a fracture mechanics based concept is described. It consists of three parts: • Finite element simulation of the fillet rolling process to calculate the residual stresses • Simulation of residual stress redistribution due to cyclic load • Assessment of fatigue cracks starting from notch roots and propagating under compressive residual stresses by means of fracture mechanics.     

Berechnung der Schwingfestigkeit festgewalzter Kurbelwellen

Predicting the fatigue strength of fillet-rolled crankshafts Since three years Darmstadt University of Technology uses finite element method for simulation of fillet rolling process. Now, together with Daimler-Benz AG, a fracture mechanics based concept has been successfully applied predicting the fatigue strength of fillet-rolled crankshafts. For these parts conventional assessment of fatigue behaviour shows several disadvantages. The new concept reduces time and costs for development and design. It consists of three parts:

• calculation of residual stresses induced by fillet rolling and affected by crankshaft and roller geometry, rolling load and work hardening data of material
• simulation of residual stress redistribution due to cyclic load
• assessment of fatigue cracks starting from notch root and propagating under compressive residual stresses by means of linearelastic fracture mechanics.

     

Crack extension by alternating shear

A comparison of the slip line flow field at the tip of a sharp crack and of a blunted crack shows that a sharp crack can be extended by alternating shear until it becomes blunted. Crack tip blunting is associated with high strain concentration and fracture by hole growth and coalescence. Crack extension by alternating shear has been obtained in fully plastic, plane strain sharply notched, singly and doubly grooved tensile specimens. Electron fractography shows crack extension by alternating shear at the tip of cleavage and fatigue cracks. It is shown that fatigue crack propagation is the result of repeated cyclic crack extension by alternating shear.     

Der Einfluß von Festigkeit und Druckeigenspannungen auf die Wechselfestigkeit von Stählen bei höheren Temperaturen

Influence of Hardness and Comprehensive Residual Stresses on the Fatigue Limit of Steels under Elevated Temperatures The room temperature fatigue behaviour under alternating stresses of bcc steels is characterized by two stationary states existing below two different reversed stress limits: Below the one no crack initiation occurs, below the other no crack propagation can be found even after an unlimited number of stress cycles. The fatigue endurance of unnotched parts is determined by the crack initiation conditions that can be improved by higher hardness of the material. The fatigue strength of notched parts under reversed stresses is decidently determined by the minimum stress required to propagate a crack; this stress can be raised by compressive residual stresses. – At elevated temperatures these two stationary states are not further existent and there are no alternating stress amplitudes that can be endured either without crack initiation or without crack propagation to fracture. Both influencing parameters hardness and compressive residual stresses are dependend on the temperature, this can be explained by Snoek's and by Cottrell's mechanisms and with the temperature depending release of residual stresses corresponding to the temperature sensitive yield point.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

In situ observation of cyclic fatigue crack propagation of SiC-fiber/SiC composite at room temperature

In situ observation of cyclic fatigue crack propagation of SiC-fiber reinforced SiC composite at room temperature has been carried out by laser microscopy. Both smooth (unnotched) and notched specimens are used for tension-tension cyclic fatigue tests. Cracks initiate at the comers of large pores during loading in smooth specimens. In notched specimens cracks are formed at the interfaces between fibers and matrix that are connected to the notch. The balance between the fiber bridging in the wake of propagating crack tip and the breakage of bridged fibers by the degradation of interfaces maintains a steady cyclic crack propagation. Crack propagation rate gradually decreases with time after the maximum load being applied.     

Schwingfestigkeitssteigerung durch Festwalzen

Improvement in Fatigue Properties by Means of Deep Rolling Deep rolling has an almost 60 years old tradition and today it is an important process especially for automobile structural parts. The development of deep rolling was greatly influenced by the Institute of Material Science of the Technical University in Darmstadt. After a short historical review the general mechanism of mechanical strengthening is discussed. Then new experimental results on ductile cast irons and a case hardened steel are given. The improvement in fatigue strength of notched specimens out of these materials is even higher than that observed on steel in previous investigations. However the experiments also indicate that mechanical strengthened parts obviously have no real fatigue limit. Measurements of crack propagation on nodular cast iron specimens show that the propagation rate of cracks in the notch root is extremely reduced by compressive residual stresses. However no real crack arrest could be observed.     

Messung von Festwalzeigenspannungsverteilungen an Bauteilen

Measurement of Deep-Rolling Residual Stress-Distributions on Components In many practical cases surface layers of components are the most heavily stressed material zones. In order to improve the fatigue strength and the wearability of components thermal, thermochemical and mechanical surface treatment methods like induction hardening, case hardening, nitriding, shot peening and deep-rolling are applied for several years. The effect of these methods depends on the increase of strength and on the production of compressive residual stresses in the heavily stressed surface layers. The mechanical processes also affect the surface roughness which may be reduced by choosing suitable process parameters. Due to the mechanical surface treatment by deep-rolling fatigue strength improvements up to 200% are possible [1], and the compensation of the notch effect was observed for notched specimen [2]. In the industry the deep-rolling is applied on e. g. crankshafts, screws, valve shafts and actuation shafts. The direct control of surface layer properties, like residual stresses and hardening, by x-ray measurements on axial sections of the components is presented here as a method for quality insurance of rolled parts. The measuring method may also be used to verify results of FEM-simulations. FEM-simulations are applied to estimate the modification of the residual stresses due to preparation.     

Behaviour of small cracks during their propagation from Vickers indentations in coarse-grain steel: An experimental investigation

In this investigation we look at the influence of the local residual stresses caused by Vickers-pyramid indenting on the initiation and early propagation of small cracks from indentations in coarse-grain martensitic steel. The size of these indentations is comparable to the grain size. Specimens with and without a local residual stress field were tested on a rotary bending machine. A focused ion beam and a scanning electron microscope were used to reveal the influence of those stresses on the location of the cracks’ initiation and the mechanism of the small-crack propagation. The existing local residual stresses assist in the initiation of two cracks at a level lower than the fatigue limit. The early small-crack propagation is gradually obstructed by the residual stress-field configuration until the cracks become non-propagating cracks. At levels higher than the fatigue limit, both cracks succeed in breaking through the compressive stressed domain and link together. From that moment the crack begins to behave as a long crack, penetrating outside the indentation into the tensile-stressed domains.     

Größeneinfluß und Dauerfestigkeitseigenschaften unter Besonderer Berücksichtigung optimierter Oberflächenbehandlung

Size Effect and Fatigue Properties with Respect to Optimized Surface-Treatment. A hyperbolic function describes the geometrical size effect of notched specimens made from heat treated steel. An estimation of fatigue properties of components under one level fatigue tests is possible, if there are comparable materials and surface properties. The fatigue properties of specimens are well described by standardized stress-N graphs. The slope of the stress-N graphs in the range of load cycle depends on the concentration factor and not on the size effect. The fatigue properties of components are largely increased by thermal and mechanical surface strengthening. For the determination of the improvement of fatigue properties it is important to known the initiation of cracking. The improved fatigue properties of inductive surface hardened smooth specimens can be explained by the initiation of cracking below the surface. Mechanically strengthened notched specimens start cracking on the surface. The increase of fatigue properties for these specimens is explained by compressive residual stresses. The fatigue properties of notched specimens can be improved by the optimisation of mechanical strengthening, to higher values than for smooth surface strengthened specimens. This is due to compressive residual stresses. They decrease the tensile stresses which are responsible for crack propagation. If the tensile stress is below fatigue limit for initiation of cracking the crack arrests immediately.     

Two-phase crack propagation approach to fatigue life prediction of preloaded notched members

Experiments with preloaded notched members of 2024-T3 aluminum alloy have shown that preloads in a wide range, even including those which create overall yielding, increase the fatigue lives of the members. Evidence suggests that the extended fatigue life is primarily due to the residual compressive stress generated at the notch root which retards the propagation of small cracks. The finite-element method (FEM) was employed to evaluate the residual compressive stress at preloaded notches. Prediction of fatigue lives of preloaded notch specimens was based on the crack propagation with two phases: small-crack propagation within the notch stress field resulting from the preloads and crack propagation outside the notch field. The effective stress-intensity-factor range for small cracks was calculated using the local stress at the notch field obtained by FEM. The theoretical values based on this model are in good agreement with experimental data.     

Festwalzen und Schwingfestigkeit

Deep Rolling and Fatigue Strength The fatigue properties of specimens and components are largely increased by deep rolling. Depending on geometrical shape of components and material strength the compressive residual stresses and the increased surface hardness made by deep rolling have a different effect on the improvement of fatigue strength. The fatigue properties of smooth specimens and components with a sufficient toughness can be raised by increase of surface hardness, whereas in case of notched parts the influence of permanent compressive residual stresses is dominant. The application of deep rolling in case of crankshafts shows a clear superiority of mechanical strengthening procedure to thermal surface strengthening. If there are some reasons to improve the wear behaviour beside the fatigue strength it is commendable to combine thermal and mechanical surface strengthening.     

Experimental evaluation of the effect of residual stress field on crack growth behaviour in C(T) specimen

The effects of the residual stress field resulting from shot peening and the indentation technique were investigated in relation to fatigue crack closure and crack growth behaviour. Compact Specimens of 20NiCrMo2 were used in this investigation. The regions of residual stress field were located behind the fatigue crack tip. Crack closure behaviour was measured with back face strain and crack mouth opening displacement gauges. Crack length was monitored by the compliance and microscopic methods. Residual stress was measured by the incremental hole-drilling method. Subsequently the closure level, propagation rate and resulting crack growth retardation were studied. Crack closure and attendant growth retardation were shown to be dependent on the residual stress field. Residual stresses produced by shot peening and indentation were both compressive. The maximum value of residual stress for both operations were on the surface and at the same intensity. However, the residual stress induced by the indentation technique was deeper. The results showed that the closure effect was stronger in the case of indentation technique.     

Evaluation of fibre bridging stress of short fatigue cracks in SCS-6/Ti-15-3 composite

Single‐edge notched specimens of a unidirectional SiC long fibre reinforced titanium alloy, were fatigued under four point bending. The propagation behaviour of short fatigue cracks from a notch was observed on the basis of the effects of fibre bridging. The branched fatigue cracks were initiated from the notch root. The fatigue cracks propagated only in the matrix and without fibre breakage. The crack propagation rate decreased with crack extension due to the crack bridging by reinforced fibres. After fatigue testing the loading and residual stresses in the reinforced fibres were measured for the arrested cracks by the X‐ray diffraction method. The longitudinal stresses in the reinforced fibres were measured using high spatial resolution synchrotron radiation. A stress map around the fatigue cracks was then successfully constructed. The longitudinal stress decreased linearly with increasing distance from a location adjacent to the wake of the matrix crack. This region of decreasing stress corresponded to the debonding area between the fibre and the matrix. The interfacial frictional stress between the matrix and the fibre could be determined from the fibre stresses. The bridging stress on the crack wake was also measured as a function of a distance from a notch root. The threshold stress intensity factor range, corrected on the basis of the shielding stress, was similar to the propagation behaviour of the monolithic matrix. Hence the main factor influencing the shielding effect in composites is fibre bridging.     

Impact of slide diamond burnishing additional parameters on fatigue behaviour of 2024‐T3 Al alloy

One of the methods for increasing fatigue life of symmetric rotary metal components is slide diamond burnishing (SDB). This method is implemented on conventional and computer numerical control machine tools by means of simple equipment, which is its main advantage. The SDB basic parameters are diamond insert radius, burnishing force, feed rate, and burnishing velocity. The additional ones are number of passes, working scheme, and lubrication conditions. The effect of SDB additional parameters on the fatigue behaviour of 2024‐T3 Al alloy was experimentally studied. Groups of smooth and notched hourglass‐shaped specimens were slide burnished using different combinations of additional SDB parameters and then were subjected to bending fatigue tests. The residual stresses, introduced by SDB, were measured by X‐ray diffraction technique. The near‐surface microstructure of the slide‐burnished specimens was investigated. Based on the results obtained, it was established that SDB produces two main effects, which depend on SDB additional parameters. The essence of the macroeffect is creation of residual compressive stresses in the superficial and subsurface layers. This stresses retard the formation and growth of fatigue macrocracks and thus increase the lifetime of slide‐burnished components. The microeffect is expressed in modifying the microstructure of the surface and subsurface layers, correspondingly, refining the grain and homogenizing and reducing the pores in the material. Such microstructure is characterized by increased plasticity and fatigue crack resistance. The fatigue life depends on the combination of these two effects. Thus, the desired fatigue behaviour of the slide‐burnished component can be ensured through an appropriate selection of the governing additional SDB parameters.     

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.     

Experimental Investigation Into the Fatigue of Welded Stiffened 350WT Steel Plates Using Neutron Diffraction Method

Abstract: The propagation of fatigue cracks under constant amplitude cyclic loading was studied in welded stiffened steel plates. The residual stresses in the stiffened plates were measured using the neutron diffraction strain‐scanning technique. The neutron diffraction measurements indicated that, in general, the residual stresses were tensile near the welded stiffeners and compressive between the stiffeners and ahead of the starter notch tips. Fatigue testing indicated that the fatigue crack growth rates of the stiffened plates were, in general, lower than that of a corresponding unstiffened plate, especially near the notch tips, where compressive residual stresses existed. An analytical method, using Green's function, was developed to predict the fatigue crack growth rates. Reasonable accuracy was obtained.     

Fatigue crack propagation into the residual stress field along and perpendicular to laser beam butt‐weld in aluminium alloy AA6056

Laser beam butt welds in Al‐alloys are very narrow and are accompanied by steep residual stress gradients. In such a case, how the initial crack orientation and the distance of the notch tip relative to the weld affect fatigue crack propagation has not been investigated. Therefore, this investigation was undertaken with two different crack orientations: along the mid‐weld and perpendicular to the weld. Fatigue crack propagation ‘along the mid‐weld’ was found to be faster in middle crack tension specimens than in compact tension specimens. For the crack orientation ‘perpendicular to the weld’, the relative distance between the notch tip and the weld was varied using compact tension specimens to generate either tensile or compressive residual stresses near the notch tip. When tensile residual stresses were generated near the notch tip, fatigue crack propagation was found to be faster than that in the base material, irrespective of the difference in the initial residual stress level and whether the crack propagated along the mid‐weld or perpendicular to the weld. In contrast, when compressive weld residual stresses were generated near the notch tip, fatigue crack arrest, slow crack propagation, multiple crack branching and out of plane deviation occurred. The results are discussed by considering the superposition principle and possible practical implications are mentioned.