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.     

GROWTH OF FATIGUE CRACKS EMANATING FROM NOTCHES IN SiC PARTICULATE ALUMINUM COMPOSITE

Abstract— The initiation and growth of cracks emanating from blunt notches in 6061-Al alloy reinforced with 25% particulate Sic metal matrix composite were investigated. To elucidate the role of aging condition of the matrix on the fatigue behavior, the studies were carried out at T6 and overaged conditions. The results show that the number of cycles required for initiation of fatigue cracks are not influenced with the notch severity and the aging condition of the matrix. The overaging heat treatment resulted in slower fatigue crack growth rates. The failure of the Sic particles during the fatigue process is given as the reason for the both observed initiation and crack growth characteristics. It is also shown that the growth rate of cracks emanating from blunt notches can be accurately described by an equivalent stress intensity factor range Δ K _eq. This could provide an adequate engineering method for design against fatigue failure from various stress concentrations for this composite system.     

Vorhersagemodell für die Wachstumsraten kurzer Risse auf der Basis von Kmax‐konstant‐Versuchen an M(T)‐Proben

Prediction model for the growth rates of short cracks based on K_max‐constant tests with M(T) specimens The fatigue crack growth behaviour of short corner cracks in the Aluminium alloys Al 6013‐T6 and Al 2524‐T351 was investigated. The aim was to determine the crack growth rates of small corner cracks at stress ratios of R = 0.1, R = 0.7 and R = 0.8 and to develop a method to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T)‐specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The pre‐cracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a Focussed Ion Beam. The results of the fatigue crack growth tests with short corner cracks were compared with long fatigue crack growth test data. The short cracks grew at ΔK‐values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK‐values and the same stress ratios. A model was developed on the basis of K_max‐constant tests with long cracks that gives a good and conservative prediction of the short crack growth rates.     

Studies on fatigue crack growth for airframe structural integrity applications

A review is made of efforts at the National Aerospace Laboratories in the development of fatigue crack growth prediction technology for airframe applications. The research was focused on extension of rainflow techniques for crack growth analysis and development of accelerated crack growth calculation methods for spectrum loading. Fatigue crack closure forms a crucial element of modelling and fractographic techniques were developed for its study. These, combined with binary coded event registration enabled crack growth and closure mapping for part-through cracks in metallic materials. Experimental research on short cracks at notches led to discovery of the hysteretic nature of crack closure, which explains well-known history-sensitive local mean stress effects in notch root fatigue. Optical fractography of failures obtained under simulated service conditions revealed that short cracks do not exhibit any more scatter than long cracks at comparable growth rates. The nature of multi-site crack initiation and growth of small cracks at notches was investigated and the effort extended to lug joints that are widely used in airframe applications. Results from this work suggest the possibility of modelling crack growth from a size smaller than 50 microns through to failure, thereby accounting for a major fraction of total life. The work described in this paper enjoyed the strong support of Dr S R Valluri, Prof R Narasimha and Dr K N Raju. Financial support for the effort was provided by Aeronautical Research & Development Board, Aeronautical Development Agency and Department of Science and Technology.     

Prediction of non propagating cracks

An explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop. Predicted lengths of these cracks based on solutions for the intensity factor are in good agreement with the experimental data. Intensity factor trends for cracks in notches are shown to vary from an initial decrease to a minimum value followed by an increase and eventual convergence with the trend for the equivalent long crack for sharp notches to the blunt notch curves that continuously increased during their approach to the long crack trend. The type of trend exhibited by a given notch depends both on notch geometry and notch size. In blunt notches the maximum value of the threshold stress for crack propagation is at initiation. However, for sharp notches the peak value of the threshold stress vs crack length curves shifts to a finite length. Stresses above the initiation level but below this peak stress level result in fatigue cracks which start but do not propagate to failure. Predicted values of the fatigue limit stresses for a variety of sizes in a circular and an elliptical notch are in good agreement with experimental results.     

Fracture mechanics of surface fatigue crack growth by ductile striation space measurement in notched Waspaloy

Ductile striation space (DSS), a parameter to predict actual cracks in both direction of length and depth, is proposed for the surface fatigue crack behaviors on notched Waspaloy. Three different lengths (1, 2 and 4 mm) of artificial notches are formed as the initial surface crack for an applied maximum stress of 1,103 MPa at the stress ratio R of 0.05. These notches are similar with the appearance of the surface cracks found from the survey of compressor disk. The results show that, all initial crack sites in the depth direction started from the multiple origination sites. The DSS parameter was clearly confirmed, and it also proves the high effectiveness of the measurement in the range of the stress intensity factors for acquiring the crack growth rate on the fractured surface. The surface cracks on Waspaloy at room temperature in an atmosphere perfectly follow the relation of ΔK versus da/dN and db/dN, even though there are, respectively, earlier and later timing differences on the initiation of cracks for the notch sizes of 1 and 4 mm. The results of ΔK versus da/dN and db/dN relations show a similar slope for three different kinds of notches.     

Fatigue and fracture of a Ni–P amorphous alloy thin film on the micrometer scale

Fracture and fatigue tests have been performed on micro‐sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm³, approximately 1/1000th the size of ordinary‐sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro‐sized specimens. In fracture toughness tests, fatigue pre‐cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro‐sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro‐sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro‐sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro‐sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, K_IC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro‐sized specimens to satisfy these requirements. Plane‐stress‐ and plane‐strain‐dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro‐sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.     

Short crack initiation and growth at 600 °C in notched specimens of Inconel718

The natural initiation and growth of short cracks in Inconel®718 U-notch specimens has been studied at 600 °C in air. U notches were introduced through broaching, and hardness traces and optical microscopy on cross-sections through the U notch broaching showed that the broaching process had introduced a deformed, work hardened layer. Fatigue tests were conducted under load control using a 1-1-1-1 trapezoidal waveform, on specimens with as-broached and polished U-notches. Multi-site crack initiation occurred in the notch root. Many of the cracks initiated at bulge-like features formed by volume expansion of oxidising (Nb,Ti)C particles. In unstressed samples, oxidation of (Nb,Ti)C particles occurred readily, producing characteristic surface eruptions. Scanning electron microscopy on metallographic sections revealed some sub-surface (Nb,Ti)C oxidation and localised matrix deformation around oxidised particles. A mechanism for crack initiation by carbide expansion during oxidation is discussed. Surface short crack growth rates in the notch root of polished specimens were measured using an acetate replica technique. Observed short-crack growth rates were approximately constant across a wide range of crack lengths. However, there was a transition to rapid, accelerating crack growth once cracks reached several hundred micrometers in length. This rapid propagation in the latter stages of the fatigue life was assisted by crack coalescence. Polishing the U-notch to remove broaching marks resulted in a pronounced increase in fatigue life.     

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.     

Initiation and growth behaviour of small internal fatigue cracks in Ti‐6Al‐4V via synchrotron radiation microcomputed tomography

Small internal fatigue cracks initiated in Ti‐6Al‐4V in the very high cycle regime were detected by synchrotron radiation microcomputed tomography (SR‐μCT) at SPring‐8 in Japan. The initiation and growth behaviours of the cracks were nondestructively observed, and the da/dN‐ΔK relationship was measured and compared with that obtained in a high vacuum environment. SR‐μCT revealed that more than 20 cracks were initiated in one specimen. The crack initiation life varied widely from 20% to 70% of the average fatigue life and had little influence on the growth behaviour that followed. The initiation site size of each internal crack detected in one specimen was comparable with the size of the fracture origins obtained in ordinary fatigue tests. These results suggest that the surrounding microstructures around the initiation site are likely a dominant factor on the internal fracture rather than the potential initiation site itself. The internal crack growth rates were lower than 10^?10 m/cycle, and extremely slow rates ranging from 10^?13 to 10^?11 m/cycle were measured in a lower ΔK regime below 5 MPa√m. The internal crack growth rate closely matched that of surface cracks in a high vacuum, and the reason for the very long life of internal fatigue fractures was believed to result from the vacuum‐like environment inside the internal cracks.     

Creep–fatigue crack growth behaviour based on EBSD observations for notched specimen made of directionally solidified Ni-base superalloy

Abstract

In order to characterise the creep–fatigue crack growth behaviour of a directionally solidified Ni-base superalloy, an investigation into damage behaviour based on the electron backscattered diffraction (EBSD) method using notched specimens has been carried out. The average misorientation in the vicinity of notches increases linearly up to the initiation of cracks with the increasing creep strains under creep or creep–fatigue conditions, whereas under fatigue conditions fatigue cracks grew without an increase in misorientation. The stress holding time clearly influenced the growth behaviour of creep–fatigue cracks and the appearance of misorientation development. However, it was shown that the relationship between the average misorientation and the relative notch opening displacement was independent of test conditions such as temperatures, stresses and stress wave forms.

It is concluded that the misorientation analysis of damaged samples based on the EBSD method allows the prediction of the initiation of creep–fatigue cracks and their growth behaviours.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

The effect of bi-modal and lamellar microstructures of Ti-6Al-4V on the behaviour of fatigue cracks emanating from edge-notches

This paper is aimed at evaluating the influence of bi‐modal and lamellar microstructures on the behaviour of small cracks emanating from notches in α+β titanium Ti‐6Al‐4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on double‐edge‐notched specimens. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 88 and 58% of the 0.2% material yield stress. Crack closure effects were measured by an extensometric technique and discussed. Variations in crack aspect ratio were determined and considered in the ΔK calculation. Corresponding results were discussed by considering the effect of the yielded region at the notch tip calculated by elastic–plastic finite element modelling of the fatigue tests. The importance of the bi‐modal and lamellar microstructures on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. The crack growth rate data obtained were compared with those measured using standard C(T) specimens (long crack).     

ESTIMATING INITIATION TIMES OF SECONDARY FATIGUE CRACKS IN DAMAGE TOLERANCE ANALYSIS

Abstract— Fatigue cracking of complex structure often involves several interacting cracks developing in a sequence of crack growth, arrest and reinitiation. A "combined" method of damage tolerance analysis is presented which employs fracture mechanics concepts to calculate crack growth and fatigue data from notched coupons with the appropriate notch radius for the crack initiation phase. The notched coupon data, plotted as peak elastic notch stress vs cycles to crack initiation, are shown to be applicable even when limited yielding occurs at the notch root. For several practical reasons it is recommended to select the initial crack size, a _i, for the crack growth phase to be as large as possible, but in accord with two selection criteria. First, a _i, must be within a notch-root region wherein the elastic stress distributions near a variety of notches are virtually identical. Secondly, a _i must be small enough not to significantly influence the stress distributions for other cracks. The Combined Method is illustrated by means of an example involving fatigue crack growth along a widthwise row of holes in 305 mm wide test panels.     

AN APPROACH TO MEASURE THE SHAPES OF THREE-DIMENSIONAL SURFACE CRACKS DURING FATIGUE CRACK GROWTH

This study presents a technique for measuring shapes of three dimensional surface cracks continuously during fatigue crack growth. The technique uses a laser interferometric system to measure crack compliance and a photomicroscopic system to measure surface crack length. Using a compliance expression for surface cracks, valid for the range of crack aspect ratios (a/c) of 0.2 to 2.0, aspect ratio calculations employing compliance and surface crack length measurements are demonstrated for cracks growing from EDM notches of different geometries (shallow or deep). The experimentally determined aspect ratio variations during cyclic crack growth are shown to be in good agreement with the expected variations in aspect ratio, predicted using the stress intensity factor equations for surface cracks. The effects of deviations in the compliance measurement location from the center of the surface crack due to assymetric crack growth are also accounted for through corrections of compliance measurements for crack-asymmetry. The fatigue crack growth rates of surface cracks, after incorporating the variations in aspect ratio in the calculations, agreed with the large-crack growth data for all crack geometries.     

Behavior of short fatigue cracks initiated from a notch in 8090 Al-Li alloy

The rates of growth of short fatigue cracks initiated from a notch are much greater than the rates of growth of long fatigue cracks for the same values of K. A decrease in the strength of materials caused by aging affects the behavior of long cracks. The geometric form of the notch strongly affects the behavior of short cracks. The growth rate of a short crack initiated from a sharp notch decreases and attains a minimum value at a length of 0.45 mm, which is far beyond the region of its influence. However, short cracks initiated from blunt notches exhibit slower growth in the region of stress concentration than outside this region. Strain fields induced by deformation of the tip of the notch are not the only factor inhibiting the propagation of short cracks from notches. To explain the behavior of a short crack initiated at a notch, one must take into account some other factors, in particular, crack closure.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 39–44, January – February, 1995.     

THE NUCLEATION AND GROWTH OF SHORT FATIGUE CRACKS BOTH AT PLAIN SURFACES AND NOTCHES

Abstract— The problem of the nucleation and growth of short fatigue cracks is addressed from an energetic point of view. It is explained that vanishingly small cracks can only nucleate and grow at the expense of the release of some locally stored energy during the fatigue deformation. This is necessary because an external loading system alone cannot provide a positive driving force for the growth of a crack whose length is below a critical value. The concept of the local driving force is used to explain the nucleation and growth of short fatigue cracks both at plain surfaces and at notches. With this approach a meaningful definition can be given of a "short fatigue crack" and a sound physical interpretation of the Kitagawa-Takahashi plots is provided. The conditions for the existence of non-propagating cracks are clearly established and the relationship between the stress concentration factor at the root of notches and the fatigue limit is explained. The paper sets up a physical framework for the sound understanding and treatment of short fatigue cracks and the microstructural parameters which control their growth.     

Influence of bulk damage on crack initiation in low‐cycle fatigue of 316 stainless steel

To investigate the effect of bulk damage on fatigue crack initiation, crack initiations due to low‐cycle fatigue of Type 316 stainless steel were observed by electron backscatter diffraction (EBSD) and scanning electron microscopy. The EBSD observations showed that local misorientation developed inhomogeneously due to the cyclic strain, and many cracks were initiated from the slip steps and grain boundaries where the local misorientation was relatively large. The crack initiations could be categorized into two types: enhancement of the driving force by geometrical discontinuity (slip steps and notches), and reduction of material resistance against crack initiation caused by accumulated bulk damage at grain boundaries. In particular, more than half of the cracks were initiated from grain boundaries. However, in spite of the significant bulk damage, the fatigue life was extended by removing the surface cracks under strain of 1 and 2% amplitude. The stress state at the microstructural level was changed by the surface removal, and the damaged portion did not suffer further damage. It was concluded that although bulk damage surely exists, the fatigue life can be restored to that of the untested specimen by removing the surface cracks.     

EXAMINATION OF SHORT-CRACK MEASUREMENT AND MODELLING UNDER CYCLIC INELASTIC CONDITIONS

The opening and closure behaviour of short fatigue cracks is seen as one of the important phenomena which control fatigue life of components where a major part of life consists of the growth of short cracks. Therefore attempts are undertaken to experimentally assess and to model the behaviour of short cracks with respect to opening and closure. In this paper crack opening results obtained by Sunder et al. through SEM evaluation of striation patterns of 2000 series aluminium alloys are examined and compared to predictions using a model recently developed for fatigue life prediction based on fracture mechanics of short cracks. Sunder's technique for crack opening measurements involves particular load sequences with increasing and decreasing load ranges applied to notched specimens with naturally nucleated surface cracks where crack opening levels are identified by steady-state striation widths for increasing load ranges. A detailed review of Sunder's results, however, indicates a number of inconsistencies and contradictions which are discussed. Opening and closure behaviour of short fatigue cracks, in particular for inelastic conditions, is compared to predictions obtained with the above-mentioned model which incorporates a constant strain opening and closure assumption. For inelastic conditions that may develop at notches this assumption means that cracks would close at considerably lower stress levels as compared to the opening stress which becomes important when effective (local) stress-strain ranges are to be determined for fatigue life prediction under spectrum loading. The constant strain assumption is supported by a number of experimental observations from the literature as discussed in the paper. The approximative nature of this assumption and further details of the model are pointed out which show a need for further developments.