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.     

CRACK CLOSURE: A CONCEPT OF FATIGUE CRACK GROWTH UNDER EXAMINATION

Abstract— In recent literature it is asserted that the concept of crack closure in fatigue fracture mechanics is not capable of explaining fatigue crack growth behaviour. The reasons given are that both asperity induced crack closure and plasticity induced crack closure should be either negligible or non-existent. We have re-considered these hypotheses since their correctness would completely change the established picture of fatigue crack growth. In order to get mathematically tractable systems the present studies are confined to long cracks loaded in mode I. The results suggest that in case of asperity induced crack closure the proposed hypothesis is only true in special cases and the demonstration of the non-existence of plasticity induced crack closure is proved to be wrong.     

A CRACK CLOSURE MODEL FOR PREDICTING THE THRESHOLD STRESSES OF NOTCHES

A model is proposed to estimate the threshold stress range of a notched component. The model considers the variation of crack closure with crack length in the presence of a notch. The threshold stress range was found from the condition that the minimum value of effective threshold stress intensity range of a crack emanating from a notch equals the effective threshold stress intensity range of a “long” crack. The effects of notch depth, of notch acuity, of notch and specimen type, of load ratio, and of material properties on the threshold stresses were considered. Experimental data reported in the literature were used to assess the validity of the model. It was found that the model correctly predicts the behavior of cracks in notched components.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

The effect of notch plasticity on the behaviour of fatigue cracks emanating from edge-notches in high-strength β-titanium alloys

The present paper is aimed at investigating the behaviour of fatigue cracks emanating from edge-notches for two different microstructures of the Ti-6246 alloy, produced by two specific thermo-mechanical treatments and defined as β-annealed and β-processed, respectively. Pulsating four point bending tests were performed on double-edge-notched specimens. The 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’s yield stress. Plastic deformation at the notch tip initially produced a local stress redistribution followed by elastic shake down due to the high cyclic strain hardening rates exhibited by both microstructures, as confirmed by finite element modelling. Crack closure effects, measured by an extensometric technique, and variations in crack aspect ratio were considered in the ΔK calculation. The obtained crack growth rate data were compared with those of long cracks measured on standard C(T) specimens as well as of microcracks measured on round, unnotched S-N type of specimens to evaluate the intrinsic fatigue crack propagation resistance of the two microstructures. The contribution of notch plasticization to crack closure was estimated by finite element modelling.     

On the Frost–Dugdale plot for non‐propagating cracks

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

Propagation of short fatigue cracks from notches in a Ni base superalloy: experiments and modelling

A notched specimen containing a semicircular slot (0.1 mm deep) was designed to simulate the growth of three-dimensional short cracks under a stress concentration. Fatigue tests were performed on N18 superalloy at 650 °C with trapezoidal loading cycles. A high-resolution optical measurement technique proved to be capable of detecting half-surface crack increments as small as 10 μm, and the potential drop method was found to be inappropriate for very small crack lengths. The stress intensity factor, Δ K , was calculated using a weight functions method. Non-uniform stress fields were determined by FEM modelling using elasto-viscoplastic constitutive equations. The plasticity-induced crack closure effect was calculated within the specimen using viscoplastic FEM modelling. The prediction of crack aspect ratio was used to investigate differences of closure along the crack front. The role of notch plasticity on these differences is discussed. Using these calculations, it is shown that the apparent differences between the growth behaviour of short and long cracks can be largely accounted for.     

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.     

Displacement controlled fatigue crack growth in inelastic notch fields: Implications for short cracks

Much has been written documenting the crack growth from notches which suggests that LEFM does not consolidate such data in a manner consistent with those of compact tension and other specimens with long cracks. Such crack growth data are reviewed and causes for the observed “short crack” effect are advanced. Situations where the crack is contained within the inelastic field of a notch are explored at length. A postulate is advanced to characterize crack growth for this case in terms of a pseudoplastic stress intensity factor defined in analogy to LEFM as well as a simple approach to deal with local crack closure. The postulate is shown to be consistent with experimental observations. Predictions of the growth of cracks in the inelastic field are made and shown to confirm observed growth rates and trends.     

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.     

On the relationship and the short fatigue crack threshold

Murakami and Endo have used the parameter to successfully predict the endurance limits and the threshold levels for components, which contain small defects or cracks. The present paper uses a modified linear–elastic fracture mechanics (LEFM) approach to examine the mechanistic basis for these correlations. The modifications include consideration of the endurance limit rather than the threshold level as a factor controlling fatigue crack growth in the very short crack growth range, consideration of elastic–plastic behaviour, and consideration of the role of crack closure in the wake of a newly formed crack. Predictions based upon the modified LEFM behaviour are found to be consistent with the earlier predictions of Murakami and Endo.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

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.     

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.     

Growth of cracks under far-field cyclic compressive loads: Numerical and experimental results

Crack growth from a notch tip, under the influence of fully compressive far-field cyclic loads, is investigated both numerically and experimentally in notched specimens of a lower strength steel and an aluminum alloy. Such cracks, emanating from the root of the notch, progressively decelerate until complete crack arrest occurs. Analyses of the stress state along the crack plane indicate that while the extent of the residual tensile stress field diminishes with an increase in crack length, there is a progressive increase in crack closure during crack advance. Approximate numerical calculations of the crack closure loads are in reasonable agreement with experimental results.     

Investigation of small fatigue crack initiation and growth behaviour of nickel base superalloy GH4169

Surface replication method was utilized to monitor the small fatigue crack initiation and growth process of single‐edge‐notch tension specimens fabricated by nickel base superalloy GH4169. Three different stress levels were selected. Results showed that small fatigue cracks of nickel base superalloy GH4169 initiated from grain boundaries or surface inclusions. The small fatigue crack initiation and growth stages took up about 80–90% of the total fatigue life. Multiple major cracks were observed in the notch root, and specimen with more major cracks seemed to have smaller fatigue life under the same test conditions. At the early growth stage, small crack behaviour might be strongly influenced by microstructures; thus, the crack growth rates had high fluctuations. However, the stress level effect on the small fatigue crack growth rates was not distinguishable for the three different stress levels. And no clear differences were found among the crack initiation lives by using replication technique.     

Restraint of fatigue crack growth by wedge effects of fine particles

This paper presents some experimental results which demonstrate restraint of fatigue crack growth in an Al–Mg alloy by wedge effects of fine particles. Fatigue test specimens were machined from a JIS A5083P‐O Al–Mg alloy plate of 5 mm thickness and an EDM starter notch was introduced to each specimen. Three kinds of fine particles were prepared as the materials to be wedged into the fatigue cracks, i.e. magnetic particles and two kinds of alumina particles having different mean particle sizes of 47.3 μm and 15.2 μm. Particles of each kind were suspended in an oil to form a paste, which was applied on the specimen surface covering the notch zone prior to the fatigue tests. In order to make some fracture mechanics approaches, in situ observations of fatigue cracks were performed for the two cases using a CCD microscope, with a magnification of ×1000. The crack length and the crack opening displacement (COD) at the notch root, δ, were measured. First it was ensured by control tests that the wedge effect of the oil itself was negligible. Then it was found that the large size alumina particles were not effective in restraining crack growth because the paste was difficult to make due to the large particle size and the particles could not enter the cracks properly. However, both of the magnetic particles and the small size alumina particles effectively restrained crack growth, especially the latter which produced 143–350% increase in the lifetime to failure. From the in situ observations, in the case of the small size alumina particles, a pronounced retardation of crack growth was observed immediately after the crack length exceeded 0.4 mm, and this is considered to be due to the range of COD value, δ_max ? δ_min , being strongly affected by the wedge effects of the particles. The crack retardation effect continues almost through the entire lifetime if the alumina paste is re‐applied at specified intervals, while the effect is apparently lost after the crack length exceeds ～2 mm when such re‐painting is not continued. After the fatigue tests, some macro‐ and microfractographic analyses were performed using a CCD microscope, a SEM and an EPMA (electron probe microanalyser), in order to examine the mechanism of fatigue crack restraint by the wedge effects of the fine particles. From those analyses, it was reasoned that the fine particles that entered a fatigue crack are subjected to cyclic pressures between the crack faces and then form a kind of wedge which causes significant levels of crack closure that restrain crack growth.     

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.     

Crack initiation under far-field cyclic compression and the study of short fatigue cracks

A procedure involving crack initiation under far-field cyclic compression is used to study the fatigue behavior of small flaws which are ˜0.3–0.5 mm in length and are amenable to linear elastic fracture mechanics (LEFM) characterization. This technique enables the determination of the threshold stress intensity range at which crack growth begins for small flaws and provides insight into some closure characteristics. Cracks were propagated in notched specimens of a bainitic steel subjected to fully compressive remote cyclic loads, until complete crack arrest occurred after growth over a distance of only a fraction of a mm at a progressively decreasing velocity. Following this, physically small flaws were obtained by machining away the notch. For the loads examined, the results indicate that the extent of damage left at the tip of the crack grown (and arrested) under remote compression is not large enough to affect subsequent tensile fatigue crack growth, when closure effects are not significant (e.g. at high load ratios). At high load ratios, the growth of small linear elastic cracks is identical to that of corresponding long flaws subjected to the same stress intensity range, which corroborates the similitude concept implicit in the nominal use of LEFM. At low load ratios, however, short tensile cracks propagate substantially faster than the longer flaws and exhibit lower threshold stress intensity range levels. Such apparent differences in their growth rates seem to arise, to a large extent, from the differences in their closure behavior, as indicated clearly from various aspects of the compression method. Global measurements of closure, with their inherent uncertainties, however, cannot account completely for the anomalous behavior of short flaws and for the effect of load ratio on short crack growth. Closure of short flaws begins to develop after growth over a minimum distance of about 0.5 mm in this steel. The significance and limitations of the compression technique are discussed and possible mechanisms responsible for the differences between long and short fatigue cracks are outlined.     

EFFECT OF CYCLE MEAN STRAIN ON SMALL CRACK GROWTH IN ALLOY 718 AT ELEVATED TEMPERATURES

The influence of the cyclic compressive excursion on the fatigue crack growth behavior of small surface cracks in Alloy 718 at 650°C is experimentally studied. Test conditions were chosen to simulate the cyclic plasticity found at notch locations in high temperature structural components. During cycling, the crack lengths were continuously monitored using the direct current potential drop method while the near field crack mouth opening displacement and global cyclic stressstrain behavior were measured using a laser interferometry technique and mechanical extensometry, respectively. Two aspects related to cyclic compressive excursion have been studied; crack closure and crack tip plasticity. Attempts have been made to use several modified ΔK expressions as well as ΔJ_eff to account for the effects of closure and decrease crack tip plasticity. It was concluded that the compressive excursion is most prominent in this alloy in its effect on the global plasticity and the subsequent loss of constraint. Closure was not found to be significant in the consolidation of test data.