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.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

Crack growth from naturally occurring material discontinuities under constant amplitude and operational loads

This paper discusses how cracks that grow from small naturally occurring material discontinuities under operational load spectra behave. The growth of small cracks under a representative maritime aircraft flight load spectrum is discussed first. The results of this study, when taken in conjunction with the authors previous studies into cracks growing under combat aircraft load spectra, illustrate how for cracks that grow from small naturally occurring material discontinuities under operational load spectra crack growth can often be easily and accurately computed. It is also shown that the Hartman–Schijve variant of the NASGRO crack growth equation is able to accurately represent the growth of small cracks in two different rail steels. It is further shown that the growth of both small and long cracks can be described by a family of da/dN versus ΔK curves and that, for 7050-T7451, the experimental procedures commonly used to determine a closure free da/dN versus ΔK curve produce curves that are consistent with those obtained using the Hartman–Schijve equation and allowing for small variations in the term ΔK_thr.     

Short crack threshold estimates to predict notch sensitivity factors in fatigue

The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Δσ_n is between Δσ₀/K_t and Δσ₀/K_f, where Δσ₀ is the fatigue limit, K_t is the geometric and K_f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value ΔK_th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from ΔK_th and Δσ₀, resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa–Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of ΔK_th(a) estimate. In this work, a generalization version of El Haddad–Topper–Smith’s equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K_f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature.     

Acoustic emission study of fatigue crack closure of physical short and long cracks for aluminum alloy LY12CZ

Crack closure of physical short and long cracks of LY12CZ aluminum alloy during fatigue process was investigated using acoustic emission (AE) technique. Results showed that the effective fatigue crack growth curve (da/dN vs. ΔK_eff) of physical short and long cracks obtained by the AE technique was consistent with the effective fatigue crack growth curve at high stress ratio (R = 0.8), which implied that the AE technique could measure the crack closure level, especially for physical short crack. The growth rate of physical short crack was much higher than that of long crack at the same ΔK, and the lower crack closure level of short crack was the main reason.     

Short cracks initiated in Al 6013-T6 with the focused ion beam (FIB)-technology

The fatigue crack growth behaviour of short corner cracks in the Aluminium alloy Al 6013-T6 was investigated. The aim was to determine the crack growth rates of small corner cracks at a stress ratio of R = 0.1, R = 0.7 and R = 0.8 and to find a possible way 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 precracks 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 the 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 created on the basis of constant K_max-tests with long cracks that gives a good and conservative estimation of the short crack growth rates.     

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.     

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.     

Calculating crack growth from small discontinuities in 7050-T7451 under combat aircraft spectra

This paper supplements previous work which showed that the crack growth rate in a large range of metallic materials fitted a variant of the Hartman–Schijve equation where da/dN is a function of (ΔK − ΔK_thr)^α, where ΔK_thr is a parameter that reflects the apparent fatigue stress intensity threshold of the material, and α is approximately 2. For the case of 7050-T7451 aluminium alloy the same equation is shown to fit both long and short crack growth data once the appropriate ΔK_thr is chosen for each specific data set. This equation is used here to produce accurate predictions of the fatigue crack growth in 7050-T7451 aluminium alloy specimens with both a low and high stress concentration subjected to two combat aircraft loading spectra. Thus, it is postulated that if long crack data are fitted to the variant of the Hartman–Schijve equation then accurate predictions can be made in the short crack regime for a wide range of materials.     

Evaluation of overload effects on fatigue crack growth and closure

Fatigue crack propagation tests with single tensile peak overloads have been performed in 6082-T6 aluminium alloy at several baseline ΔK levels and stress ratios of 0.05 and 0.25. The tests were carried out at constant ΔK conditions. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. The observed transient post-overload behaviour is discussed in terms of overload ratio, baseline ΔK level and stress ratio. The crack closure parameter U was obtained and compared with the crack growth transients. Experimental support is given for the hypothesis that plasticity-induced closure is the main cause of overload retardation for plane stress conditions. Predictions based on crack closure measurements show good correlation with the observed crack growth rates for all the post-overload transients when discontinuous closure is properly taken into account.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

The influence of cyclic stress intensity threshold on fatigue life scatter

Understanding factors that contribute to scatter in fatigue lives of metallic structures (particularly airframes) subjected to identical spectrum is critical to maintaining safety and optimising designs. This paper first briefly discusses the sources of scatter, and then concentrates on the effect of variations in the “cyclic stress intensity threshold” (ΔK_thr) on fatigue crack growth. It shows that a version of the NASGRO equation can be used to account for the crack growth scatter seen in a number of classical fatigue experiments by accounting for variations in ΔK_thr. This is an important outcome for safety and is particularly useful when considering lead cracks for which ΔK_thr is small (approaching zero) as these cracks appear to commence growing soon after introduction into service.     

The application of asymptotic solutions to a semi-elliptical crack at the root of a notch

This paper presents an approximate method based on asymptotic solutions for estimating the stress intensity factor K for semi-elliptic surface cracks at stress concentrations. The proposed equation for estimating K makes use of the near-notch and remote-notch solution to interpolate over the entire range from shallow to deep cracks. The near-notch solution is obtained by means of the stress concentration factor. For cracks located in the remote stress field, K is obtained by considering the crack to be located in a smooth plate with a crack depth equal to the sum of the notch depth and the actual crack depth. The accuracy of the predictions is assessed using numerical calculations and solutions found in the literature.     

A simple model of stress intensity range threshold and crack closure stress

The cyclic stress intensity threshold (Δ$\text{K}{}_{\mathrm{TH}}$) below which cracks will not propagate varies with length for short cracks. A model is proposed which relates Δ$\text{K}{}_{\mathrm{TH}}$ to the crack closure stress arising from fracture surface roughness. This is used to predict a variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length for surface cracks in Ti 6Al-2Sn-4Zn-6Mo alloy, based upon measured values of crack opening displacement arising from roughness. The predicted variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length is found to be similar to that obtained from the empirical model of Δ$\text{K}{}_{\mathrm{TH}}$ proposed by El Haddad et al.[5]. The application of the new model to estimate the value of crack closure stress arising from crack tip plasticity for short surface cracks is also discussed.     

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.     

Fatigue crack growth and damage tolerance

The problems arising as a result of aging aircraft, rail and civil infrastructure have focused attention on tools for predicting the growth of cracks from small naturally occurring material discontinuities. To this end, the present paper discusses on the difference between the analysis tools needed for ab initio design and sustainment, modelling of cracks that grow from small naturally occurring material discontinuities and ways to determine the short crack da/dN versus ΔK data from long crack American Society for Testing and Materials (ASTM) tests. It also discusses how existing equations can be used to predict short crack growth and how to account for the variations seen in crack growth histories. Attention is also focused on the recent Federal Aviation Administration limit of validity ruling and the effect of the environment on widespread fatigue damage in civil transport aircraft.     

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.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

SMALL CRACK GROWTH IN THE ALUMINIUM–LITHIUM ALLOYS 8090 AND 8091

The relationship between microstructure and the fatigue behaviour of small cracks has been examined for the aluminium–lithium alloys 8090 and 8091 after peak ageing at 170°C. Duplex ageing and pre-stretching were used to vary the distribution of S'precipitates and thus the distribution of slip. No effect of S'distribution an small crack growth was observed in either alloy. This is thought to be due to a combination of the lack of closure and lower overall slip reversibility in small cracks. Small cracks in 8091 were found to grow slower than in 8090 due to differences in grain shape rather than texture. Small cracks in both alloys were observed to grow much faster than long cracks for equivalent ΔKs. This difference was reduced when small crack data were compared with long crack data generated at R= 0.7 due to the reduced closure. The use of ΔJ made long and small crack growth rates still more comparable.