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An increase of testing frequency to reduce the testing time could affect the fatigue behavior of metallic materials. The current paper investigates the effect of testing frequency on the high and very high cycle fatigue behavior of AA2024, Ti-6Al-4V, and Inconel 718 alloys tested at 20, 90, and 1000 Hz. To quantify the effect of testing frequency a two-parameter Weibull distribution and Basquin's equation were utilized as well as the threshold stress intensity factor range was determined. Fatigue crack initiation sites were evaluated on the fracture surface with respect to different testing frequencies. The results showed that changes in the testing frequency significantly influence the mechanical response of the Ti-6Al-4V alloy, while no substantial impact on the fatigue properties of AA2024 and Inconel 718 alloys was identified. The findings of the study contribute to a more complete knowledge of the frequency sensitivity of the alloys and provide valuable insights for the design and evaluation of materials used in high-frequency applications. [ABSTRACT FROM AUTHOR]

Abstract Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities, so it has been widely utilised in the fatigue field. However, most ML methods are inexplicable black-box models that are difficult to apply in engineering practice. Symbolic regression (SR) is an interpretable machine learning method for determining the optimal fitting equation for datasets. In this study, domain knowledge-guided SR was used to determine a new fatigue crack growth (FCG) rate model. Three terms of the variable subtree of ΔK, R-ratio, and ΔK th were obtained by analysing eight traditional semi-empirical FCG rate models. Based on the FCG rate test data from other literature, the SR model was constructed using Al-7055-T7511. It was subsequently extended to other alloys (Ti-10V-2Fe-3Al, Ti-6Al-4V, Cr-Mo-V, LC9cs, Al-6013-T651, and Al-2324-T3) using multiple linear regression. Compared with the three semi-empirical FCG rate models, the SR model yielded higher prediction accuracy. This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities, so it has been widely utilised in the fatigue field. However, most ML methods are inexplicable black-box models that are difficult to apply in engineering practice. Symbolic regression (SR) is an interpretable machine learning method for determining the optimal fitting equation for datasets. In this study, domain knowledge-guided SR was used to determine a new fatigue crack growth (FCG) rate model. Three terms of the variable subtree of ΔK, R-ratio, and ΔKth were obtained by analysing eight traditional semi-empirical FCG rate models. Based on the FCG rate test data from other literature, the SR model was constructed using Al-7055-T7511. It was subsequently extended to other alloys (Ti-10V-2Fe-3Al, Ti-6Al-4V, Cr-Mo-V, LC9cs, Al-6013-T651, and Al-2324-T3) using multiple linear regression. Compared with the three semi-empirical FCG rate models, the SR model yielded higher prediction accuracy. This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model. [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate the influence of chunky graphite on the characteristics of fatigue crack propagation in heavy section spheroidal graphite cast iron. Samples containing and not containing chunky graphite were cut from a large ingot of spheroidal graphite cast iron. The fatigue crack propagation test conformed to ASTM. Stress ratio R was 0.1, and the specimen used was of the 1CT type with a thickness of 12.5 mm, and humidity RH = 0%. In the samples containing chunky graphite, the slope of the linear approximation m at the IIb stage of fatigue crack propagation becomes larger and fatigue crack growth rate becomes faster than the spheroidal graphite samples. The reason seems to be that crack propagates along the graphite connected to the chunky graphite. The decrease in the threshold stress intensity factor range ?Kth of the chunky graphite samples was smaller than the decrease in tensile strength. In the chunky graphite samples, the fracture surface roughness became large and the crack closure induced by fracture roughness occurred conspicuously. The threshold stress intensity factor range decreased due to the influence of the chunky graphite. However, it was found that threshold stress intensity factor range does not decrease as much as the tensile strength due to the effect of the crack closure induced by fractured surface roughness. [ABSTRACT FROM AUTHOR]

In this study, the effects of various heat treatment procedures on the mechanical properties of the Ti-15V-3Al-3Sn-3Cr metastable β titanium alloy were investigated. Single-step and duplex aging treatments were applied to the alloy at low and high aging temperatures. Duplex aging treatments were carried out by selecting two different pre-aging times and temperatures: 10 h at 300 °C and 24 h at 250 °C. Thus, the effects of pre-aging on the mechanical properties of the alloy were examined. Optimum tensile properties were obtained in the duplex-aged samples, which was aged at 550 °C for 20 h after being pre-aged at 250 °C for 24 h. While fine, high volume fraction and uniformly dispersed α phases increased the tensile strength and % elongation of the alloy in the aging treatment, the fatigue crack propagation rate also increased. Also, it was observed that the threshold stress intensity factor range (ΔKth) increased with the aging treatment. While the lowest ΔKth value was obtained at the solution-treated sample, the highest ΔKth value was obtained in the sample to which duplex aging treatment was applied depending on precipitation of fine and high volume fraction of α phases. [ABSTRACT FROM AUTHOR]

In this study, we investigated long fatigue crack growth perpendicular to a soft-hard material interface comprising the same Young’s moduli but different yield strengths. We determined the degree of fatigue crack growth retardation attributable to the interface under the constant stress intensity factor range (Δ K ) using the plasticity-induced crack closure analysis with the Dugdale model. We subsequently determined the threshold stress intensity factor range (Δ K th ) under a constant stress amplitude (σ a ). Under a constant Δ K , the retardation degree was primary dependent on the two materials’ yield strength ratio. Under a constant σ a , Δ K th was dependent on both the yield strength ratio and the distance between initial crack tip and interface. [ABSTRACT FROM AUTHOR]

Fretting fatigue process have many features such as early stage crack initiation at contact edge, very slow crack propagation and fatigue failure after very long life operation of machinery. In previous paper [1,2,3] we present fretting fatigue process model and fretting strength and life estimation using fracture mechanics and wear process approaches. But, the estimation of fretting wear process require a large amount of labor, so this precise wear estimation method is not suitable for actual design site. In this paper we try to present simple fretting fatigue limit estimation method based on the assumption that in the final stage of wear process the contact pressure distributions near contact edges converge to a uniform. And the validity of this estimated result can be confirmed by comparing with experimental results. [ABSTRACT FROM AUTHOR]

An investigation was conducted into the influence of statically-applied, mode I, crack-opening load on the threshold condition for propagation of a shear-mode fatigue crack in a bearing steel. Torsional fatigue test was carried out at an R of −1 using a hollow cylindrical specimen into which a semi-elliptical, small slit was axially introduced. A static axial compressive stress was simultaneously applied to suppress crack branching. A coplanar, shear-mode, non-propagating fatigue crack emanating from the slit was attained by appropriate control of shear stress amplitude. Internal pressure was then applied to generate a hoop stress as a static crack-opening stress, σ θ static . Consequently, the threshold shear-mode stress intensity factor range, Δ K τth , was significantly decreased with increase of the static mode I stress intensity factor. To further understand the contribution of σ θ static to the reduction in Δ K τth , microstructural observations for the cross-sections of a non-propagating crack were conducted using a scanning electron microscope in conjunction with the electron backscatter diffraction analysis. The results revealed that the excess loading of σ θ static accounts for the change in the crack-path, resulting in a further reduction in Δ K τth . [ABSTRACT FROM AUTHOR]

A new ΔK-decreasing test method of the metal film was developed. The film was adhered to a through elliptical hole in a base plate and was fatigued in accordance with the displacement constraint along the hole-circumference in the base plate subjected to a cyclic stress. Commonly, a stress intensity factor range was increased with a crack propagation under a constant stress amplitude but was decreased toward the hole-edge because of the difference in thickness between the film and the base plate in this ΔK-decreasing test method. The decrease in a stress intensity factor with a crack propagation was calculated by FEM analysis and the optimum aspect ratio of an elliptical hole was determined. Using the ΔK-decreasing test method, the crack propagation test was conducted for metal films. As a result, the fatigue crack propagation rate was decreased and was arrested near the hole-edge under the constant stress amplitude to the base plate. The threshold stress intensity factor ranges were obtained for some kinds of metal film and the accuracy of the testing method was discussed.

• Fatigue crack growth of hydrogen-charged 17–4 PH steel was investigated. • Threshold stress intensity factor range was not degraded by hydrogen. • Frequency dependence of crack growth acceleration by hydrogen was predicted. • A newly model was proposed as a substitute for ordinary acceleration model. • Its model incorporated an interaction of cycle- and time-dependent crack growth. Effect of hydrogen on the fatigue crack threshold and fatigue crack growth (FCG) behavior of 17–4 PH steel was investigated using a circumferentially notched specimen with a stress concentration factor of 6.6 precharged in a 100 MPa hydrogen gas environment. Fatigue life tests were performed in air at room temperature at a stress ratio of −1 and test frequencies of 0.001–10 Hz. Although the FCG rate was accelerated, it was discovered that the fatigue crack threshold was not degraded by the hydrogen. The H-induced FCG acceleration ratio was predicted by a new model considering cycle- and time-dependent FCGs. [ABSTRACT FROM AUTHOR]

• Plasticity-induced crack closure analysis using the Dugdale-model. • Work hardening effects introduced in the Dugdale-model. • Material indices of Δ K th for mechanical cracks of arbitrary length are clarified. • The discretization errors in space and time are discussed. • Using conclusions, past Δ K th databases are discussed from the mechanical viewpoint. The fatigue limits of smooth materials and various notched materials are determined by their non-propagating limit after the growth of a fatigue initiated crack; thus, the characterization of the threshold stress intensity factor range (Δ K t h ) is important for fatigue design. The material dependencies of Δ K t h for small and long cracks differ significantly; however, the physical meaning for this has not adequately examined. In this study, the material indices of Δ K t h for mechanical cracks of arbitrary length were clarified by plasticity-induced crack closure analysis using the Dugdale-model, which considers the work hardening effects. The discretization errors in space and time were discussed in detail to provide a mechanically well-founded conclusion. Furthermore, databases of past Δ K t h values are discussed from the mechanical perspective using this conclusion. [ABSTRACT FROM AUTHOR]

• Equivalent crack growth model incorporates the effect of stress ratio. • Equivalent driving force yields same growth rate as combined effects of applied stress intensity range and stress ratio. • Curves of growth rate versus equivalent driving force for different R-ratios have common threshold. • The ratio of any two driving forces at two stress ratios is equal to the ratio of their thresholds. • Ratio of growth rates of two equivalent curves is a power function of the ratio of their threshold. An equivalent crack growth model that accounts for the effect of stress ratio is proposed for the correlation and prediction of crack growth under different stress ratios. A previously proposed equivalent driving force ΔK eq that yields the same growth rate (da/dN) R as combined applied stress intensity factor range ΔK R and stress ratio, R is modified, and its corresponding equivalent growth rate (da/dN) eq is derived. This yields an equivalent crack growth model of (da/dN) eq versus ΔK eq capable of collapsing data of different R-ratios unto a common curve. The model was validated with excellent agreement between the model and published data. [ABSTRACT FROM AUTHOR]

The threshold stress intensity factor range (Δ K th ) of water-quenched Fe–0.017C (wt.%) fully ferritic steel was determined using room-temperature fatigue tests on micro-notched specimens. The experimentally determined Δ K th was approximately 40.5% higher than conventionally predicted results. This extraordinary resistance to transgranluar fatigue crack propagation likely results from the strain–age hardening. [ABSTRACT FROM AUTHOR]

Based on the structural concept of threshold stress intensity factor ranges, the model, describing the growth kinetics of physically small and long cracks, was constructed. The model permits the calculation of lifetime on the growth of physically small and long cracks at regular cyclic uniaxial loads by the data on static mechanical characteristics and a microstructure of the initial material. The model validity was corroborated by fracture toughness results in symmetric cyclic plane bending of VT3-1 titanium alloy specimens in different microstructural states. Calculated kinetic fatigue fracture diagrams are in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

The ranges of the threshold stress intensity factor (SIF), Δ K IIth and Δ K IIIth , for small shear-mode cracks in bearing steel are measured using torsional fatigue testing under static compression. The threshold values are described as a function of the crack size and the crack-face interference. In addition, to simplify the evaluation of the shear-mode threshold, a single parameter, K τ , is introduced to represent the SIF of shear-mode cracks. Moreover, a practical expression for approximating K τ is proposed on the basis of the area parameter model. Finally, the threshold SIF range Δ K τth is found to exhibit a dependence on the crack size similar to that of small mode I cracks, i.e., Δ K τth ∝ ( area ) 1 / 3 , for the regime of small shear-mode cracks with area values ranging from 0.01 to 1 mm. [ABSTRACT FROM AUTHOR]

Abstract: The 35CrMo alloy steel was nitrocarburized and post-oxidized in salt bath and the 109 cycles fatigue tests were carried out. The results show that for the untreated specimens all the cracks initiate from the surface while for the treated specimens the cracks originate from the subsurface in short fatigue life regime and from internal inclusion in longer fatigue life regime. The treated specimens do not fracture in very high cycle fatigue regime and the fatigue limit increases by 51% after the treatment. No granular-bright-facet is observed in the vicinity of a non-metallic inclusion on the fracture surface. [Copyright &y& Elsevier]

Abstract: In order to propose a prediction expression of a threshold stress intensity factor range (AK th ) for magnesium alloys with small crack, rotating bending fatigue tests in three magnesium alloys which have a different hardness and low carbon steel (JIS S10C) were carried out. In these tests, the AK of a crack propagation lower limit from an annealed pre-crack as the AK th was measured. One of the three magnesium alloys have the same Vickers hardness (HV) as the low carbon steel, however the AK th was half of the low carbon steel. In order to make this difference clear, the authors focused on an effective threshold stress intensity factor range (AK ef f ith ), because there is large difference in the AK eff j h which is not negligible to evaluate the AK th between magnesium alloys and steel. Considering the difference in the AK ef f Jh , a prediction expression was proposed based on Murakami''s prediction expression which can predict the AK th in various metals by applying only two parameters i.e. the HV and an initial crack size. However, the prediction expression cannot evaluate the AK th of the magnesium alloys. In this expression, Young''s modulus which is proportional to the AK effth was used to modify Murakami''s prediction expression. In addition the new prediction expression was speculated to be accurate. [Copyright &y& Elsevier]

The influence of R ratio in the range 0·05-0·4 on the ambient temperature fatigue crack growth behaviour of an austenitic stainless steel weld, SS 316(N), has been studied. Results indicate that the cyclic threshold stress intensity factor ΔKth increases with decreasing R ratio. The data are compared with those for SS 316, SS 316L and SS 316L(N) base materials from the literature, and various approaches dealing with the R ratio effects are examined. Zhang's model considering the contribution of the crack tip plasticity to the fundamental fatigue crack propagation process does provide a consistent interpretation for the data. [ABSTRACT FROM AUTHOR]

Abstract: The stress and displacement fields near the bonding edge, sharp notch, and contact edge show singularity behaviors, so methods of evaluating the strength of these points using maximum stresses calculated by a numerical stress analysis, such as the finite element method, are generally not valid. We have previously presented a new method of evaluating the strength of these singular points using two stress singularity parameters H and λ. The difficulty with this method was in obtaining the critical value of the intensity of the stress singularity parameter H c for each order of stress singularity λ. Then we have developed a method of formularizing critical value of stress singularity parameter H c for each order of stress singularity λ by utilizing critical distance stress theory. Firstly we apply this method to the delamination strength evaluation. The estimated delamination criteria H c(λ) agrees well with the experimental results. Then we apply this method to general sharp notch corner and contact edge fatigue problems. In these cases the fatigue-crack initiation criteria can be derived from two typical strength parameters, namely, fatigue limit σ w0 and threshold stress intensity factor range ΔK th. These estimated critical H th(λ) value agrees well with the experimentally measured value. Using this simple critical distance stress approach we estimated the fretting fatigue-crack initiation criteria for any contact edge angle and optimized the contact edge geometry. Moreover, we can apply this new strength criterion to stress singularity fields for general stress-concentration structures. [Copyright &y& Elsevier]

Abstract: In fretting fatigue process the wear of contact surfaces near contact edges occur in accordance with the reciprocal micro-slippages on these contact surfaces. These fretting wear change the contact pressure near the contact edges. To estimate the fretting fatigue strength and life it is indispensable to analyze the accurate contact pressure distributions near the contact edges in each fretting fatigue process. So, in this paper we present the estimation methods of fretting wear process and fretting fatigue life using this wear process. Firstly the fretting-wear process was estimated using contact pressure and relative slippage as follows:where W is the wear volume (depth), K the wear coefficient, P the contact pressure, S the slippage. And then the stress intensity factor for cracking due to fretting fatigue was calculated by using contact pressure and frictional stress distributions, which were analyzed by the finite element method. The S–N curves of fretting fatigue were predicted by using the relationship between the calculated stress intensity factor range (ΔK) with the threshold stress intensity factor range (ΔK th) and the crack propagation rate (da/dN) obtained using CT specimens of the material. And then fretting fatigue tests were conducted on Ni–Cr–Mo–V steel specimens. The S–N curves of our experimental results were in good agreement with the analytical results obtained by considering fretting wear process. Using these estimation methods we can explain many fretting troubles in industrial fields. [Copyright &y& Elsevier]

In this paper, push–pull fatigue tests of notched specimens under R=−1, 0 and 0.5 are carried out on annealed 0.1 % carbon steel and quenched-tempered 0.5 % carbon steel with H rm B simeq 600. The fatigue limit of a long crack, sigma w2, is obtained from that of a notched specimen with a sharp and deep notch whose radius is smaller than the branch point rho0. Using the present and past sigma w2 data, the effect of the positive mean stress on the dK w of the long crack is evaluated using 3.2 H rm B ( simeq sigma rm B) and sigma rm S(3.2 H rm B), where dK w is the stress intensity factor range for predicting the fatigue limit of a metal with an arbitrary crack, sigma rm S is the lower yield stress or 0.2% proof stress, sigma rm B is the ultimate tensile strength and H rm B is the Brinell hardness. Although the sigma w2 decreases with the mean stress, sigma w2 is cut off by the threshold stress sigma we of the plastic deformation at the crack tip. For the quantitative prediction of the fatigue limit of a cracked steel with an arbitrary crack length under a positive mean stress, the sigma w2 and sigma we values are approximated by simple formulae. [ABSTRACT FROM AUTHOR]

In this paper, the result from rotating bending fatigue tests of notched specimens are carried out on aluminum cast alloys and high strength steels with HB ≈ 600 are reported. The threshold stress intensity factor range under a stress controlled condition, ΔKw, is introduced for the purpose of predicting the fatigue limit of a metal with an arbitrary crack. The ΔKw value of a long crack, ΔKwU L, is obtained from the fatigue crack propagation limit σw2 of specimens with a sharp and deep notch; ΔKw increases with crack length, and ΔKwUL is an upper limit of ΔKw. Since there are few σw2 data of steels with HB ⩾ 400, the σw2 values are evaluated by the fatigue crack initiation limit predicted using Linear Notch Mechanics and the relation between σw1 and σw2 at the branch point. Using ΔKwUL values of many metals with a long crack, the ΔKwUL values are approximated with a simple formula. Moreover the lower limit value of ΔKw versus the crack length, ΔKwLL, is proposed. Then using the ΔKw and ΔKwUL formulae and the ΔKwLL value, the smallness of a fatigue crack is clarified. [ABSTRACT FROM AUTHOR]

The influence of periodic overloads on the fatigue crack propagation behavior in the near threshold regime of physically (extrinsically) short cracks and long cracks is investigated. The overload ratio and the number of base amplitudes were 1.8 and 1000 cycles, respectively. A 20 vol.% SiC particle reinforced 359 cast aluminum alloy and a 17 vol.% SiC particle reinforced 2124 aluminum alloy are examined. In the Paris regime, the two alloys exhibit a different behavior. In the 2124 reinforced alloy, the overloads induce a reduction of the mean crack propagation rate which is typical for ductile metals. On the other hand, the mean crack propagation rate increases in the 359 reinforced cast alloy which is caused by the generation of micro-cracks during the overload, mainly due to particle fracture.In the near threshold regime, the behavior of both alloys is very similar. The effective threshold is not affected by the overload, i.e. if the base amplitudes are smaller than the effective threshold they do not contribute to crack propagation.The initial crack propagation rate of closure free pre-cracks is not influenced by the interaction of the base amplitudes and the overloads. After a relatively short extension of this extrinsically short crack, the periodic overloads begin to dominate the propagation behavior especially for base amplitudes smaller than the long crack threshold of the stress intensity range. [Copyright &y& Elsevier]

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK IIth . The relationship ΔK IIth > ΔK Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory-roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory-roofs were formed by crack branching into mode I. Crack branching started from small semi-elliptical cracks nucleated by shear at the tip of the original circumferential crack. [ABSTRACT FROM AUTHOR]

In order to examine the threshold condition for the fatigue limit of materials containing a small crack under cyclic torsion, reversed torsional fatigue tests were carried out on 0.47% C steel specimens containing an initial small crack. Initial small semi-elliptical cracks ranging from 200 to 1000 μm in length were introduced by the preliminary tension–compression fatigue tests using specimens containing holes of 40 μm diameter. The threshold condition for the fatigue limit of the specimens containing artificial small defects under rotating bending and cyclic torsion are also reviewed. Crack growth behaviour from an initial crack was investigated. The torsional fatigue limit for a semi-elliptical small crack is determined by the threshold condition for non-propagation of Mode I branched cracks. The torsional fatigue limit of specimens containing an initial small crack can be successfully predicted by the extended application of the √area parameter model in combination with the σθmax criterion. [ABSTRACT FROM AUTHOR]

• Δ K th is dependent on the Δ K decreasing rate. • This study performed PICC analysis with the Dugdale model. • The dependence of material properties on Δ K th of long crack was studied. • The rate value proposed by ASTM is valid for all materials within 10% error. The threshold stress intensity factor range Δ K th can be obtained using the Δ K decreasing method. Because Δ K th is dependent on the Δ K decreasing rate, the rate is regulated by the American Society of Testing Materials standard. However, the rate was derived under specific conditions, and its applicability to materials with physical properties different from ordinary steel has not been clarified. To address this issue, this study performed plasticity-induced-crack-closure analysis with the Dugdale model. The dependence of material properties on Δ K th of long crack was determined for steel, aluminum and magnesium. The results showed that the rate value proposed by the standard is valid for all materials with different yield strengths and different Young's moduli within 10% error. [ABSTRACT FROM AUTHOR]