Non-propagating crack behaviour at giga-cycle fretting fatigue limit

Fretting fatigue fracture of industrial machines is sometimes experienced after a long period of operation. It has been a question whether the fatigue limit which means infinite life really exists in fretting fatigue or not. Fretting fatigue tests in ultra high cycle region up to 10⁹ cycles were performed. Test results showed that the S‐N curve had a knee point around 2 × 10⁷ cycles and a clear fatigue limit was observed in the giga‐cycle regime for partial slip conditions. An electropotential drop technique was applied to detect the crack growth behaviour under the contact pad. The real‐time measurement of crack depth during the fretting fatigue test at the fatigue limit showed that a crack initiated at an early stage and then ceased to grow after 2 × 10⁷ cycles and the crack became a non‐propagating crack. These results indicated that the fatigue limit exists in fretting fatigue and infinite endurance is achieved by the mechanism of forming a non‐propagating crack.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Experimental study on very high cycle fatigue of martensitic steel of 2Cr13 under corrosive environment

Rotating bending fatigue test at very high cycle regimes was carried out on martensitic steel of 2Cr13 in air and 3.5% NaCl environment. The result showed that the S–N curve presents a stepwise tendency over the range of 10⁶–10⁸ cycles in both air and 3.5% NaCl environment. In air fatigue, cracks initiated from the sample surface and inclusions at subsurface and no typical fish eye feature in very high cycle fatigue were observed for all samples tested up to 6 × 10⁸ cycles. In 3.5% NaCl solution, a fatigue limit over the range of 10⁶–10⁸ cycles exhibited with the corrosion fatigue strength reduced by 47% compared to the air fatigue. Multiple cracks initiated from surface and the number of crack origins increased with increasing stress level and surface proportion of fatigue propagation increased as number of cycles increased.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

Fatigue behaviour of SiCp-reinforced aluminium composites in the very high cycle regime using ultrasonic fatigue

The fatigue behaviour of a 2009/SiC/15p‐T4 DRA composite has been examined in the very high cycle fatigue (VHCF) regime where 10⁷≤N_f≤ 10⁹ cycles. Ultrasonic fatigue was used to achieve the very high cycle counts. Careful processing yielded a composite with a very homogeneous particle distribution with minimal clustering. Fatigue crack initiation was observed almost exclusively at AlCuFe inclusions with no crack initiation observed at SiC particle clusters. Fatigue lives at a given stress level exhibited minimal scatter and subsurface crack initiation was observed in all cases. This behaviour is consistent with the presence of a low number density of critical inclusions that are responsible for crack initiation very early in fatigue life.     

Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel

Axial loading fatigue tests were carried out to study the influence of inclusion on high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel (AISI 11). The fatigue strength of 1538 MPa with endurance life of 10⁷ cycles were obtained by stair-case method. The fatigue specimens were also subjected to a constant maximum stress of 1650 MPa to investigate the relationship among inclusion origin size (10-30 μm), fish-eye size (70-130 μm) and fatigue life (10⁵-10⁷ cycles). The fatigue life was found to be dependent on the inclusion size and the crack propagating length. A compressive residual stress of 300-450 MPa turned out to be present at the specimen surface, and finally induced the interior failure mode. Further investigation into the correlation between stress intensity factors of inclusion origin and corresponding stages of fatigue crack growth and fatigue life revealed that the high cycle fatigue behavior was controlled by crack propagation. According to the fractographic investigation, two distinct zones were observed in fish-eye, representing Paris-Law and fast fatigue crack growth stage, respectively. Threshold stress intensity for crack propagation of 3.9 MPa√m was obtained from the well correlated line on the ΔK_I-log N_? graph. The fracture toughness can also be estimated by the mean value of stress intensity factor ranges for fish-eye.     

Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

Investigation of crack initiation and propagation behavior of AISI 310 stainless steel up to very high cycle fatigue

Fatigue behavior up to very high cycles for AISI 310 stainless steel has been investigated. The fatigue crack initiated from the surface of the material. It was found that up to 10⁶ cycles, cracks initiated from the carbide precipitates at grain boundaries. However, above 10⁶ cycles, the cracks initiated from persistent slip bands found at the surface of the specimen. At lower stress levels, slip bands were developed without initiating the cracks. The horizontal asymptote S–N curve from 10⁶ to 10⁹ cycles was attributed to the development of slip bands all over the surface of the specimen, before crack initiation.     

Effect of stress ratio on very high cycle fatigue properties of Ti-10V-2Fe-3Al alloy with duplex microstructure

In fatigue critical applications, Ti-10 V-2 Fe-3 Al alloy components are expected to endure cyclic loading with cycles above 109. To assess their operating safety, S-N relations of Ti-10 V-2 Fe-3 Al alloy in very high cycle fatigue(VHCF) regime are of concern and have been investigated in this work. Fatigue behavior including S-N curves and crack initiation mechanisms is reported. Two transitions of fatigue crack initiation mechanism, from internal crack initiation to surface crack initiation and from α_p cleavage to α_s/βdecohesion, occur when the stress ratio(R) and stress level are reduced. Fatigue limits exist at N_f = 6 × 10~7 cycles for all stress ratios except for 0.5. In the VHCF regime two kinds of internal crack initiation mechanisms exist, i.e., coalescence of cluster of α_p facets and α_s/β decohesion. Their mutual competition depends on the stress ratio and can be interpreted in terms of different stress character required for promotion on different internal crack initiation mechanism. Small crack propagation is discussed to be life controlling process under the stress ratio range from-0.5 to 0.1 during VHCF regime while under the stress ratio 0.5 VHCF, life almost refers to the life required for crack initiation.     

Crack growth process in GBF area of SUJ2 bearing steel in very high cycle fatigue regime

Abstract

The crack growth process in GBF of high strength bearing steel JIS SUJ2 is qualitatively investigated by low–high two-step variable amplitude loading (TSAL) tests. It is demonstrated that the GBF size reduces with the increase in applied stress amplitude, and that the GBF size at a given stress amplitude is a constant which is independent of inclusion size at the crack origin. The fatigue life at a given stress amplitude, which is proportional to ?8 power of the inclusion size, reduces with increasing inclusion size. It was shown by TSAL tests that GBF was formed at the earlier stage (approximate 10⁵ cycles corresponding to less than 1% total fatigue life in the regime N_f≧10⁷ cycles) and propagated hardly until near to the final life (more than 90% total fatigue life). After that the GBF crack will propagate rapidly to the ultimate size in a short time.     

On the relationship between fatigue limit,threshold and microstructure of a low-carbon Cr-Ni steel

The relationship between the fatigue limit stress range, Δσ_w, the threshold stress intensity factor, ΔK_th, and microstructure of low-carbon 12CrNi3A steel has been investigated. Non-propagating microcracks were observed on the surface of smooth specimens which has been subjected to at least 5 × 10⁶ cycles at the fatigue limit stress. The size of the cracks depended on the characteristic sizes of the microstructure of the material. Scanning electron microscopy showed that the fractographic characteristics in the near-threshold region of fatigue macrocrack growth were similar to those in the fatigue microcrack initiation region. This implies that the fatigue limit and fatigue threshold of the material have a similar physical meaning, both signifying the resistance of the material to the propagation of fatigue cracks. The relationship ΔK_th = 1.12Δσ_W √πα was shown to be valid, where a is a material parameter relating to microstructure, rather than to the length of a macrocrack. The results also showed that the value of a depends on the material and microstructure, and that both Δσ_W and ΔK_th will change if the microstructural characteristics of the material change.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Effect of small scale notches on the very high cycle fatigue of AISI 310 stainless steel

Fatigue behaviour of AISI 310 stainless steel has been investigated up to very high cycles. The fatigue crack initiation sites were found at the surface of the material. Persistent slip bands developed at the surface of the specimens led to the crack initiation. At lower stress levels, shallow persistent slip bands were found at the surface of the specimens, and the fatigue limit was obtained. Notched specimens showed lower fatigue lives. Notched specimens with higher stress concentration factor (K_t) showed higher fatigue strength reduction factor (K_f). It was found that shallow notches of depth ~100 µm may reduce the fatigue life substantially.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths

This paper is concerned with the use of the Modified Wöhler Curve Method (MWCM) applied in conjunction with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of mechanical components subjected to multiaxial cyclic loading and experiencing stress concentration phenomena. In more detail, our engineering approach takes as its starting point the idea that accurate estimates can be obtained by simply assuming that the value of the critical length, L_M, to be used to evaluate fatigue damage in the medium–cycle multiaxial fatigue regime is a function of the number of cycles to failure, N_f. In other words, the MWCM, which is a bi‐parametrical critical plane approach, is suggested here to be applied by directly post‐processing the linear‐elastic stress state damaging a material point whose distance from the notch tip increases as N_f decreases. According to the main feature of the TCD, the above L_M versus N_f relationship is assumed to be a material property to be determined experimentally: such an hypothesis results in a great simplification of the fatigue assessment problem because, for a given material, the same critical length can be used to estimate fatigue damage independent of the considered geometrical feature. The accuracy of the devised approach was checked by analysing about 150 experimental results we generated by testing V‐notched cylindrical samples made of a commercial cold‐rolled low‐carbon steel. The above specimens were tested under in‐phase and out‐of‐phase combined tension and torsion, considering the damaging effect of superimposed static stresses as well. Moreover, in order to better check its accuracy in assessing notched components subjected to complex loading paths, our method was also applied to several data sets taken from the literature. This extensive validation exercise allowed us to prove that the MWCM applied along with the TCD is successful in estimating medium‐cycle multiaxial fatigue damage (N_f values in the range 10⁴–10⁶), resulting in predictions falling within the widest scatter band between the two used to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that the proposed approach predicts multiaxial fatigue lifetime by post‐processing the linear elastic stress fields in the fatigue process zone: this makes our method suitable for being used to assess real components by performing the stress analysis through simple linear‐elastic FE models.     

Modeling and Failure Analysis of a Broken Railway Axle: Effects of Surface Defects and Inclusions

In the present work, the fatigue behavior of an axle was analyzed using modeling and experimental approaches. A failed axle was used for experimental studies. The experimental results were then analyzed in order to model and predict the fatigue life of axle. The three-dimensional finite element analysis was used to simulate the fatigue behavior of axle. The growth of a machining defect, 2 μm initial crack length, was simulated versus applied cycles. The changes in the stress intensity factor as a function of crack length were modeled as well. The model predicted that after about 5 × 10⁸ cycles there was an abrupt increase in the crack length, reaching a critical value of about 65 mm at around N _f = 5 × 10⁹ cycles, indicating that the longer the crack, the higher its growth will be. The experimental results were then compared with the modeling predictions. It is shown that the latter are in a good agreement with the former. The results obtained in this study do give a basis for evaluation of single scratch or notch produced by improper machining.     

Driving forces for localized corrosion‐to‐fatigue crack transition in Al–Zn–Mg–Cu

Research on fatigue crack formation from a corroded 7075‐T651 surface provides insight into the governing mechanical driving forces at microstructure‐scale lengths that are intermediate between safe life and damage tolerant feature sizes. Crack surface marker‐bands accurately quantify cycles (N_i) to form a 10–20 μm fatigue crack emanating from both an isolated pit perimeter and EXCO corroded surface. The N_i decreases with increasing‐applied stress. Fatigue crack formation involves a complex interaction of elastic stress concentration due to three‐dimensional pit macro‐topography coupled with local micro‐topographic plastic strain concentration, further enhanced by microstructure (particularly sub‐surface constituents). These driving force interactions lead to high variability in cycles to form a fatigue crack, but from an engineering perspective, a broadly corroded surface should contain an extreme group of features that are likely to drive the portion of life to form a crack to near 0. At low‐applied stresses, crack formation can constitute a significant portion of life, which is predicted by coupling macro‐pit and micro‐feature elastic–plastic stress/strain concentrations from finite element analysis with empirical low‐cycle fatigue life models. The presented experimental results provide a foundation to validate next‐generation crack formation models and prognosis methods.     

Fatigue life estimation after crack repair in 6005 A-T6 aluminium alloy using the cold expansion hole technique

In this paper, the hole drilling (HD) and the cold expansion (CE) processes, which were used as a technique for crack repair, were investigated in order to estimate the beneficial effects on fatigue crack initiation (FCI). The FCI life is defined as the number of cycles to initiate a new crack of 0.2 mm on the surface of the specimen. Three hole radii and three degrees of cold expansion (DCE%) values were tested after a crack propagation period. Crack retardation after the CE process was observed. This phenomenon is due to two mechanisms: retardation owing to both geometric and mechanical effects, which is produced by the stress concentration at the drilled hole, and the large strain‐induced compressive residual stresses around the hole. In this report, the influence of the loading conditions was studied. For high values of the stress intensity factor range ΔK_ρ around the hole (based on the pseudo crack length a + ρ), the number of cycles corresponding to crack initiation N_i is low. At the edge of the hole, the maximum stress range can be approximated by the following formula: Δσ_max = 2ΔK_ρ /√πρ , where ρ is the hole radius and ΔK_ρ is the related stress intensity factor range.The FCI life extension, defined by the number of cycles corresponding to crack re‐initiation N_i , is related to the relative maximum stress range ratio R_σ = [(Δσ_max )/(Δσ_max )_th ] where (Δσ_max )_th is the value of the threshold maximum stress range obtained when N_i = 2 × 10⁶ cycles. The relationship between N_i and R_σ may be written as a power function.     

A statistical evaluation of micro‐crack initiation in thermally cut structural elements

The paper presents a numerical modelling of fatigue crack initiation in thermally cut structural elements by using improved Tanaka–Mura crack nucleation model. The main goal of the study is to analyse the influence of different grain orientations generated with Voronoi tessellation on the crack initiation period. The numerical modelling of the crack initiation period is performed on the test specimens made of high strength steel with martensitic microstructure. Because the specimens are assumed to be thermally cut without any additional treatment, surface roughness is taken into account in the numerical simulation. Several computational analyses with different grain orientations are performed on the each stress level. Therefore, the stress cycles interval [N₁, N₂] in which the crack is expected to be initiated with the probability P(N) is determined by using statistical analyses of obtained computational results. Experimental testing is also performed on the uniaxial test machine by stress ratio R = 0.1.     

A probabilistic approach for thermal shock fatigue life of glass

This paper presents a probabilistic approach for predicting fatigue life of glass subjected to near‐ΔT_C (critical temperature difference) thermal shock which exhibits little subcritical crack extension. First, thermal shock fatigue life N_f was derived as a function of temperature difference ΔT, fracture probability F and Biot's modulus β from the slow crack growth concept in conjunction with the Weibull distribution model. Next, thermal shock fatigue tests as well as flexural tests were performed for borosilicate glass to measure ΔT_C and N_f versus ΔT. The parameters associated with slow crack growth were then determined from the experimental results while the heat transfer coefficient h or β was obtained with the aid of finite element analysis. Thirdly, the thermal shock fatigue diagram (ΔT?N_f curves) was depicted for various values of β. Finally, crack length was simulated on the basis of the present approach.