Inertial effects on fatigue crack growth

In this paper, a cohesive zone model is used to study the influence of inertial effects on crack growth considering cyclic loading in homogenous rate‐independent materials. Quasi‐static and dynamic solutions are compared in order to establish the conditions in which the inertial effects become important in the analysis. It is discussed how speed and frequency of the loading and specimen sizes modify crack growth characteristics. In general, an increase in the loading frequency leads to a higher propagation velocity. Very high loading frequencies may lead to the formation of microcracks ahead of the crack tip and may change the failure mode of the cracked structure from crack propagation to uniform debonding. This work shows that inertial effects are specially noticeable for frequencies in the kHz range. However, applied frequencies close to natural frequencies of the cracked specimen can give rise to strong inertial effects and then a substantial reduction of fatigue life for much lower frequencies. This work also shows that critical frequencies depend on the specimen size.     

Stress intensity factors for cracked triangular cross‐section thin‐walled tubes

For one kind of finite‐boundary crack problems, the cracked equilateral triangular cross‐section tube, an analytical and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate and the principle of virtual work. Different from the classical crack extension energy release rate, the crack surface widening energy release rate can be defined by the G*‐integral theory and expressed by stress intensity factors. This energy release rate can also be defined easily by the elementary strength theory for slender structures and expressed by axial strains and loads. These two forms of crack surface widening energy release rate constitute the basis of a new analysis method for cracked tubes. From present discussions, a series of stress intensity factors are derived for cracked equilateral triangular cross‐section tubes. Actually, the present method can also be applied to cracked polygonal tubes.     

Evaluation of temperature‐sensitive fatigue crack propagation of a high‐speed railway wheel rim material

The fatigue crack growth rate (FCGR) of ER8C high‐speed railway wheel rim material was tested at various service temperatures. The temperature sensitivity of fatigue crack propagation was evaluated, and the effect of temperature on the crack propagation mechanism was analyzed. The obtained results indicate a fatigue ductile‐to‐brittle transition (FDBT) point at ?20°C for the ER8C wheel rim materials. A reverse relationship was found between FCGR and temperature for the near threshold and Paris regimes when the temperature was below the FDBT point. However, no evident changing rule was found when the temperature was above this transition point. An evident fatigue crack propagation mode transition was found from lamellar tearing to intergranular cracks, which was related to the FDBT for the near‐threshold regime.     

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

Non‐planar mixed‐mode growth of initially straight‐fronted surface cracks,in cylindrical bars under tension,torsion and bending,using the symmetric Galerkin boundary element method‐finite element method alternating method

In this paper, the stress intensity factor (SIF) variations along an arbitrarily developing crack front, the non‐planar fatigue‐crack growth patterns, and the fatigue life of a round bar with an initially straight‐fronted surface crack, are studied by employing the 3D symmetric Galerkin boundary element method‐finite element method (SGBEM‐FEM) alternating method. Different loading cases, involving tension, bending and torsion of the bar, with different initial crack depths and different stress ratios in fatigue, are considered. By using the SGBEM‐FEM alternating method, the SIF variations along the evolving crack front are computed; the fatigue growth rates and directions of the non‐planar growths of the crack surface are predicted; the evolving fatigue‐crack growth patterns are simulated, and thus, the fatigue life estimations of the cracked round bar are made. The accuracy and reliability of the SGBEM‐FEM alternating method are verified by comparing the presently computed results to the empirical solutions of SIFs, as well as experimental data of fatigue crack growth, available in the open literature. It is shown that the current approach gives very accurate solutions of SIFs and simulations of fatigue crack growth during the entire crack propagation, with very little computational burden and human–labour cost. The characteristics of fatigue growth patterns of initially simple‐shaped cracks in the cylindrical bar under different Modes I, III and mixed‐mode types of loads are also discussed in detail.     

Strength and fatigue strength of a similar Ti‐6Al‐2Sn‐4Zr‐2Mo‐0.1Si linear friction welded joint

Strengths for monotonic and cyclic loadings of similar overmatching Ti‐6Al‐2Sn‐4Zr‐2Mo‐0.1Si (Ti6242) linear friction welds (LFW) were studied and compared with the parent material (PM) behaviour. Non‐destructive synchrotron observations revealed the presence of pores in the weld interface. The weld centre zone (WCZ) showed a higher strength leading to lower macroscopic ductility of the cross‐weld samples. Local strain and normalized strain rate have been assessed by stereo digital image correlation (DIC) and revealed an early plastic activity at yielding in the vicinity of the WCZ attributed to residual stresses. For the target life, the fatigue strength was slightly reduced but compromised by a strong scatter. Indeed, an internal fish‐eye fatigue crack initiation was found on an unexpected dendritic defect that was very different from the PM microstructure and the known martensitic α′ in the WCZ. The dendritic defect was linked to surface contamination prior to welding and led to melting.     

Transferability of specimen J–R curve to straight pipe with circumferential surface flaw

Specimen J–R curve is extensively used for structural integrity of large components. It is well known that J–R curve heavily depends on constraint level ahead of crack tip in remaining ligament. In earlier work, it was demonstrated that J–R curve from Three Point Bending (TPB) specimen is transferable to straight pipe with circumferential through wall crack. In this paper, the transferability of J–R curve is investigated from TPB specimen to pipe with circumferential surface crack. A 16 in. diameter pipe with circumferential surface crack and TPB specimen machined from same piping material (SA333Gr6 Steel) are tested. Consequently, 3D finite element analysis (FEA) has been performed on surface cracked pipe and TPB specimen. Crack‐initiation load is also predicted for surface cracked pipe by FEA and compared with experimental result. J–R curve is calculated for the pipe using experimental data, that is, load, load line displacement and crack growth. J–R curve of pipe is compared with TPB specimen and it is found that the pipe is predicting much higher J–R curve than TPB. This difference of J–R curve is investigated by evaluating stress triaxiality in remaining ligament for both cases. Stress triaxiality is quantified using triaxiality factor (h) ahead of crack tip for pipe and TPB specimen. It is found that the TPB specimen has considerably higher constraint level than pipe with surface crack, which is well supported by trend of J–R curves for specimen and pipe. A study has also been carried out to investigate the effect of internal pressure on the stress triaxiality. It is found that there is negligible difference in stress triaxiality because of internal pressure. The stress triaxiality is re‐established as a qualitative parameter to assess the transferability of J–R curve from specimen to component.     

Corrosion fatigue behaviour of a 15Cr‐6Ni precipitation‐hardening stainless steel in different tempers

Systematic fatigue experiments, including both high‐cycle axial fatigue (S–N curves) and fatigue crack growth (FCG, da/dN–ΔK curves), were performed on a precipitation‐hardening martensitic stainless steel in laboratory air and 3.5 wt% NaCl solution. Specimens were prepared in three tempers, i.e. solution‐annealed (SA), peak‐aged (H900) and overaged (H1150) conditions, to characterize the effects of ageing treatment on the corrosion fatigue (CF) resistance. S–N results indicated that fatigue resistance in all three tempers was dramatically reduced by the aqueous sodium chloride environment. In addition, the smooth‐surface specimens in H900 temper exhibited longer CF lives than the H1150 ones, while those in SA condition stood in between. However, for precracked specimens, the H1150 temper provided superior corrosive FCG resistance than the other two tempers. Comparison of the S–N and FCG curves indicated that early growth of crack‐like defects and short cracks played the major role in determining the CF life for smooth surface. The differences in the CF strengths for the S–N specimens of the given three tempers were primarily due to their inherent differences in resistance to small crack growth, as they were in the air environment.     

Fatigue crack propagation characteristics of high‐tensile steel wires for bridge cables

The viability of single edge cracked sheet test method for rapidly determining the crack propagation characteristics of steel wires was investigated. First, fatigue tests under 3 different stress ratios were conducted on the sheet specimens which were manufactured from a kind of widely used cable wires. The test data were analysed, and the crack growth rates of sheet specimens were constructed by Walker model. Then, a series of fatigue tests were performed on notched round‐bar specimens to verify the predictability of Walker model parameters. Moreover, the experimental results obtained in different studies on crack propagation characteristics of steel wires were discussed. The results show that the crack propagation characteristics of sheet specimens behave a certain dependence on depth. The sheet crack growth laws can be well used to predict the fatigue life of notched bar specimens when the mechanical heterogeneity is considered. For bridge cable steels, the rational values for the exponent parameter of Paris law, m, should be close to 3.     

Crack closure in friction stir weldment using non‐linear model for fatigue crack propagation

The fatigue crack propagation in a friction stir‐welded sample has been simulated herein by means of two 3‐dimensional finite element method (FEM)‐based analyses. Numerical simulations of the fatigue crack propagation have been carried out by assuming a residual stress field as a starting condition. Two initial cracks, observed in the real specimen, have been assessed experimentally by performing fatigue tests on the welded sample. Hence, the same cracks have been placed in the corresponding FE model, and then a remote load with boundary conditions has been applied on the welded specimen. The material behaviour of the welded joint has been modelled by means of the Ramberg‐Osgood equation, while the non‐linear Kujawski‐Ellyin (KE) model has been adopted for the fatigue crack propagation under small‐scale yielding (SSY) conditions. Owing to the compressive nature of the residual stress field that acts on a part of the cracked regions, the crack closure phenomenon has also been considered. Then, the original version of the KE law has been modified to fully include the closure effect in the analysis. Later, the crack closure effect has also been assessed in the simulation of fatigue propagation of three cracks. Finally, an investigation of the fracture process zone (FPZ) extension as well as the cyclic plastic zone (CPZ) and monotonic plastic zone (MPZ) extensions have been assessed.     

Prediction of crack initiation plane direction in high‐cycle multiaxial fatigue with in‐phase and out‐of‐phase loading

A new method for predicting crack plane direction in high‐cycle multiaxial fatigue is proposed. This method considers material properties and loading conditions. Two situations are considered: (i) in‐phase loading, where the crack plane direction only depends on the loading condition and material properties have little influence on it, and (ii) out‐of‐phase loading, where the crack plane direction is affected by both loading conditions and material properties. The prediction accuracy is assessed by comparison with several experimental results, including different loading conditions and materials. The results show that the proposed method provides a good prediction capability for these experiments.     

Intrinsic material length,Theory of Critical Distances and Gradient Mechanics: analogies and differences in processing linear‐elastic crack tip stress fields

The Theory of Critical Distances (TCD) is a bi‐parametrical approach suitable for predicting, under both static and high‐cycle fatigue loading, the non‐propagation of cracks by directly post‐processing the linear‐elastic stress fields, calculated according to continuum mechanics, acting on the material in the vicinity of the geometrical features being assessed. In other words, the TCD estimates static and high‐cycle fatigue strength of cracked bodies by making use of a critical distance and a reference strength which are assumed to be material constants whose values change as the material microstructural features vary. Similarly, Gradient Mechanics postulates that the relevant stress fields in the vicinity of crack tips have to be determined by directly incorporating into the material constitutive law an intrinsic scale length. The main advantage of such a method is that stress fields become non‐singular also in the presence of cracks and sharp notches. The above idea can be formalized in different ways allowing, under both static and high‐cycle fatigue loading, the static and high‐cycle fatigue assessment of cracked/notched components to be performed without the need for defining the position of the failure locations a priori. The present paper investigates the existing analogies and differences between the TCD and Gradient Mechanics, the latter formalized according to the so‐called Implicit Gradient Method, when such theories are used to process linear‐elastic crack tip stress fields.     

The influence of partial surface shot peening on fatigue crack growth behaviour of a high‐strength ferritic steel

The effects of partial surface shot peening on the fatigue crack growth behaviour of a ferritic steel have been experimentally investigated in this paper. Dog‐bone specimens fabricated from Optim700QL were tested under tension‐tension fatigue loads. Three distinct extents of partial shot peening, with respect to the crack tip and specimen symmetry line, were tested. The fatigue crack growth results from these experiments have been compared with those obtained from the same specimen geometry but with no peening. The results show that the residual stress fields formed ahead of the initial notch tip due to the partial peening process play a significant role in the fatigue crack growth behaviour of the material and effectively result in accelerated crack propagation at the midwidth of the specimens. It has been shown in this study that partial peening can lead to a fatigue crack growth rate around twice as fast as that of the unpeened specimen.     

A methodology for predicting creep/fatigue crack growth rates in Ti 6246

A methodology has been developed which is capable of predicting creep/fatigue crack growth rates at ambient and elevated temperatures in Ti 6246. Predictions are based on finite element analysis and strain-control testing of plain specimens. The prediction of fatigue crack growth rates for a given crack configuration and cyclic plastic zone size is assumed to be consistent with the processes leading to crack initiation in plain specimens. Such an assumption leads to the conclusion that a similar stress–strain profile will lead to similar lives in both the plain specimens and in the cyclic plastic zone ahead of a crack in a notched specimen. Therefore, fatigue crack growth results from the accumulation of damage in the cyclic plastic zone ahead of the crack tip. Once the damage accumulated in this element of material becomes critical, the crack propagates through the damaged region into a new region of virgin material where the process of damage accumulation begins again. The creep/fatigue model is described and assessed with reference to measured fatigue crack growth rate data for Ti 6246 at 20 °C and 500 °C.     

The effect of T‐stress on crack‐tip plastic zones under mixed‐mode loading conditions

In this paper, the influence of T‐stress on crack‐tip plastic zones under mixed‐mode I and II loading conditions is examined. The crack‐tip stress field is defined in terms of the mixed‐mode stress intensity factors and the T‐stress using William's series expansion. The crack‐tip stress field is incorporated into the Von Mises yield criteria to develop an expression that determines the crack‐tip plastic zone. Using the resultant expression, the plastic zone is plotted for various combinations of mode II to mode I stress intensity factor ratios and levels of T‐stress. The properties of the plastic zone affected by T‐stress and mixed‐mode phase angle are discussed. The observations obtained on plastic zones variations are important for further fatigue and fracture analyses for defects in engineering structures under mixed‐mode loading conditions.     

Interior failure mechanism and life prediction of surface‐treated 17Cr‐Ni steel under high and very high cycle fatigue

The understanding of very high cycle fatigue (VHCF) mechanisms is critical to the development of life prediction approach. For this purpose, high cycle fatigue (HCF) and VHCF properties of a surface‐treated 17Cr‐Ni steel were investigated under axial loading with stress ratio of 0. This steel exhibits the constantly decreasing S‐N characteristics associated with the inclusion‐fisheye induced failure under the HCF and the inclusion‐FGA (fine granular area)‐fisheye induced failure under the VHCF. The cyclic pressing plays an important role in the FGA formation process, but the FGA still can be observed for the stress ratio of zero due to the slight crack closure effect. Two life modelling approaches associated with related failure mechanisms in the HCF and VHCF regimes are proposed based on the agreement between experimental and predicted results.     

Fatigue lifetime estimation of railway axles

The railway axles are subjected to cyclic loading during their operation. Their load is of long-term nature, therefore a real risk of fatigue failure exists. This failure could lead to derailment of the whole train with serious consequences. To prevent such scenario, the railway axles have to be safely removed from operation before their final failure occurs.This paper presents methodology for the residual fatigue lifetime prediction of the railway axle based on the linear elastic fracture mechanics concept. The methodology contains estimation of the critical position of initial crack, prediction of the fatigue crack front shape development during crack propagation, separation of the bending and press-fitting contributions to the axle load, experimental measurement of the crack growth kinetics of EA4T steel and subsequent estimation of the residual fatigue lifetime of railway axle. Part of the presented study is also devoted to the probability aspects of determination of material characteristics describing fatigue crack propagation and retardation effects caused by existence of plastic zone ahead of propagating fatigue crack. Described methodology is already applied in the design process of new railway axles in Bonatrans company.     

Fatigue thresholds of holed components under in‐phase and out‐of‐phase torsional and axial loadings

The resistance‐curve (R‐curve) method was applied to the prediction of the fatigue thresholds of notched components under in‐phase and out‐of‐phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin‐walled tubular specimen of medium‐carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack was nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in‐phase and for out‐of‐phase loadings with 45° phase difference. For out‐of‐phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

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

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