The formal analogy between Tanaka–Mura and Weibull models for high‐cycle fatigue

The micro‐mechanical model for fatigue crack initiation proposed by K. Tanaka and A. Mura in 1981 is analysed and rewritten in a different form, which allows highlighting its formal analogy with an empirical model previously introduced by W. Weibull in 1934. The result is a unified phenomenological model that can be used for both fatigue data fitting and life predictions. Strengths and limitations of the model are discussed and a case study of experimental data fitting is presented. In the example application, the model parameters of 18NiCrMo5 carburized steel are obtained through the likelihood maximization over fatigue test data. A comparison between the estimated parameters for the material in two different conditions (untreated and deep cryogenically treated) is then given to confirm the micro‐mechanical changes that should be induced by the cold processing and to point out the direction for further investigations.     

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.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Local strain accumulation in fatigue crack propagation process of Ti‐6Al‐4V alloy

Fatigue crack growth behaviours of the titanium alloy Ti‐6Al‐4V, with two different microstructures, at different maximum stresses were identified by digital image correlation technique. Full‐field strains were monitored around fatigue cracks after consecutive cycles in fatigue crack growth experiments. Results indicated that the Ti‐6Al‐4V alloy with a bi‐modal microstructure had a better fatigue resistance than that with a primary‐α microstructure. Typical behaviours of small cracks and the evolution of multi‐scale fatigue cracks were clarified. The strain accumulations around the micro‐notch and fatigue crack increased with increasing number of load cycles. On the basis of von Mises strain mapping, it was found that crack growth rate could be characterized by crack‐tip plastic zone size.     

Cyclic behaviour of 12% Cr ferritic‐martensitic steel upon long‐term on‐site service in power plants

The strain‐controlled and stress‐controlled low‐cycle fatigue behaviour of served 12% Cr ferritic–martensitic steel is conducted at room temperature. Continuous softening is observed at both control modes, and the fitting results show that the fatigue properties of 12% Cr steel are not reduced significantly after 230 000 h service at 550 °C/13.7 MPa. Scanning electron microscopy has been employed to investigate the microstructure evolution after long‐term service. It is proved that the decomposition of martensite laths structure and the coarsening of carbides at grain/lath boundaries are the main reasons why the pipe bursts after 180 000 h service at 550 °C/17.1 MPa. The fracture under both control modes has been observed by using scanning electron microscopy, and it indicates coarse carbides along grain/lath boundaries are favourable sites for micro‐crack nucleation and the secondary cracks along the fatigue striations are formed by the connection of micro‐cracks nucleated during fatigue behaviour.     

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

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

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

A dislocation barrier model for fatigue limit – as determined by crack non-initiation and crack non-propagation

Fatigue damage is caused by cyclic slip, and cyclic slip is driven by dislocation glide force. In order to cause fatigue damage, the cyclic glide force has to overcome the resistance of the primary and secondary dislocation barriers. Based on this cyclic damage process, the following diverse fatigue phenomena are synthesized into an integral and self-consistent analysis: Fatigue damage occurs in persistent slip bands (Hempel, 1956; Smith, 1957; Forsyth, 1957, 1961, 1963), and a nucleated fatigue micro crack is a shear crack (Forsyth, 1961). Pre-cracking fatigue damage is confined to the surface layer of a stressed metal (Wood et al., 1963). Fatigue limit is inversely related to grain size as shown in brass (Sinclair and Craig, 1952), in mild steels (Klesnil, Holzmann, Lukáš and P. Ryš 1965; Yoshikawa and Sugeno, 1965; and Taira, Tanaka, and Hoshina, 1979), and in ferritic-martensitic steel, (Kunio, Shimizu, and Yamada, 1969). Forrest and Tate (1964) found fatigue cracks in fine-grained brass at an alternating stress even below the fatigue limit. The cracks were within the boundaries of single grains. But they found no cracks in coarse-grained brass below the fatigue limit. The analysis synthesizes all of these experimental observations. The analysis is based on a realistic physical model. With a better understanding of the model and an improved calculation of the glide force, quantitative evaluations of the resistance of the dislocation barriers would eventually be possible. The needs for additional research are pointed out. A number of means of improving fatigue strength, based on the analysis, are suggested or explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

微观组织与裂纹闭合效应对40CrNiMo钢疲劳短裂纹扩展的影响

对具有粗、细晶粒组织的40CrNiMo 钢进行了疲劳短裂纹扩展试验研究。试验和分析结果表明,短裂纹扩展的偏折强烈,裂纹闭合效应较小。粗晶组织比细晶组织的裂纹偏折更大,粗糙度诱发闭合效应更强,因而裂纹扩展较幔。微观组织通过对闭合效应的作用进而影响了疲劳短裂纹的扩展行为。     

Relationships between crack opening displacement,alloy variables,and crack detection sensitivity

Alloy grain size is known to influence both the propagation path and the closure stress of surface fatigue cracks in many alloys. The general trend is for the path to be more tortuous and the closure stress to be larger, the larger the grain size. By use of Ti Al-4V and Al 7075-T6, the effects of grain size on the nondestructive detection of surface cracks which might arise from closure stress and path irregularity variables were evaluated. Titanium specimens were inspected using an acoustic harmonic generation technique, and it was discovered that the major source of harmonic signals was grain sized crystallographic cracks. Harmonic signals were larger during fatigue in an 8-µm compared to a 4-µm grain sized alloy, as there were more grain sized cracks in the large grain material. Crack closure was found to be extremely important in determining the reflected acoustic amplitude obtained in inspecting small (100–1000 µm) cracks in Al 7075-T6 using a critical angle technique. Average received amplitudes were an order of magnitude smaller for cracks at zero load than for those opened by a tensile stress. The scatter in the reflected amplitude was also large, apparently as the result of variations in the degree of the closure from crack to crack. For the 7075 material, the important effect of larger grain size was to increase the irregularity of the crack path, making the small cracks more visible acoustically at azimuthal angles not normal to the crack plane.     

Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

Effects of annealing and quenching on fatigue behaviour in type 444 ferritic stainless steel

In order to understand the effects of annealing and quenching on fatigue behaviour in type 444 stainless steel, fully reversed axial fatigue tests have been performed using smooth specimens of heat‐treated materials in laboratory air and 3%NaCl aqueous solution. Three materials subjected to different heat treatments, annealing at 960 and 1000 °C, and water‐cooling at 960 °C, were prepared. In laboratory air, the fatigue limit of the annealed specimens was lower than that of the as‐received specimen and decreased with increasing annealing temperature. The subsequent grain coarsening from the heat treatments was primarily responsible for the lower fatigue strength in the annealed specimens. The fatigue strength of the water‐cooled specimen was lower than that of the corresponding annealed specimen. In the annealed specimens, cracks were generated within ferritic grains, while in the water‐cooled specimen, at or near grain boundaries. In 3%NaCl solution, the fatigue strengths of all specimens decreased compared with those in laboratory air. Only in the water‐cooled specimens, crack initiation at grain boundary and intergranular crack growth were observed, indicating the most sensitive to corrosion environment.     

Influence of bulk damage on crack initiation in low‐cycle fatigue of 316 stainless steel

To investigate the effect of bulk damage on fatigue crack initiation, crack initiations due to low‐cycle fatigue of Type 316 stainless steel were observed by electron backscatter diffraction (EBSD) and scanning electron microscopy. The EBSD observations showed that local misorientation developed inhomogeneously due to the cyclic strain, and many cracks were initiated from the slip steps and grain boundaries where the local misorientation was relatively large. The crack initiations could be categorized into two types: enhancement of the driving force by geometrical discontinuity (slip steps and notches), and reduction of material resistance against crack initiation caused by accumulated bulk damage at grain boundaries. In particular, more than half of the cracks were initiated from grain boundaries. However, in spite of the significant bulk damage, the fatigue life was extended by removing the surface cracks under strain of 1 and 2% amplitude. The stress state at the microstructural level was changed by the surface removal, and the damaged portion did not suffer further damage. It was concluded that although bulk damage surely exists, the fatigue life can be restored to that of the untested specimen by removing the surface cracks.     

Initiation and propagation behaviour of fatigue cracks in hard-shot peened Type 316L steel in high cycle fatigue

Observations of fatigue crack growth behaviour were made during rotating‐bend testing of hard‐shot peened Type 316L steel. From the results of these observations, the crack that developed in the axial direction was observed and the mechanism of the fatigue crack properties was clarified as follows: (1) Small circumferential surface fatigue cracks were detected at 60% of the fatigue lifetime. These cracks propagated very slowly in both the circumferential and radial directions. (2) When a radial crack reached a depth of between 150 and 350 μm, axial fatigue cracks were formed. (3) In the next stage, either the radial or the axial fatigue cracks continued propagating, or an inwards growing radial crack formed from the axial crack. (4) In the final stage, the circumferential surface crack began to grow rapidly and resulted in fracture. (5) The fracture type of hard‐shot peened Type 316L is a particular type of surface fracture.     

On propagation of short rolling contact fatigue cracks

Recent accidents involving railway rails have aroused demand for improved and more efficient rail maintenance strategies to reduce the risk of unexpected rail fracture. Numerical tools can aid in generating maintenance strategies: this investigation deals with the numerical modelling and analysis of short crack growth in rails. Factors that influence the fatigue propagation of short surface‐breaking cracks (head checks) in rails are assessed. A proposed numerical procedure incorporates finite element (FE) calculations to predict short crack growth conditions for rolling contact fatigue (RCF) loading. A parameterised FE model for the rolling‐sliding contact of a cylinder on a semi‐infinite half space, with a short surface breaking crack, presented here, is used in linear‐elastic and elastic–plastic FE calculations of short crack propagation, together with fracture mechanics theory. The crack length and orientation, crack face friction, and coefficient of surface friction near the contact load are varied. The FE model is verified for five examples in the literature. Comparison of results from linear‐elastic and elastic–plastic FE calculations, shows that the former cannot describe short RCF crack behaviour properly, in particular 0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is required instead.     

High-cycle fatigue properties in Ti–5% Al–2.5% Sn ELI alloy with large grain size at cryogenic temperatures

High‐cycle fatigue properties were investigated for Ti–5% Al–2.5% Sn ELI alloy with a mean α grain size of 80 μm, which had been used for liquid hydrogen turbo‐pumps of Japanese‐built launch vehicles. At cryogenic temperatures, the fatigue strength in high‐cycle region did not increase in proportion to increments of the ultimate tensile strength and the fatigue strengths at around 10⁶ cycles were about 300 MPa independent of test temperatures. Fatigue cracks initiated in the specimen interior independent of the test temperatures of 4 K, 77 K and 293 K. At 4 K and 77 K, several crystallographic facet‐like structures were formed at crack initiation sites. On the other hand, there were no facet‐like structures that could be clearly identified at the crack initiation sites at 293 K. Low fatigue strengths in longer‐life region at cryogenic temperatures could be attributable to the formation of large sub‐surface crack initiation sites, where large facet‐like structure are formed.     

On the determination of material parameters in crack initiation laws

Crack initiation along slip bands can be described by the Tanaka–Mura relation and its extensions. These relations are based on dislocation theory and determine the number of load cycles to reach a critical dislocation density for a given value of the resolved shear stress along the potential crack path. An important material parameter in these relations is the critical shear stress which is a threshold value for crack initiation, i.e. the number of cycles to crack initiation becomes infinitely high if the resolved shear stress along the potential crack path stays below this threshold value. This critical shear stress is determined using a database for microcrack initiation, microcrack growth, and coalescence obtained with a martensitic steel. The number of cracks per unit area, the so‐called crack density, was derived from this database as a function of the number of load cycles. These experimentally observed values of the crack density are compared to values obtained by simulating the crack initiation process using a random cell structure as a mesoscopic unit cell. A best fit is obtained for values of the critical shear stress between 110 and 160 MPa with the uncertainty both related to simplifications in the model and to limitations of the experimental analysis.     

Experiments and model predictions for fatigue crack propagation in riveted lap‐joints with multiple site damage

In this paper, the growth of long fatigue cracks up to failure in aircraft components is studied. A deterministic model is presented, able to simulate the growth of fatigue through cracks located at rivet holes in lap‐joint panels. It also includes criteria to assess the link‐up of collinear adjacent cracks in a MSD scenario. To validate the model, a fatigue test campaign was carried out on riveted lap‐joint specimens in order to produce experimental crack growth and link‐up data. Accurate measurements of naturally occurred surface cracks were automatically performed by the Image Analysis technique, thus allowing the tests to run 24 h a day. The comparison between experimental tests and numerical simulations is good, thus confirming the model as a useful tool for the assessment of fatigue life of aircraft riveted joints.     

Analysis of fatigue crack behaviour based on dynamic response simulations and experiments for tensile-shear spot-welded joints

Fatigue crack initiation and propagation behaviours were studied based on the dynamic response simulation by the three‐dimensional finite‐element analysis (FEA) and dynamic response experiments for tensile‐shear spot‐welded joints. The entire fatigue propagation behaviour from the surface elliptical cracks at the initiation stage to the through thickness cracks at the final stage was taken into consideration during the three‐dimensional FEA dynamic response simulations. The results of the simulations and experiments found that the fatigue cracks of spot‐welded joint from initial detectable crack sizes to crack propagation behaviour could be described by three stages. Approximately one‐half of the total fatigue life was taken in stage I, which includes micro‐crack nucleation and the small crack growth process; 20% of the total fatigue life in stage II, in which the existing surface crack propagates through the thickness of sheet and 30% of the total fatigue life in stage III, during which the through thickness crack propagates along the direction of plate width to the final failure. According to the relationship between the crack length and depth and the dynamic response frequency during the simulated fatigue damage process, the definition of fatigue crack initiation and propagation stages was proposed. The analysis will provide some information for the fatigue life prediction of the spot‐welded structures.     

Long fatigue life critical crack lengths*

A model based on surface strain redistribution and crack closure is presented for prediction of the endurance or fatigue limit stress by determining the threshold stress and critical length of short cracks that develop under microstructural control. The threshold stress first decreases with crack size to a local minimum then increases to a local maximum corresponding to the fatigue limit stress. This occurs at the critical crack length corresponding to about four grain diameters. The model is capable of determining the threshold stress range and depth of propagating and non‐propagating surface cracks as a function of stress ratio, material and grain size. The microstructure is shown to be particularly significant in the very long life regime (N_f ≈ 10⁹ cycles). When the surface cracks become non‐propagating, internally initiated cracks continue growing slowly, eventually reaching the critical crack length with failure occurring after a very high number of cycles (10⁷ < N_f < 10⁹ cycles).