Predicting the total fatigue life in metals

When a metal specimen is subjected to cyclic loading, a large number of initiated cracks will initiate in its volume. The specimen forms a sample of initial cracks: the larger specimen, the larger is the sample. In previous work of the author it was shown that the fatigue limit can be predicted by estimating the largest expectable crack depth with the help of statistics of extremes. In this paper it is shown that the fatigue crack initiation time above the fatigue limit can be predicted in an analogous manner. Instead of estimating the largest crack size with the distribution of maxima, prediction of the shortest expectable initiation time is obtained using the distribution of minima. Good agreement with extensive set of experimental data was obtained.The presented method offers a new way for estimating the total fatigue life of a component. When estimates of the crack initiation life and the critical crack size are obtained, the stable crack growth can be computed using Paris law. The estimate of the total fatigue life is obtained as the sum of initiation and crack growth lives. A method for constructing design curves for finding the crack initiation life for any material is presented.     

Fatigue limit of new precipitation-hardened aluminium alloy with distinct fatigue crack propagation limit

The goal of this study was to confirm the presence of fatigue limit in a plain specimen of a new precipitation-hardened aluminium alloy. The alloy was fabricated by adding 0.53% excess Mg to the standard 6061-T6 aluminium alloy with a balanced Mg₂Si composition. There were two challenges in this study: verification of the existence of fatigue limit in this new alloy and interpretation of the large scatter in specimen life at the low stress level amplitude. For the former, the existence of a fatigue limit was confirmed by a coaxing effect test. For the latter, the initiation and growth behaviors of a small fatigue crack at low stress amplitude were observed by plastic replica method not only with an optical microscope but also with a scanning electron microscope (SEM). The study results showed that the large scatter in specimen fatigue life at the low stress level amplitude was due to the anomalous initiation and growth behaviors of the small fatigue crack, which in turn was strongly influenced by local conditions. Finally, a conservative S–N curve of this new alloy evaluated by using a plain specimen could be obtained where a distinct knee point showed at cycles of about 10⁶.     

Fracture behaviour of a TiAl alloy under various loading modes

Tensile tests, compression tests, in situ tensile tests, bending tests, tensile fatigue tests and bending fatigue tests were carried out for a TiAl alloy. Based on the global experimental results and microscopic observations of the fracture surfaces and cracking behaviour on the side surfaces of tested specimens, the fracture mechanisms of fully lamellar (FL) TiAl alloys under various loading modes are summarized as following: (1) Cracks initiate at grain boundaries and/or interfaces between lamellae. (2) When a crack extends to a critical length, which matches the fracture loading stress the crack propagates catastrophically through entire specimen. (3) The crack with the critical length can be produced promptly by the applied load in the tensile and bending test or be produced step-by-step by a much lower load in the fatigue tensile test. (4) For fatigue bending tests, the fatigue crack initiates and extends directly from the notch root, then extends step-by-step with increasing the fatigue bending loads. The fatigue crack maybe extends through entire specimen at a lower fatigue load or triggers the cleavage through the whole specimen at a higher load. (5) In compressive tests, cracks initiate and propagate in directions parallel or inclined to the compressive load after producing appreciable plastic strains. The specimen can be fractured by the propagation of cracks in both directions.     

Evaluation of corrosion fatigue crack propagation life at low-pressure steam turbine rotor groove

The corrosion fatigue crack propagation life of Christmas-tree type rotor groove with three hooks is studied. Each corner of the hook can be a candidate for crack initiation site therefore the condition where cracks initiate and propagate simultaneously at several hook corners must be considered. When a blade is inserted in the rotor groove, narrow gap is introduced unavoidably between the rotor groove and the blade root. The effect of this narrow gap on the crack behavior must also be considered. A procedure was presented to assess the crack initiation and propagation behavior under such a condition. Using the procedure, crack initiation and propagation behavior was evaluated for several gap conditions. It was revealed that the gap condition had little effect on the relation between crack depth at the third hook corner and life consumption ratio (ratio of loading cycle to final failure life). A corrosion fatigue test was performed using a rotor groove model specimen, and the results were compared with the evaluation results.     

Fatigue crack initiation life prediction for aluminium alloy 7075 using crystal plasticity finite element simulations

An experimentally-validated approach for predicting fatigue crack initiation life of polycrystalline metals is developed based on crystal plasticity finite element (CPFE) simulations. In this approach, the microstructure used in the simulations possesses statistically the same grain size and crystallographic orientations as those obtained from electron back-scatter diffraction experiments. A backstress model is incorporated into the CP constitutive model to describe the mechanical behaviour of aluminium alloy (AA) 7075 under cyclic loading. The key variables of the prediction model, the energy efficiency factor and plastic strain energy density, are calibrated using a fatigue test on a round-notched AA7075 specimen at room temperature. The proposed approach is then validated by using another fatigue test to predict 69.1–87.3% of the experimentally measured fatigue crack initiation life. The effects of the microstructure and texture on the energy efficiency factor and fatigue life prediction are quantitatively determined. It is shown that for a given range of energy efficiency factors a similar range of life prediction is obtained. Since the proposed approach considers the heterogeneity of the microstructure, it can well capture the grain scale deformation localisation and therefore improve the precision of fatigue life prediction.     

Naked eye observations of microstructurally short fatigue cracks

An experimental methodology is described whereby interactions between cracks and microstructural barriers, and the consequent non-uniform propagation rates are observed without the assistance of any microscopy technique. This experimental procedure consists in increasing the grain size of Al1050 and Al1100 aluminum alloys specimens until the centimeter scale by applying a series of mechanical and heat treatments. By properly adjusting the strains, temperatures and furnace times of both stages a very precise control of the microstructural size is achieved. Once the thermomechanical treatment is completed and the sought microstructural size is obtained, a small circular notch is machined on each specimen in order to initiate the cracks at the desired location, and the samples are subjected to mode I fatigue loading. The fluctuating crack growth rate, the twist and tilt angles of the crack-plane at grain boundaries and crack arrest and branching can be easily observed with the naked eye. Production of secondary crack branches caused by roughness induced closure has also been observed. Tests were performed varying grain size and notch diameter and it was observed that the distance between successive minima in crack growth rate correlates well with the grain size of the specimens. .     

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.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

PREDICTING FATIGUE CRACK INITIATION LIFE OF AN ALUMINIUM ALLOY AT LOW TEMPERATURES

Abstract— A simple approach to predict the fatigue crack initiation (FCI) life of notches at low temperatures is developed. The stress cycle to initiate a 0.25 mm crack at a notch tip is presented as a function of an equivalent stress amplitude. The results of the study indicate that the FCI life of an aluminium alloy increases with decrease in temperature and the effect of temperature on the FCI resistance can be predict in the form of an FCI coefficient C and the FCI threshold. The coefficient C is the parameter controlling FCI resistance in the low cycle fatigue region and it can be calculated from the elasticity modulus and the strain hardening exponent. The threshold is the parameter governing FCI resistance in the high cycle fatigue region and its value depends mainly upon the endurance limit. The temperature- dependence of the endurance limit can be predicted by a thermal activation model. By means of this approach, the fatigue crack initiation life at low temperatures can be predicted from the material tensile properties without any additional low temperature fatigue tests and without any empirical modification so long as the endurance limit of the metal at room temperature is predetermined. The results suggest that this approach is applicable to other aluminium alloys.     

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.     

On the miner's damage hypothesis in notched specimens with emphasis on scatter of fatigue life

The subject of cumulative damage in fatigue is extremely complex and various discussions have been made for the conformity of experimental results with Miner's linear damage hypothesis. It seems, however, that one of the limitations of the conventional linear damage rule is that the nominal cycle ratio based on the mean value of scatter of fatigue life for a group of specimens does not represent the correct cycle ratio for individual specimen. The object of this study is to propose a method to evaluate the cumulative cycle ratio for each particular specimen, with emphasis on scatter of life. According to the statistical considerations of crack propagation curves obtained experimentally with a large number of mild steel notched specimens, it is confirmed that fatigue life of individual specimen will be estimated from the rate of crack growth at earlier stage of fatigue. From the results of two-level step tests, it is shown that the inherent cumulative cycle ratio for each specimen is calculated, and it also enables to evaluate the effect due to stress interaction associated with change of stress level.     

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.     

Microstructural effects on the short crack behaviour of a stainless steel weld metal during low-cycle fatigue

An experimental study into microstructural effects on short fatigue crack behaviour of 19 stainless steel weld metal smooth specimens during low-cycle fatigue is performed by a so-called ‘effective short fatigue crack criterion’. This material has a mixed microstructure in which it is difficult to distinguish the grains and measure the grain diameter. The columnar grain structure is made up of matrix-rich δ ferrite bands, and the distance between the neighbouring rich δ ferrite bands is an appropriate measurement for characterizing this structure. Particularly, the effective short fatigue cracks (ESFCs) always initiate from the bands of δ ferrite in the matrix in the weakest zone on one of the specimen surface zones which is orientated in accordance with the inner or outer surface of welded pipe from which the specimens were machined. These cracks exhibit characteristics of the microstructural short crack (MSC) and the physically small crack (PSC) stages. The average length of the ESFCs at the transition between MSC and PSC behaviour is ≈40 μm, while the corresponding fatigue life fraction is ≈0.3 at this transition. Different from previous test observations, the growth rate of the dominant effective short fatigue crack in the MSC stage still shows a decrease with fatigue cycling under the present low-cycle fatigue loading levels. A statistical evolution analysis of the growth rates reveals that the short fatigue crack growth is a damage process that gradually evolves from a non-ordered (chaotic) to a perfectly independent stochastic process, and then to an ordered (history-dependent) stochastic state. Correspondingly, the microstructural effects gradually evolve from a weak effect to a strong one in the MSC stage, which maximizes at the transition point. In the PSC stage, the effects gradually evolve from a strong to weak state. This improves our understanding that the short crack behaviour in the PSC stage is mainly related to the loading levels rather than microstructural effects.     

Fatigue crack initiation in Hastelloy X – the role of boundaries

In polycrystalline metals, microstructural features such as grain boundaries (GBs) influence fatigue crack initiation. Stress and strain heterogeneities, which arise in the vicinity of GBs, can promote the nucleation of fatigue cracks. Because of variations in grain size and GB types, and consequently variations in the local deformation response, scatter in fatigue life is expected. A deeper quantitative understanding of the early stages of fatigue crack nucleation and the scatter in life requires experimental and modelling work at appropriate length scales. In this work, experiments are conducted on Hastelloy X under fatigue conditions, and observations of fatigue damage are reported in conjunction with measurements of local strains using digital image correlation. We use a recent novel fatigue model based on persistent slip band–GB interaction to investigate the scatter in fatigue lives and shed light into the critical types of GBs that nucleate cracks. Experimental tools and methodologies, utilizing ex situ digital image correlation and electron backscatter diffraction, for high resolution deformation measurements at the grain level are also discussed in this paper and related to the simulations.     

载荷方向和焊缝余高对氩弧焊缝疲劳性能的影响

采用疲劳寿命测试和观测断口方法,研究焊接方向和焊缝余高对TC2钛合金氩弧焊缝疲劳性能的影响。结果表明:同种焊接方向,保留焊高试件的疲劳寿命低于去焊高试件;同种焊缝余高处理方式,斜焊试件的疲劳寿命高于直焊试件。去焊高试件于气孔缺陷处萌生裂纹,保留焊高试件疲劳裂纹起源于焊趾。裂纹扩展初期,裂纹均在焊缝内扩展,有明显的疲劳条带;扩展后期,斜焊试件裂纹穿过焊缝进入母材,存在典型的韧性疲劳条带。直焊试件疲劳瞬断区韧窝少而浅;斜焊试件在母材瞬断,韧窝多且密。     

A PROPOSED CRITERION FOR FATIGUE THRESHOLD: DISLOCATION SUBSTRUCTURE APPROACH

Abstract— A model for fatigue threshold has been proposed based on the dislocation subgrain cell structure that evolves at the crack tip in steels during the fatigue deformation process. The stabilized subgrain cells that develop in the material act as impenetrable barriers to dislocations in slip band pile-ups that emanate from the fatigue crack tip. The blocking of these dislocations tends to limit crack growth that occurs by crack tip emission of dislocations, thereby leading ultimately to the fatigue threshold condition. The grain size effect on threshold is deduced to be an indirect effect as it is proposed that the subgrain cell size is the controlling substructural parameter at the threshold stress intensity level. The subgrain cell size is shown to be proportional to the one-third power of the initial grain size.     

Further trials of a strain hardening index of fatigue damage

Previous cyclic-strain, smooth-specimen fatigue tests of α–β titanium alloys displayed an anomolous endurance enhancement for some of the alloy conditions. This could be explained by associating resistance to fatigue damage directly with the stress-normalized plastic strain hardening rate at the point of maximum cyclic tensile stress. Since this rate also controls the extent of stress-relaxation-induced tensile creep strain in each cycle, it was thought that fatigue damage might be associated with it. To test this hypothesis, data with varied load hold time, and over a full range of cyclic life, is reported here for some of the previously reported alloys of Ti-6A1-4V, as well as for an A36 steel plate. Notch fatigue tests of the A36, combined with those of Yoder et al. for the titanium alloys, are compared to the smooth specimen data. Results tend to support the damage-inhibiting role of the plastic strain hardening rate, but not of the creep strain portion of each cycle. Notch fatigue data agrees with smooth specimen trends if Neuber's rule is used to characterize the stress concentration factor, particularly with the A36 steel. As with Yoder's notch fatigue results, smooth specimen LCF life, though quite different in the range less than 10³ cycles, tends to converge near the endurance limit, thus mitigating adverse effects of alloy conditions which favor resistance to fatigue crack propagation in α-β titanium alloys.     

Fatigue behaviour of bare and pre-corroded magnesium alloy AZ31

Constant amplitude fatigue tests have been performed using smooth specimens of a rolled AZ31 magnesium alloy in order to assess the fatigue behaviour of the material. The tests were periodically interrupted and replicas were taken from the surface of the specimens in order to reveal crack initiation and early crack propagation. Based on the derived S–N curve a very high stress sensitivity of the fatigue life can be concluded; it may be attributed to the inability of the material to accumulate fatigue damage in terms of cyclic plasticity at the early stage of fatigue. Fatigue cracks initiate already after few fatigue cycles between strain incompatibility points (e.g. grain boundaries) due to difficulties in satisfying the von Mises criterion. The initiation and propagation mechanisms of the fatigue cracks are characterized as cleavage. Furthermore, the corrosion susceptibility of the material has been investigated in a salt spray environment. It becomes evident that the presence of corrosion damage, in terms of corrosion pitting, results in the development of stress concentration, facilitating essentially the initiation and propagation of fatigue cracks. Thus, the fatigue limit is reduced to 50% of the respective value of the un-corroded material.     

The physics of fatigue crack initiation

The fatigue life of a component can be expressed as the sum of two segments of life: (a) the number of loading cycles required to initiate a crack and (b) the number of cycles it takes that crack to propagate to failure. In this review, the primary emphasis is relating the fatigue crack initiation to the microstructure of the material. Many studies have focused on this phenomenon over the years and the goal of this paper is to put this work in perspective and encourage future work of fatigue in polycrystals based on the material’s microstructure. In order to address fatigue, it is necessary to understand the mechanisms that facilitate crack initiation. Slip irreversibilities exist in a material and accumulate during fatigue loading. At the defect level, irreversibilities are a result of dislocations: annihilating, cross-slipping, penetrating precipitates, transmitting through grain boundaries, and piling-up. These slip irreversibilities are the early signs of damage during cyclic loading. The dislocations subsequently form low-energy, stable structures as a means to accommodate the irreversible slip processes and increasing dislocation density during cyclic forward and reverse loading. The result is strain localizing in a small region within the materials, i.e. persistent slip bands and dislocation cells/bundles. Strain localization is a precursor to crack initiation. This review paper will focus on experimental observations of strain localization and the theory and numerical analysis of both slip irreversibilities and low energy configuration defect structures. This fundamental understanding is necessary to study persistent slip bands in FCC metals and alloys including the appropriate characterization, theory, and modeling. From this fundamental knowledge both micromechanical and crystal plasticity models can be used to predict crack initiation, which are also reviewed. Finally, this review ends with a discussion of the future of fatigue modeling and experiments.