STATISTICAL INVESTIGATION OF THE BEHAVIOUR OF SMALL CRACKS AND FATIGUE LIFE IN CARBON STEELS WITH DIFFERENT FERRITE GRAIN SIZES

Abstract— In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.     

SCATTER IN SMALL CRACK PROPAGATION AND FATIGUE BEHAVIOUR IN CARBON STEELS

In order to investigate the physical basis of scatter in fatigue behaviour, rotatory bending of smooth fatigue specimens was carried out using two steels with different microstructures (ferrite/pearlite and tempered martensite). Fifteen or sixteen specimens were fatigued at each stress, and the initiation and propagation behaviour of a crack which led to the final fracture were examined for all the specimens. The emphasis was to investigate the scatter characteristics of fatigue behaviour based on the scatter of small crack propagation data. The data were analysed by assuming the Weibull distribution, and a statistical investigation of the physical basis of scatter was performed, i.e. the distributions for fatigue life, crack propagation life and growth rate of small cracks were established and the relation between the scatter in those distributions was studied.     

THE AIR FATIGUE AND CORROSION FATIGUE OF A 13% Cr TURBINE BLADE STEEL

Abstract— Reasons for data scatter from fatigue tests on a high strength 13% Cr steel are discussed and data is presented for corrosion fatigue of this steel in a condensing steam environment. Rotating bend tests were performed at 50 and 3 Hz and tension-tension fatigue tests at 0.016 Hz and R =0.1. Some specimens were periodically inspected to identify sites of fatigue crack initiation. The role of inclusions in initiating fatigue cracks was investigated and it was found that the population of larger inclusions in the steel matched that at fatigue crack initiation sites. Comparison of fatigue lives from polished and abraded specimens indicated that there is little point in producing highly polished surfaces for this steel to try and improve fatigue life unless the inclusion content can be reduced in size and number. Corrosion fatigue data is presented indicating the magnitude of the reduction of fatigue life caused by condensing pure steam and condensing chlorinated steam.     

Initiation and propagation of fatigue cracks in cast IN 713LC superalloy

Fatigue life, initiation and propagation of cracks at 800 °C in a cast Ni-base superalloy IN 713LC were experimentally studied in high-cycle fatigue region. Load symmetrical cycling and cycling with high tensile mean load were applied. Both crystallographic crack initiation resulting in long Stage I crack growth and non-crystallographic Stage II propagation were observed. High scatter of fatigue life data was explained by: (i) variability in microstructural conditions for crystallographic crack initiation and propagation and by (ii) influence of casting defect size distribution. The fractographic observation supports the slip band decohesion mechanism of crack initiation and an important role of cyclic slip localization in persistent slip bands.     

疲劳裂纹扩展行为的跨尺度分析方法

该文以跨尺度应变能密度因子作为裂纹扩展的控制参量, 建立了跨尺度疲劳裂纹扩展模型。疲劳破坏全过程可用该模型进行统一描述, 而不必划分成疲劳裂纹形成与扩展两个不同阶段, 采用不同的理论分别进行分析。以LY12 铝合金板为例, 采用上述模型, 精确拟合出不同循环特征下的S-N试验曲线。当考虑材料微结构的影响时, 疲劳试验数据的发散性也可拟合出来。研究表明:材料初始缺陷及微结构在疲劳过程中的演化特性, 对于构件的疲劳寿命有显著影响, 是疲劳试验数据发散的主要原因。     

CORROSION FATIGUE OF AN HSLA STEEL

Abstract— Single-pitted specimens of an HSLA steel, were tested in laboratory air and in 1 M NaCl solution to study the influence of a corrosive environment on its fatigue life.
The growth of fatigue cracks and the partitioning of the fatigue life into fatigue crack initiation and fatigue crack propagation were studied by photographing the pit and the cracks developing on it periodically during testing. Non-propagating or dormant surface cracks were not observed in this study. Fractography using SEM showed the locations of fatigue crack initiation. The mechanisms of corrosion fatigue were studied by performing tests in 1 M NaCl at different test frequencies. Corrosion pits proved to be crack initiation sites. Hydrogen embrittlement was found to be unimportant in the corrosion fatigue of HSLA steel in this study. The 1 M NaCl corrosive environment appeared to reduce the fatigue life of this material by a dissolution mechanism. The effect of pit depth was studied by testing specimens having various pit depths. An effect of pit size was apparent. Fatigue life decreased with increasing pit depth. Pit depth, rather than the ratio of pit depth to pit diameter, influenced fatigue behaviour. A non-damaging pit depth was found.     

BIMODAL CONCEPT OF HIGH-CYCLE FATIGUE LIFE PREDICTION FOR CONSTANT AND VARIABLE AMPLITUDE FATIGUE

A bimodal concept for the prediction of the high-cycle fatigue life of structural details subjected to constant- or variable-amplitude loading is considered in this paper. The total fatigue life was separated into two phases: crack initiation and crack propagation. The portion of life spent in crack initiation was estimated by using S–N data obtained on smooth specimens. A fracture mechanics concept was used to calculate the portion of life spent in crack propagation, and the S–N curve, including the fatigue limit of a structural detail, was determined by using material properties and the geometry of the detail. The bimodal concept was applied to a welded stiffener and the results are compared with experimental data reported in the literature.     

FATIGUE STRENGTH OF A ROTOR STEEL SUBJECTED TO TORSIONAL LOADING SIMULATING THAT OCCURRING DUE TO CIRCUIT BREAKER RECLOSING IN AN ELECTRIC POWER PLANT

Abstract— The fatigue strength of notched specimens of a rotor steel was examined under variable torsional loading which simulates turbine-generator oscillations resulting from the high speed reclosing of transmission-line circuit breakers. The local stress-strain response at a notch root was analysed using Neuber's rule and the resulting complex strain sequences applied to smooth specimens. Using the rain flow analysis and the linear summation rule, fatigue lives of the smooth specimens were successfully predicted from constant amplitude fatigue life data in association with the cyclic stress-strain curve obtained by the incremental step method. Experimental crack initiation lives for notched specimens subjected to variable torsional loading were in excellent agreement with the theoretical curves derived from results on smooth specimens. According to the view that fatigue damage is equated to crack length, the propagation life of a mode II crack along the notch root was predicted to be actually coincident with the life to crack initiation at the notch root denned in this study, i.e. the life at the stage of finding a continuous circumferential crack.     

STATISTICAL INVESTIGATION OF THE EFFECT OF LABORATORY AIR ON THE FATIGUE BEHAVIOUR OF A CARBON STEEL

In order to clarify the effect of the atmospheric conditions on fatigue damage, rotary bending fatigue tests were carried out on smooth specimens of a normalized 0.37% carbon steel in controlled laboratory air. The air conditions used in the tests were moist air at 20 °C, moist air at 35 °C and dry air at 35 °C. The influence of atmosphere on crack initiation and propagation behaviour was investigated in detail based on successive observations of the surface. Experimental results showed that the fatigue life was superior at 20 °C compared to 35 °C by a factor of 2, while the effect of moisture was small compared to that of temperature. The statistical investigation of crack initiation and propagation behaviour indicated that the temperature strongly affects the crack initiation process; conversely, moisture plays an important role in the propagation process of cracks smaller than 0.3  mm. Moreover, the distribution characteristics of crack initiation life, crack propagation life, fatigue life and crack growth rate were analysed by assuming either a Weibull distribution or a log-normal distribution.     

Statistical description of the effect of Zr addition on the behavior of microcracks in Cu–6Ni–2Mn–2Sn–2Al Alloy

As possible substitutes for high-strength Cu–Be alloys, Cu–6Ni–2Mn–2Sn–2Al alloys have been developed. To clarify the physical background of the effect of trace Zr on the fatigue strength of such alloys, the initiation and propagation behavior of a major crack that led to the fracture of the tested specimens was monitored. When the stress amplitude was less than σ _a = 350 MPa, the fatigue life of the alloys with Zr was about 2–2.5 times larger than that of the alloy without Zr. When σ _a > 350 MPa, the effect of Zr addition on the fatigue life dramatically decreases as the stress amplitude increases. The increased fatigue life due to Zr addition resulted from an enhancement of the crack initiation life and microcrack growth life. The enhanced crack initiation life was mainly attributed to the strengthening of grain boundaries due to the precipitation of SnZr compounds. A statistical analysis of the behavior of multiple cracks was made to quantitatively evaluate the scatter in fatigue behavior. The statistical analysis supported the conclusions obtained from the behavior of a major crack.     

Damage tolerant design of cast components based on defects detected by 3D X-ray computed tomography

This paper presents the application of 3D X-ray computed tomography (XCT) in deterministic fatigue strength analysis of relatively large cast components and also probabilistic fatigue design of heavy-section castings. To this end, more than 100 fatigue specimens were cut from a rejected wind turbine hub casting. XCT was used to find the 3D map of defects in selected fatigue specimens. All fatigue specimens were axially tested at R = −1 at room temperature and fatigue life scatter was established. Fractography analysis of broken specimens was performed. For CT scanned specimens, the defect sizes and positions obtained by XCT, in conjunction with the (nearly homogeneous) stress distribution of the specimens were used to predict the fatigue life and also the position of the fatigue crack initiation site. The predicted fatigue life and crack initiation position for CT scanned specimens were compared with experimental results. The obtained defect distribution by XCT was used in a random defect analysis to establish the scatter of fatigue life for the analyzed specimens. The predicted fatigue life scatter was compared with experimental results. The comparison showed that random defect analysis can successfully predict the scatter of fatigue life and may be used to find the probability of failure of cast components, based on the given defect distribution.     

“Size effect” in the fatigue behavior of Friction Stir Welded plates

Comparative fatigue tests were carried out on Friction Stir Welded specimens of a 2195-T8 aluminum–lithium alloy that differed significantly in width. The width of the larger specimens was over thirteen times greater than that of the small specimens. Fatigue results showed a clear “size effect”, i.e. fatigue life of large specimens was about 40% of the corresponding value of small specimens. The Equivalent Initial Flaw Size methodology was adopted to correlate the two sets of results. Fatigue crack initiation life was disregarded with respect to crack propagation life, and fatigue life was evaluated only as propagation of a small pre-existing defect. Following this methodology, test results of small specimens were used to evaluate the initial equivalent flaw contained in each specimen. It was assumed that this data followed a normal distribution. The equivalent initial flaw in larger specimens was evaluated by simple geometrical considerations. A very good assessment of mean fatigue life and scatter in the fatigue results of large specimens was obtained by simulating the propagation of these defects. Calculations were carried out by taking also welding residual stresses into account, but the results demonstrated that this effect was not significant.     

基于Beach Marking方法的钢结构疲劳裂纹检测研究

研究裂纹的形成和扩展规律是钢结构疲劳断裂的一个重要课题。该文讨论了一种十分经济有效的检测钢结构疲劳裂纹萌生与扩展的方法,即Beach Marking方法。首先简要总结了该方法的发展历史和研究现状,并系统归纳了其基本原理和关键问题。同时,通过焊接H型钢梁的试验案例,探索该方法应用在大尺寸构件上的实际效果,并具体展示该方法的设计步骤和应用过程。试验表明,Beach Marking方法简单实用,关键在于设计合理的疲劳荷载序列;通过分析疲劳断口上留下的疲劳弧线,并结合断裂力学理论,可以获得疲劳裂纹的扩展规律和参数,为钢结构疲劳寿命数值分析提供科学依据。     

CRACK GROWTH ARRESTING PROPERTY OF A HOLE AND BRINELL-TYPE DIMPLE

Abstract— Fatigue tests of sheet specimens having a central crack were carried out to study the effects of holes and dimples on the arrest of fatigue crack propagation. Two holes were drilled at some distance from, and at either side of, a crack tip, and the dimple of a certain diameter was introduced by pressing steel balls in the specimen at a crack tip. Results showed that the two holes produced an increase in crack propagation life (about 3 times) when the holes were drilled at an appropriate distance. On the other hand, the effect of a dimple on the fatigue strength was remarkably large, i.e. in the greatest case a 2.2 times increase in the fatigue endurance limit of cracked specimens and about a 50 times increase in the crack propagation life, at stresses above the fatigue limit. The main reason for the remarkable recovery of fatigue strength was the residual compressive stresses produced by the dimple. To evaluate the effect of residual compressive stresses on the da/dN vs. δK relation, a simple model is proposed. By using this model, the effect of residual stresses on crack propagation can be estimated quantitatively. Furthermore, the fatigue life of dimpled specimens was estimated based on the model.     

Effects of Shot‐Peening on Fretting Fatigue Crack Growth Behavior in Ti‐6Al‐4V

Abstract: The effects of shot‐peening on fretting fatigue crack growth behaviour in titanium alloy, Ti‐6A1‐4V were investigated. Three shot‐peening intensities: 4A, 7A and 10A were considered. The analysis involved the fracture mechanics and finite element sub‐modelling technique to estimate crack propagation lives. These computations were supplemented with the experimentally measured total fretting fatigue lives of laboratory specimens to assess the crack initiation lives. Shot‐peening has significant effect on the initiation/propagation phases of fretting fatigue cracks; however this effect depends upon the shot‐peening intensity. The ratio of crack initiation and total life increased while the ratio of the crack propagation and total life decreased with an increase of shot‐peening intensity. Effects of residual compressive stress from shot‐peening on the crack growth behaviour were also investigated. The fretting fatigue crack propagation component of the total life with relaxation increased in comparison to its counterpart without relaxation in each shot‐peened intensity case while the initiation component decreased. Improvement in the fretting fatigue life from the shot‐peening and also with an increase in the shot‐peening intensity appears to be not always due to increase in the crack initiation resistance from shot‐peened induced residual compressive stress.     

Fatigue behaviour prediction of steel reinforcement bars using an adapted Navarro and De Los Rios model

Fatigue cracks tend to initiate on the rebar surface and therefore, the surface conditions may control their fatigue behaviour. This study investigates the influence of surface microstructure and roughness dispersion on the scatter and fatigue life of hot rolled (HR)–cold worked (CW) and quenched and self-tempered (QST) rebars. The stochastic nature of the fatigue life is mainly affected by the scatter of short cracks in the crack initiation phase. A model adapted from Navarro and De Los Rios (N–R) was developed to predict the crack initiation, including short crack growth, and long crack propagation phases. The crack initiation phase includes the dispersion inherent to the grain size, grain orientation ratio and multiple phases i.e., ferrite–pearlite and martensite as well as the roughness dispersion determined on the rebar surface and the influence of the rib geometry. The stress concentration factor due to the rib geometry was considered as a constant parameter. In the long crack propagation phase, all microstructural features are considered as constants. The model results were compared to experimental data from the literature.     

Pre-strain effect on fatigue strength characteristics of SUH660 plain specimens

Precipitation particles in precipitation-strengthened materials are considered to be cut by pre-strain treatment, which affects the fatigue strength. In this study, fatigue tests were performed on precipitation-strengthened stainless steel SUH660 to investigate the effect of pre-strain on fatigue crack initiation and propagation characteristics. Fatigue test results showed that pre-strained specimens have a shorter fatigue crack propagation life compared to non-strained specimens; this is the opposite of results observed in carbon steel. The accelerated fatigue crack growth observed in pre-strained specimens was first assumed to be caused by precipitate cutting. A dislocation accumulation model for the fatigue crack tip in the precipitation-strengthened material was then suggested. Buff-polished specimens were also used for the fatigue tests, and the results showed that the work-hardened layer had a significant impact on the fatigue strength and fatigue life.     

Effect of local cold working on the fatigue life of 7475-T7351 aluminium alloy hole specimens

Different degrees of cold working (ranging from 0% to 5.58%) were applied to the hole of plate specimens of 7475-T7351 aluminium alloy. These specimens were then subjected to cyclic loading. In each test, the crack initiation was detected and subsequently the crack length was monitored, using a video camera system. The experimental results were analysed in order to determine the cold working effect on the fatigue initiation period, on the propagation life and finally on the overall fatigue life. It was found, for example, that the propagation life improvement factor for a degree of cold working of 5.58% is about 43.0 and 4.9 for applied nominal stresses of 191 and 300 MPa, respectively. For the same conditions, the fatigue life improvement factor is about 3.2 and 1.5. A numerical analysis was also performed, using three-dimensional finite element method to establish the stress and strain distributions resulting from the superposition of the cold working process and the fatigue loading. Then, the results were used in connection with the non-cold worked hole data for calculating the cold worked plate initiation period according to the strain-life concept; for determining the propagation life, the weight function technique was applied. The predictions are very close to the experimental results.     

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.     

Verwendung von statistischen Grundlagen für die Lebensdauervorhersage bei schwingender Beanspruchung

A concept to describe the fatigue lifetime by using statistical methods In order to spend time and money, cyclic loading tests have been usually undertaken with a relative small number of specimens. On the other hand, it is well established that fatigue life data, i.e. the cycle number of crack initiation N_i as well as the cycle number of total failure N_f show a scatter for a given load level. Therefore, fatigue live predictions must be undertaken using statistical methods. In this case it has to be taken into account that the quantity N_f consists of two parts, i.e. crack initiation and propagation. The first one has to be calculated in a statistical manner, whereas the second one with deterministic methods. Therefore, a superposition of statistical and deterministic parts has to be taken into account. Up to now it was estimated that in all cases the failure results from the same damage mechanism. In this case a scatter of fatigue life may be described by the Weibull distribution and characterised by the location parameter and the Weibull exponent. By using the correct density function, all fatigue life data N_i can be plotted in a failure probability P_v(N_i) vs. N_i plot. In case of some Al-alloys no linear dependence between P_v and N_i has been found, indicating that more than one type of defect spectrum may initiate the failure. Indeed, in AlMgSi cold worked specimens two types of cracks, e.g. surface as well as corner cracks, have been found that initiate the failure of the specimens. If was possible to correlate each type of crack with an individual Weibull distribution. By using this procedure, fatigue life can be estimated better than before.