A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

NEAR THRESHOLD FATIGUE CRACK PROPAGATION BEHAVIOUR OF A HETEROGENEOUS MICROSTRUCTURE

The threshold regime of a heterogeneous, pearlitic-ferritic microstructure was investigated at R= 0.1. Not only did the ΔK_th values vary depending on the test procedure in that da/dN vs ΔK curves before and after ΔK_th determination were not identical but transition ΔK values also differed. The observations are correlated with inherent micro- structural features.     

THE EFFECT OF CRACK LENGTH ON FATIGUE THRESHOLD

This paper puts forward a new method for analysing the behaviour of very short fatigue cracks. A probability function is introduced into the definition of the growth threshold, which rationalises the scatter in experimental data produced using an aluminium bronze alloy. This probability function can be visualised in terms of the microstructure of the material.
It is shown that, in this material as in mild steels, fatigue crack initiation is not the critical stage. Initiation occurs relatively easily, but the cracks so formed may grow to only a few grain diameters in length before being arrested; thus it is the behaviour of cracks of this length which is critical in determining the fatigue strength of the material.
These observations, when combined with the probability functions, allow estimation of the probability of failure of a component or structure in service with greater confidence than the methods used at present.     

CRACK CLOSURE: A CONCEPT OF FATIGUE CRACK GROWTH UNDER EXAMINATION

Abstract— In recent literature it is asserted that the concept of crack closure in fatigue fracture mechanics is not capable of explaining fatigue crack growth behaviour. The reasons given are that both asperity induced crack closure and plasticity induced crack closure should be either negligible or non-existent. We have re-considered these hypotheses since their correctness would completely change the established picture of fatigue crack growth. In order to get mathematically tractable systems the present studies are confined to long cracks loaded in mode I. The results suggest that in case of asperity induced crack closure the proposed hypothesis is only true in special cases and the demonstration of the non-existence of plasticity induced crack closure is proved to be wrong.     

PREDICTION OF THE FATIGUE THRESHOLD FOR A CRACKED BODY USING SHAKEDOWN THEORY

Abstract— In this paper, the fatigue threshold Δ K _th of a cracked body is studied. Unlike other approaches given in the literature, the shakedown theory is used for predicting Δ K _th. A crack is considered as a sharp notch, the radius of which, at the threshold stress level, is a material constant. The threshold of crack propagation is explained as being due to shakedown of the cracked body, and a simple but reasonable model is derived. The value of Δ K _th is found to be proportional to the yield stress multiplied by the square root of the effective crack tip radius. Using this model, Δ K _th is calculated for some materials. Comparison of the predicted fatigue thresholds with those obtained by experiments, or by using other approaches, indicates that our model provides satisfying results.     

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.     

13SiMnNiCrMoV钢切口疲劳裂纹萌生门槛值

本文研究在13SiMnNiCrMoV 结构钢中用尖裂纹的应力强度因子来反映三点弯曲缺口试样的疲劳裂纹萌生规律。当 R=0.1,f=100Hz,试样尺寸 B×W×L=12.5×25×117mm 时,缺口名义应力幅的门槛值为Δσ_(th)=3315ρ~(0.352) MPa,0.5mm≤ρ≤5mmΔK_(th)=250ρ~(0.352) MPam~(1/2)门槛值与ρ有关。同时得到缺口裂纹萌生的循环次数 N_i 与名义应力幅Δσ、缺口曲率半径ρ的定量关系是N_i=3.98×10~(22)ρ~(1.62)/Δσ~(4.85),N_i≤10~(5.5)并讨论了(ΔK_1/ρ~(1/2))_(th)与ρ无关的结论。     

PREDICTING THE EFFECTS OF LOAD RATIO ON THE FATIGUE CRACK GROWTH RATE AND FATIGUE THRESHOLD

The effect of the load ratio, R, on fatigue crack growth behaviour is analysed on the basis of the recently proposed inelastic discrete asperities model. A wide range of load ratios, both positive and negative, are examined. Particular emphasis is placed on compressive excursions, i.e. negative R loadings. The inelastic discrete asperities model is a micro-mechanical analysis based on the plastic crushing of a single asperity (or multiple asperities) located on the crack face close to the crack tip and under dominantly plane strain conditions. Experimental data have indicated that the primary crack face contacts which obstruct closure are immediately adjacent to the crack tip, although segments of the crack face more distant from the crack tip are not neglected. However, the more distant asperities are a part of the past crack advance history which does not influence current behaviour. By use of this model, it is shown that the effect of the load ratio can be adequately predicted once some baseline information on mechanical material properties and surface roughness is provided. The model also provides useful trend information and explains many of the observed phenomena, e.g. the ‘saturation’ of the compressive underload effects. For a constant applied nominal stress intensity factor range, ΔK_nom , it is shown that the effective stress intensity factor range, ΔK_eff , initially decreases as the positive R decreases (corresponding to the increasing influence of closure), reaches a minimum around R = 0, and then starts increasing with negative R (corresponding to the plastic crushing of the asperities which reduces closure), eventually reaching a saturation level below ΔK_nom . Conversely, for an assumption of a constant ΔK_eff , the applied ΔK_nom increases as the positive load ratio decreases, reaching a maximum around R = 0, and then decreases with more negative R values, eventually reaching again a saturation level (above ΔK_eff ). It is also shown that the effect of material hardness can be directly analysed based on this model.     

A MODEL FOR THE EFFECT OF A GASEOUS ENVIRONMENT ON THE LEFM FATIGUE THRESHOLD CONDITION OF STEELS

Using a different approach to those methods involving hydrogen-embrittlement and crack-closure mechanisms a previously developed model is extended to predict the commonly observed effects of yield strength and a gaseous environment on the long-crack fatigue crack growth threshold. The model assumes the existence of two intrinsic thresholds namely an upper bound value and a lower bound value related to, respectively, K_max-controlled cleavage and δK-controlled reversed shear mechanisms of crack growth in a critically stressed volume at the crack tip. This new development assumes that nascent hydrogen atoms, liberated from moisture in the environment, assist in reducing dislocation mobility thereby rationalizing experimental observations on low strength materials in moist laboratory air when compared to a dry inert environment. Quantitative predictions of fatigue thresholds in laboratory air and inert environments show good agreement with experimental data for several low and high strength steels. This alternative procedure may be found to be useful in practical design applications when reasonably fast and accurate estimates are required.     

THE INFLUENCE OF SPECIMEN GEOMETRY ON NEAR THRESHOLD FATIGUE CRACK GROWTH

Abstract— The near threshold fatigue behavior of a nickel base superalloy and a wrought 2024 aluminum alloy is examined as a function of specimen geometry. Experimental results revealed that for a given value of Δ K in Region I, crack growth rates were observed to increase as the specimen loading became more symmetric with respect to the load line. Compact tension type specimens exhibited lower crack growth rates than the more symmetrically loaded center cracked tension specimens. Consideration of the observed discrepancies is given in terms of the near field crack tip stress distribution and deformation behavior of the material affecting crack advance.     

THE EFFECT OF ENVIRONMENT ON CRACK CLOSURE AND FATIGUE THRESHOLD*

Abstract— The threshold value for fatigue crack growth of a medium carbon steel was increased when the test-environment was changed from air to an aggressive H₂S-containing brine. This increase in fatique threshold was shown to be caused by corrosion product-induced crack closure. Further, the fatigue threshold and crack closure level were shown to be dependent on the growth rate history in approaching threshold. The differences in fatigue crack growth rate and fatigue threshold resulting from test procedure and growth rate history were significantly reduced by employing the effective stress intensity concept.     

A CALCULATION OF THE THRESHOLD STRESS INTENSITY RANGE FOR FATIGUE CRACK PROPAGATION IN METALS

Abstract— In this paper the strain distribution and the plastic zone size at a fatigue crack tip are discussed. From this analysis and considering the critical condition for plastic-blunting, a simple analytical formula for calculating the threshold stress intensity range for fatigue crack propagation at R= 0 is proposed. It is found that calculated values are in good agreement with existing experimental results.     

THE INFLUENCE OF TEST VARIABLES ON THE FATIGUE CRACK GROWTH THRESHOLD

Abstract— A microcomputer controlled fatigue crack growth and threshold testing system has been used to investigate the influence of test variables on the measured values of Δ K _th, the threshold for fatigue crack growth, using a C-Mn steel. The work has examined: (1) the influence of crack length and test management; (2) the basic material scatter from repeated testing; (3) the effect of unloading rate C where C = (1/Δ/ K )(d Δ K /d a ); (4) the effect of step unloading; (5) the influence of minimum stress intensity factor, K _min . Comparisons have been made between the results of this computer controlled work and those published previously but made using a manual load shedding technique. The results of Δ K _th and fatigue crack growth rates are in general agreement with previous data and confirm the K _min dependence of Δ K _th and d a /d n. The value of Δ K _th is shown to be generally independent of the other test variables for a wide range of conditions and is reproducible with a low degree of scatter.     

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.     

THE THRESHOLD STRESS INTENSITY RANGE IN FATIGUE

Abstract— The parameters are considered that control the threshold stress intensity in fatigue and relationships existing between these parameters are examined. A new relation is derived which is shown to be consistent with experimental data for a 0·15%C, 1·5%Mn steel.     

THE EFFECTS OF MOISTURE ON THE FATIGUE CRACK GROWTH BEHAVIOUR OF A LOW ALLOY STEEL NEAR THRESHOLD

Abstract— The influence of moisture on the fatigue crack growth behaviour near threshold of a 2NiCrMoV rotor steel has been investigated. At a high stress ratio ( R = 0.6), moisture enhances fatigue crack growth rates by approximately 60% compared with the growth rate in dry air. The effect would appear to be due to the influence of hydrogen which is confined to a volume of material at the crack tip considerably smaller than the plastic zone. At a low stress ratio ( R = 0.14), the growth rates in moist air can be very much lower than in dry air. This difference is closely associated with the formation of oxides on the fracture surface—moisture modifying the type and extent of oxidation which is observed. Observations of transient crack growth following environmental changes, suggest that fracture surface oxides within approximately 0.3 mm of the crack tip exert a strong retarding influence on crack growth although oxides up to at least 3 mm from the tip may also have some retarding effect.     

CONSIDERATION OF MULTIAXIALITY IN FATIGUE LIFE PREDICTION USING THE CLOSURE CONCEPT

Abstract— Based on fracture mechanics a model has been developed for predicting the fatigue lifetime to initiate a crack of technical size (2 a ∼ .5mm) in engineering components under multiaxial-proportional loading. Using material data determined for uniaxial loading, the model describes and evaluates the elasto-plastic multiaxial notch stresses and strains using the effective range of the J -integral, Δ J _eff, as a crack tip parameter. Mean stresses, load sequence effects and various modes of crack propagation due to variable amplitude loading with individual multiaxiality ratios can be explicitly considered. The prediction accuracy of the model is demonstrated using experimental fatigue life data determined with unnotched specimens of FeE460 and A15083 for proportional fully-reversed constant and variable amplitude loading with various multiaxiality ratios.     

HIGH CYCLE FATIGUE AND THRESHOLD BEHAVIOUR OF POWDER METALLURGICAL Mo AND Mo-ALLOYS

Abstract A detailed characterization of the room temperature fatigue properties of powder metallurgical Mo, Mo–W and Ti–Zr–Mo (TZM) alloys is presented. In particular the factors affecting fatigue crack nucleation and growth behaviour are described. Fatigue tests were carried out by conventional rotating-bending and compared with results from a time-saving 20 kHz resonance push-pull test method. Fatigue strength data were determined by a statistical evaluation of test results from a sufficiently large number of specimens. The results show an increase in fatigue strength with alloying additions. Fatigue cracks were observed nucleating at highly localized slip bands at the specimen surface with the fatigue crack zones comprising only a small fraction of the total specimen cross-section. Fatigue crack growth rates at low stress intensities and threshold stress intensity values for crack growth were determined for a stress ratio of R =– 1 using a 20 kHz resonance test method. These latter values were found to be sensitively dependent on microstructure, composition and processing history.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.