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.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Fatigue notch sensitivity of steel blunt-notched specimens

The notch sensitivity of three steels with similar plain fatigue limits was analysed and modelled. The analysis was made by using a model previously derived which estimated the fatigue limit of blunt notched components by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers. The analyses show how the first two or three microstructural barriers define the fatigue limit and the fatigue notch sensitivity of blunt notched specimens.     

THE SIZE OF PLASTIC ZONES AND FATIGUE CRACK GROWTH BEHAVIOUR OF THREE FORMS OF A Ti–6Al–2.5Mo–1.5Cr ALLOY

The effect of microstructure on the fatigue properties of Ti–6Al–2.5Mo–1.5Cr alloy was investigated. The experimental results for both the fatigue crack initiation and propagation behaviour, as well as the dynamic fracture toughness ( K _Id ) showed clearly that a lamellar microstructure is superior to two other structures. It was found that, as in the case of steels, the initiation and subsequent growth of cracks in the titanium specimens with a sharp notch may also occur on loading levels below the threshold values of the K factor (Δ K _th ) determined for long fatigue cracks. In addition, measurements by interferential-contrast of the plastic zone size on the surface of specimens revealed that the different rate of crack growth at identical values of Δ K in individual structural states can roughly be correlated with the size of the plastic zone. A general relationship between the fatigue crack growth rate and plastic zone size, the modulus of elasticity and the role of crack tip shielding is discussed.     

MICROSTRUCTURE AND FATIGUE PROPERTIES OF A WELDED DUPLEX STAINLESS STEEL

Abstract— In response to the increasing structural applications in duplex steels for welded structures, fatigue behaviour of a SAF 2304 grade duplex stainless steel was investigated, considering both the base metal and GTAW welded joints. Fatigue curves and fatigue limits under rotary bending fatigue were obtained. The study focused attention on the microstructural features of fatigue crack propagation of the two series of experiments, thereby permitting an evaluation of the tortuous crack path of welded joints and the mechanisms related to threshold microstructural barriers.     

INFLUENCE OF LOW-INTENSITY SHOT PEENING ON THE FATIGUE STRENGTH OF AN Al/Al

Metal matrix composites are increasingly utilized in engineering applications because of their favourable strength/weight ratio. However, their applications are still limited because of their relatively poor fatigue resistance, which could be improved by using some appropriate surface treatment. In this paper, an Al/Al₂ O₃ (20%) composite material is considered. In particular its fatigue strength is examined to verify if, how and when shot peening can be used to improve the performances of MMC components that are cyclically loaded. Fatigue tests allow one to evaluate the influence of shot peening on the fatigue limit of both smooth and notched specimens. Residual stress measurements, fracture surface analyses and metallographic examinations allow one to evaluate the role of residual stresses, hardening and grain distortion on the improvement that can be achieved with this treatment. On the basis of these results, some guidelines are drawn on how to optimize the choice of peening parameters.     

高强度渗碳钢制构件的断裂分析

利用化学分析、金相检验、扫描电镜以及电子探针微区分析等方法对高强度20CrNiMo渗碳钢制矿岩牙轮钻头和汽车发动机活塞销的断裂原因进行了分析。结果表明,两构件的断裂是由于锻轧温度过高,引起硫化物在晶界上的再析出所造成的。指出了要重视这类渗碳钢的缺口敏感性及对钢中非金属夹杂物的检验方法。     

PREDICTION OF FATIGUE FAILURE IN A CRANKSHAFT USING THE TECHNIQUE OF CRACK MODELLING

Abstract— A new technique, known as crack modelling, is used here to predict fatigue failure in a crankshaft component. The technique uses a linear elastic finite element (FE) analysis to derive a stress intensity factor ( K ) for the component under load. The novel feature of the technique is that K is calculated without introducing a crack into a component; the stress field around the maximum stress point is examined and compared to that for a standard centre-cracked plate. The fatigue limit for a crankshaft was successfully predicted, when compared to experimental data. The only material parameter required for this prediction was the threshold stress intensity range, ΔK_th.     

FATIGUE LIFE PREDICTION OF NOTCHED COMPOSITE COMPONENTS

Abstract— The local stress/strain approach has been used to predict the fatigue lives of notched composite components. The method was based on a microstress analysis and the application of a multiaxial fatigue parameter incorporating the alternating strain components on the critical plane. This parameter was able to correlate the fatigue lives obtained under a variety of multiaxial loading and geometrical configurations, enabling a generalized fatigue life curve to be determined on the basis of limited experimental data.
The ability of the multiaxial fatigue parameter to relate the fatigue behaviour of composites was illustrated by predicting the locations of crack initiation sites in a unidirectional silicon carbide fibre reinforced titanium plate containing a circular hole tested under constant amplitude cyclic loading. The same approach was also successfully employed to predict the fatigue lives of graphite reinforced epoxy composite tubes with circular holes tested under several combinations of cyclic tension and torsion.     

SURFACE CRACKS AND THE FATIGUE LIMIT OF METALS

Abstract— A technique based on indenting a sphere into a material has been developed for measuring the yield strength of metals at various depths from the surface. Proceeding from the experimentally established reduction in the yield strength of the metal surface layer and cyclic crack growth resistance characteristics, the authors suggest a model simulating fatigue fracture based on the continuum mechanics assumptions which allows the fatigue limit to be estimated on the basis of a critical non-propagating fatigue crack size for components of various thickness in tension-compression or in bending; considering stress concentrations under both alternating and oscillating loads in the presence of near-surface stresses. Theoretical predictions using the model for three martensitic stainless steels and a titanium alloy showed a fair agreement with experimental data.     

LOW CYCLE FATIGUE LIVES OF NOTCHED COMPONENTS

Abstract— In low cycle fatigue situations, the plastic behaviour of the material at the root of stress concentrators is of prime importance in determining the cyclic life. However, simple procedures such as Neuber's rule do not adequately describe the development of plastic behaviour at a notch root, while the expense of a finite element analysis is not justified in many instances. This paper describes a simple, approximate numerical method of calculating plastic notch stresses and strains that would be of use in such situations. The usefulness of the technique is demonstrated by comparing low cycle fatigue lives predicted from notch plastic strains with those determined by fatigue testing of smooth specimens subjected to similar plastic strain ranges.     

LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS

Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r_s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, r_s is presented. As an alternative to ΔK the range Δσ_s of the cyclic normal stress at a point situated at the fixed distance s=r_s/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ_s at the prescribed distance is used instead of ΔK since nowadays Δσ_s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ_s is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσ_s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ_s (πrr_s)^½ instead of ΔK the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue-fracture activation region r_s is derived in terms of the fatigue limit Δσ_FL obtained from S-N tests and of the threshold value ΔK_th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r_s= (ΔK_th/Δσ_FL)²/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ_s must be greater than Δσ_FL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσ_s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ_s > Δσ_FL.     

Growth of very long “short cracks” initiated at holes

The initiation and growth behavior of very long microstructurally short fatigue cracks formed at circular holes is described. Very long here means cracks which are several millimeters or even centimeters long. Microstructurally short refer to the fact that these cracks, in spite of their physical length, are still smaller than the grain size of the material and thus exhibit the characteristic features of such cracks. Growth retardation or even halt at grain boundaries and fluctuating crack growth rates can readily be observed with the naked eye by employing a experimental technique which allows one to increase the grain size of Al1050 Aluminum alloy until the centimeter scale by applying a series of mechanical and heat treatments. Once the thermo-mechanical treatment is completed and the desired grain size obtained, a circular notch is machined on each specimen, and the samples are subjected to fatigue loading. With this method, interactions between cracks and microstructural barriers can be studied with an unprecedented level of ease and detail. An interesting observation is that the location of the crack initiation point along the hole contour varies greatly with the ratio between the hole diameter and the grain size: for large ratios, the initiation point is located close to the point corresponding to the maximum circumferential stress (the horizontal symmetry axis in our case), but for smaller ratios, however, the point of crack initiation moves markedly away from the symmetry axis.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

TORSIONAL FATIGUE OF A MEDIUM CARBON STEEL CONTAINING AN INITIAL SMALL SURFACE CRACK INTRODUCED BY TENSION–COMPRESSION FATIGUE: CRACK BRANCHING,NON-PROPAGATION AND FATIGUE LIMIT

In order to examine the threshold condition for the fatigue limit of materials containing a small crack under cyclic torsion, reversed torsional fatigue tests were carried out on 0.47% C steel specimens containing an initial small crack. Initial small semi-elliptical cracks ranging from 200 to 1000 μm in length were introduced by the preliminary tension–compression fatigue tests using specimens containing holes of 40 μm diameter. The threshold condition for the fatigue limit of the specimens containing artificial small defects under rotating bending and cyclic torsion are also reviewed. Crack growth behaviour from an initial crack was investigated. The torsional fatigue limit for a semi-elliptical small crack is determined by the threshold condition for non-propagation of Mode I branched cracks. The torsional fatigue limit of specimens containing an initial small crack can be successfully predicted by the extended application of the √area parameter model in combination with the σ_θmax criterion.     

ESTIMATION OF THE FATIGUE LIMIT BY PROGRESSIVELY-INCREASING LOAD TESTS

Abstract— On the basis of fatigue data derived from a large number of experiments, the load progression methods of Locati and Prot as well as a method operating on a thermometric basis have been comparatively evaluated in an experimental and analytical (statistical) study. The last-named thermo-method can provide useful estimates for a fatigue limit corresponding with ca. 0 to 5% probability of fracture with only 1 to 3 experiments. The Prot-method, set up and evaluated in a certain way, provides a useful estimate of the fatigue limit and, additionally, an approximate indication of the width of the transition range of the corresponding Wöhler-type tests after experiments on not less than about ten specimens. The load progression, contrary to the original Prot-concept, must not necessarily be applied in a continuous mode, but can occur stepwise with increments Δσ smaller than ca. 15 Nm^-2.     

FATIGUE CRACK GROWTH BEHAVIOUR OF FIBRE-METAL LAMINATE GLARE-1 AND METAL LAMINATE 7475 WITH DIFFERENT BLUNT NOTCHES

Abstract— The fatigue crack growth behaviour of the fibre metal laminate "GLARE-1" has been investigated for different blunt notches in Constant Amplitude (CA) tests. In order to investigate the influence of the fibres, the same laminate material but containing no fibres (Laminate 7475) was also tested. The fatigue crack growth properties of GLARE-1 are superior to those of Laminate 7475. GLARE-1 shows lower crack growth velocities at the same K_nom values and in addition the crack growth rates decrease with increasing crack length. The Laminate 7475 shows typical metal behaviour for single crack propagation and accelerating crack growth with increasing crack length. In GLARE-1, multiple crack propagation takes place. The cracks propagate independent of each other and have similar crack growth rates, in part due to closure effects caused by the unbroken fibre layers.
The crack growth rates of specimens having a small root radius are higher in both materials than in specimens with a large notch radius. In GLARE-1, the superiority of a larger notch radius is more pronounced than in the Laminate 7475 and is attributed to a stronger crack closure effect owing to fibre bridging. The reason for the higher bridging capability in specimens containing larger notches is that less fibres are broken or damaged in the notch vicinity.     

超声疲劳试验中载荷频率对材料疲劳性能的影响

用超声高频疲劳试验方法获得的40Cr钢和50车轴钢的疲劳性能大于常规低频疲劳试验结果,表明超声加载频率对疲劳性能存在影响,这种影响可归因于应变速率的影响.采用一个超声加载频率修正系数对超声疲劳性能试验中载荷频率对疲劳性能的影响进行修正.超声加载频率修正系数近似等于常规低频疲劳条件下的疲劳强度系数与超声高频疲劳条件下的疲劳强度系数的比值,该修正系数也可通过不同应变速率下材料的断裂强度的比值来近似地确定.