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.     

Grain size effects on notch sensitivity

This work presents experimental results on the fatigue behavior of cracks growing from circular notches under axial loading conditions for a very wide range of notch size to grain size ratios, including cases where the notch size is of the order of, or even smaller, than the grain size. Notch sensitivity is evaluated and the well-known dependence on grain size is clearly demonstrated. It was found that for the same specimen geometry and loading conditions, the influence of the stress concentration is directly dependent on the relationship between the notch size and the grain size.     

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.     

玻璃钢材料疲劳极限的灰色预测

本文应用灰色系统理论对玻璃钢复合材料的疲劳性能进行研究，建立了不同交变应力与对数循环次数之间的生成函数，通过生成函数对玻璃钢材料疲劳极限预测，效果较好。     

各种平均应力下高周疲劳极限间的定量关系

疲劳极限是材料工程应用中的一个重要特性参数,但它并不是材料常数。在不同循环载荷作用下,材料会有不同的疲劳极限值。疲劳极限值很大程度上依赖于循环载荷中的平均应力或最大应力幅值,两者之间的关系是材料自身固有的特性关系。因为在接近疲劳极限的低循环应力幅下,S-N曲线受疲劳极限控制,所以在工程应用中对其定量关系有迫切的需求,但现有的经典经验关系只能对其进行非常粗略的估算,不能满足工程应用中有关寿命设计的需要。现状是只能通过大量的实验,得出其实验关系。该文提出了一种函数形式的关系式,该关系式可以足够精确地描述各种材料的疲劳极限和平均应力之间的关系,且只包含三个材料常数。只要这三个材料疲劳特性常数被事先确定,则任意疲劳载荷下的疲劳极限值,都可由该关系式估计得到,因此可以作为材料本身固有的疲劳强度的状态关系式使用。     

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.     

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。     

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.     

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.     

基于锁相红外热成像技术对铝合金铆接结构件疲劳极限的快速测定

该文将锁相红外热成像技术应用到2A12铝合金材料制成的铆接结构试件疲劳极限的快速测定上,将锁相红外热成像技术获得的结果与现有的该种材料在不同应力集中系数和应力比下疲劳极限试验数据进行插值得到的结果进行了对比,并与通过传统的阶梯法获得的试验结果进行了对比,验证了对于过盈量不大的普通铆接结构件来说,可以将锁相红外热成像技术应用到疲劳危险点处于多轴应力状态的金属铆接结构试件疲劳极限的快速测定上。     

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.     

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. .     

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.