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.     

Effect of small notch and absorbed hydrogen on the fatigue fracture in two-step stress test within fatigue limit diagram

It is usually regarded as a common understanding that fatigue failure would not occur if all stresses were kept within fatigue limit diagram. However, it was shown that fatigue failure occurred in some special cases of variable amplitude loading condition even when all stresses were kept within fatigue limit diagram in the case of small-notched specimen. The cause of such a phenomenon was examined using two-step stress pattern for low alloy steel SCM440H. In the case of constant stress amplitude loading, non-propagating crack was formed only at low mean stress and not formed at high mean stress. However, in the case of two-step stress pattern in which the first step stress was chosen as  R  =−1 and the second step stress was with high mean stress, a non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred by the stresses within fatigue limit diagram. In this study, the effect of notch size and shape were examined. The effect of absorbed hydrogen was also investigated. Absorption of 0.3 ppm hydrogen caused more reduction of fatigue limit.     

A mechanistic approach to critical-distance methods in notch fatigue

One approach to the prediction of notch fatigue limits is the Neuber method in which stresses are averaged over a critical distance ahead of the notch. In recent years this theory has been updated by the discovery of an analytical method for finding the critical distance for a given material, which shows that the appropriate distance is 2 a _o , a _o being El Haddad's short-crack constant. The present author has advocated this approach, which he has called the Line Method (LM) and has tested it extensively against experimental data. However the method still remains essentially empirical; the aim of the present paper was to try to link this approach to the known mechanisms of crack growth at a notch. It is proposed that the LM is successful because it expresses the conditions necessary for growth of a small crack located at the notch root. The argument is developed by starting from the resistance curves used to predict non-propagating cracks and by linking the LM with the expression for stress intensity, K , derived by the crack-line loading method. The results provide some mechanistic justification for the use of the LM for sharp, crack-like notches; its success for other types of notch (i.e. blunt notches and short notches) requires a different explanation.     

Notch sensitivity of Ti-based unidirectional metal matrix composites under tensile and fatigue loading

Neuber's rule and the notch equivalent crack length concept were utilized to predict the effect of notches on the fracture strength and fatigue limit of unidirectional metal matrix composites. For the examination of the fracture strength, the strain of the notch is compared to that required for debonding or fracture of the fibres. The notch effect under fatigue loading is determined by examining the ability of the notch to achieve premature debonding.     

A simple method to analyse the notch sensitivity of specimens in fatigue tests

A simple method to analyse the notch sensitivity of specimens in fatigue tests is presented. The parameter m, which can be used to measure the notch sensitivity, the nominal stress and the stress concentration factor (K_t) are used to establish the method. In order to verify the feasibility of the method, notch fatigue test results from our group and literatures were collected. The results reveal that an optimal value of parameter m does exist for each material. Life predictions indicated that the model is able to describe the life evolution for notched specimens under high cycle fatigue and low cycle fatigue tests. Because the geometry effect is accounted for K_t, the method is suitable for the conditions when the notch geometries and the absolute dimensions are similar to the tested 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.     

钛合金试样无效断裂分析

对钛合金条件疲劳极限测定中的无效断裂试样进行了分析。分析结果表明 ,对于疲劳缺口敏感系数较大的金属材料 ,夹持力不宜过大 ;同时 ,对于圆形横截面试样 ,可以靠增加夹持部分与最大应力处的横截面面积之比D2 d2 来减轻或消除夹持力对疲劳性能检测结果的影响。对于本试验中的钛合金材料 ,当D2 d2不小于 3 .5时 ,试样发生有效断裂。     

Fracture mechanisms and fracture mechanics at ultrasonic frequencies

Performing fatigue tests at ultrasonic frequencies, e.g. 20 000  Hz, allows one to perform experiments beyond 10⁹ and 10¹⁰ cycles within half a day or a week, respectively. The testing technique has led to the construction of fatigue machines of high technical standard. Use of the ultrasound technique to study the mechanisms of crack initiation in pure metal single crystals, in cast alloys with voids being crack initiation sites, and in complicated fibre-reinforced laminates is reported. Likewise, use of ultrasonic loading to study the mechanisms of crack propagation is discussed, as well as LEFM principles; especially when these principles cannot be applied. It is shown how crack growth retardation with increasing crack length is attained in fibre-reinforced laminates by the effect of fibre bridging. Additional experimental possibilities, e.g. random loading, variation of mean load, superposition of shear loads, variation of temperature and environment, and not only axial but also torsional loading at ultrasonic frequency, and recent research results are discussed.     

Effect of notch on fatigue behaviour of a directionally solidified superalloy at high temperature

The effect of notch types and stress concentration factors (K_t) on low cycle fatigue life and cracking of the DZ125 directionally solidified superalloy has been experimentally investigated. Single‐edge notched specimens with V and U type geometries were tested at 850 °C with stress ratio R = 0.1. High temperature in situ optical method was used to observe crack initiation and short crack propagation. Scanning electron microscope observation of fracture was used to analyse the failure mechanism. The results reveal that fatigue resistance decreases with K_t increasing from 1.76 to 4.35. The ratcheting is found to be affected by both K_t and the nominal stress from the displacement–force curve. In situ observations indicate that the cracking does not occur at the notch apex but at the location where the max principal stress or Hill's stress is the highest. According to the scanning electron microscope observations, the failure of the notched specimens strongly depends on the anisotropy microstructures.     

Fatigue limit evaluation of notches,small cracks and defects: an engineering approach

In this paper, the average stress method for the fatigue limit evaluation of stress raising geometrical features is revised and extended. In particular, an analytical close‐form approach was used and the linear elastic stress equations were modified by taking into account the effect of nominal stress on the local stress distribution. Hence, the average tangential stress was correctly evaluated over a distance of 2a₀, where a₀ was El Haddad's short crack constant, for long and small notches as well as for crack‐like notches. When this model is applied to a wide range of geometrical features subjected to mode I fatigue loading, the classical shape of the curves of the Kitagawa–Takahashi diagram was obtained for changes in crack‐like notch size. Similarly, notch sensitivity was estimated by reducing the notch tip radius. The accuracy of the proposed method in predicting fatigue limits was then checked by using experimental data taken from the literature and generated on testing specimens weakened by rounded and sharp notches as well as by small artificial defects.     

On the notch sensitivity of flax fibre metal laminates under static and fatigue loading

Damage progression and failure characteristics of open‐hole flax fibre aluminium laminate (flax‐FML) specimens subjected to quasi‐static tensile or tension‐tension fatigue loading were experimentally investigated. Notched and unnotched flax‐FML composites exhibited brittle fracture with little or no fibre pull‐out and minimal delamination at the aluminium/adhesive interface. The flax‐FMLs were tested to failure under tension‐tension fatigue loading conditions (R ratio of 0.1; frequency of 10 Hz; applied fatigue stresses ranging between 30% and 80% of the respective ultimate tensile strength values). The fatigue cycles to failure decreased with the increase in the applied fatigue stress and hole diameter. A phenomenological modelling technique was developed to evaluate the fatigue life of an open‐hole flax‐FML composite. Fatigue tests on specimens subjected to a maximum load equivalent to 35% of the respective tensile failure strength were interrupted at around 85% of the corresponding fatigue life. The accumulated fatigue damage in these specimens was characterised using X‐ray computed tomography. For benchmarking purposes, the fatigue performance and related damage progression in the flax‐FML composite were compared with those of the glass‐FMLs.     

Fracture mechanics transfer function for two-dimensional noncircular flaws

A transfer function that converts an irregularly shaped two-dimensional crack into an equivalent circular crack of equal propagation lifetime is proposed. The methodology extends the exact elliptical to circular crack transfer function to other noncircular cracks with geometries that slightly deviate from the elliptical. Results for rectangular, symmetric dumbbell, and asymmetric dumbbell cracks are presented.     

On the design and test of equivalent configurations for notch and fretting fatigue

This work investigates the possibility of designing fretting and notch fatigue experiments that are nominally equivalent in terms of damage evaluated by a multiaxial fatigue model. The methodology adopted to carry out this search considered a cylinder‐on‐flat contact geometry and a V‐notched plate. The loading conditions and geometries of the experimental configurations were adjusted to obtain the same decay of the multiaxial fatigue index from the hot spot up to a critical distance. Aluminium alloy 7050‐T7451 was used in the experimental evaluation of the methodology. Considering the well‐known scatter of fatigue data and the limited number of specimens available, the obtained results suggest that the use of the notch analogy in fretting fatigue is appropriate.     

A unified treatment of the mode I fatigue limit of components containing notches or defects

The paper addresses the estimation of the fatigue limit of components weakened either by U- and V-shaped notches or by defects, all under mode I stress distributions. When the influence of the opening angle is absent, a single formula is able to summarise both the notch sensitivity and the sensitivity to defects. Fatigue limit assessments need two material parameters, namely the plain fatigue limit and the threshold value of the long crack stress intensity factor range. The formula is compared with about 90 fatigue limits taken from the literature. Material properties and specimen geometries are given in detail. Afterwards, in the case of V-notches with large opening angles, the formula is modified, but without involving additional material parameters. A generalised Kitagawa diagram is obtained, that encompasses fatigue behaviour of stress raisers of different size, opening angle and notch tip radius.     

Fatigue crack growth rates under sequential mixed-mode I and II loading cycles

One common mode of failure that occurs in rolling bodies such as gears, bearings and rails is due to the fatigue process. Several research workers suggest that rolling contact fatigue cracks are subjected to mixed mode I and II loading cycles. It is believed that the correct modelling of loading cycles can help us to study the mechanics of crack growth because fatigue comprises a major safety consideration in the design process. Experiments have been performed under nonproportional mixed-mode I and II loading cycles with fixed degrees of overlap, so that coplanar cracks were produced. Three empirical crack propagation laws have been established which are related to both mode I and mode II effective stress intensity factor ranges.     

Mean stress and plasticity effect prediction on notch fatigue and crack growth threshold,combining the theory of critical distances and multiaxial fatigue criteria

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σ_fl,R = ?1/σ_YS, such as 7075‐T6 (σ_fl,R = ?1/σ_YS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σ_fl,R = ?1/σ_YS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD.     

Theoretical fatigue–effective notch stresses at spot welds

Notch stress formulae are derived for the application of a notch stress approach to the fatigue assessment of spot welds. A keyhole notch is assumed to describe the edge of the weld spot between the overlapping plates. The stress fields at the keyhole notch under 'singular' and 'non-singular' in-plane loading modes inclusive of the stress concentration factors K _t are derived from the relevant Airy stress functions. The formulae are applied to typical loading cases of spot welds and compared with finite element solutions. Fatigue-effective notch stresses inclusive of fatigue notch factors K _f are calculated by applying the microstructural support hypothesis of Neuber. The notch stresses at the keyhole are also derived for out-of-plane shear loading based on the relevant harmonic stress functions. The multiaxial notch stresses at the weld spot edge are thus completely described.     

Two measurement techniques for determining effective stress intensity factors

Two methods were studied for determining crack closure and locking effects under combinations of mixed mode I and II loading, namely the strain gauge and the surface replica methods. They demonstrated that strain gauges are able to detect the mode I crack closure but not mode II crack locking. As an alternative, the surface replica method is suggested as a practical technique for measuring mode II crack locking effects. The effective mode II stress intensity factor range can be estimated by comparison of the actual measured sliding range between a pair of crack faces and the theoretical sliding range.     

Fracture mechanics solutions to spot welds

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.     

Fracture mechanics and scale effects in the fatigue of railway axles

Fatigue of railway axles is one of the basic problems of fatigue. However, in spite of the criticality of this component, modern approaches have not been used for addressing a critical revision of traditional design. The scope of this paper is to study the scale effects in fatigue limit and in crack growth rate for a high strength steel used for high speed railway axles.Fatigue limit tests on micro-notched specimens led to the determination of fatigue thresholds for small cracks of the examined steel. This allowed us to successfully analyse the `scale effect' and the fatigue strength of full-scale axles in terms of threshold stress for short cracks emanating from small non-metallic inclusions.A series of crack propagation tests on small scale specimens lead to the definition of an EPFM crack propagation model which has been successfully compared with propagation data on full-scale components. These results support the application of the crack propagation model for the determination of axle inspection intervals.