Fracture mechanics and notch sensitivity

A diagram valid for the analysis of the fatigue limit of cracks and notches centred in an infinite plate was recently proposed by the authors of the present work with the aim to make explicit the bridging at the fatigue limit between defect sensitivity (correlated to the length parameter a₀, according to El Haddad–Topper–Smith's definition) and notch sensitivity (correlated to a*, where a* is a particular notch depth corresponding to the intersection between the ΔK_th and Δσ₀/K_t curves). The expression being valid, defect sensitivity and notch sensitivity were seen as two sides of the same medal. Such a diagram is now extended to finite size components by simply introducing the shape factor α commonly used in fracture mechanics. The obtained critical defect size is termed a_D, which is a material and geometry dependent parameter, in order to distinguish it from a₀, which is a material parameter. As a consequence the critical notch depth a_N is introduced, such that . This results in the proposal of a ‘universal’ diagram able to summarize experimental data related to different materials, geometry and loading conditions. The diagram, the validity of which is checked by means of several results available in the literature, is applied both to the interpretation of the scale effect and to the surface finishing effect.     

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.     

Fatigue life behaviour of TiAlN and TiAlN/CrN coated notched P20 steel specimens

The performance of single layer TiAlN and multilayered TiAlN/CrN physical vapour deposition coatings deposited on AISI P20 steel substrate in affecting overall fatigue resistance of notched specimens was assessed and compared with the performance of the uncoated counterparts. V‐shaped circumferential notches on cylindrical specimens were adopted for fatigue tests. Surface coating characteristics such as hardness, elastic modulus and microstrains were measured and found to be different and often larger than those of the steel substrate. Unlike the un‐notched (smooth) coated specimens, which are known to exhibit large improvements in fatigue life in the high cycle fatigue regime, considerable reductions in fatigue life of the coated notched samples were observed. This was understood to be because of the coating's brittleness, which induces at the notch tip early and frequent fatigue crack initiations, especially in the case of multiple layered coatings. Scanning electron microscope images showed more crack initiation sites in both the coated specimens compared with the uncoated specimen. Also, presence of dimples on the surface confirmed dimple rupture mechanism in the ductile steel substrate in the coated and uncoated specimens.     

Fatigue strength of high strength dual-phase steel sheet

Fatigue tests have been carried out on lean-alloyed dual-phase steels with tensile strengths ranging from 300–800 MPa. Smooth specimens and specimens with punched holes were tested. The fatigue strength of dual-phase steel was found to be similar to that of other types of steel (eg solution hardened or microalloyed steels) of equal tensile strength. The fatigue strength increases with increasing yield strength. For notched specimens it is also related to the yield ratio. Work and bake hardening increase the fatigue strength of smooth specimens in proportion to the increase in yield strength. For notched specimens this effect is less and is dependent on the yield ratio. Bake hardening of material which was not work hardened also increased the fatigue strength. The notch sensitivity of low yield ratio dual-phase steel is found to be low. The notch sensitivity seems to increase with increasing yield ratio.     

Fatigue tests of notched specimens made from butt joints at steel

The weld toe as well as the weld root of joints acts as a geometrical notch, which decreases the fatigue strength of welded components. Local approaches used for fatigue assessment account for the local stress concentration when referring to the notch stress as a fatigue parameter. This applies also to the approaches based on the notch stress intensity factor like, for example, the averaged strain energy density, neglecting the actual notch radius and considering a sharp notch as a simplification. A uniform S‐N curve valid for different types of welded joints and failure locations was derived from re‐analyses of fatigue test results as documented in literature. The fatigue tests described in this paper aimed at validating that energy‐based S‐N curve by dedicated tests on artificially notched specimens. At first, four parameters were investigated in order to estimate their influence on the fatigue strength and to select appropriate notch geometries for the final step of the test campaign. The advantages of these tests are that both the exact notch geometry and the local stress range at the notch, including misalignment effects, were identified and considered in experimental data analysis. This paper presents the results of the rather comprehensive testing activities and comparisons with the design‐S‐N curve mentioned, yielding unexpected fatigue behaviour. This can be explained by the short crack propagation life.     

FATIGUE LIMIT OF BLUNT-NOTCHED COMPONENTS

The position and effective resistance of microstructural barriers and their relation to the fatigue strength of blunt-notched specimens are analysed and modelled for three low-carbon steel microstructures. A relationship for the notch size effect on the basis of the experimental evidence that the fatigue limit (both plain and notched) represents the threshold stress for the propagation of the nucleated microstructurally short cracks, was derived. The derived relationship characterizes the fatigue notch sensitivity 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, and was experimentally verified for two notch geometries in three microstructures: ferrite, ferrite–bainite and bainite–martensite.     

Requirements for stress gradient‐based fatigue assessment of notched structures according to theory of critical distance

Notches, local stress raisers within structural components, are one of the most important locations for fatigue crack initiation. It is well known that fatigue is governed by the effective stresses in the vicinity of notches. Within this study, differences in prediction accuracy between different types of theory of critical distance methods, that is, point and line methods, are systematically investigated in conjunction with a sensitivity study regarding mesh refinement, assumed strength hypothesis and material behaviour. For this purpose, a finite element analysis parameter study on notched structures is performed and recommendations for the application of stress gradient methods are presented. Difference in effective stress of up to 30%, and hence a significant difference in fatigue life (e.g., 185% for a slope of S‐N curve of k = 4), is found for typical notch shapes, for example, in welded joints.     

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small‐notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two‐step stress and repeated two‐step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step 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 even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non‐propagating crack and a mean stress change.     

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.     

Fatigue assessment of laserbeam welded PM steel components by the notch stress approach

The local fatigue strength of a laserbeam weld of a complex engine component, which joins a PM with a formed sheet component, was assessed by the notch stress concept with the fictitious reference radius of r_ref = 0.05 mm. First, simplified specimens, following the main geometric dimensions of the parts, were manufactured. On these specimens the fatigue strength was identified by tests and the notch stresses calculated by finite element analysis. Based on these results a design SN‐curve was derived to assess the fatigue strength of the engine component. The numerical assessment of the welded joint was verified by proof tests with the component. The assessment could be improved by considering statistical and stress gradient dependent size effects according to the concept of the highly stressed volume.     

Fatigue strength of carbon steel specimens having an extremely shallow notch

In order to elucidate how the principal dimensions of a notch as small as grains affect the fatigue strength of carbon steel, rotating bending fatigue tests were carried out on annealed 0.45% C steel specimens having an extremely small artificial notch whose depth is either 5 or 10μm. The fatigue processes at notched parts were observed successively.In these extremely shallow notches, the parameter controlling fatigue limits for fracture σ_w was the notch depth, independently of notch sharpness. On the other hand, the crack initiation limits in the notches σ_W1 were determined by a single K_tσ_W1 — χ relation obtained from the tests on ordinary notches, where K_t is the stress concentration factor and χ is the stress gradient at the notch root.These results were studied on the basis of the characteristics of crack initiation process, the stress intensity variations at the crack tip and the stress distribution near the notch root.     

Effect of submillimeter size holes on the fatigue limit of a high strength tool steel

The very high cycle fatigue and small fatigue crack growth behaviour of a generic tool steel material for diesel fuel injector application are described. The small crack growth tests for the tool steel material with and without the hardening heat treatment revealed the mechanisms of crack propagation and threshold behaviour. Based on the small fatigue crack propagation threshold value, an elastic plastic fracture mechanics methodology for the prediction of the endurance limit of specimens with submillimeter holes is proposed. The advantages of the new methodology are discussed in relation to existing methodologies for endurance limit prediction of specimens with small holes.     

Determining fatigue life of bent and tensioned elements with a notch,with use of fictitious radius

The work presents verification of Neuber's fictitious radius method, used in fatigue life calculation of notched elements and welded joints. Stress values, calculated according with fictitious radius method, were compared with smooth specimens Basquin fatigue curves, and number of cycles was read. However, obtained calculated number of cycles of fatigue life does not correspond to experimental fatigue life, especially in a low cycle fatigue range. Hence, different equivalent microstructural length values were calculated for different loading levels. It was observed that equivalent microstructural length depends on loading level and type of loading. Finally, equivalent microstructural length was presented in a linear regression equation, as dependant on loading level and its relation to yield strength.     

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.     

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.     

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.     

On the estimation of fatigue failure under fretting conditions using notch methodologies

ABSTRACT According to experimental evidence, the early stages of fatigue crack propagation under fretting conditions are strongly influenced by the stress gradient generated in the material near the contact zone. This suggests that the crack growth process can be analysed using methodologies similar to those employed to predict the fatigue behaviour of notched elements. This paper assesses the applicability of a number of models originally developed for notched components to fretting fatigue problems. The ability of such models to predict fatigue failure is discussed and compared with experimental results for Al 7075‐T6 specimens that were subjected to fretting fatigue under spherical contact.     

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.     

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.