This review is a brief survey of three-dimensional effects at cracks and sharp notches. The overall aim is to review developments over the past 50 years leading up to the current state of the art. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack or notch tip. It is also restricted to static loading and to constant amplitude fatigue loading. An enormous amount of theoretical and experimental information relevant to three-dimensional effects has been published in the past five decades, so the review is, of necessity, highly selective. Theoretical topics covered are linear elastic fracture mechanics, including Volterra distorsioni, stress intensity factors, corner point singularities, crack front line tension, displacement analysis of cracks and notches, and through thickness distributions of stresses and stress intensity factors. Crack path topics covered are fatigue crack path constraints, determination of fatigue crack paths, oscillating crack fronts in thin sheets and the transition to slant crack propagation in thin sheets. Plane strain fracture toughness testing, including standards, is covered. Overall, it can be concluded that the existence of three-dimensional effects at cracks and sharp notches has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important.

Characterization of very high cycle fatigue (VHCF) performance is of significant issue for ensuring long-term durability and reliability of machinery and structural components due to the growing industrial demands and significant requirements of the advanced systems. In this study, VHCF characteristics of nanocrystallized skins (nanoskin) on JIS SCM435 (AISI 4137) steels were investigated as three different nanoskins on the surface, which was fabricated by altering the static load of ultrasonic nanocrystal surface modification (UNSM) treatment. The fatigue characterization, which shows linearly proportional correlation in the range of 80–120 µm depth of subsurface, was subjected to severe plastic deformation by altering the static loads of UNSM treatment to 40, 70 and 100 N, respectively. The fatigue strength increased up to 30% in the regime of VHCF. The improved strength mainly resulted from the generation of nanocrystalline structure, the enhanced surface uniformity, hardness and residual stress.

In this paper, ductile fracture behaviours of 304 stainless steel pipes with two circumferential surface cracks under pure bending are simulated using finite element damage analyses. Simulations are based on the stress-modified fracture strain model with the concept that the critical accumulated damage for progressive cracking is assumed to be dependent on an element size. The proposed method can predict not only maximum loads but also complex ductile fracture patterns observed in experiments.

The energy dissipated to the surroundings as heat in a unit volume of material per cycle, Q, was recently proposed as fatigue damage index, and it was successfully applied to rationalise fatigue data obtained by carrying out stress-controlled and strain-controlled fatigue tests on AISI 304 L stainless steel plain and hole specimens. In this paper, it is shown that the Q parameter is independent on thermal and mechanical boundary conditions occurring during experiments. After that, additional stress-controlled fatigue tests on plain and notched specimens characterised by smaller notch tip radii than those tested previously have been performed. Present data have been compared with previous ones, and it was found that all available results can be synthesised in terms of the energy parameter Q into a unique scatter band, independently on the testing conditions (stress-controlled or strain-controlled) and on the specimens' geometry (plain or notched). About 100 data were included in the statistical analysis to characterise the energy-based scatter band of the material. Finally, some limitations of applicability of the experimental technique adopted in the present paper are discussed.

To accurately perform the fatigue assessment of engineering components subjected to in-service multiaxial fatigue loading, the adopted design criterion must properly be calibrated, the used information usually being the fatigue strength under both pure uniaxial and pure torsional fatigue loading. Because of the complex fatigue response of metallic materials to multiaxial loading paths, the only reliable way to generate the necessary pieces of calibration information is by running appropriate experiments. Unfortunately, because of a lack of both time and resources, very often, structural engineers are requested to perform the multiaxial fatigue assessment by guessing the necessary fatigue properties. In this complex scenario, initially, the available empirical rules suitable for estimating fatigue strength under both pure axial and pure torsional fatigue loading are reviewed in detail. Subsequently, several experimental results taken from the literature and generated by testing metallic materials under a variety of proportional and non-proportional multiaxial loading paths are used to investigate the way such empirical rules affect the accuracy in estimating fatigue strength, the damage extent being evaluated according to the modified Wöhler curve method. Such a systematic validation exercise allowed us to prove that under proportional loading (with both zero and non-zero mean stresses), an adequate margin of safety can be reached even when the necessary calibration information is directly estimated from the material ultimate tensile strength. On the contrary, in the presence of non-proportional loading, the use of the empirical rules reviewed in the present paper can result, under particular circumstances, in a non-conservative fatigue design.

This paper presents the application of weight function method for the calculation of stress intensity factors (K) and T-stress for surface semi-elliptical crack in finite thickness plates subjected to arbitrary two-dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two-dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T-stress solutions. This method is used to derive the weight functions for both K and T for semi-elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T-stress solutions for several linear and nonlinear two-dimensional stress distributions. These derived weight functions are particularly useful for the development of two-parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).

The fatigue results of a high-pressure die cast of AZ91D magnesium alloy revealed the presence of different types of casting defects, which account for the large scattering in the number of cycles until failure. In this paper, this magnesium alloy has been analysed, and in an effort to reproduce the same surface and material conditions exhibited in automotive service components, the fatigue test samples were manufactured using a die that employs the same casting process and equipment. To examine the fracture surface of all the fatigue tests, a scanning electron microscope was used, and the source of the failure, so as to relate fatigue life with casting defect type, was identified. Five casting defect types that influence the fatigue behaviour were observed and classified: (a) isolated pores (blowholes), (b) micro-porosity areas, (c) circular shrinkage cavities associated with the contraction and geometry of the casted specimen, (d) surface burrs associated with the die-casting mould and (e) the presence of oxides or inclusions.

The subject of this paper is to investigate the capability of the relative stress gradient to properly represent the beneficial effect of residual stress states on the fatigue life of Ti-6Al-4V specimens, with notches of different severity. The research was developed considering notched and un-notched specimens with different geometries and different shot-peening treatments. The results were determined by running fatigue experimentation under rotating bending and by developing a novel predictive model based on the relationship between the local fatigue limit and a generalized form of the relative stress gradient, accounting for the peening-induced residual stresses. The proposed tool for fatigue limit estimation was completed by a stochastic analysis, which considered the variability of the involved parameters, in particular the residual stress entity. This made it possible to finally determine the component failure probability in a general, efficient and accurate way.

Welded steel connections of infrastructures are susceptible to fatigue failure. Advanced carbon fibre reinforced polymer (CFRP) has been demonstrated promising for fatigue strengthening of steel structures. Limited research was conducted on CFRP strengthening of welded connections. This paper focuses on the application of ultra high modulus (UHM) CFRP plates with a modulus of 460 GPa to strengthen steel plates with longitudinal fillet weld attachment using five CFRP strengthening configurations. A series of fatigue tension tests were carried out with constant amplitude fatigue loading. Beach marking technique was adopted to record the crack propagation process. Effects of CFRP bond length, bond width and bond locations on fatigue performance of welded steel joints were investigated. The experimental results showed that UHM CFRP plates could generally increase the fatigue life of the welded steel joints. It seems better to apply CFRP on the welding side of the specimen to achieve longer fatigue life. Then, the effects of weld and weld attachment on the CFRP strengthening efficiency was further studied by comparing experimental results of non-welded steel plates with single side UHM CFRP plate strengthening. Finally, the classification method was adopted to assess the strengthening efficiency of the UHM CFRP plate to the steel plates with longitudinal weld attachment.

The present paper discusses the evolution of a critical plane-based multiaxial high-cycle fatigue criterion, known as Carpinteri–Spagnoli criterion. By proposing appropriate changes to the original formulation, the extended versions of the aforementioned criterion are able to assess smooth and notched metallic structural components subjected to different fatigue loading conditions, such as multiaxial in-phase and out-of-phase synchronous cyclic loading, asynchronous cyclic loading and random loading. The results obtained through this criterion are compared with some experimental results related to relevant data reported in the literature.

The paper presents a numerical modelling of fatigue crack initiation in thermally cut structural elements by using improved Tanaka–Mura crack nucleation model. The main goal of the study is to analyse the influence of different grain orientations generated with Voronoi tessellation on the crack initiation period. The numerical modelling of the crack initiation period is performed on the test specimens made of high strength steel with martensitic microstructure. Because the specimens are assumed to be thermally cut without any additional treatment, surface roughness is taken into account in the numerical simulation. Several computational analyses with different grain orientations are performed on the each stress level. Therefore, the stress cycles interval [N₁, N₂] in which the crack is expected to be initiated with the probability P(N) is determined by using statistical analyses of obtained computational results. Experimental testing is also performed on the uniaxial test machine by stress ratio R = 0.1.

The thick plate induces the variation of mechanical properties and fracture toughness, especially in cold regions. At the low temperature, the brittle behaviour of steel becomes worse. A series of tests (such as uniaxial tensile test and three-point bending test) were carried out at low temperature to investigate the mechanical properties and fracture toughness of structural steel plates of Q345B with thickness of 60 to 150 mm, as well as the fracture toughness of 150 mm thick butt welded plate. The test specimens are all manufactured from plates along thickness with small size, and the tensile test specimens included through-thickness specimens additionally. The ductility index (percentage reduction of area) and the fracture toughness index (critical CTOD values) all decrease with the temperature decreases and the distance from plate surface increases. The results obtained in this paper provide technical basis for preventing brittle fracture of thick plate steel structures in cold regions.

Crack initiation in Ti-6242 has been observed to occur in a grain with a hard orientation for basal slip neighbouring a grain with a soft orientation. Because there is significant variability in microstructural features and crack initiation life, it is useful to explore the effects of the variability of the microstructural components through a probabilistic sensitivity analysis. In this paper, a probabilistic crystal plasticity finite element model of a hard−soft grain combination (2 grains) was exercised considering the Schmid factor of the soft grain, the misorientation angle between the two grains, and the soft grain size as random variables. A probabilistic sensitivity analysis of the time-to-crack initiation was then employed in order to ascertain the relative importance of the random variables. The results indicate that the variance in the Schmid factor accounts for the majority of the variance in the time-to-crack initiation. A local sensitivity analysis found that larger Schmid factors result in smaller mean life and larger variance. The neighbouring soft grain size was found to be less important than the Schmid factor and misorientation angle.

The paper deals with the effect of the weld bead geometry on the fatigue strength of a joint, mainly focusing on geometry change due to post-weld grinding. The weld toe burr grinding usually has a positive effect on the fatigue strength; however, excessive material removal at the weld throat can decrease its strength. This effect was experimentally evaluated and compared with proper numerical estimations. By means of the numerical evaluations of the effective stress, obtained by the implicit gradient method, the estimation of the geometric component of the grinding process is possible. With this procedure, it is possible to analyse a real joint, geometrically modelled by laser scanner acquisition, and also to assess the excessive net section reduction in a grinding operation.

Aluminium foam sandwiches are subjected to four-point bending fatigue test considering the effect of geometric parameters of panels, such as core and plate thickness, and loading mode, such as arm distance.

Fatigue strength curves are expressed in terms of different stress amplitude parameters calculated using an analytical model based on laminated plate classical theory and a solid finite element method model. Despite, the notable fatigue data scatter, originated by foam intrinsic inhomogeneity, experimental fatigue curves are coherent and allow obtaining unified fatigue curves.

The present study evaluates ratcheting response of materials by means of the Armstrong–Frederick (A–F) hardening rule, the modified A–F rule (Bower's model), and further modifications of the hardening rule based on new introduced coefficients. The implemented modifications on the A–F-based hardening rule aims to address stages of ratcheting over stress cycles. The modified hardening rule predicts the ratcheting strain rate decay over stage I and the constant rate of strain accumulation during stage II. The modified hardening rule consisted of the coefficients of the hardening rule controlling stress–strain hysteresis loops generated over stress cycles during ratcheting process (Bower's modification on A–F rule) plus the coefficients controlling rates over stages of materials ratcheting deformation. Stress–strain-dependent coefficients in the modified rule are responsible to compromise overprediction of ratcheting of A–F during stage I and the premature plastic shakedown beyond stage I induced by Bower's model. Ratcheting strain rate coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting in stages I and II and enabled the modified hardening rule to predict ratcheting strain over a prolonged domain of stress cycles. The modified hardening rule was employed to assess ratcheting response of 304, 42CrMo, 316L steel and copper samples under uniaxial loading conditions. The predicted ratcheting values based on the modified hardening rule and the experimental ratcheting strains were found in good agreements.

Fatigue and crack propagation tests are carried out on 7075-T73 open hole aluminium alloy specimens. A remarkable increment of fatigue life due to the Split Sleeve Cold Expansion^TM process is observed, further improved by applying the process twice on the same hole. Comparable increments are obtained by using the StressWave^TM method. Specific tests are performed in order to point out a possible relaxation of the residual stresses due to fatigue loading. The results obtained reveal no relaxation phenomena in the tested specimens.

The compressive residual stress around cold expanded holes is numerically evaluated. Dedicated experiments based on the Sachs method are conducted to confirm the residual stress prediction.

Since 1948, ductile cast irons (DCIs) are able to combine the toughness of steels with the good castability of grey irons. They are widely used in a number of applications, for example wheels, gears, and crankshafts in cars and trucks. Their fatigue crack propagation resistance depends on loading conditions, chemical composition, matrix microstructure and graphite elements morphology (graphite volume fraction, graphite elements nodularity, graphite elements distribution and dimensions).

In this work, a ferritic DCI was investigated focusing fatigue crack propagation micromechanisms: step by step fatigue crack propagation tests were performed considering compact-type specimens, and crack propagation micromechanisms were investigated by means of scanning electron microscope and digital microscope lateral surfaces observations, considering different loading conditions. Furthermore, overloads were also considered during fatigue crack propagation, investigating their influence on DCI fatigue crack propagation micromechanisms.

A cyclic cohesive zone model (CZM) combined with the extended finite element method for the fatigue crack initiation and propagation in ductile materials was investigated under different loading conditions in C(T) specimens. Detailed experimental verification confirmed the known CZM could not predict effects of the loading ratio in fatigue crack properly. Including the loading ratio into the damage evolution equation described the loading ratio correctly. The CZM was used to predict both fatigue crack nucleation and propagation in a deep notched C(T) specimen. The simulations displayed reasonable agreement with experimental data in the stable stage of fatigue crack propagation and showed the potential for a unified description of fatigue crack nucleation and growth.

The crack propagation behaviours of polymethyl methacrylate material with double holes under the directional controlled blasting are studied using dynamic caustic method. A series of dynamic caustic patterns at the propagating crack tip under the explosive loading are recorded using the digital high-speed camera. Some important dynamic fracture characterizations and parameters about two main cracks are determined including the crack path, the propagating speed and the crack tip stress intensity factors. The fracture mechanisms of the double blasting holes are analysed. The results provide the important experimental basis for evaluating and designing the directional controlled blasting for the rock tunnel and the rock face excavation.

In the present contribution, the fracture behaviour of specimens made of isostatic graphite and weakened by inclined key-hole notches is investigated. Different loading mixities are considered varying the inclination angle of the notch with respect to the direction of the applied load.

The new data permit to enlarge the scarce number of results available in the literature for the same material under prevalent in-plane shear loading.

A criterion based on local energy is used for the fracture assessment to summarise all the data in a single scatter band independent of the notch geometry and mode mixity. The local energy-based criterion allows to predict with sound accuracy the critical loads of the specimens independent of the mode mixity from pure mode I to prevalent mode II. A final synthesis is reported in the paper, summarising the new data together with previous results on the same material from U-notched specimens subjected to mode I + II loading.

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.

The crack tip stress-induced martensitic transformation and the resulting stress distribution in a nickel–titanium (NiTi)-based shape memory alloy have been analysed. In particular, the effects of temperature, within the stress-induced transformation regime, in single edge crack specimens have been studied by a recent analytical model, finite element simulations and experimental measurements. The results of the analytical model have been compared with those obtained from finite element simulations, carried out by using a special constitutive model for shape memory alloys, and good agreements have been observed. Furthermore, full field numerical results have been used to better understand the evolution of the volume fraction of martensite in the crack tip region. Finally, experimental measurements have been carried out, by using single edge crack specimens obtained from commercially available NiTi sheets by electro-discharge machining. The results have been analysed by linear elastic fracture mechanics theory, and the analytical model has been used to calculate modified stress-intensity factors for shape memory alloys. A slightly increase of the critical stress-intensity factor has been observed with increasing the testing temperature, and this result is in accordance with the model calculations, which indicate a toughening effect, i.e. a reduction of the crack tip stress intensity factor.

This work aims at evaluating the fracture surfaces of tensile samples taken from a new kind of ductile iron referred to as ‘dual-phase Austempered Ductile Iron (ADI)’, a material composed of ausferrite (regular ADI microstructure) and free (or allotriomorphic) ferrite. The tensile fracture surface characteristics and tensile properties of eight dual-phase ADI microstructures, containing different relative quantities of ferrite and ausferrite, were studied in an alloyed ductile cast iron. Additionally, samples with fully ferritic and fully ausferritic (ADI) matrices were produced to be used as reference. Ferritic–pearlitic ductile irons (DI) were evaluated as well. For dual-phase ADI microstructures, when the amount of ausferrite increases, tensile strength, yield stress and hardness do so too. Interesting combinations of strength and elongation until failure were found. The mechanisms of fracture that characterise DI under static uniaxial loading at room temperature are nucleation, growth and coalescence of microvoids. The fracture surface of fully ferritic DI exhibited an irregular topography with dimples and large deformation of the nodular cavities, characteristic of ductile fracture. Microstructures with small percentages of ausferrite (less than 20%) yielded better mechanical properties in relation to fully ferritic matrices. These microstructures presented regions of quasi-cleavage fracture around last-to-freeze zones, related to the presence of ausferrite in those areas. As the amount of ausferrite increased, a decrease in nodular cavities deformation and a flatter fracture surface topography were noticed, which were ascribed to a higher amount of quasi-cleavage zones. By means of a special thermal cycle, microstructures with pearlitic matrices containing a continuous and well-defined net of allotriomorphic ferrite, located at the grain boundaries of recrystallised austenite, were obtained. The results of the mechanical tests leading to these microstructures revealed a significant enhancement of mechanical properties with respect to completely pearlitic matrices. The topographies of the fracture surfaces revealed a flat aspect and slightly or undeformed nodular cavities, as a result of high amount of pearlite. Still isolated dimple patterns associated to ferritic regions were observed.

We investigated the asymptotic problem of a kinked interface crack in an orthotropic bimaterial under in-plane loading conditions. The stress intensity factors at the tip of the kinked interface crack are described in terms of the stress intensity factors of the interface crack prior to the kink combined with a dimensionless matrix function. Using a modified Stroh formalism and an orthotropy rescaling technique, the matrix function was obtained from the solutions of the corresponding problem in transformed bimaterial. The effects of orthotropic and bimaterial parameters on the matrix function were examined. A reduction in the number of dependent material parameters on the matrix function was made using the modified Stroh formalism. Moreover, the explicit dependence of one orthotropic parameter on the matrix function was determined using an orthotropic rescaling technique. The effects of the other material parameters on the matrix function were numerically examined. The energy release rate was obtained for a kinked interface crack in an orthotropic bimaterial.

In polycrystalline metals, microstructural features such as grain boundaries (GBs) influence fatigue crack initiation. Stress and strain heterogeneities, which arise in the vicinity of GBs, can promote the nucleation of fatigue cracks. Because of variations in grain size and GB types, and consequently variations in the local deformation response, scatter in fatigue life is expected. A deeper quantitative understanding of the early stages of fatigue crack nucleation and the scatter in life requires experimental and modelling work at appropriate length scales. In this work, experiments are conducted on Hastelloy X under fatigue conditions, and observations of fatigue damage are reported in conjunction with measurements of local strains using digital image correlation. We use a recent novel fatigue model based on persistent slip band–GB interaction to investigate the scatter in fatigue lives and shed light into the critical types of GBs that nucleate cracks. Experimental tools and methodologies, utilizing ex situ digital image correlation and electron backscatter diffraction, for high resolution deformation measurements at the grain level are also discussed in this paper and related to the simulations.

Hindered by the distinctive toughness requirements of the current European standards, the high-strength low-alloy (HSLA) steels are rarely applied to the pressure vessels industry. The reason is that the design rules specified by the standards define local plastic deformation as limit state. This results in an over-conservative application of materials. To achieve an effective, economical and energy-efficient use of HSLA steels, a strain-based criterion, the damage curve, which considers crack initiation instead of the beginning of plastic deformation as limit state, is proposed in this study for the improved design rules. In the view of the interaction of microstructure and mechanical properties of materials, the new design rule is derived on the basis of the correlation of microstructural features of HSLA steels with the micromechanical damage models. The experimental verification of the result is furthermore investigated with sufficient agreement so that the general applicability of the procedure can be expected. However, further studies for a reliable parameter calibration are necessary.

Use of high-strength concrete can lead to more economical design reducing the material requirements, weight of structure and extended service life of structure. The effect of fatigue loading is more prominent on the structures using high-strength concrete. Bond between concrete and reinforcing bars is a major factor affecting the performance and sustainability of reinforced concrete structures. Less research is available on the effect of low cyclic fatigue loading on the bond strength of high-strength concrete. In this research, reinforced concrete beams (1165 × 150 × 225 mm) were tested under low cyclic loading with different stress range levels. It can be concluded that the bond strength of high-strength concrete is more than for normal-strength concrete. Low-cyclic fatigue loading decreased the bond strength under monotonic loading by about 43–45%. Energy dissipation during cycling is found to be good. At higher cycles, energy dissipation decreased because of local damages in front of bar ribs. With the increase in number of cycles, change in slip behaviour was found.

Shipbuilding in blocks, as being usual on all larger shipyards, requires that the blocks will finally be welded together manually or semi-automatically, that is, with butt-welds in transverse direction that have to withstand relatively high dynamical loads. Modern shipbuilding aims at lightweight construction with thin plates that may have a plate thickness down to 4 mm. Previous investigations showed that manually produced butt-welds in such thin structures did not reach the calculated fatigue life as required in the rules. Up to the present, this problem has not yet been solved, and it is questioned if all influence factors on the fatigue behaviour of real structures are correctly considered as no damage cases at butt joints that are known yet. In the investigation described here, results from small-scale specimens tested with cyclic loads will be transferred to large components, considering the effects of recorded pre-deformations induced by welding as well as measured differences in residual stresses between small-scale specimens and large components, thus clarifying how far for instance a detrimental stress ratio should be taken into account by the rules for thin plates.

Damage evolution and crack propagation in sandstone specimens have been observed by digital image correlation method. To investigate deformation and failure process of rock under different loading conditions, uniaxial compression and indentation tests were performed. Through the experiment, displacement and strain fields are simultaneously obtained that can visually display the distribution, mode and evolution of deformation and cracking in rock. Experimental results show that the damage distributes diffusely in rock at early loading stage, and the measured apparent strain increasingly concentrates with loading because of the nucleation of crack; propagation of the crack leads to the eventual failure of the specimen. Damage factor is calculated on the basis of deviation of apparent strain, and localization factor is presented to describe the level of deformation localization. The combined use of two factors can well represent the damage evolution of rock under compression.

This paper deals with the influence of interference fit coupling on the fatigue strength of holed plates made of a medium-carbon forging steel (35 KB2), heat treated by quenching followed by tempering, up to a hardness of about 350 BH, obtaining a sorbitic microstructure. Tensile and impact tests showed an ultimate tensile strength of about 1100 MPa, a yield strength of about 1000 MPa, an elongation to failure of 15% and an impact toughness KV of 43 J at room temperature. Axial fatigue tests were performed on holed specimens with or without a pin, made of the same material, press fitted and still left into their central hole. The tension–tension fatigue tests have been performed with a stress ratio R = 0.1. The effect on fatigue strength was investigated both experimentally and numerically. Three different conditions were investigated by using open hole specimens, specimens with 0.6% of nominal specific interference and specimens with 2% of nominal specific interference. The experimental stress-life (S–N) curves pointed out an increased fatigue life of the interference fit specimens, compared with the open hole ones. The numerical investigation was performed in order to analyse the stress field by applying an elastic plastic 2D simulation, with commercial finite element software. The stress history and distribution around the interference-fitted hole indicate a significant reduction of the stress amplitude produced by the external loading (remote stress) because a residual and compressive stress field is generated by the pin insertion.

In this paper, the fatigue behaviour of some ductile irons for structural applications is analysed in terms of strain–life, stress–life and cyclic stress–strain curves. Push–pull, strain-controlled fatigue tests were carried out on ferritic, pearlitic, isothermed and austempered ductile irons. The same tests were executed on a structural steel for comparison purposes. The experimental data were processed according to the common practice as well as to a recent procedure proposed by the authors, which ensures the compatibility conditions are satisfied in a strict sense. Conversely, if the common practice is applied, compatibility conditions are satisfied only approximately. Finally, the results of the experimental fatigue tests on the different materials are compared and discussed in view of application to structural components.

This note reviews the means for fatigue damage rates estimation using scaled Laplace distributed loads. The model is suitable for the description of stresses containing transients of random amplitudes and locations. Moment method to estimate model parameters is given. Explicit formulas to compute rainflow damage rate as a function of excess kurtosis are presented. Laplace model is used to describe the variability of forces measured at some location on a cultivator frame. Validation of the model and uncertainty analysis in fatigue damage predictions is given.

Bending fatigue prediction accuracy of steel wheel can hardly be guaranteed without clearly understanding the influence of stamping process on fatigue. In this research, multi-step stamping processes of spoke were analysed by different finite element simulation techniques. Major influences of stamping process on fatigue property were distinguished. Data-mapping technique was used to transfer information between stamping and fatigue analysis models. Difference material experiments were carried out to research the influence of prestrain on material properties. Modified E-N function was established according to the theoretical analysis and material experiment results. Bending fatigue finite element simulation was carried out, and result matched experiment well both in position and cycle life.

As an engineered material, ultra-high toughness cementitious composite (UHTCC) exhibits the characteristics of pseudo strain hardening and multiple cracking under uniaxial tension. It can be applied as the reinforcing and protective material of concrete structures. In this paper, static and fatigue flexural tests were carried out on UHTCC-layered concrete composite beams, for which UHTCC layer was used on the tension side. Under both static and fatigue loads, plane section assumption was suitable for such composite beams, and a good bond strength was achieved between the two layers. For static specimens, the UHTCC layer enhanced the ductility of the concrete layer. While under cyclic loads, because of the reinforcing effect of UHTCC, more than one crack were formed in the concrete layer, which led to a ductile deformation. Furthermore, the fatigue damage process of the composite beam was analysed.

Fatigue crack initiation life prediction is a fundamentally challenging problem that is of prime importance as a significant portion of the fatigue life is spent in the initiation phase. In spite of the extensive efforts of research over the past two decades, the concept of crack initiation still remains as an enigma in science. The major challenges in predicting crack initiation life in industry are the evaluation of the crack initiation parameters such as the maximum resolved shear stress range, maximum slip band width and the energy efficiency coefficient. In this paper, we show that the energy efficiency can be successfully estimated with good accuracy by performing lattice level crystal plasticity-based computational simulations on representative models. The lattice level plasticity-based finite element computations are reported for the case of single crystal copper in this work, and the results show that this strategy leads to higher accuracy than the existing idea of approximating the efficiency factor. The results show that this strategy could be of great use in improving the reliability in prediction of crack initiation life. The effectiveness of this computational procedure would greatly reduce the financial investments necessary to perform experimental analysis of all structures to determine the crack initiation parameters, as it would require just a single measurement to quantify the measurement of efficiency.

This work evaluates the limit stress of the thermo-elastic phase of deformation by thermo-analysing the surface of a specimen during a static traction test.

By adding a temperature curve measured over a small area of the surface to the classical stress–strain curve, it is possible to evaluate a limit temperature T₀ that is coincident with the beginning of the curve's nonlinear trend. The corresponding stress value is as estimation of the fatigue limit of the component under analysis.

The authors derive an expression to evaluate temperature during a mono-axial static traction test. As an example, temperature curves recorded during traction tests performed on two notched steel specimens are reported and compared with this proposed expression. The change to the linearity in the temperature curve during the static traction test is evident in these examples and the corresponding stress value is an estimation of the fatigue limit of the component under analysis.

Each welded connection between blades and band or crown of a Francis hydraulic turbine runner can be considered as a T-joint subjected to pure bending induced by the water action. A semi-elliptical crack is assumed to exist at the surface of one of the aforementioned welded connections. The actual geometry of the T-joint can be simplified, that is, only the cracked plate (representing the blade) under a given stress distribution acting on the defect faces is examined. A numerical procedure already proposed by the authors to compute the stress-intensity factor (SIF) along the crack front is here applied by introducing some changes to simplify such computations. The obtained values of SIF are compared with some results available in the literature.

The low-cycle fatigue behaviour of a cast Al–12Si–CuNiMg alloy, with a high content of Si, is investigated at 200, 350 and 400 °C. The fatigue test results show that the alloy exhibits symmetrical hysteresis loops, moderate cyclic softening and higher fatigue resistance at higher temperature. The fracture surface analysis reveals that more tear ridges are formed at higher temperature, which strongly affect the fatigue resistance. Furthermore, evaluation of the material fatigue resistance using an energy-based Halford–Marrow model indicates that the material's ability to absorb and dissipate plastic strain energy is enhanced as temperature increases.

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large-sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.

This study aimed to investigate crack behaviour at the internal and external surfaces of the cement layer in total hip replacement. A three-dimensional model of the femur with the cemented prosthesis was developed and analysed. Cracks were placed on the internal, external and both internal and external surfaces of the cement layer. Stress intensity factors were measured during gait. Results revealed that the stress intensity factors modes I and III were the most dominant in the crack propagation in the cement layer. The domain of mode I was the medial and lateral sides of the cement layer. Meanwhile, the domain of mode III was the anterior and posterior sides of the cement layer. The stress intensity factor and distance from the distal end indicated an inverse relationship. The internal and external cracks had no significant interaction. Moreover, stress intensity factors at the external surface of the cement layer were higher than those on the internal surface.

This paper postulates a crack growth model for pipeline steels in near-neutral pH soil environments, on the basis of the experimental results reported in literature and the fundamental understanding of the corrosion fatigue crack growth dominated by hydrogen embrittlement mechanism. The comparison with the laboratory data indicates that this model can provide reasonable predictions for the dependence of the crack growth rates on the stress intensity factor, stress ratio, loading frequency, solution pH and electrochemical potential.

This paper investigates the fatigue strength assessment of web-core steel sandwich panels. The production of these structures is made possible by laser stake welding. The investigation in this study considered two series of panels, one being an empty steel structure and the other filled with in situ polyurethane foam in order to increase the panel stiffness. Both series were tested under cyclic bending loading condition (R = 0) until one of the panel joints failed completely. A 3D panel bending response was analysed using finite element method. The J-integral values at the panel joints were obtained by means of plane strain finite element analysis and by using displacements from 3D panel response. The influence of the weld geometry on the J-integral value was investigated. It was found that the J-integral value is similar in the cases of the average and critical geometry. The contact between the joint plates is possible in some cases, but its influence proved to be insignificant for the fatigue strength assessment. The study further shows that by using the average geometry, the J-integral approach was able to identify the critical panel joints and present the fatigue strength results from both panel series in a narrow scatterband. The fatigue strength at two million cycles obtained for the panels within this study was in agreement with the laser stake welds and other steel joint types from previous studies. However, the slope of the panels fatigue resistance curve was found to be shallower than in the case of joints.

This paper presents a new data analysis technique to rapidly identify the region of stable crack growth in crack tip opening angle (CTOA) testing of a modified double cantilever beam. The technique basically used the load–displacement data from CTOA testing on API X65 steel, which demonstrated a region of constant slope after the peak load. In total, 22 data points (out of 90) fell in this region, for which the variation of CTOA versus crack length remained almost constant. The CTOA measurement was conducted from crack edges and from a fine reference grid, using photographs from two cameras in front and rear sides of the CTOA specimen. As the visual analysis of the individual photographs is tedious and rather lengthy, the presented technique can be easily used for rapid and precise identification of the mean CTOA from those data in the constant slope region of the load–displacement plot.

This Special Issue celebrates the first 30 years of the existence of the Italian Group on Fracture (IGF). In that time, the fractographic imaging capability afforded by scanning electron microscopes had undergone a technological revolution, offering unparalleled opportunities to characterize very fine fracture surface features and to characterize chemical species and microstructure via such techniques as energy dispersive spectroscopy (EDS), wavelength dispersive spectroscopy (WDS) and electron backscatter diffraction (EBSD). A wavelength-dispersive spectrometer uses the characteristic X-rays generated by individual elements to enable quantitative analysis (down to trace element levels) to be performed with spot sizes as small as a few micrometres. This complements EDS where a user can acquire a full elemental spectrum in only a few seconds but where energy peaks may overlap among different elements, particularly those corresponding to X-rays generated by emission from different energy-level shells (K, L and M) in different elements. It then becomes easier to acquire a quantitative elemental map alongside excellent fracture surface images. This paper considers some of the areas in fractography where the increased capability of modern scanning electron microscopes confers advantages.

First, fatigue tests were performed on butt-welded joints made of novel direct quenched ultra high strength steel with high quality welds. Two different welding processes were used: MAG and Pulsed MAG. The weld profiles, misalignments and residual stresses were measured, and the material properties of the heat-affected zone were determined. Fatigue tests were carried out with constant amplitude tensile loading both for joints in as-welded condition and for joints after ultrasonic peening treatment. Finally, in fatigue strength predictions, the crack initiation phase was estimated using the procedures described by Lawrence et al. [Lawrence F V, Ho N J and Mazumdar P K (1981) Predicting the fatigue resistance of welds. Annu. Rev. Mater. Sci, 11, 401–425]. The propagation phase was simply estimated using S–N curves for normal quality butt welds, which may contain pre-existing cracks or crack-like defects eliminating the crack initiation stage.

The influence of cyclic creep accumulation rate on the damage evolution of MDYB-3 polymethyl methacrylate (PMMA) was experimentally investigated. Fatigue tests were carried out at four stress levels by stress control mode. The steady cyclic creep accumulation stage was observed occupying a substantial proportion of all specimens fatigue processes. Cyclic creep strain growth speed and relaxed modulus degradation rate were deduced as two important indicators for describing the damage evolution characteristics. Linear evolution relations of cyclic creep strain and modulus degradation with cycle times were retrieved from different terms of hysteresis loops. A preliminary model was proposed to be able to estimate the damage extent at different cyclic stress levels. The life predictions by the proposed model were compared with the experiment results and the classical power S–N model, which were demonstrated as a good estimation for the fatigue life. It is feasible to make durability evaluations by the characteristics of steady cyclic creep for multiaxis directed PMMA material.

Stable tearing is a recurring process in which fatigue crack growth is interspersed by substantial jumps of crack growth, commonly at the central cross-section of the component while the crack front nearer the surface lags behind. These tearing bands have been observed to start very early during fatigue life and can make up the majority of the fatigue fracture surface. This paper presents the development of predictive models, in which the tongue-shaped stable tearing band is first idealised as trapezoidal shape, and then two alternative fracture criteria are formulated with the aid of the finite element (FE) method and the Forsyth stable tearing concept. Parametric solutions of the stress intensity factor at the front of the trapezoidal crack front are obtained using the FE method. Comparisons between the model predictions and experimental results indicate that both models produce satisfactory prediction of the stable tearing crack jump length in aluminium alloy coupons of varying cross-sectional thickness.

Constraint can be divided into two conditions of in-plane and out-of-plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in-plane and out-of-plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in-plane and out-of-plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in-plane and out-of-plane constraints based on crack-tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in-plane and out-of-plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in-plane constraint, out-of-plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint-dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.

This paper proposes a numerical approach based on a steady-state algorithm to predict the rolling contact fatigue crack initiation in railway wheels in practical conditions. This work suggests taking into account the cyclic hardening of the wheel's material and one of its originality is to conduct a complete numerical approach whatever the loading level. The main stages are the characterization and modelling of the material behaviour, the determination of the stress–strain fields using a numerical steady-state method and the application of a high cycle fatigue criterion. Computations were made with the Abaqus FE commercial software. Three cases are studied: rolling with or without sliding and skating. The numerical results give several types of mechanical responses: elastic or plastic shakedown. Otherwise, the results show that the location where the shear stress is maximal is not the same as where the risk of crack is the highest.

In this paper, a fracture mechanics method was applied for the evaluation of crack behaviour in anisotropic paperboard subjected to biaxial uniform loading. The experiment was performed to determine the crack propagation angle and the fracture strength of paperboard under biaxial loading with the cruciform specimen optimized by FEM simulation. The effects of biaxial loads on the critical stress ratio and crack propagation angle for various inclination angles were investigated. The experimental results were compared with theoretical results, which were calculated by using the Normal Stress Ratio Criteria. The experimental results for crack propagation angle and critical stress show good agreement with theoretical results.

In this paper, the arbitrary Lagrangian Eulerian formulation is employed for finite element modelling of dynamic crack propagation problem. The application phase simulation of computational dynamic fracture is applied to model by which the crack propagation history and variation of crack velocity are predicted using the material dynamic fracture toughness. The dynamic solution of problem is accomplished using the implicit time integration method. The convective terms due to mesh-material motion are taken into account via the convection equation. A robust and efficient mesh motion technique, that its equations need not to be solved at every time step, is employed in Eulerian phase. The mesh connectivity is preserved during the analysis. So, the successive remeshing of model is eliminated. When the dynamic fracture criterion is satisfied for crack growth, the presented algorithm allows the crack to advance by splitting the material particle at the crack tip. The dynamic energy release rate is calculated at each time step to determine dynamic stress intensity factor. The predicted results are compared with those obtained through the experimental study and remeshing technique cited in the literature. The proposed computational algorithm leads to an accurate and efficient simulation of dynamic crack propagation process.

Subsurface crack mode II propagation parallel to the contact surface is a damage mechanism leading to dramatic failure in many components subjected to cyclic loading. A weight function (WF) was elaborated for calculating the applied mode II stress intensity factor (SIF) of a crack in a two-dimensional half-space in plane strain condition, for crack completely closed and frictionless contact between the crack faces. With respect to other methods, the WF allows faster SIF calculation, thus being suitable for simulation of many repeated load cycles and fatigue crack propagation. The WF was applied for simulating a case of rolling contact experiments found in the literature, and good agreement between experimental and numerical results was obtained, showing the effectiveness of the WF method in damage tolerant design.