Three-dimensional (3D) finite element analyses are carried out on single-edge bend [SE(B)] specimens for which the *J*-integral resistance curves (*J–R* curves) have been experimentally determined to develop the constraint-corrected *J–R* curves for the X80 grade pipe steel. The constraint parameters considered in this study include *Q _{HRR}*,

The relations between fatigue strength and other mechanical properties especially the tensile strength of metallic materials are reviewed. After analyzing the numerous fatigue data available, the qualitative or quantitative relations between fatigue strength and hardness, strength (tensile strength and yield strength) and toughness (static toughness and impact toughness) are established. Among these relations, the general relation between fatigue strength *σ*_{w} and tensile strength *σ*_{b}, *σ*_{w} = *σ*_{b}(*C* − *P* ⋅ *σ*_{b}), where *C* and *P* are parameters, (hereafter, the general fatigue formula) can well predict the fatigue strength with increasing the tensile strength in a wide range for many materials such as conventional metallic materials, newly developed materials and engineering components. On the basis of the experimental results of many materials, the fatigue damage mechanism, especially for high-strength steels, is proposed. It is suggested that the general fatigue formula can provide a new clue to predict the fatigue strength and design the materials by adjusting material parameters *P* and *C* adequately.

The paper is focused on failure assessment of the shaft of a pumped storage unit. The shaft failure occurred during normal operation of the hydropower unit after 35 years of service. Three different methods are applied in order to assess its lifetime. Firstly, a finite element analysis was performed in order to obtain the static stress distribution and to apply a strain-based crack initiation for the shaft under torsion load. The number of cycles for crack propagation was obtained using the Paris law for mode III. More precisely, the lifetime assessment of the shaft is obtained based on a low-cycle fatigue analysis for estimating the number of cycles for crack initiation and then followed by that for fatigue crack propagation. Secondly, an analytical estimation based on failure assessment diagram is carried out for circumferential crack in order to determine the safe/unsafe region, where the shaft can operate with a crack. The failure assessment diagram for mode III loading was plotted in order to obtain the critical circumferential crack using the stress intensity factor solution and three analytical solutions for plastic zone. Thirdly, the theory of critical distance is employed for estimating the shaft life under torsional loading. A good agreement is obtained between the estimated results and experimental data for the shaft life and the crack length.

Threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. In the present paper, a theoretical model of a periodically kinked crack is proposed to describe the influence of the crack deflection degree on the fatigue behaviour. The kinking of the crack is due to a periodic self-balanced microstress field having length scale *d*. By correlating the parameter *d* with a characteristic material length (e.g. average grain size in metals, maximum aggregate size in concrete), the present model is applied to interpret some experimental findings related to crack size effects in fatigue of materials. Well-known experimental results concerning three different situations (fatigue threshold, fatigue short crack growth and fatigue crack growth in the Paris regime) are analysed.

Welding processes often lead to pronounced weld termination points (start/end), which are prone to fatigue events such as crack initiation. The fatigue of weld ends under shear loading, especially in thin sheet structures, is not sufficiently explored yet. In the present investigation, the real geometry of welds was obtained by scanning the three-dimensional surface, especially of weld ends. Cryogenic breaking of the weld opened the view to the weld root geometry and especially to the critical location, where the weld root migrates to a weld toe at the weld end. In the experimental part of this research, fatigue testing of thin sheet plane and cylindrical specimens as well as large components containing weld ends was performed. Based on the data, weld end life curves have been obtained. The notch stress concept and a fracture mechanics based approach were applied for describing the results of fatigue tests providing sufficient accuracy.

In the present paper, the fatigue strength estimation capabilities of the modified C-S (Carpinteri-Spagnoli) criterion are improved by employing the Maximum Rectangular Hull (MRH) method proposed by the first author. The C–S criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach and takes into account both shear stress (Mode II) and normal stress (Mode I) mechanisms to evaluate the orientation of the critical plane. The fatigue damage parameter used is given by a nonlinear combination of the equivalent normal stress amplitude, *N*_{a,eq}, and the shear stress amplitude, *C*_{a}, acting on the critical plane. In the present paper, the shear stress amplitude is evaluated through the MRH method. Some experimental data available in the literature are compared with the theoretical estimations, concluding that the multiaxial fatigue strength evaluations provided by the C–S criterion are improved when *C*_{a} is computed applying the MRH method instead of the Minimum Bounding Circle (MBC) method.

This work provides some ecological criteria for fatigue designers so that they can quantitatively consider the ecological impact as a factor during the process of design. In particular, during the selection of materials for fatigue applications, two kinds of applications have been examined. The first one is related to components under cyclic loading with no energy consumption during their use, as a pipe under variable pressure. In this case, the highest impact takes place during the material production phase. The second application refers to components used in means of transport, as planes or cars components. For them, the highest environmental impact occurs during the use phase, through fuel consumption. For both applications, a parameter is provided, named *Ecological-Fatigue Factor*, that combines both the ecological impact and the fatigue endurance of the materials. For the two applications, a ranking of materials based on the Ecological-Fatigue Factor is given. Great differences can be found between the two rankings.

Linear elastic fracture mechanics has enabled the research community to solve a wide variety of problems of practical and scientific interest; however, it has historically suffered from two main shortcomings. Firstly, it predicts physically unrealistic singular stresses and strains at crack tips. Secondly, microstructural effects are lacking, so that a major source of size-dependent behaviour is not captured. Gradient-enriched elasticity overcomes both these shortcomings: singularities are avoided, so that crack-tip stresses can be used to assess integrity, and the inclusion of microstructural terms implies that size effects can be captured. In this investigation, it is shown that gradient-enriched crack tip stresses can directly be used to model the transition from the short to the long crack regime. The accuracy of this approach was validated by a wide range of experimental results taken from the literature and generated under both static and high-cycle fatigue loading. This high level of accuracy was achieved without having to resort to phenomenological model parameters: the extra constitutive coefficient was simply the (average) grain size of the material.

The present paper reviews and contains simple modifications to extend the applicability of global and local fatigue concepts to thin-welded specimens with pronounced weld terminations (starts/ends). Experimental fatigue data reported by Kaffenberger and Vormwald have been used for the validation of the proposed procedures. Special attention is paid to the notch strain concept. The material state is explicitly considered by means of corresponding strain–life curves in conjunction with P* _{SWT}*, P

Climate change and sustainability have driven enormous development programmes for offshore wind. These large structures are mainly fabricated of welded steel tubular and plate sections not dissimilar to structural details commonly encountered in the ship, and offshore oil and gas sectors, but design requirements differ significantly due to environmental aspects, loading regime and low capital expenditure and operational expenditure requirements. There is therefore a requirement to quickly update corrosion fatigue knowledge and data bases in order to assist operations and designers to optimise structures with respect to fatigue strength and cost. This paper reviews seawater corrosion fatigue and potential approaches to developing appropriate test procedures and analysis methods to produce reliable and meaningful corrosion-fatigue behaviour under stochastic loading conditions and sets out some fundamental principles for any such testing programme.

The effects of wire brush hammering on low cycle fatigue behaviour of AISI 316 austenitic stainless steel has been investigated on turned samples through an experimental study combining strain controlled fatigue tests, scanning electron microscope examination and X-ray diffraction analysis. An increase in fatigue life by 266% was reported at an imposed strain amplitude of Δ*ε _{t}*/2 = 0.2%. This improvement is limited to Δ

Sandwich panels are more and more used in load bearing structures because of their high specific stiffness and high specific strength. Impact energy absorption is a characteristic required for some specific application, that is, in high-speed transportations. In this article, the impact response of a new sandwich panel made up of two polyethylene skins separated by lightweight polyethylene foam, built with an innovative manufacturing process called rotational moulding, is investigated by both the impact test and the finite element analysis. To characterize the low-velocity impact response of this new material, three homogenous polyethylene sandwich panels, 44 ± 1 mm thick, are studied under seven impact test energy levels, from 5 to 70 J. Experimental tests have allowed obtaining absorbed energy and the load–time plot for each impact energy level. Furthermore, a quantitative analysis of the damage is presented. Finally, a finite element model was implemented to evaluate the damping effect of the core.

Spray-formed hypereutectic aluminium silicon alloy DISPAL® S232–T6x is cycled with variable amplitude at ultrasonic frequency up to the very high cycle fatigue (VHCF) regime under fully reversed tension–compression loading. The Powder Metallurgy alloy is tested using a Gaussian cumulative frequency distribution of load cycles, and lifetimes are compared with constant amplitude data. Miner calculation delivers mean damage sums between 0.5 and 0.9 for mean lifetimes between 8 × 10^{7} and 1.6 × 10^{10} cycles, respectively. Cracks are initiated at voids, at inclusions or at distributed inhomogeneities (porous areas or oxides) at the surface or in the interior. *In situ* analysis of vibration properties indicates that cracks are formed and start growing from the beginning of fatigue cycling, even if failure occurs in the very high cycle fatigue regime. Crack initiation stage is negligible. Lifetime prediction calculation is performed using an adapted Paris-law and considering lifetime as cycles necessary to propagate an initial crack to failure. Measured and predicted mean lifetimes differ by factor 0.4–1.0. Large crack-initiating defects strongly reduce the fatigue lifetimes, which is successfully covered in the crack propagation model.

The aim of this work is to understand the influence of notches under thermomechanical fatigue (TMF) in a directionally solidified Ni-base superalloy. Experiments were performed utilizing linear out-of-phase and in-phase TMF loadings on longitudinally oriented smooth and cylindrically notched specimens. Several notch severities were considered with elastic stress concentrations ranging from 1.3 to 3.0. The local response of the notched specimens was determined using the finite element method with a transversely isotropic viscoplastic constitutive model. Comparing the analysis to experiments, the locations observed for crack nucleation in the notch, which are offset from the notch root in directionally solidified alloys, are consistent with the maximum von Mises stress. Various local and nonlocal methods are evaluated to understand the life trends under out-of-phase TMF. The results show that a nonlocal invariant area-averaging method is the best approach for collapsing the TMF lives of specimens with different notch severities.

Fatigue crack growth behaviours in different welding zones of laser beam welded specimens were investigated using central crack tension specimens for 6156 aluminium alloy under constant amplitude loading at nominal applied stress ratio *R* = 0.5, 0.06, −1. The experimental results showed that base metal (BM) exhibited superior fatigue crack resistance compared to weld metal (WM) and heat-affected zone (HAZ). Crack growth resistance of WM was the lowest. The exponent *m* values for BM and HAZ at different stress ratios are close and around 2.6, while *m* for WM at different stress ratio is around 4.7. The discrepancy between crack growth rates for WM and BM is more evident with increasing stress ratio, while it is a little change for HAZ and BM. Change of the microstructure in WM deteriorates the resistance of fatigue crack growth compared to BM. It was mainly due to grain boundary liquation and dissolving of second-phase particles in the weld region. It was also found that the variety of fatigue crack resistance for different welding zones is in conformity with the change of hardness. BM with the highest hardness exhibited the maximum resistance for fatigue crack, and WM with the lowest hardness exhibited the minimum fatigue crack resistance.

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti-6Al-4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.

Semi-empirical notch sensitivity factors *q* have been used for a long time to quantify notch effects in fatigue design. Recently, this old concept has been mechanically modelled using sound stress analysis techniques, which properly consider the notch tip stress gradient influence on the fatigue behaviour of mechanically short cracks. This mechanical model properly calculates *q* values from the basic fatigue properties of the material, its fatigue limit and crack propagation threshold, considering all the characteristics of the notch geometry and of the loading, without the need for any adjustable parameter. This model's predictions have been validated by proper tests, and a criterion to accept tolerable short cracks has been proposed based on it. In this work, this criterion is extended to model notch sensitivity effects in environmentally assisted cracking conditions.

This paper is aimed at the approximation of the stress and displacement fields both in the vicinity and also at a larger distance from the crack tip in test specimens utilised for the determination of the fracture characteristics of quasi-brittle materials. A novel geometry is considered, which, with changes in the specimen's shape proportions, offers a wide variety of crack tip constraint levels and consequently also a broad range of extents/shapes of the nonlinear zone evolving around the crack tip. The combination of (four-point) bending and wedge splitting tests of notched prismatic specimens is proposed and numerically investigated. Several variants of boundary conditions are modelled. The stress intensity factor *K*, the *T*-stress and the coefficients of even higher-order terms of the Williams series are determined and subsequently utilised for analytical approximations of the stress field. The agreement between the analytical and numerical solution depending on the distance from the crack tip and the number of terms of the series, and taking into account the analytical expression, is discussed. The presented approach is expected to be a suitable technique employed as part of a procedure being developed for the estimation of the fracture process zone extent in silicate composite materials. Such materials are characterised by their quasi-brittle fracture response, which is caused by the softening of the material in the nonlinear zone. It is shown that changes in specimen proportions and/or the positions of supports slightly influence the crack tip constraint level resulting in possible differences in the width of the nonlinear zone.

The characteristics of dislocation configurations under thermo-mechanical fatigue cycling were investigated in [001] oriented nickel-based single-crystal superalloys. Thermo-mechanical fatigue tests were performed on TMS-75 (without hold time) and TMS-82 (with hold time) superalloys. The specimens were subsequently studied by transmission electron microscopy under two-beam conditions. In TMS-75 superalloy, cross-slipping is the main characteristic for the low number of dislocations. In TMS-82 superalloy, more complex process of dislocation configurations has been demonstrated in detail, involving five stages: after the first stress relaxation, after the first tensile plastic deformation, after the second stress relaxation, after 30 cycles and after rupture. In addition, for TMS-82 superalloy, there is a reversible movement behaviour of stacking faults that occur in compression and disappear in tension. After rupture, the number of dislocation is related to the hold time. Longer hold time could generate a higher degree of stress relaxation and produce more dislocations with climbing characteristic.

Many biological materials are generally considered composites, made of relatively weak constituents and with a hierarchical arrangement, resulting in outstanding mechanical properties, difficult to be reached in man-made materials. An example is human bone, whose hierarchical structure strongly affects its mechanical performance, toughness in particular, by activating different toughening mechanisms occurring at different length scales. At microscale, the principal toughening mechanism occurring in bone is crack deflection. Here, we study the structure of bone and we focus on the role of the microstructure on its fracture behaviour, with the goal of mimicking it in a new composite. We select the main structural features, the osteons, which play a crucial role in leading to crack deflection, and we reproduce them in a synthetic composite. The paper describes the design, manufacturing and characterization of a newly designed composite, whose structure is inspired to the Haversian structure of cortical bone, and that of a classic laminate developed for comparative reasons. We conclude with a critical discussion on the results of the mechanical tests carried out on the new composite and on the comparative laminate, highlighting strengths and shortcomings of the new biomimetic material.

The problems arising as a result of aging aircraft, rail and civil infrastructure have focused attention on tools for predicting the growth of cracks from small naturally occurring material discontinuities. To this end, the present paper discusses on the difference between the analysis tools needed for *ab initio* design and sustainment, modelling of cracks that grow from small naturally occurring material discontinuities and ways to determine the short crack d*a*/d*N* versus Δ*K* data from long crack American Society for Testing and Materials (ASTM) tests. It also discusses how existing equations can be used to predict short crack growth and how to account for the variations seen in crack growth histories. Attention is also focused on the recent Federal Aviation Administration limit of validity ruling and the effect of the environment on widespread fatigue damage in civil transport aircraft.

Pedagogically speaking, crack initiation–growth–termination (IGT) belongs to the process of fracture, the modelling of which entails multiscaling in space and time. This applies to loadings that are increased monotonically or repeated cyclically. Short and long crack data are required to describe IGT for scale ranges from nano to macro, segmented by the SI system of measurement. Unless the data at the nano scale can be connected with the macro, IGT remains disintegrated. The diversity of non-homogeneity of the physical properties at the different scale ranges results in non-equilibrium. These effects dubbed as non-equilibrium and non-homogeneous are hidden in the test specimens and must be realized. They can be locked into the reference state of measurement at the mi-ma scale range by application of the transitional functions and transferred to the nano-micro and macro-large scale ranges.

The aim of this work is to convert the ordinary crack length data to those referred to as short cracks that are not directly measurable. All test data are material, loading and geometry (MLG) specific. The results obtained for the 2024-T3 aluminium sheets hold only for the MLG tested. The differences are more pronounced for the short cracks. These effects can be revealed by comparing the incremental crack driving force (CDF) for the ma-mi range the ma-large range and the na-mi range The CDF is equivalent to the incremental volume energy density factor (VEDF). The incremental mi-ma CDF is found to be 10–10^{5} kg mm^{−1} for cracks 3–55 mm long travelling at an average velocity of 10^{−5} mm s^{−1}. The crack velocity rises to 10^{−3} mm s^{−1} when the incremental CDF is increased to 10^{5}–10^{6} kg mm^{−1}, while the crack lengths are 49–260 mm. The crack velocity for the na-mi range of 0.040–0.043 mm slowed down to 10^{−8} mm s^{−1}, and the incremental CDF reduces further to 10^{−8}–10^{−2} kg mm^{−1}. Note that changed several orders of magnitude while the crack advanced from 0.040 to 0.044 mm. Such behaviour is indicative of the highly unstable nature of nanocracks.

All results are based on using the transitionalized crack length (TCL). The TCL fatigue crack growth increment Δ*a* is postulated to depend on the incremental CDF Δ*S* or ΔVEDF. The form invariance of , and is invoked by scale segmentation to reveal the multiscale nature of IGT that is inherent to fatigue crack growth. While the choice of directionality from micro to macro is not the same as that from macro to micro, this difference will not be addressed in this work.

The article presents two-stage fatigue life evaluation of a stiffened aluminium aircraft fuselage panel, subject to ground–air–ground pressure cycles, with a bulging circumferential crack and a broken stringer. As a worst-case scenario, it is assumed that double cracks start at the edge of a rivet hole both in the skin and in the stringer simultaneously. In the first stage, fatigue crack growth analysis is performed until the stringer is completely broken with the crack on the fuselage skin propagating. After the stringer is completely broken, the effect of bulging crack on the fatigue life of the panel is investigated utilizing the stress intensity factors determined by the three-dimensional finite element analyses of the fuselage panel with the broken stringer. It is concluded that bulging of the skin due to the internal pressure can have significant effect on the stress intensity factor, resulting in fast crack propagation after the stringer is completely broken.

The fracture behaviour of Fe_{78}Si_{9}B_{13} metallic glass under laser shock loading was investigated. Morphologies of the fracture surface and laser irradiated surface were characterized using scanning electron microscope. The results show that the fracture surface consists of sliding region and final fracture region with crack propagation. Liquid droplets and melted belts are scattered on the fracture surface as the notable features compared with fracture surface morphology under quasistatic loading, indicating the significant temperature increase in shear bands during dynamic loading. The primary and secondary shear bands are distributed on the specimen surface resulting from the simultaneous operation of multiple shear bands at high strain rates. Ripples with the characteristic spacing of about 1 µm are generated on the laser irradiated surface because of the interaction of laser pulse with solid surface.

Hydrogen is known to have a deleterious effect on most engineering alloys. It has been shown repeatedly that the strength of steels is inversely related to the ductility of the material in hydrogen gas. However, the fatigue properties with respect to strength are not as well documented or understood. Here, we present the results of tests of the fatigue crack growth rate (FCGR) on API X70 from two sources. The two materials were tested in air, 5.5 and 34 MPa pressurized hydrogen gas, and at both 1 and 0.1 Hz. At these hydrogen pressures, the FCGR increases above that of air for all values of the stress intensity factor range (Δ*K*) greater than ~7 MPa · m^{1/2}. The effect of hydrogen is particularly sensitive at values of Δ*K* below ~15 MPa · m^{1/2}. That is, for values of Δ*K* between 7 and 15 MPa · m^{1/2}, the FCGR rapidly increases from approximately that found in air to as much as two orders of magnitude above that in air. Above 15 MPa · m^{1/2}, the FCGR remains approximately one to two orders of magnitude higher than that of air.

A transient behaviour is observed in the numerical analysis of plasticity induced crack closure at the beginning of crack propagation, as the residual plastic field is being formed. The extent of crack propagation prior to plasticity induced crack closure measurement has a major influence on the accuracy of numerical prediction and on computation time. The objective here is to quantify and understand the minimum propagation, Δ*a _{stb}*, required to obtain stabilized crack opening values. For plane stress state, Δ

In the present version of the truss-like discrete element method (DEM), masses are considered lumped at nodal points and interconnected by means of unidimensional elements with arbitrary constitutive relations. In previous studies of non-homogeneous concrete cubic samples subjected to nominally uniaxial tension, it was verified that numerical predictions of fracture using DEM models are feasible and yield results that are consistent with the experimental evidence so far available, including the prediction of size and strain rate effects. In the DEM formulation, material failure under compression is assumed to occur by indirect tension. In previous simulations, it was verified that the response is satisfactorily modelled up to the peak load, when a sudden collapse usually occurs, characteristic of fragile behaviour. On the other hand, experimental stress versus displacement curves observed in small specimens subjected to compression typically present a softening branch, in part due to sliding with friction of the fractured parts of the specimens. A second deficiency of DEM models with a perfectly cubic mesh is that the best correlations with experimental results are obtained with material parameters that differ in tension and compression. This paper examines another cause of the excessively fragile behaviour of DEM predictions of the response of concrete elements subjected to nominally uniaxial compression, which is due to the regularity of the perfect cubic mesh, unable to capture nonlinear stability effects in the material. It is shown herein that the introduction of small perturbations of the DEM regular mesh significantly improves the predicting capability of the model and in addition allows adopting a unique set of material properties, which are independent of the nature of the loading.

In this research, the effect of adding carbon nanofibers (CNFs) on fatigue life of epoxy resin under flexural bending fatigue loading conditions was investigated. The fatigue tests of specimens were performed under displacement-controlled bending loading at different displacement amplitudes at room temperature. Due to the addition of CNFs, a remarkable improvement in fatigue life of epoxy resin was observed. For instance, 24-fold improvement in fatigue life for 0.25 wt% CNF/epoxy nanocomposites at a strength ratio of 0.43 observed in comparison with the neat epoxy resin.

This paper presents further assessments of the previously reported round-robin fatigue data obtained from high-frequency mechanical impact (HFMI)-improved longitudinal welds. A detailed statistical analyses of geometry measurements of HFMI-treated weld toe profiles are presented. The fatigue analyses based on notch stress as defined by the International Institute of Welding are performed using the finite element method. Notch stresses are assessed based on both the fictitious weld toe radius and the addition of measured actual notch radius to the fictitious radius. While no large differences are observed between the results of methods, the former one is found to be more practical and faster to implement from the end-user point of view.

Literature datasets showed that gigacycle fatigue properties of materials may be affected by the specimen risk-volume, i.e., the part of the specimen subjected to applied stress amplitudes above a prescribed percentage of the maximum applied stress amplitude. The paper proposes a Gaussian specimen shape able to attain large risk-volumes for gigacycle fatigue tests, together with a general procedure for its design: wave propagation equations are analytically solved in order to obtain a specimen shape characterised by a uniform stress distribution on an extended length and, as a consequence, by a larger risk-volume. The uniformity of the stress distribution in the Gaussian specimen is numerically verified through a finite element analysis and experimentally validated by means of strain gauge measurements.