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Since the first paper on the fatigue of metallic materials by J. Albert in 1837, tremendous numbers of papers have been published in various journals by many researchers all over the world. Based on such a long history, several papers on the very high cycle fatigue (VHCF) in the life‐time longer than 107 cycles had appeared in some journals during the period of 1980's. One characteristic finding in these works is the fact that the metallic material can fail even at the stress level lower than the conventional fatigue limit. This fact means that the conventional fatigue design of mechanical structures cannot give the safety of the practical products in the very high cycle regime. Due to this fact, fatigue properties of structural materials in very long life regime has become an important subject; and a lot of studies have been carried out, and many important results have been accumulated until now. Typical aspects on VHCF property are summarized as follows: (1) the fatigue crack tends to occur around the interior inclusion, (2) fine granular area (FGA) is formed around such an inclusion, and (3) duplex S–N characteristics appear in the VHCF regime. In this paper, a brief historical review together with the future prospect on the very high cycle fatigue of metallic materials is attempted for the sake of reference to facilitate the research in this area. Highlights: Historical review and future prospect for researches on metal fatigue.Progress of researches on very high cycle fatigue of metallic materials.Review of interior crack initiation and growth mechanisms around inclusion.Quantitative formulation of interior crack growth around inclusion. [ABSTRACT FROM AUTHOR]

The article discusses a study which was carried out to investigate the local and effective fracture behaviour of polycrystalline silicon for microelectromechanical systems (MEMS). The apparent mode I critical stress intensity factor was determined from MEMS-scale tension specimens. The distribution of values was attributed to local cleavage anisotropy and to enhanced grain boundary toughening.

This paper starts with an overview of the application of the three guidelines (GL) of the German Research Association of Mechanical Engineers (FKM). Each of these provides algorithms for calculating fatigue lives of components under constant or variable amplitude loading, however, with underlying different failure criteria, that is, technical crack initiation life (GL‐nonlinear), fatigue crack growth life (GL‐fracture mechanics), and total fracture life (GL‐linear). Since the GL‐linear only considers linear‐elastic material behavior in the fracture fatigue life calculation, the guideline is not capable for the LCF and is not able to take sequence effects into account. For a better approximation of fracture fatigue lives, the elastic–plastic material behavior has to be taken into account. This paper introduces the U‐Concept which has been evaluated from a large structural durability database from the literature with more than 1,500 experiments for constant and more than 700 experiments for variable amplitude loading. The U‐Concept is a small add‐on to the local strain approach (LSA) which is the backbone of the GL‐nonlinear. It enables (1) to directly calculate the fatigue life to total fracture based on elastic–plastic material behavior according to the LSA or (2) to estimate the remaining fatigue life from crack initiation to fracture without a crack growth simulation. Furthermore, the U‐Concept needs no experimental determined crack growth parameters, the only necessary material parameter is the ultimate tensile strength Rm. The U‐Concept is therefore easy applicable for industrial users and increases the accuracy of the approximated fatigue lives by considering the elastic–plastic material behavior. [ABSTRACT FROM AUTHOR]

MIL‐STD 1530D requires that the certification of an aircraft part employ analytical tools that are capable of modeling crack growth. It is further stated that the durability and damage tolerance (DADT) analyses should be based on linear elastic fracture mechanics (LEFM) and follow a building block approach. This paper illustrates the durability analysis required to certify an additively manufactured part by using the examples of durability tests performed on two wire arc additively manufactured (WAAM) 18Ni 250 Maraging steel specimens. Highlights: Examines the growth cracks in WAAM 18Ni 250 maraging steel specimens with rough surfaces.Reveals that cracking in specimens with rough surfaces is characterized by a single equation.Illustrates the Hartman–Schijve equation for assessing specimens with rough surfaces. [ABSTRACT FROM AUTHOR]

A computational framework of anisotropic phase field model is used to investigate the effects of effective critical energy release rate, interface property, and hole shape on the failure of composite material in this paper. This model is implemented in ABAQUS using a user‐defined element (UEL). First of all, the model is validated through a benchmark model. Second, the effective critical energy release rate is introduced, which can improve the accuracy of the simulation result. Then, the influence of strong and weak interfaces on the failure of composite material is studied. It can be found that the interface properties can change the evolution mode of crack and the final load–displacement response. Finally, the effect of hole shapes on the failure of the composite material is also explored, which shows that the bearing capacity of model can be improved by changing the shape of the hole. [ABSTRACT FROM AUTHOR]

Metal additive manufacturing technologies provide new opportunities for manufacturing complex components. However, the limited data on fracture behavior are delaying adoption in safe‐critical applications. This paper aims to evaluate the effect of orientation and the intra‐build design parameters on EBM Ti6Al4V fracture toughness using a design of experiments. Three builds comprised of over 150 compact tension samples were printed representative of the EBM build chamber, followed by microstructural characterization, X‐ray microcomputed tomography, and fracture toughness testing per ASTM E399. The average fracture toughness was 65 MPa√m, with anisotropy as the largest source of variation due to crack growth behavior with respect to the build direction. Microstructure coarsening was observed with increase in height, resulting in an increase in fracture toughness, irrespective of sample geometry or orientation. Build orientation and sample location influenced the microstructure and fracture toughness and should be considered when adopting EBM components in load‐bearing applications. [ABSTRACT FROM AUTHOR]

This paper reports the damage mechanism of 30Cr1Mo1V rotor steel during thermal fatigue at 540°C. Detailed information on macro‐failure characteristics and micro‐failure mechanisms was revealed here. The results showed that both intragranular micro‐defects and intergranular micro‐crackings were formed during the fatigue process. The formation of intragranular micro‐defects was related to the dislocation tangle inside the ferrite sub‐grains, while the formation of intergranular micro‐cracking could be related to the weakening of atomic cohesion at the matrix/cementite interface. Eventually, the transgranular crackings occurred in the 30Cr1Mo1V steel. The morphology of these crackings presented an edge‐shaped discontinuity, which may propagate perpendicularly to the loading direction and cause the material to fracture. [ABSTRACT FROM AUTHOR]

The present paper deals with the J‐A concept in two‐parameter elastic–plastic approaches of fracture mechanics. The cumulative damage rule in a solid is employed to construct the quantitative elastic–plastic J‐A fracture criterion. As a result, the constraint corrected elastic–plastic fracture toughness JmatC as a function of the crack‐tip constraint parameter A, the yield stress, the strain hardening exponent and the failure stress has been proposed. The significant effect of the strain hardening exponent on the normalized constraint corrected fracture toughness is observed. The value of the normalized constraint corrected fracture toughness decreases with the increase of the applied failure stress and the decrease of the crack aspect ratio to a certain values, and then it stabilizes. Highlights: The cumulative damage rule in a solid and the J‐A concept are employed.Quantitative two‐parameter J‐A fracture criterion is proposed.The constraint corrected fracture toughness is described as a function of crack‐tip constraint.The effect of the constraint parameter A is analyzed for some standard specimens. [ABSTRACT FROM AUTHOR]

In this paper, comprehensive progressive damage analyses are performed to evaluate the effects of patch sizes and layups on restarting crack growth of single‐side repaired aluminum panels with central inclined cracks under high cycle fatigue loading. Complicated nonlinear damage behavior of adhesive bonding, composite patch, mixed‐mode cracks, and fatigue loadings require precise numerical tools to consider and analyze the coupling effects of various damages on fatigue life of such complex component. In progressive damage analysis, high cycle fatigue cohesive zone modeling is used for debonding of patch, and high cycle fatigue continuum damage model used for composite patches. Practical composite patch layups and sizes are selected in huge number of models, and the restarting crack growth life is predicted. The obtained results show the possibility of increasing the restarting crack growth life using an appropriate composite patch layup and geometry dimensions. Highlights: Restarting crack growth of single‐side repaired panels fatigue loadingComprehensive progressive damage analysesEffects of composite patch size and layup on restarting crack growthCrack growth retardation using appropriate composite patch [ABSTRACT FROM AUTHOR]

This paper investigates the fracture behavior of high‐performance grouting materials in the grouted connection section of marine structures, where they are subjected to complex stress states. This study utilizes a combination of experimental and numerical simulation methods to establish a reliable numerical simulation technique for the fracture process of high‐performance grouting materials. The mixed mode fracture behavior is analyzed using six different types of specimens, and the strain contour is analyzed using the Digital Image Correlation technique. An extended peridynamics model is proposed for the numerical simulation, which adopts a fracture criterion based on strain energy density. The accuracy of the model is verified qualitatively and quantitatively, and the simulation results are consistent with the experiments. Overall, this study provides insights into the fracture behavior of high‐performance grouting materials in complex stress states and presents a reliable numerical simulation technique for the fracture process. Highlights: Different fracture criteria were used to analyze the four points bending test results.Digital Image Correlation technique was adopted to predict the crack initiation position and failure mode.The failure mode, failure angle, and fracture toughness of material were discussed.An extended peridynamics model is established for failure analysis of grouted material. [ABSTRACT FROM AUTHOR]

This paper develops a mesoscopic numerical method for evaluating the fracture energy of concrete. In this method, concrete is modeled as a three‐phase composite material, composed of mortar, coarse aggregate, and the interface between them. The actual mixed‐mode I–II crack growth path in mode I fracture tests is traced by applying crack propagation criteria. After verifying the numerical method by a series of three‐point bending tests, the effects of aggregate location, aggregate size, and crack propagation path on the fracture energy of concrete are evaluated. It is found that for the fracture mode of crack bypassing aggregates, the actual fracture energy of concrete is significantly affected by the aggregate location but independent of the aggregate size and the crack propagation path. Highlights: A mesoscopic numerical method is proposed for the fracture energy of concrete.The actual mixed‐mode I–II crack growth path is traced by applying crack growth criteria.The actual fracture energy of concrete is significantly affected by aggregate location.The actual fracture energy of concrete is independent of crack growth path. [ABSTRACT FROM AUTHOR]

The papers summarize recent findings in numerical and theoretical models aimed to assess the fracture and fatigue behavior of structural components as well as new interesting set of data combined with new experimental techniques. Thus, this VSI embraces different works aimed to understand the material behavior using advanced approaches, disruptive fracture mechanics concepts, and advanced experimental techniques for fatigue crack behavior assessment. Also, the effect of different manufacturing processes on the fatigue and crack propagation behavior is addressed.3,4 Other works are focused on fracture mechanics formulations. [Extracted from the article]

This paper presents a novel high‐resolution direct analysis of mating AA7050‐T7451 fracture surfaces at crack lengths from 0.1 to 1.3 mm (Kmax of 4.51 to 16.39 MPa√m) for the purpose of analyzing the fatigue growth mechanisms. The various fractographic features observed at these crack lengths were then compared to the known accelerative effects of an applied loading sequence that contained underloads at regular intervals. A correlation was found between some of the observed features and the local fatigue crack growth rate. This study provides new insight into the prominent mechanisms that dictate crack growth rate and ultimately should assist with developing crack growth prediction methods that more accurately represent the physics of the fatigue crack growth mechanisms. Highlights: Mating fatigue surfaces are compared at high resolution in AA7050‐T7451.Striation features are shown to significantly differ on mating surfaces.Fissuring from underloads is found to occur at all investigated crack lengths.This fissuring may be mechanistically linked to underload acceleration effects. [ABSTRACT FROM AUTHOR]

Thermomechanical fatigue (TMF) crack growth of Alloy 718 when the cycle includes long high‐temperature tensile dwells is often accelerated because sustained‐load crack growth occurs during the dwells and a temperature affected zone (TAZ) develops ahead of a crack tip that reduces fatigue crack growth resistance upon application of a cycle after the long dwell. This paper presents new TMF and sustained‐load tests that aim to study and characterize the TAZ development and growth ahead of semi‐elliptical and single‐edge cracks. The influence of constraint on crack growth is assessed. This investigation focuses on a coarse‐grained (CG) Alloy 718 at 650°C. By comparing the crack growth behavior between a fine‐grained and CG microstructure after a long tensile dwell, a modification of the TAZ growth prediction model that includes the influence of grain size is proposed. Using this improved model for TAZ growth and acceleration, the TMF crack growth prediction of surface cracks is improved. Highlights: Temperature affected zone (TAZ) develops during tensile dwells in Alloy 718.The extent of TAZ is reduced when grains are larger.The extent of TAZ is also dependent on the constraint near the crack tip.A new grain size dependent TAZ growth model improves TMF predictions. [ABSTRACT FROM AUTHOR]

The numerical approach is a vital means for evaluating the stability of flawed rocks. In this paper, the extended non‐ordinary state‐based peridynamics (NOSB‐PD) theory is employed to simulate the fracture process of rocks containing two pre‐existing flaws. Two stress criteria, including the maximum tensile stress criterion and the Mohr–Coulomb criterion, are implemented into the NOSB‐PD numerical method to respectively judge the tensile and shear failure of rock materials. The effects of inclination angles and ligament angles on the crack initiation and coalescence modes for flawed rocks are investigated based on the numerical results. The numerical results are in good agreement with the previous experimental results. The fracture mechanism of flawed rocks is revealed based on the evolutionary distribution characteristics of the maximum principal stress field and shear stress field obtained by the extended NOSB‐PD theory. Highlights: The extended non‐ordinary state‐based peridynamics (NOSB‐PD) theory is employed.The fracture characteristics of flawed rocks are investigated by the extended NOSB‐PD.The fracture failure mechanism of flawed rocks is revealed by the extended NOSB‐PD. [ABSTRACT FROM AUTHOR]

To better solve the issues of steady crack extension with broad plasticity and the crack‐related problems in general yielding situations when the assumption of small‐scale plastic yielding fails, it is of great significance to further study the macroscopic mechanism of crack extension. In this paper, a new insight into the elastic–plastic crack extension is proposed on the foundation of critical storage of elastic strain energy (SESE). The feasibility of the new methodology is validated by designing and implementing two different experimental schemes in three typical elastic–plastic materials. The experimental results indicate that the critical SESE decreases linearly with the increase of crack length and U‐notch initial length. Besides, the SESE release rate is obtained through experimental and theoretical methods, and they are in the same order of magnitude and their value sequences are also accordant with all tested materials. Therefore, this investigation provides a new approach to characterizing crack extension in elastic–plastic materials. Highlights: A new insight is proposed to characterize crack growth in elastic–plastic materials.A novel experimental methodology is adopted to obtain the critical SESE.The established linear correlation is well validated by two experimental schemes.By experimental and theoretical methods, G is obtained and they fit each other well. [ABSTRACT FROM AUTHOR]

Multiaxial fatigue failure is the most common problem in engineering structures. It is worth noting that short crack growth accounts for most of the fatigue life. Hence, it is necessary to study the short crack growth models for multiaxial fatigue life assessment. The primary focus of this study is to develop a hierarchical Bayesian linear regression method to estimate parameters in multiaxial fatigue crack growth model. The Bayesian method is used to estimate the intercept and slope of the regression equation for each loading path and ensemble test datasets. The method of this work was demonstrated on three multiaxial fatigue crack growth datasets. The main results obtained in this paper were that the parameters of the multiaxial fatigue crack growth model changed significantly with different loading paths, and the parameters of the model depended on the multiaxial loading path. Highlights: An equivalent strain‐based intensity factor ΔKESA was proposed.Hierarchical Bayesian linear regression is developed for parameter estimation.Hierarchical Bayesian model considers the differences of each loading paths.The parameters of the fatigue crack growth model depend on the loading path. [ABSTRACT FROM AUTHOR]

Using artificial intelligence‐based methods in predicting material properties, in addition to high accuracy, saves time and money. This paper models and predicts the fracture toughness properties of polymer concrete (PC) composites using the deep learning method. After preparing a database consisting of 209 experimental data from 19 relevant studies, the effect of seven important variables on critical stress intensity factor (KIc) and crack tip opening displacement (CTOD) is considered. Then, the deep neural network (DNN) model is developed and trained using the prepared database. The accuracy of the DNN model is examined by implementing four statistical criteria, MSE, R2, RMSE, and MAE. Finally, the sensitivity of the KIc and CTOD to each input variable is evaluated using a partial dependence plot (PDP) analysis. While aggregate size, nanofiller content, and a/R ratio have the most positive effect on KIc, aggregates and nanofiller content have the most positive influence on CTOD. Highlights: An experimental database for fracture mechanics of polymer concrete (PC) is prepared.A deep neural network (DNN) model is developed to predict the fracture properties of PC.The effect of seven input variables on KIc and CTOD of PC is evaluated.The sensitivity of KIc and CTOD of PC is analyzed by using partial dependence plots. [ABSTRACT FROM AUTHOR]

This paper contains the in‐service fatigue fracture analysis for the first stage low‐pressure compressor disk of the aircraft engines D30KU‐154. Based on the results of the fractographic investigation on collapsed compressor disks the fatigue crack initiation and propagation principles were established. It is shown that the crack initiation in the rim part of the compressor disk is due to a high frequency loading that leads to very high cycle fatigue fracture. The total fatigue lifetime of the compressor disk is determined by simultaneous action of low amplitude loading due to blades vibration, and high amplitude loading due to flight cycle (centrifugal forces). Study of in‐service fracture of the compressor disk was based on the evaluation of numerical simulations of the stress state in the damaged zone under corresponding loading conditions. The estimation of fatigue lifetime and crack path predictions were performed based on the multiregime fatigue fracture model developed by the authors. Highlights: The two‐criteria multimode fatigue fracture model is introduced.The operational fatigue breaks in different aircraft structures are analyzed.The numerical simulations of compressor disk failure performed under different loading conditions and scenarios.The minimum fatigue lifetime was calculated for VHCF initiation and HCF crack growth scenario. [ABSTRACT FROM AUTHOR]

This contribution introduces the work of early researchers in the field of fracture mechanics and materials testing. The development in fracture mechanics around the turn of the century in Germany and Austria-Hungary is presented, and the work of pioneers, e.g. K. Wieghardt, A. V. Leon, K. Wolf, A. Smekal and P. Ludwig is critically discussed. A comparison with the developments by G. I. Inglis and A. A. Griffith is elaborated. It will be shown that the work of these pioneers—particularly the 1907 paper by Wieghardt on the development of the basic analytical equations of fracture mechanics— predates many of the later developments by several decades. The work by Wieghardt was in fact directly related to a practical failure case, and the voluminous work of Leon was mainly driven by practical needs of engineering. The reasons for the neglect of Wieghardt's fundamental paper of 1907—particularly in the Anglo-American hemisphere—are critically discussed. [ABSTRACT FROM AUTHOR]

Unloading compliance (UC) method and normalization method (NM) are two of the most commonly used methods for determining the fracture toughness of materials. However, considerable differences often exist in the fracture toughness determined by these two methods, which solicits a new method to determine the fracture toughness accurately. In this paper, the compliance of crack length differences is discovered, analyzed, and verified by experiments. Based on this compliance, a new accurate method, known as the accurate J‐R curve method (AJR), is developed and verified by test results. It is found that the J‐R curves determined by the new AJR method are more accurate than those determined by UC and NM. The developed new AJR method and the results presented in this paper can assist engineers and researchers to determine J‐R curves and fracture toughness of steels more accurately and can contribute to the body of knowledge of fracture mechanics. [ABSTRACT FROM AUTHOR]

The additional local stress concentration caused by undercut and misaligned defects could lead to lower fatigue strength of welded joints. The paper aims to investigate the effects of undercuts and misalignments on fatigue performance and reliability of Load‐carrying Cruciform Welded Joint (LCWJ) quantitatively by probabilistic statistics theory and fracture mechanics theory. Firstly, the geometrical characteristics of undercut and misalignment are summarized from the literature and our experiments. Subsequently, the probabilistic distributions of material fracture properties, the configurations of geometries, and flaws were evaluated under specific loading conditions. The fatigue strengths are further estimated by the probabilistic reliability theory by combining the actual fatigue data. The results demonstrate a clear disparity of fatigue crack growth threshold and resistances for the tested data of base metal and weldment. The level of defects determines the interval of fatigue life, and the larger the dispersion accompanying earlier fatigue failure occurs. Highlights: The effects of weld defects on fatigue strength and reliability were assessed quantitatively by the probabilistic method.FCGRs of HAZ and U‐WM are more conservative than the base metal.The SIFs in mismatched LCWJs were evaluated by the weight function theory. [ABSTRACT FROM AUTHOR]

The text discusses the Eighth International Conference on Very High Cycle Fatigue (VHCF8), which was held online from July 5 to 9, 2021, and distributed from Sapporo, Japan. The conference focused on the emerging issue of very high cycle fatigue (VHCF) in materials strength, particularly in metallic materials, polymers, and composites. The conference covered a wide range of topics, including crack initiation and propagation mechanisms, fatigue life estimation, and nondestructive approaches for internal damage analyses. After the conference, 17 high-quality papers were selected for a special issue of the journal Fatigue and Fracture of Engineering Materials and Structures (FFEMS) to highlight the research presented at the conference. [Extracted from the article]

Crack behavior at the interface between two materials is the core problem of layered material fracturing. In this paper, first, experimental tests were conducted on layered material using a drop weight test system following the caustics method. The layered material was made of poly (methyl methacrylate) (PMMA) and epoxy resin bonded with Loctite‐330 at two inclination angles (30° and 60°). A corresponding numerical simulation was carried out using continuum–discontinuum element methods. Crack propagation is found to mainly occur in mode I in the PMMA and epoxy resin but follows a mixed cracking mode at the interface. The fracture parameters of the crack tip in the layered materials changed substantially owing to the existence and change of the interface structure. After the crack enters the interface, the crack propagation speed increases significantly. Higher crack dip angles are associated with greater crack propagation speed increases after entering the interface. The simulation results indicate that the interface strength properties affect crack behavior at the interface. This effect also varies as a function of interface inclination and impact velocity. Highlights: Caustics method is used to study fracture parameters of layered material.A mixed‐mode fracture model is implemented into CDEM to simulate interface crack.Effect of strength properties on interface crack are simulated.Effect of impact velocity on interface crack are simulated. [ABSTRACT FROM AUTHOR]

Considering fracture constraint is an efficient way to describe stress-strain field and fracture toughness more accurately, so it is necessary to realise the relationship with in-plane and out-of-plane constraint for different standard specimens. In this paper, three-dimensional finite element method is applied to study the in-plane and out-of-plane constraint for both cruciform specimen and single edge notched bending specimen made from commercial pure titanium. Crack length and in-plane loading as the factors affecting in-plane constraint, and thickness as the factor affecting the out-of-plane constraint are used to study the effect on both in-plane and out-of-plane constraint in this paper. From the results, in-plane and out-of-plane constraint are both related to specimen geometries and loading styles. And there exist relationships with in-plane and out-of-plane constraint because of factors for different specimens. Depending on crack length, out-of-plane constraint increases with in-plane constraint. While depending on transverse loading, out-of-plane constraint decreases with in-plane constraint. In addition, when the in-plane constraint of a specimen is higher, in-plane constraint increases with out-of-plane constraint (thickness). When the in-plane constraint is lower, in-plane constraint almost remains unchanged with out-of-plane constraint. [ABSTRACT FROM AUTHOR]

This paper evaluates the capabilities of the recently developed CF20 cohesive fatigue model, which can predict crack initiation as well as the rates of crack propagation by relying on intrinsic relationships between a stress‐life diagram and its corresponding Paris law. The model is validated here using a partially reinforced double cantilever beam (R‐DCB) benchmark proposed in literature. The two parameters needed for the CF20 cohesive fatigue model were obtained by performing preliminary analyses of a conventional DCB. The analysis results indicate that the CF20 cohesive fatigue model can accurately reproduce the complex evolution of the delamination observed in the R‐DCB. Highlights: A 3D benchmark is analyzed using the mixed‐mode CF20 cohesive fatigue formulation.The parameters of the model are obtained from experimental results of DCB specimens.The model predicts crack growth rate and delamination shape changes during propagation.A parametric study illustrates the precision needed to accurately predict the final delamination length. [ABSTRACT FROM AUTHOR]

The traditional extended finite element method (XFEM) is suitable for simulating crack growth, but the crack‐tip stress field analysis still depends on the enriched function. In this paper, based on the numerical eigensolution of the singular displacement and stress field together with the Hellinger–Reissner (H–R) variational principle, a novel crack‐tip singular element is established to replace the enriched element in the crack‐tip region in the traditional XFEM. The stress field inside the element adopts a series expression instead of only including the leading‐order terms. The element only requires Gaussian integration at the element boundary and avoids mesh refinement in the crack‐tip region. The element can be used to analyze cracks in anisotropic materials, interface cracks, and cracks terminating at the bimaterial interface. The numerical solutions of the singular stress field in various crack forms are presented through numerical examples, which proves the effectiveness and versatility of the novel crack‐tip singular element. Highlights: An extended finite element method with a novel crack‐tip singular element is proposed.The convergence speed of the present extended finite element method is satisfactory.The compatibility between the singular element and other elements is good.The singular element has the feature of multifunction. [ABSTRACT FROM AUTHOR]

The research on the Very High Cycle Fatigue (VHCF) response of materials is fundamental to guarantee a safe design of structural components. Researchers develop models for the fatigue life in VHCF, aiming at assessing the stress–life relation and, accordingly, the probabilistic S–N (P‐S–N) curves. In the paper, the models for the stress–life relation in VHCF are comprehensively reviewed. The models are classified according to the approach followed for defining the stress–life dependency, that is, power law, probabilistic, fracture mechanics, or Paris law‐based approach. The number of failure modes that can be modeled, the statistical distribution for the fatigue life, and the characteristics of the estimated P‐S–N curves are also reviewed by analyzing the fitting capability of experimental datasets for each model. This review is supposed to highlight the strengths and weaknesses of the currently available models and guide the future research. [ABSTRACT FROM AUTHOR]

In order to predict and assess creep life for plate structures with semi‐elliptic surface cracks under high temperature condition, the accurate calculation of the creep fracture mechanics parameter C* is a critical step. In this paper, the effects of crack sizes, plate geometries, and material creep properties on the parameter C* have been investigated under tensile and bending loads by extensive finite element analyses. Based on the results, the creep influence functions Hc for calculating C* values were obtained and fitted into equations for surface cracks in plates under both loads. The equations have been verified by finite element calculations. The C* solutions were obtained through these equations which are suitable for wide ranges of crack sizes, plate geometries, and materials. [ABSTRACT FROM AUTHOR]

Abstract: This work explores the contribution to crack growth rate acceleration and deceleration that arises from plasticity‐induced shielding during an overload cycle. The CJP model of crack tip displacements and stress fields was proposed to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic‐plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been independently verified. In this paper, the CJP model is used to follow plastic zone size and shape through an overload fatigue cycle and to assess the extent that plasticity‐induced shielding accounts for the observed crack growth changes. The changes in effective stress intensity factor range during the overload demonstrate that the observed growth rate changes during overload cycles can only be partially rationalised through plasticity‐induced shielding (closure). [ABSTRACT FROM AUTHOR]

Traditional risk-based design process involves designing the structure based on risk estimates obtained during several iterations of an optimization routine. This approach is computationally expensive for large-scale aircraft structural systems. Therefore, this paper introduces the concept of risk-based design plots that can be used for both structural sizing and risk assessment for fracture strength when maximum allowable crack length is available. In situations when crack length is defined as a probability distribution the presented approach can only be applied for various percentiles of crack lengths. These plots are obtained using normalized probability density models of load and material properties and are applicable for any arbitrary load and strength values. Risk-based design plots serve as a tool for failure probability assessment given geometry and applied load or they can determine geometric constraints to be used in sizing given allowable failure probability. This approach would transform a reliability-based optimization problem into a deterministic optimization problem with geometric constraints that implicitly incorporate risk into the design. In this paper, cracked flat plate and stiffened plate are used to demonstrate the methodology and its applicability. [ABSTRACT FROM AUTHOR]

Friction stir (FS) welding is a relatively new solid-state welding process that offers high levels of joint performance with minimal preparation and little post-weld dressing. The high levels of plastic work induced in the weld zone produce a very fine grain size in the stirred region of the weld (e.g. the nugget), while the low heat input limits residual stresses to a low fraction of the proof strength of the weld metal. These effects are generally beneficial to weld dynamic performance. The peculiar thermomechanical history in the FS weld region leads, however, to particular defects with some unusual effects on crack path, whose occurrence depends partly on crack speed, or growth rate. This paper presents observations regarding specific influences of the FS welding process on crack paths and dynamic performance for 5083-H321 and 5383-H321 aluminium alloys, and proposes an explanation for the observations in terms of the weld microstructures and thermomechanical history. The insights presented in this paper can be used to inform optimisation of the weld process parameters, through on-line feedback and control of tool geometry, force footprint, torque and temperature. [ABSTRACT FROM AUTHOR]

Due to the difficulties of applying torsional loads to introduce mode III effects, there are few studies for investigating mixed mode I/III fracture in brittle materials. In this paper using three novel single or double edge‐cracked diametral compression disc shape specimens, complete ranges of mixed mode I/III are introduced. Fracture factors of the compressed disc specimens with different pre‐notch shapes are determined numerically for a wide range of notch depth and notch inclination angles. The ability of specimens was studied using mixed mode I/III fracture experiments on gypsum. Different fracture envelopes were obtained for the gypsum demonstrating the influence of disc geometry and notch type on mixed mode I/III behavior. For all samples, mode III fracture toughness (KIIIc) was approximately 1.2 to 1.8 times the corresponding value of KIc. Depending on the crack front type, ligament shape and mode mixity, different fracture surfaces were observed. While the mode I fracture surface was smooth and flat in all samples, for mixed mode I/III and mode III, rotation and partially segmentation saw tooth shape wrinkles were observed. [ABSTRACT FROM AUTHOR]

The current paper reviews application of an improved FASTRAN life‐prediction code to predict fatigue behavior of notched coupons made of an aluminum alloy and a titanium alloy. For each material, fatigue‐crack‐growth‐rate data were determined over a very wide range in rates from threshold (small‐crack region) to near fracture on standard crack‐growth specimens. In the low‐rate regime, small‐crack data were used on the aluminum alloy, whereas a compression pre‐cracking constant‐amplitude method was used on the titanium alloy. A characteristic microstructural flaw size was determined from fatigue‐test data on notched coupons under constant‐amplitude loading. These data were then used to predict fatigue behavior of similar notched coupons under various spectrum loadings. For variable‐amplitude loading conditions, an improved "rainflow‐on‐the‐fly" subroutine was used in the life‐prediction code. Comparisons are made between previous life predictions and those made with the current code under variable‐amplitude loading. In general, the new code produced longer fatigue lives than older versions. The new code worked well using the same initial microstructural flaw size for a given material under both constant‐ and variable‐amplitude loading. [ABSTRACT FROM AUTHOR]

ABSTRACT The object of this paper is to develop the load separation method for the new pipe-ring notched bend specimen. The paper presents an approach for determining the plastic load line displacement ( ηplLLD) and the plastic crack mouth opening displacement ( ηplCMOD) correction factors for pipe-ring notched bend specimens. The estimated plastic factors are possible to use in estimation approach based on load versus displacement test. The ηpl factors could be applied for fracture toughness testing of pipeline materials when standard specimens cannot be applied. Finite element method is employed for estimating the separation parameters. The notch tip radius of blunt notched specimens varies within an interval Rn = 0, 0.1, 0.25, 0.5, 0.75, 1.25, 1.5 and 2 mm. The effect of the notch tip radius on the ηpl factors is analyzed. [ABSTRACT FROM AUTHOR]

Abstract: Extensive experimental investigations show that internal defects play a key role in the very‐high‐cycle fatigue (VHCF) response of metallic materials and that crack growth from internal defects can take place even if the stress intensity factor associated to the initial defect is below the threshold for crack growth. By introducing a reduction term in the typical formulation of the threshold for crack growth, the authors recently proposed a general phenomenological model, which can effectively describe crack growth from internal defects in VHCF. The model is able to consider the different crack growth scenarios that may arise in VHCF and is enough general to embrace the various weakening mechanisms proposed in the literature for explaining why crack can grow below the threshold. In the present paper, the model is generalized in a statistical framework. The statistical distributions of the crack growth threshold and of the initial defect size are put into the model. The procedure for the estimation of the Probabilistic‐S‐N curves and of the fatigue limit distribution is illustrated and numerically applied to an experimental dataset. [ABSTRACT FROM AUTHOR]

This paper presents and compares two combined experimental‐numerical techniques for the investigation of fracture properties of additively manufactured polymer parts using digital image correlation (DIC) measurements. The first method only uses measured kinematic fields, and the second is based on finite element simulations driven by measured boundary conditions. A mini single edge notched tensile sample manufactured by fused filament fabrication with ABS is studied. It is shown that both methods locally extract J‐integrals, and the crack tip is accurately located by the FE‐based method. By comparing computed displacements to those measured via DIC, it is possible to locally check the validity of the numerical model. The initiation and propagation stages are analyzed independently thanks to two different magnifications of acquired image series. [ABSTRACT FROM AUTHOR]

ABSTRACT The present paper investigates the application of the stochastic approach when the commonly adopted Miner's linear damage rule is implemented, both in its traditional and modified forms to include the presence of a random stress threshold (random fatigue limit), below which the rate of damage accumulation is reduced. Main steps are provided to obtain the simulated distribution of the accumulated damage under variable amplitude loading. When the stochastic approach is applied in the presence of a random fatigue limit, an additional correlation structure, which takes into account the fatigue limit value, must be introduced in the analysis. If the number of cycles to failure under constant amplitude loading is Weibull (Log-Normal) distributed, then the corresponding accumulated damage is Fréchet (Log-Normal) distributed. The effects of the correlation structure on reliability prediction under variable amplitude loading are also investigated. To this aim, several experimental datasets are taken from the literature, covering various metallic materials and variable amplitude block sequences. The results show that the choice of the damage accumulation model is a key factor to value the improvement in the accuracy of reliability predictions introduced by the stochastic approach. Comparison of the predicted number of cycles to failure with experimental data shows that larger errors are non-conservative, regardless of the adopted correlation structure. When the analysis is limited to reliability levels above 80%, for these large non-conservative errors, it is the quantile approach to be closer to actual experimental data, thus limiting the overestimation of component's life. For the experimental datasets considered in the paper, adoption of a stochastic approach would improve the accuracy of Miner's predictions in 10% of cases. [ABSTRACT FROM AUTHOR]

Rolled steel plates and sections are often applied in structures in such a way that the principal load direction corresponds with the rolling direction. Examples are beams, arches, or pylons of bridges, supporting beams of ship decks, and the main elements of crane structures. However, some types of structure are subjected to a multiaxial stress state or are loaded with the main load direction perpendicular to rolling. The orientation may influence the mechanical properties. This paper studies the influence of anisotropy observed in the microstructure of rolled C–Mn steels on the tensile properties, Charpy impact values and particularly the fatigue crack growth rates. The influence of anisotropy is determined through tests performed at different orientations with respect to the rolling direction, namely, L‐T, T‐L and T‐S orientations. Samples were taken from structures that were constructed between 25 and 50 years ago from steel grades Fe510C or St52.3 (modern equivalences S355J2 or S355N). The orientation appears to have a statistically relevant influence on Charpy impact value and fatigue crack growth rate. The anisotropy ratio, defined as the ratio between the mechanical property in a certain orientation with that of the L‐T orientation, ranged between 0.30 and 0.53 for Charpy impact values. The anisotropy ratios appear correlated with the absolute Charpy value, with a correlation coefficient of ρ = −0.8. The anisotropy ratios of the crack growth in T‐L and T‐S orientations were 1.19 and 0.43, respectively. Anisotropy ratios for crack growth appear uncorrelated with anisotropy ratios for Charpy impact. The observed anisotropy may partially explain the difference between uniaxial and multiaxial fatigue crack growth as determined by others. [ABSTRACT FROM AUTHOR]

This paper presents a study on the effect of microstructure on the fatigue crack growth (FCG) rate in advanced S355 marine steels in the Paris Region of the da/dN versus ΔK log–log plot. The environments of study were air and seawater (SW), under constant amplitude sinewave fatigue loading. Fundamentally, three phenomena (crack tip diversion, crack front bifurcation and metal crumb formation) were observed to influence the rate of FCG. These phenomena appear to be a function of the material microstructure, environment and crack tip loading conditions. The three factors retarded the crack growth by reducing or redistributing the effective driving force at the main active crack tip. A crack path containing extensively the three phenomena was observed to offer strong resistance to FCG. In SW, the degree of the electrochemical dissolution of the microplastic zone appears to be an additional primary factor influencing FCG in the steels. [ABSTRACT FROM AUTHOR]

This paper summarises the findings of an international collaborative programme that focuses on the problem of the growth of cracks that arise from natural corrosion in bridge steels. The experimental data presented in this paper confirm that the bridge steel da/dN versus Δ K relationship is similar to that seen by the high-strength aerospace steels D6ac and 4340. It is then shown that the methodology developed to predict the growth of small naturally occurring cracks in aerospace materials can also be used to compute the growth of cracks that arise because of natural corrosion in bridge steels. [ABSTRACT FROM AUTHOR]

ABSTRACT Object of this paper is to emphasize some dissipative aspects of steels in high cycle fatigue from the thermographic point of view by relating anelastic and microplastic behaviours to loading levels respectively below and above the fatigue limit. To this aim, the Two Curves Thermographic Method has been modified by using both a parabola and a power curve as regression laws instead of the traditional linear ones. Two new thermal parameters have also been considered, the thermal increment and the subtended area by the thermal profile at a very low number of cycles. Experimental data referred to C45 standard and 25CrMo4 notched steel specimens have been processed using both original and modified Two Curves methodologies and both traditional and new thermographic parameters. All changes introduced in the present paper provide good results both in terms of fatigue limit values and for as concerns the rapidity of the fatigue tests. [ABSTRACT FROM AUTHOR]

BACKGROUND McClintock 1,2 was one of the first to model continuous-cycling fatigue crack growth by assuming a succession of miniature low-cycle-fatigue (LCF) specimens at the crack tip. Elements ahead of the crack amass damage until the arrival of the tip itself. Such models had been summarized by Majumdar and Morrow, 3 but the author was unaware of these papers at the time. The ideas were pursued further by Chakrabortty 4 whose paper, again unknown to the author, was published in the same issue (1979, Vol. 2) of FEMS. In the original paper 5 crack propagation is represented by successive regeneration at the crack tip, the process becoming progressively easier as the crack grows owing to an increase in strain concentration. These ‘initiation’ cycles were related to the ‘Coffin’ expression for crack initiation, thereby introducing two empirical constants k and α. The paper is of the class ‘ρ/ N’ where ρ is the assumed size of a crack-tip process zone and N is the cycles required to traverse that zone. Expressions had been previously derived linking LCF with linear-elastic fracture-mechanics (LEFM) crack growth, using the parameter Δ J. 6 (It was later shown that this was identical to using an equivalent stress intensity parameter. 7 ) It has been shown that the approach does not apply for crack depths < 180 μm. 6 At elevated temperature the Δ J approach was successful for describing crack growth in the range 0.2–1.2 mm for the cobalt-based alloy MAR-M509 at 600 °C. 8 Other studies have in fact shown 9 that crack growth rates are approximately constant below a depth of 200 μm. Even to this day short crack growth relations in LCF and their practical use are not as familiar as those in LEFM. It may justifiably be argued that for every paper published on LCF short crack growth, several hundred have appeared dealing with LEFM crack growth in terms of the ‘Paris’ law. One of the original referees' comments was that the paper 5 should have been presented in terms of LEFM. The author nevertheless defended his approach because for small cracks it was thought useful to retain the crack depth explicitly. It will be shown that LCF crack growth data have a definite part to play in the assessment of components and structures. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper deals with the rectangular tensile sheet with symmetric double edge notch cracks. Such a crack problem is called an edge notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method), two edge notch models are analyzed in detail. By changing the geometrical forms and parameters of the edge notch, and by comparing the stress intensity factors (SIFs) of the edge notch crack problem with those of the double edge cracked plate tension specimen (DECT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the edge notch on the SIFs of the DECT specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the DECT specimen So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the DECT specimen. [ABSTRACT FROM AUTHOR]

ABSTRACT In the recent years, Cohesive Zone Models (CZMs) have gained increasing popularity for modelling the fracture process [1] and also in other applications like composite de-lamination [2] solder failures [3] in circuits, etc. This can be attributed to the ability of the CZM to adapt to the nonlinearities in the process it represents by adjusting the model parameters. These parameters that are selected to represent the material behaviour in the vicinity of the crack or a damage zone are non-deterministic in nature resulting in random fracture strength estimates. Currently, there are no standardized tests for measuring the CZM parameters and their random scatter. Numerous researchers in the literature suggest values for the CZM parameters based on their experience from limited test data. Traditionally, fracture toughness is determined through coupon tests for any material system that is being analysed using Linear Elastic Fracture Mechanics to determine the fracture strength of a specimen. Since data for fracture toughness are available, this research is aimed at determining the probability density functions (PDFs) for the cohesive zone parameters that would give the same scatter in fracture strength as that obtained from the test statistics. Correlations between the model parameters were introduced to improve the accuracy of the fracture strength PDF. A finite width cracked plate was selected as a test case to demonstrate the process. This paper also presents evidence that material scatter can be isolated from the geometric effects to determine a normalized PDF of fracture strength for a given material. This normalized PDF can then be scaled, using mean fracture strength, to any crack configuration to develop a nomograph that can be used to rapidly assess risk without the need for a probabilistic fracture analysis. [ABSTRACT FROM AUTHOR]

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh. [ABSTRACT FROM AUTHOR]

In this paper, a cohesive zone model is used to study the influence of inertial effects on crack growth considering cyclic loading in homogenous rate‐independent materials. Quasi‐static and dynamic solutions are compared in order to establish the conditions in which the inertial effects become important in the analysis. It is discussed how speed and frequency of the loading and specimen sizes modify crack growth characteristics. In general, an increase in the loading frequency leads to a higher propagation velocity. Very high loading frequencies may lead to the formation of microcracks ahead of the crack tip and may change the failure mode of the cracked structure from crack propagation to uniform debonding. This work shows that inertial effects are specially noticeable for frequencies in the kHz range. However, applied frequencies close to natural frequencies of the cracked specimen can give rise to strong inertial effects and then a substantial reduction of fatigue life for much lower frequencies. This work also shows that critical frequencies depend on the specimen size. [ABSTRACT FROM AUTHOR]

In this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength. [ABSTRACT FROM AUTHOR]

The damage process in quasi‐brittle materials is characterized by the evolution of a micro‐crack field, followed by the joining of micro‐cracks, stress localization and crack instability. In network models, masses are lumped at nodal points which are interconnected by one‐dimensional elements with a bilinear constitutive relation, considering the energy consistency during the simulated process. In order to replicate the material imperfections, to render a realistic behaviour in damage localization, the model has not only random elastic and rupture properties, but also a geometric perturbation. In the present paper 2D plates with different levels of brittleness are simulated. The numerical results are presented in terms of global stress vs strain diagram, final network configuration, energy balance during the process and as geometric damage evolution. Therefore, the predictive potential of the lattice discrete element model to capture fracture processes in quasi‐brittle materials is demonstrated. [ABSTRACT FROM AUTHOR]

It is significant for structural design and maintenance to assess behaviour and life under varying load conditions. For structures operating in high‐temperature environments, creep is one mechanism responsible for material failures. In this paper, different damage accumulation rules were reviewed, and a new creep damage assessment method was proposed based on the creep damage tolerance parameter λ and load factor Φ. By introducing the creep damage tolerance parameter λ and the minimum creep rate, the loading process and creep behaviour of the material are taken into account in a damage assessment. The parameters in the model can be obtained by the simple variable load creep test, and the remaining life and strain can be predicted using uniaxial creep test data. To analyse the applicability and accuracy of this new model, the strain histories, the life of step load, and the constant load creep from experiments on a titanium alloy at 500°C were obtained, and the prediction results of the novel and previous methods were carefully investigated. [ABSTRACT FROM AUTHOR]