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• This work describes a novel hybrid methodology to extract essential information from the bulk of opaque materials. • It is based on a combination of experimental synchrotron X-ray diffraction data with a Westergaard's analytical model describing the crack tip fields. • Unlike most other full-field experimental techniques, this work is aimed at estimating the stress intensity factor in the bulk of the material in situ , thus being a great step forward in the understanding of the 3D nature of fatigue crack propagation. • The work is also pioneering in performing a parametric study of key factors that influence through thickness estimation of the stress intensity factor. In this work a novel approach to estimate in situ the stress intensity factor (SIF) through the thickness of metal specimens is presented. It is based on a hybrid methodology that combines powerful synchrotron X-ray diffraction data with an elastic analytical model describing the strain field around the crack tip. A sensitivity analysis is conducted to understand the largest sources of error and their impact on the estimated SIF values. The accuracy in locating the crack tip position was found to affect the quality of the SIF estimation. Accordingly a procedure is developed to help locate the crack tip position. The methodology is tested on ultra-fine grained aluminium alloy 5091 and on a bainitic steel. It is recommended that an area of interest having a size at least 3 times larger than the plane strain plastic zone is mapped, providing good SIF estimations (within 8%) for all cases studied. [ABSTRACT FROM AUTHOR]

Highlights • Study of crack-tip propagation with macro-scale and micro-scale analyses. • Experimental estimation of the crack-tip position and the crack orientation. • Macro-scale analysis includes estimation of the SIF (continuum mechanics) from DIC. • Micro-scale investigation includes fractography analysis with SEM. • Full-field displacement information is combined with Williams' series development. Abstract This work presents a comprehensive study for characterising the crack-tip mechanics and fatigue crack propagation in an Aluminium 2024-T351 alloy. It combines information obtained from three different sources: full-field displacement information from digital image correlation, analytical modelling of the crack-tip field and SEM fractographies. The displacement data measured around the crack-tip are fitted to a Williams' series development in order to evaluate singular and non-singular terms of the crack-tip field. The procedures also allows rigid body motion to be corrected and the crack-tip coordinates and crack orientation to be estimated. Fatigue striations from the fracture surface were analysed with SEM in order to estimate the crack growth rate for different boundary conditions. Representation of all the results together with the Paris law data of the alloy allows the procedures to be cross-validated and to fit with a good agreement micro-scale measurements with continuum mechanics estimations. [ABSTRACT FROM AUTHOR]

Highlights • New methodology for investigating the interior of engineering materials. • Estimation of the stress intensity factor in the bulk of metal alloys. • Hybrid approach combining experimental data and an elastic model describing the strain field surrounding the crack tip. • Analytical model based on Williams' series development to describe the strain field around the crack tip. • Experimental data measured in the bulk of the material with synchrotron X-ray diffraction. Abstract A generalised approach for determining the stress intensity factor in the bulk of non-transparent materials is presented. The new approach combines experimental elastic strain data, measured with powerful synchrotron X-ray diffraction, with an elastic model based on Williams' series development. The stress intensity factor is calculated using a multi-point over-deterministic method where the number of experimental data points is higher than the number of unknowns describing the elastic field surrounding the crack-tip. The tool is tested on X-ray strain measurements collected on a bainitic steel. In contrast to surface techniques the approach provides insights into the crack tip mechanics deep within the sample and makes full use of the plastic zone data. Satisfactory results are obtained with 1 term in the series development and a smaller region of interest. By increasing the number of terms, it is possible to improve the accuracy in the SIF predictions but this requires a larger region of interest. [ABSTRACT FROM AUTHOR]

Highlights • An ultrafine finite element model of a cracked component allows visualising the plastic zone in great detail. • A bi-dimensional equivalent plastic zone shape is derived from the three-dimensional yielded volume. • A correction factor for the theoretical plastic zone at plane stress conditions is determined. • Its evolution with the specimen thickness is obtained. • The numerical model has been validated with full-field digital image correlation experiments. Abstract In this work, we present a detailed numerical analysis of the evolution of the plastic zone through the thickness of compact tension aluminium alloy specimens. An ultra-fine non-linear finite element model was used to characterise with great detail the size and shape of the plastic zone for different thicknesses. The numerical plastic zone was compared in size and shape with the plane strain and plane stress Dugdale plastic zones. In general, the maximum plastic zone was found to be in the interior but closer to the surface than to the mid plane. We also propose an equivalent bi-dimensional plastic zone for converting the complex 3D distribution into a 2D plastic zone. Finally, the numerical results were validated using experimental displacement data measured optically from the surface of the specimen. [ABSTRACT FROM AUTHOR]

Abstract: In the present work, a methodology for structural health monitoring based on a combination of digital image correlation and an analytical elastic solution is presented. To this end, full‐field displacement around a crack tip in a CT sample made of 2024‐T351 Al alloy under cyclic loading was monitored at different load levels. An analytical solution based on Williams' model was used to evaluate the experimental value of the stress intensity factor (SIF) in a continuous fashion during cyclic loads. It was observed that by increasing the loading amplitude in the cyclic loading, the difference between nominal and experimental estimation of SIF increased due to the crack tip plasticity effect, which was not considered in the nominal evaluations. To consider the plasticity effect, Irwin's approach was employed. The results showed that the proposed method can successfully monitor the evolution of SIF of a sample under cyclic loading until the sudden fracture of the sample. [ABSTRACT FROM AUTHOR]

In-line inspection (ILI) has become a routine procedure in the Oil and Gas industry for performing cost-effective pipeline integrity assessments, allowing continuing monitoring and providing a basis for informed decisions in terms of repair, maintenance or a change to the operating conditions. The amount of ILI data is however immense and dealing with these data from a fitness-for-service point of view poses a significant challenge to the industry. Thus, smart methods for using ILI data in the assessment of the integrity of oil and gas transmission pipelines are essential. The aim of this paper is to propose a screening approach for reducing the amount of ILI inspection data requiring detailed structural integrity assessment. The screening approach has two main stages: (1) a geometry based filter assessing the shape of the flaw and (2) an elastic stress based filter that uses the point method, as in the Theory of Critical Distances (TCD), to identify the most severe flaws. The methodology uses the outputs from ILI (dimensions of flaws, orientation and distance from starting point) to generate a visualisation of the pits within the pipeline, a ranking of pits in terms of sphericity (roundness) and depth, to evaluate pit density and generate the models for finite element analysis. The method was tested on actual ILI data, where the number of pits in a 12.75 in. riser of 11 km length was reduced significantly (i.e. two/three orders of magnitude), such reduction depending on the level of conservatism introduced by the analyst. The tool will allow Oil and Gas owners and operators to reduce the immense amount of data obtained during pigging to a much less time-consuming set for flaw assessment. [ABSTRACT FROM AUTHOR]

The crack propagation is influenced by what happens at both the surface and the interior of the component. Traditional experimental tools allow the surface behaviour to be characterised accurately but the information obtained from the bulk is much more limited. In this work, a study of both bulk and surface behaviour is presented. The material behaviour is studied by powerful 3D ultrafine finite element analysis in terms of the crack tip plasticity for a range of different conditions. The analysis is performed on a wedged opening loaded specimen made of an Aluminium alloy. The results are then validated with full-field digital image correlation data. The validation is used to enhance the model used in our analyses. [ABSTRACT FROM AUTHOR]

Structural components are often subjected to complex multiaxial loading conditions. The study of fatigue cracks under such conditions is not easy from an experimental point of view and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that is now well known and is not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (ΔK I and ΔK II ) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under two different load levels and a range of crack lengths. All crack-tip information is obtained with a hybrid optical-analytical methodology. It combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field. [ABSTRACT FROM AUTHOR]

The current work aims at estimating the stress intensity factor deep inside the bulk from elastic strain data measured by synchrotron X-ray diffraction. Key features affecting the evaluation of the stress intensity factor are the number of terms in the analytical model describing the crack tip field, the extension and position of the area of interest of the experimental data, the effect of the experimental data collected within the plastic zone and the number of elastic strain data points used. Here a parametric study of these features is presented in terms of their influence for the stress intensity factor determination. It was found that 3 or 4 terms in Williams' expansion is often sufficient; the data should be collected from across the full range of angles around the crack tip; and the number of points/number of terms should be greater than 40. [ABSTRACT FROM AUTHOR]

Most mechanical components are subjected to the complex fatigue loading conditions, where both amplitude and direction of loading cycles change over the time. The estimation of damage caused by these complex loading scenarios are often done by simplified uniaxial fatigue theories, which ultimately leads to higher factor of safety during the final design considerations. Critical plane-based fatigue theories have been considered more accurate for computing the fatigue damage for multiaxial loading conditions in comparison to energy-based and equivalent stress-based theories. Two recently developed fatigue theories have been evaluated in this work for the available test data. Test data includes significant amount of biaxial load paths. [ABSTRACT FROM AUTHOR]

In the past two decades, crack-tip mechanics has been studied increasingly using full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), crack opening displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, the position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF by using Williams’ model. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation around the crack-tip has been examined. The comparison between nominal and experimental values of K I showed that the effect of subset size on the measured K I is negligible compared to the effect of the field of view and the position of the area of interest. [ABSTRACT FROM AUTHOR]

Two complementary experimental techniques have been used to study the evolution of crack-tip strain fields in a thin (plane stress dominated) compact tension sample following a single overload (OL) event. The total strain has been characterised at the surface by digital image correlation (DIC), while the elastic strain field in the bulk (interior) behaviour has been characterised by means of synchrotron X-ray diffraction (XRD). Surface and bulk information allowed us to visualise the evolution of the strain fields before the OL event, during the OL event, just after it and at various stages after it. Unlike previous work, complete 2D maps of elastic strains around the crack-tip were acquired at 60 µm spatial resolution by XRD. The strain data were used to estimate the effective crack driving force at the surface and at the mid plane. The DIC shows less crack opening displacement after overload and the XRD a lower crack-tip peak stress after OL until the crack has grown past the compressive crack-tip residual stress after which the behaviour returned to that for the baseline fatigue response. While the compressive residual stress introduced by the OL offsets the crack-tip stress field as it grows through the overload plastic zone, the changes in crack-tip stress over each cycle are the same before and at all stages after OL. [ABSTRACT FROM AUTHOR]

Most mechanical components experience multi-axial cyclic loading conditions during service. Experimental analysis of fatigue cracks under such conditions is not easy and most works tend to focus more on the simpler but less realistic case of uni-axial loading. Consequently, there are many uncertainties related to the load sequence effect that are now well known and are not normally incorporated into the growth models. The current work presents a new methodology for evaluating overload effect in biaxial fatigue cracks. The methodology includes evaluation of mixed-mode (KI and KII) stress intensity factor and the Crack Opening Displacement for samples with and without overload cycle under biaxial loading. The methodology is tested under a range of crack lengths. All crack-tip information is obtained with a hybrid methodology that combines experimental full-field digital image correlation data and Williams' elastic model describing the crack-tip field. [ABSTRACT FROM AUTHOR]

This work presents a new methodology for evaluating crack initiation under biaxial conditions. The methodology consists of evaluating a number of crack parameters automatically with digital processing of high-magnification images of the crack. Five different strain conditions were evaluated on a low carbon ferritic–pearlitic steel specimen with tubular shape. A hole of 150 μm diameter was drilled to enforce the crack to initiate at a particular spot. Different combinations of axial and torsional strains were analysed during the initiation stage of the crack. Fatigue crack propagation curves clearly showed oscillations due to microstructure. It was also observed that these oscillations decreased as the torsional component of the strain was increased. Driving force was also evaluated in crack opening and sliding direction through crack opening displacement and crack sliding displacement. The results demonstrate that crack opening displacement is sensitive to microstructural barriers and crack sliding displacement is sensitive to crack deviations caused by the microstructure. [ABSTRACT FROM AUTHOR]

The evolution of crack-tip strain fields in a thin (plane stress) compact tension sample following an overload (OL) event has been studied using two different experimental techniques. Surface behaviour has been characterised by Digital Image Correlation (DIC), while the bulk behaviour has been characterised by means of synchrotron X-ray diffraction (XRD). The combination of both surface and bulk information allowed us to visualise the through-thickness evolution of the strain fields before the OL event, during the overload event, just after OL and at various stages after it. Unlike previous work, complete 2D maps of strains around the crack-tip were acquired at 60µm spatial resolution by XRD. The DIC shows less crack opening after overload and the XRD a lower crack-tip peak stress after OL until the crack has grown past the compressive crack-tip residual stress introduced by the overload after which the behaviour returned to that for the baseline fatigue response. While the peak crack-tip stress is supressed by the compressive residual stress, the crack-tip stress field changes over each cycle are nevertheless the same for all Kmax cycles except at OL. [ABSTRACT FROM AUTHOR]

In the past two decades, crack-tip mechanics has been increasingly studied with full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), Crack Opening Displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, size of the images, position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF and T-stress by using Williams' model. The concept of determination of the K-dominance zone from experimental data has also explored. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation ahead of the crack tip has been examined. The comparison between theoretical and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of size of the image. [ABSTRACT FROM AUTHOR]

The crack initiation and propagation behaviour of St52-3N steel is investigated under biaxial conditions. Short crack behaviour is studied and pearlite bands are found to modify the crack growth rate. The behaviour under proportional and non-proportional (90°) loading is studied with different critical plane models; Wang–Brown, Fatemi–Socie, Smith–Watson–Topper, Liu I and Liu II. Smith–Watson–Topper and Liu I are found to best predict the crack orientation under proportional loading and Fatemi–Socie and Liu II under non-proportional loading. The best predictions in terms of fatigue life are obtained by Fatemi–Socie, both under proportional and non-proportional loads. [ABSTRACT FROM AUTHOR]

In this work we present the results of in situ synchrotron X-ray diffraction measurements of fatigue crack-tip strain fields following a 100% overload (OL) under plane strain conditions. The study is made on a bainitic steel with a high toughness and fine microstructure. This allowed a very high (60 μm) spatial resolution to be achieved so that fine-scale changes occurring around the crack-tip were captured along the crack plane at the mid-thickness of the specimen. We have followed the crack as it grew through the plastic/residually stressed zone associated with the OL crack location. We observed two effects; one when the enhanced plastic zone is ahead of the crack and one after it has been passed. Regarding the former it was found that the compressive stress at the crack-tip initially falls sharply, presumably due to the increased plastic stretch caused by the OL. This is associated with a concomitant fall in peak tensile stress at K max , the elastic excursion between K min and K max remaining essentially unchanged from before OL. Subsequently discontinuous closure as seen previously for plane stress caused by crack face contact at the OL location limits the elastic strain range experienced by the crack tip and thereby retards crack growth. [ABSTRACT FROM AUTHOR]

This work presents a novel methodology for characterising fatigue cracks under biaxial conditions on a low carbon steel. It allows both short crack and early propagation stages to be studied in tubular specimens. Short crack growth is studied with a long-distance microscope acquiring images of the bare metal surface. Results showed oscillations in crack growth rate due to microstructure. Early propagation stage is studied with high magnification Digital Image Correlation (DIC) technique for measuring displacement and strain crack-tip fields. By applying micro-speckle pattern on the metal surface it is possible to achieve high magnification for DIC technique. Ultra-fine black and white speckles were created by electro-spray technique. The validity of this novel technique is demonstrated by direct comparison with extensometer measurements, under combined tension–compression and torsion conditions. It was also possible to estimate satisfactorily the mixed-mode stress intensity factor. [ABSTRACT FROM AUTHOR]

In this paper a methodology for evaluating crack initiation under biaxial conditions is presented. The methodology consists of evaluating the crack length automatically with digital processing of high-magnification images of the crack. The methodology was applied to study five different strain conditions on a low carbon ferritic-pearlitic steel specimen with tubular shape. A hole of 150 μm diameter was drilled to enforce the crack to initiate at a particular spot. Different combinations of axial and torsional strains were analysed during the initiation stage of the crack. The setup employed allowed detection of the crack to within 6 μm from the edge of the hole on average and monitoring of the crack during early stages. Fatigue crack propagation curves clearly showed oscillations due to microstructure. It was also observed that these oscillations decreased as the torsional component of the strain was increased. [ABSTRACT FROM AUTHOR]

Highlights: [•] Evolution of closure in thick and thin CT specimens prior and after overload. [•] Closure quantified through COD and full-field K-Muskhelishvili approaches. [•] Closure is distant dependent in retardation zone for thick but not thin CT specimens. [•] Full-field K-Muskhelishvili less sensitive to measure closure load than COD. [•] Fatigue crack growth plastic zone model fit to experimental data. [ABSTRACT FROM AUTHOR]

• Novel fatigue crack growth (FCG) study of 2024-T351 aluminium alloy based on plasticity developed at the crack tip. • Combines experimental FCG data with powerful numerical model replicating the material properties, geometry and loading conditions. • Determination of crack closure level based on contact of the first node behind the crack tip. • Establishing a new nearly linear relation between da/dN and plastic component of the CTOD. In this work, fatigue crack growth (FCG) in the 2024-T351 aluminium alloy is studied using the plastic CTOD range, Δ δ p. Experimental tests were performed on 12 mm thick CT specimens in order to obtain FCG rate and in cylindrical specimens to obtain stress–strain loops. A numerical analysis replicated the experimental work in terms of material, geometry and loading conditions, but assuming pure plane strain state, in order to obtain Δ δ p. The material parameters were fitted using the experimental stress–strain loops. The experimental work showed an increase of FCG rate with the increase of stress ratio from R = 0.1 to R = 0.7 mm, which indicated the existence of the crack closure phenomenon. However, the analysis of the position of the first node behind the crack tip showed that there is no crack closure under plane strain state, while a maximum value of 36% was found for plane stress state. Therefore, the surfaces influence FCG rate even in 12 mm thick specimens. A nearly linear relation was found between da/dN and Δ δ p. The comparison with other aluminium alloys showed that there is a significant influence of material on da/dN -Δ δ p relation. The change from plane strain to plane stress state decreased FCG rate due to crack closure. Under plane strain state there is a minor influence of stress ratio in the range R = 0.1–0.7, also because there is no crack closure. Finally, a comparison was made between plastic CTOD and cumulative plastic strain at the crack tip. Well defined relations were found, showing that both parameters can be used to quantify crack tip deformation. [ABSTRACT FROM AUTHOR]

This work presents a novel methodology for characterising fatigue cracks under biaxial conditions. The methodology uses high magnification Digital Image Correlation (DIC) technique for measuring displacement and strain crack-tip fields. By applying micro-speckle pattern on the metal surface it is possible to achieve high magnification for DIC technique. The speckles were created by electro-spray technique. The validity of this novel technique is demonstrated by direct comparison with standard extensometer measurements, under tension-compression and torsion conditions. In order to image the correct region, the notch effect on the fatigue life was also evaluated. [ABSTRACT FROM AUTHOR]

This work presents an in-situ characterisation of crack-tip strain fields following an overload by means of synchrotron X-ray diffraction. The study is made on very fine grained bainitic steel, thus allowing a very high resolution so that small changes occurring around the crack-tip were captured along the crack plane at the mid-thickness of the specimen. We have followed the crack as it grew through the overload location. Once the crack-tip has progressed past the overload event there is strong evidence that the crack faces contact in the region of the overload event (though not in the immediate vicinity of the current locations of the crack tip) at Kmin even when the crack has travelled 1mm beyond the overload location. It was also found that at Kmax the peak tensile strain ahead of the crack-tip decreases soon after the overload is applied and then gradually recovers as the crack grows past the compressive region created by the overload. [ABSTRACT FROM AUTHOR]

The evaluation of stress intensity factors from experimentally determined crack-tip stress or displacement fields almost always requires that the location of the crack tip is identified beforehand. In this work, a study has been performed to compare how different methods to locate the crack-tip position from the displacement field around a crack tip obtained by digital image correlation influence the estimation of stress intensity factors. The methods used were two constrained Newton type methods: the trust-region reflective Newton method and quasi-Newton method; an unconstrained direct search method: the Nelder-Mead Simplex method; a constrained genetic algorithm; and a constrained Pattern Search (PS) method. It is shown that the Newton type methods are less accurate compared with the direct search methods studied. The PS method was found to be the most accurate. Furthermore, the PS method was found to be about twice as fast as the Simplex method and 10 times faster than a Genetic Algorithm for the same computing hardware and the same input data. [ABSTRACT FROM AUTHOR]

ABSTRACT The surface crack opening displacements are characterised by digital image correlation for a (thin) plane stress 316 stainless steel compact tension sample subjected to an overload event. This supports a traditional plasticity-induced closure interpretation showing a knee in the closure response prior to overload, an absence of closure in the accelerated growth regime followed by accentuated closure in the retardation regime. By contrast, measurement of the mid-thickness elastic strain field behind and ahead of the crack made by synchrotron X-ray diffraction shows no evidence of significant crack face contact stresses behind the crack tip on approaching minimum loading. Rather the changes during loading and overloading can mostly be explained by a simple elastic plastic analysis using a value of the yield stress intermediate between the initial yield stress and the UTS. This shows very significant compressive reverse plastic strains ahead of the crack that start to form early during unloading. At the moment it is not clear whether this difference is because of the increasing stress intensity applied as the crack grows, or for some other reason, such as prevention of the crack faces closing mid-thickness due to the reverse plastic zone. [ABSTRACT FROM AUTHOR]

The general idea of this paper is to model the mixed-mode cyclic elastic-plastic behaviour of the crack tip region at the global scale. It should be helpful, for instance, for predicting the effect of mixed mode overloads in fatigue. It is aimed at establishing a model reasonably precise (compared with elastic-plastic finite element (FE) computations) but condensed into a set of partial derivative equations so as to avoid huge elastic-plastic FE computations in the future. For this purpose, the kinematics of the crack tip region is characterized by a set of condensed variables. This is classical in linear elastic fracture mechanics (LEFM), the displacement field is approached by the product of spatial reference fields ( and ) and nominal stress intensity factors ( and ). Therefore, in LEFM, two condensed variables only, and , fully define the kinematics in the crack tip region. So as to generalize this approach to mixed mode cyclic elastic-plastic conditions, we define first the intensity factors ( and ) of the elastic spatial reference fields ( and ) and we introduce two additional spatial reference fields ( and ) and their intensity factors ( and ) to account for plastic deformation within the crack tip region. Such an approximation is shown to be reasonably precise using FE computations. Therefore, the velocity field in the crack tip region is fully defined by only four condensed variables ( and ). Using the multi-scale approach proposed herein, evolutions of and for various mixed-mode loading conditions defined by and were generated using the finite-element method (FEM). Then, it was shown that we can model these evolutions at the global scale through a yield locus, a flow rule and a kinematics hardening rule. It is also suggested how this model could be employed for predicting the effects of mixed mode plasticity on fatigue crack growth. [ABSTRACT FROM AUTHOR]

This study presents a methodology for evaluating crack closure and the effect of crack-tip plasticity on stress intensity. Full-field displacement maps obtained by digital image correlation are used to obtain the mixed-mode, crack-driving force. The methodology allows the quantification of the effect of a range of contact phenomena: effects arising from interlocking, plastic deformation of crack face asperities and wedging generated as a consequence of sliding displacements of fatigue cracks have been identified. By evaluating the effective crack-tip stress intensity factor, crack opening levels can be quantified for both mode I and mode II. Moreover, the approach can take into account plasticity effects local to the crack in determining the stress intensity factor. All the information can be extracted in a non-contacting fashion with equipment that can be easily incorporated into industrial environments. [ABSTRACT FROM AUTHOR]

A mathematical processing technique and an algorithm for the numerical correction of experimental displacement fields on the specimen surface in the vicinity of a crack tip with consideration of the displacement of a body as a rigid whole under its loading and the actual position of a crack tip were proposed. The initial experimental displacement fields in the vicinity of a fatigue crack tip of a compact specimen were determined by digital image correlation. This approach was successfully used for a compact specimen and the possibility of its expansion to obtain the distributions of the stress intensity factors and the nonsingular T stresses along the spatial crack front was shown. [ABSTRACT FROM AUTHOR]

This paper is concerned with the application of the strip yield models implemented in NASGRO to estimate fatigue crack growth under random loading. The two different strip yield model options (constant constraint-loss (CCL) and variable constraint-loss (VCL)) implemented in the software are considered and compared. In addition, three crack grow rate relations, obtained from constant amplitude data, the NASGRO material database and the literature, were also considered and compared. The capacity of the models to estimate the fatigue life and variability is analyzed by comparing simulated results with experimental data of fatigue crack growth under different stationary Gaussian random load processes on compact, C ( T ), specimens of aluminum alloy 2024-T351. The analysis performed showed that both model options provide very similar good fatigue life predictions. The estimated fatigue lives are within ±13% of the test lives with the best option. The variability of the results due to the randomness of the load is also analyzed. In this case, the variable constraint-loss option provides better estimation than the constant constraint-loss option. [ABSTRACT FROM AUTHOR]

Abstract: The study of crack tip fields in mode I is often conducted assuming a homogeneous behaviour through the thickness. Depending on the specimen thickness, a state of plane stress or plane strain is normally presumed. However, recent studies have shown a more complex behaviour along the thickness. On the one hand, plasticity-induced crack closure effects affect mainly to a small region close to the specimen surface. On the other hand, the plastic zone evolution along the thickness is not as simple as the classic dog-bone shape normally described in Fracture Mechanics textbooks. Unlike what is normally expected, the size of the plastic zone decreases in a very small region close to the surface, as we move from the interior to the surface of the specimen. These two effects can be detected if the mesh used in the finite element model is sufficiently fine. Both effects are probably related to an uneven distribution of the load along the thickness. One of the consequences of these effects on the fatigue crack growth is the curvature of the crack front which can be explained by two mechanisms. The first one is related to the crack closure effect near the surface, it would imply a smaller effective ΔK close to the surface, and therefore a slower crack growth rate. The second one (plastic zone size decrease in a small region close to surface) is probably due to ΔK being smaller near the surface than in the interior. The current work attempts to evaluate numerically both effects in order to separate their individual influence and their magnitude. This is done by evaluating the K distribution along the thickness at different planes on an Al 2024-T35 compact tension specimen under mode I nominal loading. The plastic wake effect is removed from the model in order to distinguish between both effects. [Copyright &y& Elsevier]

A study on the accuracy of the approximation of the displacement field around of crack tip in a sample made from bridge steel (S355) is main objective of contribution. Linear elastic fracture mechanics (LEFM) theory in framework of multi-parameter formulation, i.e. postulated by Williams is used to determine of coefficients of Williams power series terms. Over deterministic method was used to calculate the terms based on the least squares regression technique, applied on data from numerical simulation and experiment on S355 steel grades. Comparison between the stress fields (by principal stress σ 1 and von Mises stress sHMH) obtain from experimental measurement DIC, Hybrid method and obtain from reconstruction by using various number of Williams power terms are quantified in order to get key information around the crack tip region on bridge steel specimens. [ABSTRACT FROM AUTHOR]

Abstract: A study on the approximation of the displacement field in the vicinity of a crack tip in a compact tension specimen made from Al 2024‐T351 is presented. Components of displacements vector are expressed using the linear elastic fracture mechanics theory via Williams' power series multi‐parameter formulation. Determination of the coefficients of the terms of this series is performed using a least squares‐based regression technique known as over deterministic method for which displacements data obtained experimentally via optical measurements are taken as inputs. The displacement fields reconstructed are discussed, and several conclusions are drawn regarding the number of the Williams' power series terms considered and the region where the displacement are investigated. [ABSTRACT FROM AUTHOR]

• Fatigue resistance of additively manufactured 18Ni300 steel under multiaxial loads. • The fatigue life and crack orientation are studied for different load paths. • Analysis performed with energy based critical plane methods. • Understanding of the normal stress effect on the fatigue behaviour of 18Ni300. In this work, the uniaxial and biaxial fatigue behaviour of maraging steel (18Ni300) obtained by additive manufacturing was studied. The material was evaluated using several biaxial load paths and different load levels. The predictive capacity of the fatigue life and crack initiation angle of the critical plane methods of Liu (I and II), and Chu, Conle, and Bonnen (CCB) were evaluated. The results obtained showed that normal stresses had a strong effect on the fatigue life. In general, the best estimates of the useful life and initial crack angle prediction were obtained with the CCB method. [ABSTRACT FROM AUTHOR]

A study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from Al 2024-T351 is presented. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (ODM) for which displacements data obtained experimentally via optical measurements are taken as inputs. The stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized CT specimen via hybrid elements. [ABSTRACT FROM AUTHOR]

• First time that CJP model is used combined with SEM information in order to characterize the fatigue behaviour of aluminium alloy 2024-T351. • Application of Digital Image Correlation for study of fatigue in metals. • Exhaustive characterization of the fracture surface with SEM and extraction of experimental data for fatigue behaviour characterization. This work characterises crack growth in AA2024-T315 by combining different methods to further increase the reliability of the results. The Christopher-James-Patterson (CJP) model was fitted to experimental data obtained by digital image correlation (DIC). The effective value of the CJP stress intensity factors were successfully correlated with the ΔK-da/dN curve as obtained with Scanning Electron Microscopy measurements of the depth of striations on the fracture surface. This approach based on fitting the CJP model with DIC data and SEM observations allowed estimation of opening and closure loads and allowed the propagation rate and fracture mode to be effectively characterised. [ABSTRACT FROM AUTHOR]

• Study of the fatigue propagation from notches of AISI 18Ni300 maraging steel. • Analysis performed on the maraing steel fabricated via additive manufacturing process (laser-beam powder bed fusion). • The investigation is focused on cracks propagating from two different notch sizes and without notch under three different biaxial loading paths. • Combination of critical plane models with theory of critical distances allows effective characterisation. • The quality of the predictions is analysed both in terms of the fatigue life and the cracking orientation. The current work aims to characterise the fatigue behaviour of an additively manufactured maraging steel, AISI 18Ni300. This is a class of high-strength steel widely used in biomedical, aircraft, aerospace, offshore, and military industries thanks to its good performance in terms of strength, toughness, ductility, dimensional stability, and weldability. Laser-beam powder bed fusion (additive manufacturing) is used to fabricate this type of steel and endows it with properties that make it an excellent candidate for producing prosthetic parts, thereby facilitating a reduction in manufacturing material consumption, labour, and machining time. Given the wide range of loads biomedical components are often subjected to, the current study focused on the multiaxial behaviour of this type of steel. To this end, Fatemi–Socie (FS) and Smith–Watson–Topper (SWT) critical plane methods combined with the theory of critical distances were applied to predict the fatigue life and cracking orientation of this material, with and without notches, under three biaxial loading scenarios. Cylindrical specimens were used and these were fabricated on the base plate in the vertical orientation using a linear printing system equipped with a Nd:YAG fibre laser. The building strategy involved the deposition of 40 μm thick layers at a scan speed of 800 mm/s. The two critical plane models returned good results at low life cycle fatigue but the FS model obtained better results at high life cycle fatigue. Regarding the crack angles, SWT model produced the best predictions. [ABSTRACT FROM AUTHOR]

• The applicability of fatigue toughness under multiaxial load is explored. • A fatigue life prediction model based on fatigue toughness is introduced. • The proposed model is formulated within a linear-elastic framework. • The model showed better predictive capabilities than other well-known models. In this paper, the cumulative strain energy density, also called fatigue toughness, was used to predict the fatigue life of notched members subjected to multiaxial loading. The relationship between the total energy absorbed to fracture and the number of cycles to failure was established from uniaxial strain-controlled fatigue tests. Multiaxial fatigue tests were performed on notched round bars made of high-strength steel under proportional bending-torsion considering different normal stress to shear stress ratios and different loading orientations. The fatigue lives predicted with the proposed model were compared to those obtained with other stress-based and energy-based models. Overall, the proposed model led to good predictions, and showed better predictive capabilities than the other tested models. [ABSTRACT FROM AUTHOR]

• New multiaxial fatigue characterisation of 316 steel including high mean deformation and non-proportional load paths. • Compression induces a lower strain range thereby increasing the fatigue life. • Thorough and independent analysis of newly proposed critical plane method (Lei-Gan) indicates an acceptable performance. • The most accurate model for estimating the fatigue life of 316 steel is Liu II. • Fatemi-Socie yields the best estimations in terms of cracking angle. In this work, the fatigue behaviour of 316 stainless steel is studied with different critical plane models. Seven cylindrical samples were used for the study, being subjected to different complex loading paths, generating combined stresses along the axial and transversal sample directions, these being: individual axial stress, individual hoop stress, alternating axial and hoop stress, a proportional combination of axial and hoop stress, and a non-proportional combination of L-shaped and square-shaped axial and hoop stress. The fatigue analysis is performed using five critical plane models; named Fatemi-Socie, Varvani-Farahani, Gan-Wu-Zhong, Liu I and Liu II. The models were assessed based on their fatigue life and crack angle prediction capacity. The Gan-Wu-Zhong recently proposed critical plane model was examined and provided acceptable results for the multiaxial loads tested on 316 steel. Nevertheless, Fatemi-Socie produced the most accurate results in terms of cracking orientation and Liu II gave the best fatigue life predictions. [ABSTRACT FROM AUTHOR]

This paper presents the development of an ultra-fine grained (UFG) microstructure in Nb1Zr alloy through severe plastic deformation by accumulative roll bonding (ARB). The sheets were subjected to 5 ARB cycles, for a total equivalent deformation of 400%. The laminated composites were characterized both mechanically and microstructurally. Tensile tests revealed a four-fold increase in yield stress after 5 ARB passes. More importantly, an important reduction of the elastic modulus was detected. A Dillamore/Taylor coupled with a Goss texture measured by X-ray diffraction was found to be responsible for this reduction. Indirect and direct cell toxicity were carried out and confirmed that ARB processing has no detrimental effect in the biocompatibility of this materials. The results support this processing route as an attractive alternative for manufacturing biocompatible Nb-based implants. [ABSTRACT FROM AUTHOR]

This work aimed to study the fatigue behaviour of S355 low carbon steel under uniaxial and biaxial loading conditions and to measure the overload effects under both types of loads. The analysis is performed with a local strain approach and with damage tolerance approach. Local strain based investigation was based on Fatemi-Socie critical plane model. This allows the life reduction caused by growing the crack from a stress raiser to be quantified. The fatigue life reduction caused by applying simultaneously torsional and tension loads was also evaluated with Fatemi-Socie model. In addition, the crack opening displacement (COD) and the effective stress intensity factor (SIF) were evaluated experimentally via full-field technique of digital image correlation (DIC). Both COD and SIF have been useful to understand the transient effects caused by a 40% overload under the two types of load. In addition, COD measurements allowed the offset compliance method for evaluating the opening load to be applied on a cylindrical specimen subjected to tension load. SIF estimation was also useful to quantify the mode mixity (I + II) developed during the experiment under the two types of load. [ABSTRACT FROM AUTHOR]

• The effect of kinematic parameters on FCG was predicted numerically using the plastic CTOD. • Increasing kinematic parameters reduces non-linearly fatigue crack growth. • The kinematic parameters have a limited effect on crack closure. • The effect of kinematic saturation stress, X Sat , is more relevant than the effect of kinematic saturation rate, C X. The parametric study of the effect of material properties on fatigue crack growth (FCG) rarely has been addressed in literature. The consideration of plastic CTOD as crack driving force opened the opportunity to predict FCG rate numerically and therefore to develop parametric studies focused on the effect of loading, geometrical and material parameters. The objective here is to study the effect of kinematic saturation stress, X Sat , and kinematic saturation rate, C X , on FCG using this numerical approach. The increase of the kinematic parameters reduced the plastic CTOD and therefore the FCG rate. The variation is non-linear and the rate of variation of δ p decreases with the increase of X Sat and C X. The effect of the kinematic saturation stress, X Sat , is more relevant than the effect of kinematic saturation rate, C X. On the other hand, a small effect of kinematic hardening parameters on crack closure was found. Finally, the increase of the number of load cycles between crack increments produced a great reduction of crack closure but no effect of plastic CTOD on models without contact of crack flanks. [ABSTRACT FROM AUTHOR]

The article focuses on the 2nd International Conference on Characterisation of Crack Tip Stress Fields held in Malaga, Spain from April 15-17, 2013. It states that fracture mechanics is used to deal with crack growth phenomena in engineering materials and discusses several modern techniques for measuring displacement, strain and stress in materials including digital image correlation, electronic speckle pattern interferometry and thermography.