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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]

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]

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 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]

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]

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]

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models. [ABSTRACT FROM AUTHOR]

In this paper, a novel geometric method combined with the piecewise linear function method is introduced into the extended finite element method (XFEM) to determine the crack tip element and crack surface element. Then, by combining with the advanced mesh technique, a novel method is proposed to improve the modelling of crack propagation in triangular 2D structure with the XFEM. The numerical tests show that the accuracy, the convergence, and the stability of the XFEM can be improved using the proposed method. Moreover, the applicability of the conventional multiple enrichment scheme is discussed. Compared with the proposed method, the conventional multiple enrichment scheme has deficiency in mixed mode I and II crack. Finally, a comparative study shows that the performance of the XFEM by using the proposed method to model the crack propagation can be greatly improved. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents transient and steady‐state elastic‐plastic‐creep crack‐tip stress fields under load‐controlled loading conditions for a wide range of combinations of power‐law plastic and creep materials. The crack‐tip stress fields are characterized in terms of 2 parameters to accommodate the crack‐tip constraint effect; the C(t)‐ (or C*‐) integral and the βQ parameter (the Q‐parameter normalized with respect to the proximity parameter to plastic collapse). For practical application, the crack‐tip stress fields are re‐formulated explicitly in terms of time and crack‐tip stress fields for elastic‐plastic and steady‐state creep conditions. Comparison with detailed FE results for plane strain tension and bend specimens shows that this formulation of the crack‐tip stress fields agrees well with finite element results. [ABSTRACT FROM AUTHOR]

In this paper, we give an explicit new formulation for the three-dimensional mode I weight function of Oore-Burns in the case where the crack border agrees with a star domain. Analysis in the complex field allows us to establish the asymptotic behaviour of the Riemann sums of the Oore-Burns integral in terms of the Fourier expansion of the crack border. The new approach gives remarkable accuracy in the computation of the Oore-Burns integral with the advantage of reducing the size of the mesh. Furthermore, the asymptotic behaviour of the stress intensity factor at the tip of an elliptical crack subjected to uniform tensile stress is carefully evaluated. The obtained analytical equation shows that the error of the Oore-Burns integral tends to zero when the ratio between the ellipse axes tends to zero as further confirmation of its goodness of fit. [ABSTRACT FROM AUTHOR]

Analysis of welded structures still remains a challenge for the analyst and in fact cannot be considered as fully solved for practical applications. For many years, a large international aggregation of researchers has developed methods to assess fatigue behaviour of welded structures. Nowadays many suggestions and methods exist to estimate fatigue life of welded structures with respect to nominal, structural, notch stress or fracture mechanics approaches. All of them are still under improvement. The high motivation and many activities of experts in the International Institute of Welding (IIW) group of researchers is a good demonstration of the complexity and need for analysis methods in that field. The purpose of this paper is to provide some discussion on selected methods available. Both authors are giving lectures to transfer methods to industrial applications. It is their experience that a large amount of knowledge has been developed although proper applications require some grading and comments on the use of those methods. This paper should give some comments and recommendations for the practical application of a selection of methods already available. A hierarchical two-step procedure for the assessment of large welded structures will be described and recommended. Also benchmark results are presented on a sample structure for sake of comparison of a few selected methods. Finally a presentation of results obtained by application of selected methods on real structures in comparison with fatigue lives from experiments will be presented. The methods selected within the paper cover the approaches for modelling, structural analysis and assessment of welded structures using finite element analysis (FEA) and stress based concepts for fatigue life estimation. [ABSTRACT FROM AUTHOR]

The parametric meshless Galerkin method (PMGM) enhances the promising features of the meshless methods by utilizing the parametric spaces and parametric mapping, and improves their efficiency from the practical viewpoints. The computation of meshless shape functions has been usually a time-consuming and complicated task in the meshless methods. In the PMGM, the meshless shape functions are mapped from the parametric space to the physical space, and therefore, the necessary computational time to generate the meshless shape functions is saved. The extended parametric meshless Galerkin method (X-PMGM) even improves the parametric property of the PMGM by incorporating the partition of unity concepts. In this paper, the development of the X-PMGM is extended by incorporating a crack-tip formulation in X-PMGM for fracture analysis and prediction of crack propagation path in the damaged structures. In this formulation, meshless shape functions are enriched by discontinuous enrichment function as well as crack-tip enrichment functions. The obtained results show that the predicted crack growth path is in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The authors successfully employed the discrete element method (DEM) in numerical determinations of the response up to and beyond failure of reinforced concrete structures subjected to impact and impulsive loadings in which tensile fracture, which is reliably predicted by DEM models, often controls the dominant failure modes. However, in impact problems when penetration occurs, the reliability of the approach in predictions of the structural response of the 3D compression zone that develops at the tip of the projectile has not yet been explicitly confirmed. In this context, in view of its complexity, the performance of the method is herein assessed and compared with available experimental results in static tests. By means of numerical simulations, it was previously verified that DEM models do predict, but overestimate, the strength increase observed on concrete cubes subjected to static multiaxial compression in relation with the unconfined strength, for confining (lateral) pressures up to about 20% of the unconfined compressive stress. For higher confining stresses, however, the DEM formulation underestimates the compressive strength increase observed in cubic and cylindrical samples, for the reasons examined in the paper, in which limitations of both the numerical predictions and experimental observations are thoroughly discussed. [ABSTRACT FROM AUTHOR]

This paper presents mode I stress intensity factors for external circumferentially cracked hollow cylinders, which are assumed to be made of functionally graded materials and subjected to remote uniform tension. The conventional finite element method is improved by introducing isoparametric transformation for simulating the gradient variations of material properties in the finite elements. This improved finite element method is verified to be effective and efficient. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper is devoted to the extraction of the dynamic stress intensity factor (DSIF) for structures containing multiple discontinuities (cracks, voids and inclusions) by developing the extended finite element method (XFEM). In this method, four types of enrichment functions are used in the framework of the partition of unity to model interface discontinuity within the classical finite element method. In this procedure, elements that include a crack segment, the boundary of a void or the boundary of an inclusion are not required to conform to discontinuous edges. The DSIF is evaluated by the interaction integral. After the effectiveness of the implemented XFEM program is verified, the effects of voids, inclusions and other cracks on the DSIF of a stationary major crack are investigated by using XFEM. The results show that the dynamic effects have an influence on the path independence of the interaction integral, and these voids, inclusions and other cracks have a significant effect on the DSIF of the major crack. [ABSTRACT FROM AUTHOR]

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

ABSTRACT This paper concerns the validation of standard safety assessment procedure given in BS 7910 for cracked circular hollow section T-joint and Y-joint, using the finite element (FE) results. A robust and efficient FE mesh generator is developed to produce the 3D models of the cracked joints and to calculate the elastic J-integral ( Je) and elastic-plastic J-integral ( Jep) values of the crack respectively. In order to verify its accuracy and convergence, the plastic collapse loads ( Pc) obtained from experimental tests and FE predictions are compared; they agree very well with each other. It is also found from experimental tests that the plastic collapse loads ( Pc) predicted using the BS 7910 reduction factor ( FAR) are safe and conservative. Subsequently, the failure assessment diagrams (FADs) of five cracked T-joints and three cracked Y-joints are constructed using the FE results, following the J-integral method, which is classified as Level 3C in BS 7910. Thereafter, a comparison between the constructed FAD curves and the standard Level 2A curve is carried out, and it is observed that the safety assessment results using the standard Level 2A curve might be unsafe because some parts of the constructed FAD curves fall inside of the standard one. A penalty factor of 1.15 working on both the elastic-plastic J-integral and plastic collapse load ( Pc) is proposed to move all the constructed FAD curves just outside of the standard Level 2A curve. [ABSTRACT FROM AUTHOR]

ABSTRACT An elliptical subsurface crack under normal loading may experience mixed fracture modes due to the non-symmetrical geometry. This paper investigates the coupling of the modes of elliptical subsurface cracks subjected to a uniform normal loading. First, a three-dimensional finite element model of a crack in an infinite space has been developed and validated. Then, by moving the crack close to surface, mixed mode SIFs have been calculated for a wide range of elliptical subsurface cracks under uniform normal loading. Cracks with aspect ratios of 0.2-1.0 and ratios of crack depth to crack length from 0.05 to infinity have been investigated through 50 finite element analyses. In this range, KII/ KI and KIII/ KI ratios increase up to 68.9% and 9.4%, respectively. Three equations for mode I, II and III SIFs have been obtained by fitting to the finite element results. These equations can be used efficiently as reference SIFs for extracting the weight functions. [ABSTRACT FROM AUTHOR]

ABSTRACT The fatigue life of cracked steel members can be greatly extended by externally attached carbon fibre reinforced plastics (CFRP), which reduces the stress intensity factors (SIFs) at the crack tip. Access to cracks is sometimes limited and the CFRP has to be attached away from the cracks. There is a lack of knowledge on SIFs for such strengthening scheme. This paper presents the effects of CFRP bond locations on the Mode I SIF of centre-cracked tensile (CCT) steel plate. The Mode I SIF at the crack tip is calculated using the finite element (FE) models. A correction factor is introduced as a function of CFRP bond location and crack length. The FE results are compared and agree well with experimental tests conducted by the authors. By combining with another two factors (one considering CFRP mechanical properties and the other considering CFRP bond width) derived previously by the authors, SIF formulae are proposed for CFRP reinforced CCT steel plates. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper presents a combined experimental-numerical technique for the calculation of the J-integral as an area integral in cracked specimens. The proposed technique is based on full-field measurement using digital image correlation (DIC) and the finite element method. The J-integral is probably the most generalised and widely used parameter to quantify the fracture behaviour of both elastic and elastoplastic materials. The proposed technique has the advantage that it does not require crack length measurements nor is it limited to elastic fracture mechanics, provided that only small scale yielding is present. Evaluated are three test geometries; compact tension, three-point bend and the double torsion beam. Possible errors and their magnitude and the limitations of the method are considered. [ABSTRACT FROM AUTHOR]

ABSTRACT Specimen J-R curve is extensively used for structural integrity of large components. It is well known that J-R curve heavily depends on constraint level ahead of crack tip in remaining ligament. In earlier work, it was demonstrated that J-R curve from Three Point Bending (TPB) specimen is transferable to straight pipe with circumferential through wall crack. In this paper, the transferability of J-R curve is investigated from TPB specimen to pipe with circumferential surface crack. A 16 in. diameter pipe with circumferential surface crack and TPB specimen machined from same piping material (SA333Gr6 Steel) are tested. Consequently, 3D finite element analysis (FEA) has been performed on surface cracked pipe and TPB specimen. Crack-initiation load is also predicted for surface cracked pipe by FEA and compared with experimental result. J-R curve is calculated for the pipe using experimental data, that is, load, load line displacement and crack growth. J-R curve of pipe is compared with TPB specimen and it is found that the pipe is predicting much higher J-R curve than TPB. This difference of J-R curve is investigated by evaluating stress triaxiality in remaining ligament for both cases. Stress triaxiality is quantified using triaxiality factor ( h) ahead of crack tip for pipe and TPB specimen. It is found that the TPB specimen has considerably higher constraint level than pipe with surface crack, which is well supported by trend of J-R curves for specimen and pipe. A study has also been carried out to investigate the effect of internal pressure on the stress triaxiality. It is found that there is negligible difference in stress triaxiality because of internal pressure. The stress triaxiality is re-established as a qualitative parameter to assess the transferability of J-R curve from specimen to component. [ABSTRACT FROM AUTHOR]

ABSTRACT Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E-glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode-mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode-mixity at the crack tip, face sheet properties and core density. [ABSTRACT FROM AUTHOR]

This paper proposes a simple numerical method to simulate ductile failure behaviours of tensile plates with interacting through-wall cracks. The method is based on the finite element damage analysis using the stress-modified fracture strain damage model. To validate the proposed method, simulated results are compared with a total of 23 published experimental data of flat tensile plates with interacting through-wall cracks. Despite its simplicity, the proposed method well predicted the experimental maximum loads of tensile plates with interacting cracks, including the loads for crack coalescence. Systematic analyses are also performed to investigate the effect of the element size used in the finite element damage analysis. [ABSTRACT FROM AUTHOR]

Fracture toughness is a crucial material property in structural design with metallic materials. For resistance against crack initiation, the crack‐tip opening displacement (CTOD) (or, equivalently, the J integral) is well established. For resistance against crack extension, the "resistance curve" (J as a function of crack size) may be used for limited amounts of crack growth. However, for crack increments much larger than the material thickness, the most useful criterion for toughness characterization is the crack‐tip opening angle (CTOA). During the past three decades, standards have been introduced to enable reproducible measurement of CTOA. Simultaneously, improved computer‐aided photographic methods have been developed to measure surface CTOA during the fracture process, and analysis of the mechanics of bend specimens has enabled deduction of the CTOA from load and displacement. Elastic‐plastic finite‐element analyses using a constant‐CTOA fracture criterion have been used to simulate fracture of laboratory specimens and structural components and to transfer the properties measured from laboratory‐scale specimens to structural applications. This paper reviews the state of the art in measurement and application of CTOA. [ABSTRACT FROM AUTHOR]

In the analysis of fracture mechanics of structures using three-dimensional (3D) J-integral, an integral evaluation of line and surface is required. However, because surface integral evaluation requires the calculation of the second derivative of displacement field and commercial finite element codes cannot calculate it, then this portion of the integral is neglected in some research. In this paper, a method for computing 3D J-integral is presented using finite element analysis. In the analysis, the second derivative evaluation of displacement field is employed. The method is implemented in calculating the J-integral of some 3D cracks and results are compared to well-known reference values. The results show that the method is reliable and is suitable for applications in engineering. The portion of 3D J-integral, namely the surface integral value is investigated and it is shown that neglecting this portion can introduce considerable error in the final results. [ABSTRACT FROM AUTHOR]

This paper studies the fracture behaviour of cracked carbon nanotube (CNT)-based polymer composites by a combined numerical–experimental approach. Tensile tests were conducted on single-edge cracked plate specimens of CNT/polycarbonate composites at room temperature and liquid nitrogen temperature (77 K), and the critical loads for fracture instabilities were determined. Elastic–plastic finite element simulations of the tests were then performed to evaluate the J-integrals corresponding to the experimentally determined critical loads. Scanning electron microscopy examinations were also made on the specimen fracture surfaces, and the fracture mechanisms of the CNT-based composites were discussed. [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]

Fatigue crack closure is strongly influenced by the plastic wake developed because of the action of precedent cycles. It is related to the load sequence and is an additional difficulty for its determination. Finite-element method has been an alternative for the study of crack closure, commonly in constant-amplitude loading. However, such analyses are complex and computationally expensive, the length of the wake simulated being a critical parameter. In this paper, a comprehensive study of the effect of the plastic wake in fatigue crack closure is made. It is structured in two parts: one regarding the correct numerical modelling process and the other focussed on the influence of the wake under moderate variable-amplitude loading. After a brief description of the numerical methodology, results for different wake lengths are reported. The plastic wake is modelled with a new approach in which the final crack tip is fixed. Information regarding potential error is provided. Second, the load sequence effect is discussed. Crack closure is obtained for several load ratios, with wakes developed with different stress ratios. This permits the analysis of the influence of the load sequence over the crack-driving force compared with constant-amplitude loading. [ABSTRACT FROM AUTHOR]

In the present paper, the interfacial crack growth of fibre reinforced composites under tension–tension cyclic load was simulated through the secondary development of the commercial finite element package ANSYS. For the importance of frictional degradation on the debonded interface during fatigue process, the modified power degradation model proposed in the authors' previous work is introduced into the present finite element analysis. Energy release rates rather than stress intensity factors are calculated in terms of difference approximation and utilized in Paris formula. Both looping cyclic load, calculating energy release rate, defining debond criterion and crack propagation law; updating parameters are programmed in ANSYS parametric design language, and the relationships between the parameters (such as the damage factor) and the number of cycles are obtained; the non-uniform stiffness degradation of matrix is taken into account. The numerical results are compared and discussed with the analytical solutions and good agreement is found. At the same time, a comparison between the present investigation and an experiment study is addressed. [ABSTRACT FROM AUTHOR]

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi-static, monotonic increasing loading are investigated using three-dimensional (3D) CDM implementation in a finite element method that is based on the layer-wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle-ply composite laminates under quasi-static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted. [ABSTRACT FROM AUTHOR]

This paper provides net-section limit pressures and a reference stress based J estimation method for pipes with constant depth, internal axial surface cracks under internal pressure. Based on systematic small strain finite element (FE) limit analyses using elastic perfectly plastic materials, net-section limit pressures are firstly determined, and based on FE results, a closed-form limit pressure solution is proposed. Furthermore, based on the proposed limit pressure solution, a method to estimate elastic–plastic J is proposed based on the reference stress approach. When the reference stress is defined by the proposed (global) limit pressure, estimated J values based on the reference stress approach are overall slightly lower than FE results, implying that the method is non-conservative. By re-defining the reference using optimised reference loads, resulting J estimates agree well with FE results. [ABSTRACT FROM AUTHOR]

The experimental and numerical investigations presented in this paper were carried out to determine the splitting forces and crack propagation scenarios of naturally bedded layered slate rock. Splitting loads were determined by impact splitting of regular-sized slate blocks under plane strain test loading conditions, using a hydraulic actuator with a wedge-shaped indenter. The mechanical properties of slate blocks required for numerical analyses were obtained from detailed experimental testing. The velocity of dynamic crack propagation in slate blocks under indenting wedge impact loading was determined using a series of strain gauge sensors. Numerical studies were carried out using ABAQUS, a general purpose, finite element analysis (FEA) program. Mode I dynamic crack propagation was simulated numerically by the gradual releasing of the restrained node on the symmetric plane of the specimens. Mode I stress intensity factors were computed for different crack lengths and the results were compared with the plane strain material fracture toughness obtained from earlier experiments/FEA. Very good agreement was obtained between analysis results and the measured fracture toughness value of slate, for the applied impact splitting load. Using the equation derived from a parametric study, of results obtained from the numerical analysis of different sizes of slate blocks, the maximum theoretical impact splitting force was determined using the plane strain fracture toughness value obtained from FEA. The difference between the loads obtained from the experimental studies and the derived empirical equation, varied between + 4.96% and −32.34%. [ABSTRACT FROM AUTHOR]

Defects that form by mechanisms such as fatigue and stress corrosion cracking are influenced both by external loads on engineering structures and internal, residual stresses that are generated during the manufacture and operation. This paper describes a programme of experimental and analytical work on a high-strength, low-toughness aluminium alloy (AL2024-T351) to assess the influence of residual stress on crack opening displacement (COD) and crack-driving force (CDF) for a range of fatigue crack lengths in compact tension (CT) specimens containing a mechanically induced residual stress field. Comparison of experimentally measured and numerically predicted CODs, at the mid-plane and surface of CT specimens, show generally good agreement for cracks introduced into the finite-element model in a progressive, element-by-element manner. Cracks introduced in a simultaneous manner give larger than observed CODs. The CDFs for the progressively introduced crack are always smaller than for simultaneously introduced. These results have implications for the assessment of initiation for slowly growing cracks. [ABSTRACT FROM AUTHOR]

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three-point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step-by-step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions. [ABSTRACT FROM AUTHOR]

The extended finite element method has been successful in the numerical simulation of fracture mechanics problems. With this methodology, different to the conventional finite element method, discretization of the domain with a mesh adapted to the geometry of the discontinuity is not required. On the other hand, in traditional fracture mechanics all variables have been considered to be deterministic (uniquely defined by a given numerical value). However, the uncertainty associated with these variables (external loads, geometry and material properties, among others) it is well known. This paper presents a novel application of the perturbation method along with the extended finite element method to treat these uncertainties. The methodology has been implemented in a commercial software and results are compared with those obtained by means of a Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

A known factor that limits the performance of automotive front-end accessory serpentine belt drive is cracking of the elastomer located in the rib tip. In this paper, fracture experiments were conducted using single-edge notched tension (SENT) specimens to study the fracture behaviour of a belt rib compound. A finite-element modelling method utilizing singular elements for crack in rubber solid was proposed and implemented in both plane-stress and 3D solid models using ABAQUS. A newly developed neural-network-based model was used to represent a nonlinear elastic belt rib rubber compound. The crack finite-element model, along with the neural-network-based material model, was verified with analytical and experimental results. A global–local finite-element procedure was developed to evaluate the J-integral for mode-I through-the-thickness crack in V-ribbed belt rib. Effects of pre-crack length, pulley pre-load and backside pulley displacement were investigated. [ABSTRACT FROM AUTHOR]

The deformation and failure of spot-welded joints have been successfully modelled using a cohesive-zone model for fracture. This has been accomplished by implementing a user-defined, three-dimensional, cohesive-zone element within a commercial finite-element package. The model requires two material parameters for each mode of deformation. Results show that the material parameters from this type of approach are transferable for identical spot welds in different geometries where a single parameter (such as maximum stress) is not. The approach has been demonstrated using a model system consisting of spot-welded joints made from 5754 aluminium sheets. The techniques for determining the cohesive fracture parameters for both nugget fracture and nugget pullout are described in this paper. It has been demonstrated that once the appropriate cohesive parameters for a weld are determined, quantitative predictions can be developed for the strengths, deformations and failure mechanisms of different geometries with nominally identical welds. [ABSTRACT FROM AUTHOR]

This paper is aimed at evaluating the behaviour of small cracks emanating from notches in the Ti-6Al-4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on prismatic specimens with a central hole. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 56.6 and 100% of the 0.2% yield stress of the material. Microstructural effects were discussed. To this purpose a specific device based on the ‘in situ’ detection of cracks by photomicroscopy was developed. Corresponding results were analysed quantitatively considering the effect of the yielded region at the notch tip by elastic–plastic finite element modelling. Furthermore, information regarding the sites of fatigue crack initiation and propagation path were discussed on the basis of careful fractographic analysis of the specimens. The importance of the two phase α, β microstructure on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. Mechanically and microstructurally long cracks were correlated by linear-elastic fracture mechanics. [ABSTRACT FROM AUTHOR]

The paper introduces a weight function for the nonlocal analysis of ductile damage that has the potential to provide approximately uniform averaged field variables over a limited region. When this region is identified with the underlying microstructural length scale of the material, the method is consistent with the view that, once damage is significant, a damaging cell behaves as a uniform entity. The analyses through which these effects have been studied concerned a unit cell idealizing a periodic array of large voids, connected by material that is capable of nucleating smaller-scale porosity. [ABSTRACT FROM AUTHOR]

This research focuses on the numerical investigation of fracture loads of U‐notched specimens made of Al‐6061‐T6 and Al‐5083 under pure opening mode and mixed mode I/II loading conditions. A new methodology is introduced with the aid of the equivalent material concept (EMC) combined with the extended finite element method (XFEM) and linear cohesive zone model (CZM), and the outcomes are compared with a conventional elastic–plastic damage model. The combination of EMC and XFEM result in the numerical EMC‐XFEM model, which provides a fast and accurate method to assess the notch fracture loads and crack growth path. Considering the experimental results, a trial and error loop is performed to calibrate the ductile damage model, which is much more cumbersome than the proposed EMC‐XFEM model. Moreover, the computational cost of elastic–plastic model is much more than the EMC‐XFEM model, although both approaches provide appropriate predictions for fracture of ductile aluminum notches. Highlights: The EMC is combined with XFEM and CZM for fracture prediction of ductile U‐notched.The model is validated with the mixed mode fracture results of two ductile aluminums.The results are also compared with the numerical method of ductile damage.The accuracy and time‐efficiency of the EMC‐XFEM method is proven. [ABSTRACT FROM AUTHOR]

ABSTRACT The crack-modelling technique is a method for prediction of fatigue in components using finite element (FE) analysis. The technique, which is based on the estimation of equivalent K factors for stress-concentrators, has had some initial success in analysing components of complex shape, but this has raised a number of questions about the potential accuracy of the method and its sensitivity to the choice of operating parameters. The present paper reports on a systematic study using four different specimen types and one component geometry. Accurate estimates of equivalent K values are shown to be possible for both sharp notches and blunt notches, loaded in uniaxial tension or bending, using a very simple approach in which the stress distribution from the notch is compared to that from a standard cracked body. The method shows some sensitivity to the optimization routines used, and to some extent to the choice of the standard cracked body. It is relatively insensitive to mesh refinement and can be used with simple, elastic FE models. [ABSTRACT FROM AUTHOR]

ABSTRACT Steel rings are frequently used as crack arrestor devices in steel gas transmission pipelines to prevent the possibility of long running axial cracks. These arrestors have the effect of reducing the pipe opening as the crack propagates. This decreases the available crack driving force and, as a result, crack arrest can take place. This essentially is a second line of defence against catastrophic failure in the event that crack initiation cannot always be prevented. This paper describes a novel analysis methodology that has been developed to investigate the suitability of these crack arrestors. This is based on a fluid/structure/fracture interaction package, PFRAC. Here, a curved beam element has been implemented into PFRAC to simulate the behaviour of the arrestor. The contact conditions between the pipe wall and the arrestor, along with the various computational procedures, are described here. Several numerical results for a cracked pipe with arrestors are presented along with comparisons with pipes that do not have arrestors. [ABSTRACT FROM AUTHOR]

Fracture of compliant materials is preceded by large deformations that reshape initially sharp cracks into rounded defects. This phenomenon, known as elastic crack blunting, is peculiar of rubber‐like polymers and soft biological tissues, such as skin, vessel walls, and tendons. With this work, we aim to provide a discussion on crack‐tip blunting and its implications in terms of tearing resistance and flaw tolerance of soft elastic materials. The characteristic features of the crack‐tip zone in the framework of nonlinear elasticity are reviewed analytically and with the help of finite element analyses on pure shear cracked geometries. Specifically, the strain‐hardening behavior typical of soft biological tissues is addressed, and we illustrate its effect on crack‐tip blunting, in terms of a local radius of curvature at the crack tip. A simplified geometrically nonlinear model, proposed to describe the progressive blunting at the crack tip and its effect on flaw tolerance, is validated through finite element analyses and experimental tests on silicone samples. We show how this can lead to a simplified criterion to define the fracture condition in nonlinear soft materials. [ABSTRACT FROM AUTHOR]

The study is devoted to the development of methods for predicting the brittle fracture of a steel part with a crack. To describe the limit state of the fracture process zone, a mathematical model of the fracture process zone in an elastic–plastic stress state and the generalized brittle fracture theory have been used. The cleavage stress and the size of the fracture process zone are used as parameters for the fracture toughness of the material. A finite element analysis approach was developed to determine these parameters by considering the elastic–plastic stress state of cracked specimens. An analytical procedure for calculating the above parameters for low‐carbon and low‐alloy steels is given. The proposed models allow the analytical calculation of critical values of the stress intensity factor for specimens with cracks at negative temperatures. The development of this study is linked to the improvement of the technology for determining the physical strength criteria of materials. The application of the proposed models makes it possible to create a methodology for predicting crack resistance of welded structures of arctic design considering their geometry and structural and technological characteristics. Highlights: The crack resistance parameters are determined based on the analysis of the fracture process zone limit state.The fracture process zone size is calculated for structural steels as a function of the yield strength.The cleavage stress dependence on the yield strength and the rolled thickness is given.The presented analytic models are verified by the testing results of cracked steel specimens. [ABSTRACT FROM AUTHOR]

Damage tolerance design allows manufactures to assess fatigue crack propagation of components containing initial defects. A new modeling approach is proposed to carry out a systematic crack growth analysis based on an analytical method using reduced order models and three‐dimensional (3D) finite element (FE)‐based fatigue crack growth (FCG) analysis. 3D FE‐based FCG analysis is adopted as an advanced modeling approach for component geometries without any simplifications with respect to crack front shape or planarity of the crack path. The FE‐based FCG approach was verified and validated in two different stages: Ti‐6Al‐4V plate geometry with three different single elliptical crack configurations and Al 2024‐T3 specimens with two different multiple crack configurations. The analytical FCG approach was developed to estimate crack front evolution and crack growth life for three different elliptical cracks to verify the FE‐based approach. Experimental data of Al 2024‐T3 specimens with multi‐edge cracks was used to further validate the FE‐based FCG approach. The FE‐based FCG approach proved to be both accurate and powerful in assessing crack propagation life and crack paths of structural parts. Highlights: Analytical crack growth (CG) approach is developed for three different elliptical cracks.Finite element (FE) analysis is adopted as an advanced CG modeling approach for components.FE‐based approach is verified and validated using analytical model data and experimental data.FE‐based approach provides accurate crack propagation assessment of structural parts. [ABSTRACT FROM AUTHOR]

Wire breakage has always attracted much attention in drawing. Mastering the mechanism of drawing fracture can effectively improve the quality of steel wire. In this study, the morphology of the fracture samples is analyzed. There are obvious V‐shaped microcracks in the materials by observing the microstructure. Base on the above results, the wire models with V‐shaped microcrack of different inclinations are established via the finite element method (FEM). Besides, the multi‐pass drawing under different back tension is simulated, and the process from crack propagation caused by damage to fracture is realized. The results show that microcrack has a great influence on the drawing fracture, and inclination is a key factor. With the increase of angle, the propagation rate of crack increases accordingly. Meanwhile, back tension will increase the accumulation of damage. The larger the back tension is, the larger the crack path is, which eventually leads to the formation of pen‐tip shaped fracture. Highlights: Steel wire with central V‐shaped microcrack is more likely to occur pen‐tip fracture.The growth rate of crack increases as the angle of V‐shaped microcrack increases.The action of back tension will make the drawing fracture occur earlier.Microcrack and back tension should be avoided, to reduce the risk of drawing fracture. [ABSTRACT FROM AUTHOR]

Fatigue crack growth in Al 2024 and Al 7050 specimens was assessed experimentally and numerically. In the experimental investigation, various specimen configurations and loading conditions were used to achieve pure mode I, pure mode II, and mixed mode I/II, I/III, and I/II/III. Sample configurations were as follows: first, compact tension shear (CTS) specimen to reproduce pure mode‐I and pure initial mode‐II loading conditions; second, surface crack tension (SCT) specimen to analyze the behavior of semielliptical surface cracks in mode‐I and mixed‐mode conditions; and third, hollow cylindrical (HC) specimen with initial semielliptical surface crack to analyze fatigue crack growth under complex stress state. In the numerical study, finite element method (FEM) simulations were performed by means of FRANC3D and ABAQUS solver. The numerical predictions were validated with the experimental results. These predictions resulted to be accurate estimation of the crack growth across the broad range of the investigated loading conditions. [ABSTRACT FROM AUTHOR]

This work presents the case study of a welded overhead crane runway girder. A full‐shell global finite element model was developed and validated using strain measurements. The global model drives solid submodels of different scales. Using load spectra based on real operational data, hot spot stress and XFEM‐based fracture mechanics simulations are performed to assess the fatigue properties of two critical joints. For the fracture mechanics‐based approach, it is shown that small cracks quickly converge to the same aspect ratio. Hence, the choice of the initial crack aspect ratio was found to be inconsequential. But the aspect ratio must not be assumed to be constant during the fatigue crack growth simulations. Finally, it is shown that the size at which a crack is transferred from one submodel to a subsequent is critical for the accuracy of the fatigue crack growth simulations. [ABSTRACT FROM AUTHOR]

The objective of this work is to investigate the correlation between rim and web thickness on the crack propagation path in thin-rimmed gears, referring to bending failures. To this aim, numerical simulations have been performed, based on the 3D extended finite element method. Results related to gear models with different web and rim thickness have been interpreted in ISO Standard environment, relating the crack path to the so called gear blank factor CR, useful in cases of mating gears consisting of rims and webs. Results show that the interaction between web and rim thickness may influence the crack propagation and the corresponding safe or catastrophic failure mode. [ABSTRACT FROM AUTHOR]

Rotor discs for gas turbines are heavy components usually designed following a safe-life approach, where the low-cycle fatigue design is based on life curves with suitable probabilistic margins. However, in such a component, there is the possible occurrence of undetected defects that can propagate at each startup-shutdown cycle, and therefore, defect acceptance criteria have to be defined for the different rotor regions (considering stress distribution and temperature). Moreover, the failure risk should be evaluated considering static fracture at overspeed as a potential failure mode. In order to make such an assessment for a turbine rotor disc, a semi-probabilistic approach for the integrity assessment-based current standards has been developed. The approach has then been implemented into a code able to process axis-symmetric Finite Element (FE) analyses of the disc and to produce maps for the expected life (for a given defect size) and for the acceptable defect (for a target life). The probabilistic assessment of turbine rotor discs is first discussed together with a sensitivity study about the most significant calculation assumptions. Then, details of the semi-probabilistic code are shown together with application to a turbine disc. [ABSTRACT FROM AUTHOR]