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In response to the problem that the standard AT2 phase field model cannot effectively model quasi-brittle failure and the existence of length dependence, a new modified phase field model is presented in this paper. By introducing an additional energy, the competing relationship between elastic strain energy and dissipation energy during fracture is changed. A new crack dissipation functional is established using the energy equivalent approach. By introducing a novel rational degradation function, not only can the strength of material failure be effectively utilized, but the model can also reproduce the cohesive softening relationship. A multi-field finite element method is used to discretize the model governing equations, and the equations are solved by an efficient BFGS monolithic algorithm. Finally, some representative numerical examples are used to analyze the effects of parameters in degradation function, length scale and mesh size on the results. The presented numerical simulation results demonstrate length scale and mesh scale independence, and are in good agreement with the experimental results and previous numerical results. At the same time, the numerical results also exhibit cohesive softening properties similar to the current phase field cohesive zone model. These results verify the robustness and effectiveness of the modified phase field model presented in this paper for simulating quasi-brittle failure and brittle fracture. [ABSTRACT FROM AUTHOR]

The objective of this paper is to derive goal-oriented a posteriori error estimators for the error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the finite element method. Such error estimators are based on the well-established technique of solving an auxiliary dual problem. In a straightforward fashion, the solution to the discretized dual problem is sought in the same FE-space as the solution to the original (primal) problem, i.e. on the same mesh, although it merely acts as a weight of the discretization error only. In this paper, we follow the strategy recently proposed by Korotov et al. [J Numer Math 11:33–59, 2003; Comp Lett (in press)] and derive goal-oriented error estimators of the averaging type, where the discrete dual solution is computed on a different mesh than the primal solution. On doing so, the FE-solutions to the primal and the dual problems need to be transferred from one mesh to the other. The necessary algorithms are briefly explained and finally some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

A new damage model which takes account of void shape effect and anisotropy of the matrix material is integrated into the explicit finite element framework to predict the damage evolution which occurs under crash or stamping process. The void coalescence failure mechanism by internal necking is also considered by using a modified Thomason's plastic limit-load model. An inverse method is developed to identify the material parameters by correlating experimental and numerical measurements with tensile tests on sheet-metal strips. The pathological mesh dependence has been overcome by a non-local approach where the evolution equation for the porosity is modified by an additional term containing a characteristic internal length. In this paper the evaluation of the Laplacian is based on a least square approximation of the internal state variable around each integration points. The presented formulation is applied to an Ni-based sheet-metal (INCO 718) and an aluminium alloy (AA 5182). The effectiveness of the numerical predictions is verified carrying out a set of experimental tests with a flat-headed punch. [ABSTRACT FROM AUTHOR]

Using an analogy between dielectric breakdown and fracture of solids, this paper develops a phase field model for the electric damage initiation and propagation in dielectric solids during breakdown. Instead of explicitly tracing the growth of a conductive channel, the model introduces a continuous phase field to characterize the degree of damage, and the conductive channel is represented by a localized region of fully damaged material. Similar as in the classic theory of fracture mechanics, an energetic criterion is taken: The conductive channel will grow only if the electrostatic energy released per unit length of the channel is greater than that dissipated through damage. Such an approach circumvents the detailed analysis on the complex microscopic processes near the tip of a conductive channel and provides a means of quantitatively predicting breakdown phenomena in materials, composites, and devices. This model is implemented into a finite-element code, and several numerical examples are solved. With randomly distributed defects, the model recovers the inverse power relation between breakdown strength and sample thickness. Finally, the effect of the layered structure in a breakdown-resistant laminate is demonstrated through a numerical example. [ABSTRACT FROM AUTHOR]

This paper is aimed at modeling the propagation of multiple cohesive cracks by the extended Voronoi cell finite element model or X-VCFEM. In addition to polynomial terms, the stress functions in X-VCFEM include branch functions in conjunction with level set methods and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Cracks are modeled by an extrinsic cohesive zone model in this paper. The incremental crack propagation direction and length are adaptively determined by a cohesive fracture energy based criterion. Numerical examples are solved and compared with existing solutions in the literature to validate the effectiveness of X-VCFEM. The effect of cohesive zone parameters on crack propagation is studied. Additionally, the effects of morphological distributions such as length, orientation and dispersion on crack propagation are studied. [ABSTRACT FROM AUTHOR]

This paper deals with a basic methodology for the application of the finite element (FE) simulation and linear elastic fracture mechanics (LEFM) to predict the onset of delamination growth. The first step of the proposed methodology is the experimental characterisation of material interlaminar fracture in pure mode I (DCB test), pure mode II (ENF test) and mixed mode I+II (MMB test). In the second step, the results of the interlaminar fracture tests are translated from load/displacement data to strain energy release rates by means of test FE simulations; thus, the critical strain energy release rate (Gc), or fracture toughness are obtained as a function of mode ratio. The third step of the methodology consists of applying FE simulations to determine the strain energy release rate (G) and mode ratio for the delamination and then comparing the result to the values of the Gc curve. The main innovative aspect of the paper is that FE simulation is used as a part of the material characterisation process; in fact, data reduction of interlaminar fracture tests is carried out by means of FE simulations. In addition, regarding the practical details of FE application to the proposed methodology, some innovative aspects are introduced, such as the analysis is carried out as a non-linear geometric problem (taken into account large displacements) and considering inside each simulation different elastic properties for the material depending on whether it is under tension or compression. These aspects and the rest of the proposed methodology are validated by the experimental results presented in the paper. [ABSTRACT FROM AUTHOR]

Devices in modern technologies often have complex architectures, dissimilar materials, and small features. Their long-term reliability relates to inelastic, time-dependent mechanical behavior of such structures. This paper analyzes a three-layer structure consisting of, from top to bottom, an elastic film, a power-law creep underlayer, and a rigid substrate. The layers are bonded. Initially, the film is subject to a uniform biaxial tensile stress. A channel crack is introduced in the elastic film. As the underlayer creeps, the stress field in the film relaxes in the crack wake, but intensifies around the crack tip. We formulate nonlinear diffusion-like equations that evolve the displacement field. When the crack is stationary, the region in which the stress field relaxes increases with time. We identify the length scale of the region as a function of time. The stress intensity factor is proportional to the square-root of the length scale. For the power-law creep underlayer, this newly identified length depends on the film stress, and corrects an error in a previous paper by Huang, Prévost and Suo (Acta Materialia50, 4137, 2002). When the crack advances, its velocity can reach a steady state. We identify the scaling law for the steady velocity. An extended finite element method (X-FEM) is used to simultaneously evolve the creep strain and crack length. Numerical results are presented for the stress intensity factors of stationary cracks, and the steady velocities of advancing cracks. [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]

Recently, the advent of optical systems has made possible the fast and accurate measurement of roughness discontinuity in three dimensions. In this study, a number of 3D roughness parameters such as fractal parameter (D), amplitude parameter (A), roughness parameter Rs and Grasselli's roughness parameter (2A0θ*max/(C + 1)) have been presented to quantify the geometry of the fracture surfaces. However, all these roughness parameters are scale dependent and their values change with scale. In this paper, the variations in theses parameters have been investigated with regard to scale. For this purpose, initially, three natural fracture surfaces with the dimensions 500 × 500 mm2 were selected and then, the four mentioned roughness parameters were calculated for these three surfaces in the range from 50 × 50 mm2 to 500 × 500 mm2. Finally, to evaluate the accuracy of roughness estimation by these roughness parameters, several joint replicas from the surfaces were constructed and the direct shear tests were carried out on them. Based on the experimental results, the Grasselli's roughness parameter gives more accurate estimation of the variations in surface roughness in regard to scale. Also the effect of small-scale evenness on surface roughness has been investigated. [ABSTRACT FROM AUTHOR]

This paper exhibits the investigative work conducted on the fracture toughness and microstructure of 6061Al-graphite particulate composites. The requisite specimens were prepared using stir casting technique with graphite proportions ranging from 3 to 12% by weight. The microstructure and interfacial bonding of 6061Al-graphite particulate composites were studied. Fracture toughness investigations were carried out on 6061Al-graphite for 3%, 6%, 9% and 12% of graphite by using single-edge notch bend (SENB) specimens. The maximum fracture toughness was found for 6061Al-9%Gr for a∕W = 0.45 and the value is 17.94 MPa √ m. Examination of specimen surface of 6061Al-graphite was done using scanning electron microscope (SEM). Due to good interface bonding and uniformity in distribution, improved fracture toughness properties are achieved. [ABSTRACT FROM AUTHOR]

Bending-active elastica beam is a structural configuration that is based on the elastic deformation of an initially straight beam. This deformation occurs when horizontal displacements are applied to a sliding support, causing the beam to bend into an arched shape. Previous research has focused on the stability of small-scale bending-active structures, thus not considering material strength, which is crucial in real-scale applications and structural design. This paper investigates the short-term structural behavior of bending-active elastica beams using pultruded glass fiber-polymer composite profiles, as used in real-scale structures. A series of short-term bending and service load application experiments were performed considering different bending degrees and loading scenarios. These results were used to validate finite element modeling. They demonstrated that steeper bent beams experience material failure, while shallower ones exhibit snap-through buckling. Material failure initiates on the tensile side of the beams, with cracks initiating at locations of maximum curvature. Higher bending degrees and symmetric loading result in higher maximum loads than lower bending degrees and asymmetric loading. A strain-based failure criterion, which can serve for structural design, is derived. [ABSTRACT FROM AUTHOR]

Web holes are often made in wood I-joists to allow passage of services. Design properties of wood I-joists with a web hole are commonly developed through testing which leads to empirical design information. This paper describes a mechanics-based method to predict the strengths of wood I-joists with a circular web hole that is suitable for implementation as a design tool. Curved beam theory is used to compute stresses around a hole. Peak tensile stresses obtained from curved beam analysis agree well with those predicted using the finite-element method. Failure load is attained by the application of fracture mechanics based finite area method. The method developed is used to predict failure loads of wood I-joists of different depths with different web hole sizes. Simplification of the method leads to the development of a simple expression that can be used for engineering design. It is found that the predicted strengths are in a good agreement with the corresponding test results. The calculation method developed can potentially replace the testing approach generally adopted by the wood I-joist industry. [ABSTRACT FROM AUTHOR]

Abstract: Crack-path prediction for crack-turning problems in stiffened structures is an important issue in modern aircraft design processes because the ability of modeling a crack-path correctly allows the engineer to predict lifecycles and maintenance cycles more appropriate. In this paper the method of material forces as a simple method to describe crack-turning problems is introduced. At first, simple problems are examined, in order to make sure that the computed numerical results are comparable to known analytical results. Thereafter a simple academic example of a stiffened structure is shown and the crack-path is predicted by means of an implementation of the material force method in a finite element analysis formulation. The results of these computations have been compared to the results achieved by several known methods for computing the stress intensity factors, the crack-path and the energy release rate. It can be seen that computations of the material force deliver all necessary information to describe a crack by linear elastic fracture mechanics. [Copyright &y& Elsevier]

This paper describes a theoretical model and related computational methods for examining the influence of inhomogeneous material properties on the crack driving force in elastic and elastic-plastic materials. Following the configurational forces approach, the crack tip shielding or anti-shielding due to smooth (e.g. graded layer) and discontinuous (e.g. bimaterial interface) distributions in material properties are derived. Computational post-processing methods are described to evaluate these inhomogeneity effects. The utility of the theoretical model and computational methods is demonstrated by examining a bimaterial interface perpendicular to a crack in elastic and elastic-plastic compact tension specimens. [ABSTRACT FROM AUTHOR]

The paper presents a reliable and efficient method for solving problems on a large set of domains with different geometries. In applications these geometries might be idealizations of a mechanical structure with multiple damage. The method is designed, and used, to analyse large three-dimensional problems. The present paper formulates the method and presents the theory for a simple model problem, i.e., the Laplace equation in two dimensions. In the numerical implementation of the splitting scheme, the p-version of the finite element method and strongly graded meshes are used. This approach provides high accuracy and error control. The exponential rate of convergence of the method is shown and practically exemplified. A numerical example shows the effects of various choices of parameters on the accuracy of the method. A complex problem related to aircraft safety, which was solved using the present method, is used to exemplify the generality and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/δ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from `complete slip before opening' to `opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks. [ABSTRACT FROM AUTHOR]

The present paper deals with the measurements of the critical Crack Tip Opening Angle by using an instrumented test. There is a comparison between the analysis of results made by a well known kinematic model and those given by finite element analysis based on a cohesive model for node release. Analysis is performed both on simple specimens and on back slotted ones. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings. [ABSTRACT FROM AUTHOR]

This paper explores the fracture process based on finite element simulation. Both probabilistic and deterministic methods are employed to model crack initiation, and several commonly used criteria are utilized to predict crack growth. It is concluded that the criteria of maximum tensile stress, maximum normal stress, and maximum Mises stress, as well as the Coulomb-Mohr criterion are able to predict the initiation of the first crack. The mixed-mode criteria based on the stress intensity factor (SIF), energy release rate, and the maximum principal stress, as well as the SIF-based maximum circumferential stress criterion are suitable to predict the crack propagation. [ABSTRACT FROM AUTHOR]

Corrosion will compromise safety operation of oil and gas pipelines, accurate determination of failure pressure finds importance in residual strength assessment and corrosion allowance design of onshore and offshore pipelines. This paper investigates failure pressure of high strength pipeline with single and multiple corrosions using nonlinear finite element analysis. On the basis of developed regression equations for failure pressure prediction of high strength pipeline with single corrosion, the paper proposes an assessment procedure for predicting failure pressure of high strength pipeline with multiple corrosions. Furthermore, failure pressures predicted by proposed solutions are compared with experimental results and various assessment methods available in literature, where accuracy and versatility are demonstrated. [ABSTRACT FROM AUTHOR]

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C-Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σref/σy) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σref/σy<<1. [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: Developing a robust predicting methodology on the interfacial fracture energy of dissimilar materials is urgently needed to meet the mechanical strength requirements for investigating novel materials and subsequent device structures with the bonded types of multi thin films. Thus, this paper provides an overview of useful approaches according to linear-elastic interfacial fracture mechanics, such as J-integral method, modified virtual crack closure technique (MVCCT), and analytical solutions derived from the relationship between the stress field of delaminated tip and crack tip opening displacements to compare their estimated capability of cracking energy. A popular technique for determining the interface adhesion of thin coatings is the four-point bending test (4-PBT). The testing vehicles of 4-PBT allow a more thorough validation of the foregoing predicted approaches based on finite element analysis compared with the simulated results with related experimental data. The critical energies of 18J/m2, 78.53J/m2, 52.01J/m2, and 71.02J/m2 for the bonded interfaces of SiO2/SiLK, Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked nano-scaled thin films are precisely judged, respectively. The predicted results of the J-integral method match well with the MVCCT estimation. The results reveal that the opening fractured mode is dominant at the beginning of the crack advances along the bonded interface of Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked films as the interfacial crack length increases. Moreover, the essential trends of dependences for the modulus ratio and thickness ratio of stacked thin films on interfacial energy release rate are logically identified and investigated. Therefore, this paper could be regarded as a design guideline of interfacial fracture behavior for stacked films utilized in the development of advanced device technologies. [Copyright &y& Elsevier]

This paper presents results of strength and fracture toughness properties of low-carbon high-strength Hardox-400 steel. Experimental tests were carried out for specimens of different thickness at wide temperature range from −100 to 20 °C. The dependences of the characteristic of material strength and fracture toughness on temperature based on experimental data are shown. Numerical calculation of the stress and strain distributions in area before crack tip using the finite element method (FEM) was done. Based on results of numerical calculation and observation of the fracture surfaces by scanning electron microscope (SEM), the critical local stress level at which brittle fracture takes place was assessed. Consideration of the levels of stress and strain in the analysis of the metal state at the tip of the crack allowed to justify the occurrence of the brittle-to-ductile fracture mechanism. On the basis of the results of stretch zone width measurements and stress components, the values of fracture toughness at the moment of crack initiation were calculated. [ABSTRACT FROM AUTHOR]

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place. [ABSTRACT FROM AUTHOR]

Abstract: Surface cracks with aspect ratio can occur in pipes subjected to corrosion attacks. There are few studies on stress intensity factors for semi-elliptical surface cracks with such high aspect ratio. With the failure rate for cast iron pipes unacceptably high there is a need to examine the accuracy of the prediction of stress intensity factors for pipes with high aspect ratio. However, little research has been undertaken on stress intensity factors with high aspect ratio. This paper attempts to develop a method to determine the stress intensity factors for pipes with high aspect ratio semi-elliptical internal surface cracks and subjected to any service load. Two analytical models are presented to determine the stress intensity factors in terms of influence coefficients. A three-dimensional finite element model is employed to derive a solution to analytical models. Based on numerical results it is found in the paper that the maximum stress intensity factor for surface cracks with high aspect ratio occurs at different point to that with low aspect ratio and hence may lead to different modes of failure. The paper concludes that the method presented in the paper can be used to determine the stress intensity factors for pipes with surface cracks of a large range of aspect ratios. This will enable more accurate prediction of the strength of pipes with various longitudinal semi-elliptical surface cracks. [Copyright &y& Elsevier]

A critical aspect in the design of tubular bridges is the fatigue performance of the structural joints. The estimation of a fatigue crack life using the linear elastic fracture mechanics (LEFM) theory involves the calculation of stress intensity factors (SIF) at a number of discrete crack depths. The most direct way is to carry out modeling by either the finite-element method (FEM) or the boundary-element method (BEM). For tubular joints commonly found in tubular bridges and off-shore structures, due to the complicated geometry resulting from the tube intersections and welding, the construction of the numerical model often becomes a complex process. This paper presents two different model construction techniques that have been developed independently at the Swiss Federal Institute of Technology (EPFL) and the Nanyang Technological University (NTU), Singapore, that are based in the BEM and the FEM, respectively. The SIF values obtained by these two methods are compared. It is found that as long as consistent geometric models are employed, compatible SIF values can be obtained by both approaches. The best and the most consistent values are obtained for the deepest point along the crack front and should be used for fatigue-life computations. [ABSTRACT FROM AUTHOR]

The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasi-brittle materials, such as concrete. The work is limited to two-dimensions, and therefore, the fracture modes of interest are mode I (pure tension) and mode II (pure shear). The constitutive model has been implemented in the context of the finite element method using interface elements. The fracture is simulated through a discrete crack represented by the interface with a cohesive crack stress-separation relation derived from the model, which is based on a fracture criterion, together with a flow rule and a softening law. The model is used for simulating results from an experimental study on beams with centric and eccentric notches of high and normal strength concretes, and explaining other test results available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports experimental results of the debonding propagation of bundled-fibers specimens subjected to a tensile stress wave. In addition, the paper also presents a dynamic debonding model for the problem on the basis of the cohesive zone model, and verifies the model by comparing the predicted debonding to the experimental data. The established numerical model is used to study the propagation mode of the debonding, and the result suggests that in this particular specimen design and loading condition, the debonding initiated in a mixed mode condition. However, the mode II quickly increased and dominated the mode I during an early debonding propagation up to certain extend where the mode mixity became constant. [Copyright &y& Elsevier]

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]

Intermediate crack-induced debonding (IC debonding) is a common failure mode of RC beams strengthened with externally bonded fiber-reinforced polymer (FRP) reinforcement. Although extensive research has been carried out on IC debonding, much work is still needed to develop a better understanding of the failure mode and a more reliable strength model. This paper presents an advanced finite-element (FE) model on the basis of the smeared-crack approach for predicting IC debonding failure. Existing FE models of the same type are generally deficient in capturing localized cracks (both their pattern and widths). This deficiency is overcome in the proposed FE model through the accurate modeling of interfaces between the concrete and both the internal steel and the external FRP reinforcements. The capability and accuracy of the proposed model are demonstrated through comparisons of its predictions with selected test results. The importance of accurate modeling of localized cracking is also explained using numerical results obtained from the FE model. [ABSTRACT FROM AUTHOR]

Abstract: Before thermal cycling or thermal exposure, tensile failure of atmospheric plasma spraying (APS) thermal barrier coatings (TBCs) usually occurs by spallation of the ceramic coating at or near the bond coating, due to the accumulation of microcracks damage. In the current paper, finite element geometric models based on the real microstructural image of TBCs are generated, and the microcracks growth induced by the uniaxial tensile loading is simulated by employing LS-DYNA code with a failure criterion determined by maximum tensile stress of yttria partially stabilized zirconia (YSZ). Additionally, the modified Brazilian disc specimens with a central hole are used to obtain the intrinsic static failure criterion of non-defective YSZ. By means of a statistical method in conjunction with finite element method (FEM) results, the tensile bond strength of APS TBCs is calculated as 40MPa in this paper. Meanwhile, damage accumulation and microcrack growth can be observed vividly by simulation processing. The numerical simulation result agrees well with the corresponding experimental result. It is shown that the methodology developed in this paper is very efficient in understanding damage evolution in TBCs. [Copyright &y& Elsevier]

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]

The concept of a stress singularity is a cornerstone of modern fracture mechanics. A new mode of stress singularity, the out-of-plane singular mode or K O mode, was recently identified for V-shaped notches subjected to in-plane loading. This new mode is coupled with the shear mode and related to Poisson’s effect. The previous studies based on the first order plate theory focused on the derivation of a characteristic equation describing the strength of this singularity and provide no information regarding the intensity, extent and relevance of this mode to practical problems. This paper aims to fill this gap. The approach utilises the 3D finite element method and a standard regression technique for characterisation of the notch singular modes. A comprehensive study of the influence of Poisson’s ratio, plate thickness and notch opening angle on the value of the notch stress intensity factor associated with this mode is conducted for infinite plates. Additionally, to demonstrate the relevance of this new singular mode to practical problems an investigation of the out-of-plane mode and associated three-dimensional effects are presented for the case of a welded lap joint. Main areas of further research are also identified. [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]

The effectiveness of FRP rehabilitation of deteriorating and under-strength reinforced concrete beams depends not only on the properties of the FRP material, but also on the characteristics of other materials in the system, characteristics of the bond, and the relative nature of properties of materials at the interfaces. Response is also affected by the cracked condition of the beam prior to the external bonding of the FRP. This paper reports on a fundamental investigation into the effect of various design parameters using a finite element analysis approach, which not only provides characteristics of response but also enables identification of damage mechanisms and their progression to failure. It is shown that the highest level of strengthening is not always due to use of maxima of the parameters, but rather on the interaction between them. Interface bond strength and fracture energy are shown to have a significant effect on load capacity, ductility and transition of failure modes from debonding within concrete, to FRP rupture, and to debonding within the adhesive itself. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new virtual crack closure-integral method (VCCM) for quadratic tetrahedral finite element to compute the energy release rates/stress intensity factors. The formulations, numerical implementations and some numerical results of proposed VCCM are presented in this paper. Proposed VCCM enables us to adopt the tetrahedral finite element in 3D crack problems and us to use automatic mesh generation programs. Therefore process time to perform 3D crack analysis drastically reduces compared with the case of hexahedral elements. [Copyright &y& Elsevier]

This paper presents an analysis of interacting cracks using a generalized finite element method (GFEM) enriched with so-called global-local functions. In this approach, solutions of local boundary value problems computed in a global-local analysis are used to enrich the global approximation space through the partition of unity framework used in the GFEM. This approach is related to the global-local procedure in the FEM, which is broadly used in industry to analyze fracture mechanics problems in complex three- dimensional geometries. In this paper we compare the effectiveness of the global-local FEM with the GFEM with global-local enrichment functions. Numerical experiments demonstrate that the latter is much more robust than the former. In particular, the GFEM is less sensitive to the quality of boundary conditions applied to local problems than the global-local FEM. Stress intensity factors, computed with the conventional global-local approach showed errors of up to one order of magnitude larger than in the case of the GFEM. The numerical experiments also demonstrate that the GFEM can account for interactions among cracks with different scale sizes, even when not all cracks are modeled in the global domain. [ABSTRACT FROM AUTHOR]

The paper presents the modeling and simulation of crack growth in three points bend specimen realized in elastic-plastic materials. After the exposition of the theoretical aspects, an application is presented, solved in two ways, which shows the feasibility of the method. For solving the problem the finite element analysis was used. [ABSTRACT FROM AUTHOR]

Over the past years, with increasing traffic volumes and higher wheel loads, fatigue damage in steel parts of typical orthotropic steel bridge decks has been experienced on heavily trafficked routes. A demand exists to find a durable system to increase the fatigue safety of orthotropic steel bridge decks. A solution might be to enhance the stiffness of the traditional orthotropic bridge deck by using a cement-based overlay. In this paper, an orthotropic steel bridge deck stiffened with a cement-based overlay is analyzed. The analysis is based on nonlinear fracture mechanics, and utilizes the finite-element method. The stiffness of the steel deck reinforced with an overlay depends highly on the composite action. The composite action is closely related to cracking of the overlay and interfacial cracking between the overlay and underlying steel plate (debonding). As an example, a real size structure, the Faro\ bridges located in Denmark, are analyzed. The steel box girders of the Faro\ bridges spans 80 m, and have a depth of 3.5 m, and a width of 19.5 m. The focus of the present study is the top part of the steel box girders, which is constructed as an orthotropic deck plate. Numerous factors can influence the cracking behavior of the cement-based overlay system. Both mechanical and environmental loading have to be considered, and effects such as shrinkage, temperature gradients, and traffic loading are taken into account. The performance of four overlay materials are investigated in terms of crack widths. Furthermore, the analysis shows that debonding is initiated for a certain crack width in the overlay. The load level where cracking and debonding is initiated depends on the stress-crack opening relationship of the material. [ABSTRACT FROM AUTHOR]

This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results. [ABSTRACT FROM AUTHOR]

Abstract: The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and asymptotic partition of unity enrichment (PUM) of the standard finite element approximation spaces. Level set methods have been recently coupled with X-FEM to help track the crack geometry as it grows. However, little attention has been devoted to employing the X-FEM in real-world cases. This paper describes how X-FEM coupled with level set methods can be used to solve complex three-dimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/I-DEAS®). The paper briefly describes how object-oriented programming shows its advantages to efficiently implement the proposed methodology. Due to enrichment, the latter method allows for multiple crack growth scenarios to be analyzed with a minimal amount of remeshing. Additionally, the whole component contributes to the stiffness during the whole crack growth simulation. The use of level set methods permits the seamless merging of cracks with boundaries. To show the flexibility of the method, the latter is applied to damage tolerance analysis of a complex aircraft component. [Copyright &y& Elsevier]

A damage detection and assessment method has been developed in this paper using the concepts of inverse method and fracture mechanics. The objectives are to detect, locate, and quantify any damage that has occurred within a beam during its service using displacement measurements taken at arbitrary points along it. Grobner bases are used to check the compatibility among the measured displacement data. Any incompatibility among those measured values indicates some damage. The curvatures are computed using the finite-difference technique. These curvatures show abrupt change at damaged locations. The damage is quantified in terms of crack length, and an analytical model is developed using a cracked-beam finite element. [ABSTRACT FROM AUTHOR]

Abstract: Goal-oriented a posteriori error estimators are presented in this paper for the error obtained while approximately evaluating the J-integral in linear elastic fracture mechanics using the finite element method. The J-integral provides a criterion for crack propagation of a pre-existing crack. Therefore, its reliable and accurate evaluation is of considerable importance in engineering applications to prevent failure of structures. This can be achieved by goal-oriented adaptive finite element methods based on the well-established strategy of solving an auxiliary dual problem in order to control the error of a (non)linear functional, here the J-integral. In this paper, two principally different goal-oriented adaptive strategies are presented. The first strategy rests upon equilibrated residual error estimators based on local Neumann problems, whereas the second one makes use of averaging techniques. The paper is concluded by a numerical example that illustrates our theoretical results. [Copyright &y& Elsevier]

Abstract: This paper explores the use of the theory of critical distances (TCD) in the prediction of high-cycle fatigue behaviour in engineering components. Theories of this type have been in use for over 50 years in various forms, and recently have been brought up to date by linking them with linear elastic fracture mechanics (LEFM). The TCD represents a major extension of LEFM, allowing it to be used for short cracks as well as for stress concentrations of arbitrary geometry, using the results of finite element analysis (FEA) or other computer-based methods. A number of different realisations of the TCD exist: several of these express the critical distance as a function of material fatigue limit (Δσ 0) and crack propagation threshold (ΔK th). This paper illustrates the application of the TCD to a case study on the failure analysis of a large maritime vehicle component in three different designs. Unusually, the increasing of a fillet radius did not prevent fatigue failures from occurring: the TCD was able to explain this, due to its ability to accurately predict notch sensitivity effects. Further applications of the TCD, to problems not only in fatigue but also in brittle fracture in various materials, are also discussed. [Copyright &y& Elsevier]