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Highlights • CRB test was numerically simulated including asymmetry of loading. • CRB specimens made directly from polyethylene pipes were examined regarding the residual stress. • Influence of crack asymmetry on results of CRB test was evaluated. • Small effect of the residual stresses on CRB test was demonstrated. Abstract The Cracked Round Bar (abbreviated as CRB in the following) test is used as standardized accelerated testing method for simple ranking of polyethylene pipes based on measuring number of cycles to failure of the cyclically loaded CRB specimen. It can also be used for the slow crack growth rate evaluation of the tested material. This paper deals with the issue of asymmetrically growing cracks in CRB specimens and possible influence of the asymmetry on the results of CRB tests, both the number of cycles to failure and the crack growth rates. It is assumed that the asymmetry is caused by presence of residual stress in the CRB specimens. In the first part of the paper, residual stress in two polyethylene pipes (produced using different extrusion speed) is investigated. Then CRB specimens made from these pipes are also examined regarding the residual stress and the results are compared. The found residual stress distributions are used as input for the following finite element method (FEM) simulation of crack growth in the CRB specimens. The FEM model results are then evaluated and fatigue crack growth rates for asymmetrically growing cracks are calculated. They are compared to the results for symmetrically growing cracks and influence on the results and its significance is discussed. In the end, CRB specimen lifetime prediction is carried out and the influence of the asymmetry on the obtained number of cycles to the failure is also addressed. [ABSTRACT FROM AUTHOR]

Continuum models of fracture should be equipped with a localization limiter to prevent pathological discretization sensitivity of finite element simulations. Moreover, stiffness recovery, called also crack closing effect, should be reproduced in the modelling of quasi-brittle materials when reversed loading is applied. In this paper the efficiency of two different established damage-plasticity models for concrete is assessed from the viewpoint of the two above-mentioned aspects. The first description is the so-called concrete damaged plasticity model, available in the ABAQUS package. In this model the plasticity theory is not only augmented with stiffness degradation and recovery, but also with the crack band approach and viscoplastic regularization. The gradient-enhanced damage description, which is the second one considered, can also be coupled to plasticity. In this model additional averaging equation prevents the pathological discretization sensitivity of fracture simulations. Two fields, displacements and averaged strain measure, are interpolated and suitable finite elements are programmed by the authors in the FEAP package. Basic concepts of the numerical analysis of the crack closing phenomenon are reviewed. Both models are capable of avoiding mesh-sensitivity, but it is achieved in a different manner and it is shown in the paper that the users of ABAQUS should employ the crack band options with particular care. Representative examples in the context of the examined issues are demonstrated: uniaxial tension of a bar and a cantilever beam. The results obtained using both the models are compared and the effects of regularization and crack closing are illustrated. [ABSTRACT FROM AUTHOR]

This paper addresses the numerical simulation of plasticity and ductile fracture of large scale structures (e.g. ships, railcars, automobiles) fabricated with welds that exhibit appreciably lower strength than the plate material, often referred to as weld undermatching. It has been observed, both numerically and experimentally, that for such structures the weld undermatching often leads to plasticity and fracture being limited to the weld and heat affected zone (HAZ). While the large size of the structures of interest precludes the use of a refined three-dimensional element mesh capable of capturing the details of the weld/HAZ behavior, cohesive zones are ideal for capturing the overall effects of undermatched weld plasticity and fracture on a structural scale. This paper focuses on establishing a systematic calibration process for determining the cohesive zone constitutive behavior and examining the validity of this approach in the context of mode I tearing of a large welded two-layer AA6061-T6 sandwich panel. First, test data from a welded coupon is used to calibrate the cohesive law. Tearing fracture of this panel is examined using the established cohesive law to represent weld/HAZ along with elastic-plastic shell elements, with in-plane dimensions much greater than the layer thickness, to represent the parent metal. It was verified that, for this structure, plasticity was indeed confined to the welds and heat affected zones, and that the behavior of the panel was captured with reasonable fidelity. [ABSTRACT FROM AUTHOR]

In Part I of this paper, quasi-static fracture toughness tests were reported which were carried out on two carbon fiber reinforced polymer materials. One laminate was unidirectional and the second was composed of plies fabricated from a twill fabric. In Part II, which is presented here, micro-computerized tomography was performed providing a relationship between the observed experimental behavior and the micromechanical structure of the materials. This was carried out for the double cantilever beam (DCB), mixed mode bending (MMB) and end-notched flexure (ENF) specimens. Load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to obtain better insight into the failure mechanisms observed for DCB and ENF specimens. [Display omitted] • Quasi-static fracture toughness testing was reported on in Part I of this paper. • Micro-computerized tomography was carried out on many of the specimens. • Damage mechanisms on the micro-scale were assessed. • Numerical simulations were carried out by means of a cohesive zone model. [ABSTRACT FROM AUTHOR]

• A modified GTN model considering the effects of anisotropy and shearing on micropore evolution is introduced. • The constitutive model is compiled into a VUMAT subroutine for numerical simulation to accurately predict the plastic deformation of aluminum alloy sheet. • The parameters in constitutive model are calibrated by inverse FE method and the validity of the modified GTN model is verified through the uniaxial tensile experiment. • A FE model of the mould-sheet coupling system is further developed to improve the forming performance. Traditional GTN meso-damage model, neglecting the effect of anisotropy or shearing on the evolution of microvoid, leads to the lower predictive capabilities of forming defects for aluminum alloy sheets. In this paper, a modified constitutive model of aluminum alloy sheet considering the effect of both anisotropy and shearing is proposed, and the corresponding model parameters are calibrated by inverse finite element method and uniaxial tensile test of the smooth strip sheet without hole. Then, the constitutive equation of the modified model is compiled into a VUMAT subroutine using backward Euler integration algorithm and FORTRAN language to perform subsequent numerical simulation in ABAQUS/Explicit, the validity of the proposed shear-corrected GTN model is also verified through the uniaxial tensile experiment of the strip sheet with a hole in the middle. Finally, finite element (FE) model of the mould-sheet coupling system is developed based on the modified GTN model, and the influence of punching speed, blank holder force, friction coefficient and dwell time on the forming performance of AA5052 aluminum alloy sheet is investigated. The results show that ductile fracture of aluminum alloy sheet is most prone to exist on the upper fillet of part. [ABSTRACT FROM AUTHOR]

[Display omitted] • Lattice beam model extended to self-healing in cementitious materials. • A new rate dependent discrete damage-healing model is presented. • Healing response derived from healing-agent chemo-physical properties. • Detailed information is provided on the size and disposition of cracking and healing zones throughout a transient analysis. • The model provides valuable information required for designing a self-healing system. • Model validated using experiments with healing under fixed and moving crack conditions. • Nature and extent of damage-healing zones determined numerically. This paper describes the development of a discrete lattice model for simulating structures formed from self-healing cementitious materials. In particular, a new approach is presented for simulating time dependent mechanical healing in lattice elements. The proposed formulation is designed to simulate the transient damage and healing behaviour of structures under a range of loading conditions. In addition, multiple and overlapping damage and healing events are considered. An illustrative example demonstrates the effects of varying the healing agent curing parameters on the computed mechanical response. The model is successfully validated using published experimental data from two series of tests on structural elements with an embedded autonomic self-healing system. The meso -scale model gives detailed information on the size and disposition of cracking and healing zones throughout an analysis time history. The model also provides an accurate means of determining the volume of healing agent required to achieve healing for all locations within a structural element. The importance of the information provided by the model for the design of self-healing cementitious material elements is highlighted. [ABSTRACT FROM AUTHOR]

• Contains practice, modeling and computation. • Dynamics is illuminated by supercomputer results of videos. • Event reconstruction and forensic assessments are made for Daallo Airlines Flight 159 bombing case. The bombing of airliners has been a tactic used by terrorists during the past 40 years. Its prevention is a major priority by homeland security officials on a worldwide basis. In efforts to aid in the investigation of such bombings, this paper provides the results of the development of mathematical modeling and computer simulation for the study of aircraft bombings and associated forensics. As an assist in the forensic study, a number of photographs are provided to depict the normally observed physical characteristics of explosives damage upon aircraft and related materials. Our study illuminates and evaluates how these characteristics can be captured by computational mechanics. Finally, we use the laptop bombing of Daallo Airlines Flight 159 as a case study to demonstrate that event reconstruction can be accomplished for the purpose of forensic investigations. Most of our supercomputer results are visualized by video animations in order to show the dynamic effects and phenomena of explosives and the associated event reconstruction. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a simple, but effective methodology to simulate opening mode fracture in high performance fibre reinforced concrete is presented. The main contribution of the paper is a technique to extrapolate the load displacement curves of three point bending experiments on fibre reinforced concrete. The extrapolation allows the full work of fracture to be determined, from which the fracture energy may be obtained. The fracture energy is used in the definition of a cohesive softening function with crack tip singularity. The softening relation is implemented in an embedded discontinuity method, which is employed for the numerical simulation of three point bending experiments. The experimental work includes a size effect study on three point bending specimens. The numerical simulation provides a satisfactory prediction of the flexural behaviour and the size effect observed in the experiments. [Copyright &y& Elsevier]

Highlights • Displacement discontinuity method is used for fracture growth numerical simulation. • Effect of friction on fracture toughness is included in fracture growth criterion. • Implementation of 3D fracture growth trajectories and intersections is outlined. • Some techniques for smoothing fracture front are presented. Abstract This paper presents some detailed implementation schemes of geometrical evolution of three dimensional crack growth for most scenarios. These include growth of isolated cracks, intersections of crack growth with body surface or another crack at interior or at front edge. The schemes have been implemented in a crack growth simulator FRACOD3D, which is based on displacement discontinuity method (DDM) for stress analysis and implements the geometrical evolution of crack growth by explicitly adding new elements along the crack front. For growth of isolated cracks, there is no need to re-mesh the old part of cracks and thus no need to recalculate the related influence coefficients in the new growth steps. For intersection of growth of a crack with body surface or interior of another crack, minimum re-mesh on the body surface or on the other crack is used by just subdividing three elements. Simulations with early versions of the explicit schemes showed that implementation of the geometrical evolution is very challenging in that the growth could lead to very unsmooth crack and affects the further numerical simulations. Some examples show that the new schemes give smooth growth. It is noted that these schemes can also be employed with other stress analysis methods which represents crack growth by adding new elements along the crack front. [ABSTRACT FROM AUTHOR]

Highlights • The dynamic fracture parameters of rocks under high temperature are measured. • A numerical procedure of rock dynamic fracture test is developed based on the laboratory tests. • Particle flow code can reproduce the mechanical behaviors of the high-temperature rock. • The simulated dynamic load test is critical for the acquisition of the critical time. • The loading rate effect and temperature dependence of dynamic fracture toughness are discussed. Abstract With the limitations of measuring techniques, limited investigation on dynamic fracture testing of rocks at high temperature is reported. In this paper, an effective measuring method of the dynamic mode I fracture toughness of high-temperature rocks, combined with laboratory tests with the Discrete Element Method (DEM), is proposed. Based on the laboratory experiments conducted, including uniaxial compressive tests under different temperature conditions, the Brazilian test and split Hopkinson pressure bar (SHPB) test, the micro-parameters of the numerical model are calibrated and the validity of the numerical model of specimens and the simulated dynamic load tests are examined. The results show that the DEM can truly reflect the mechanical properties of rocks at high temperatures, and the simulation test can capture the dynamic fracture parameters of rocks at elevated temperatures. The test data indicates that the fracture initiation toughness of specimens increases linearly with the loading rate, while the fracture initiation time detected by the measurement circle near the notch tip decreases. When the loading rate is higher than 130 GPa m1/2/s, the fracture initiation toughness has a significantly negative relationship with the temperature within the temperature range of 25–400 °C. [ABSTRACT FROM AUTHOR]

Highlights • Numerical size effect study on notched samples were carried out using a linear cohesive crack law. • For sharp notches, the size effect curve has a asymptote corresponding to Bažant's SEL. • For blunt notches, the size effect curve has a large size asymptote to the elastic limit. • An analytical size effect curve is presented for both sharp and blunt notches. Abstract This paper deals with the study of size effect on structural strength for quasi-brittle materials under mode I fracture conditions. By using a linear cohesive crack model, accurate numerical simulations were performed to compute the size effect curves for two test configurations – namely, the three-point bending test with span-to-depth ratio equal to 3 and the center crack panel test – featuring sharp notches and blunt notches whose width is also scaled with the specimen dimension. The analysis of the results shows that, as the specimen size tends to infinity, the asymptotic behavior depends on the type of notch. For sharp notches the size effect curve tends asymptotically to Bažant's Size Effect Law. On the contrary, for blunt notches the size effect curve tends to a horizontal asymptote corresponding to the elastic limit. The elastic limit can be calculated by the tensile strength reduced by the stress concentration factor at the tip of the blunt notch and it depends on the geometry of the specimen. Furthermore, the numerical results were utilized to derive the expression of a Generalized Cohesive Size Effect Curve (GCSEC) which agrees well with Bažant's Universal Size Effect Law (USEL) and with some experimental data gathered from the literature. [ABSTRACT FROM AUTHOR]

Highlights • Identifying open questions in fatigue fracture of fibre-reinforced polymer composites. • Discussing microscopic damage mechanisms and their effects on the macroscopic scale. • Discussing the physics of driving force and of fatigue damage resistance. • Identifying topics for further research in fatigue fracture of polymer composites. Abstract Where for metallic materials fatigue fracture testing has contributed significantly to understanding macroscopic and microscopic fatigue failure, the understanding of fatigue fracture in fibre reinforced polymers (FRP) still seems limited. It appears that the research on fatigue in FRPs raises more questions, rather than providing a framework for understanding the underlying mechanisms. Open questions include for example the correct formulation of the driving force and fatigue damage resistance, how to account for mixed mode loading and fibre bridging? But also the question to what extent averaging and homogenising over time- and length scales hinders the understanding in relation to the microscopic mechanisms? To contribute to the development of understanding, this paper discusses several of these open questions. The selected questions were discussed at a recent workshop on 'Physics of fatigue damage growth' at TU Delft with participants from several laboratories covering expertise on fatigue fracture testing of both metals and polymer composites. The discussion focuses on potential experimental and simulation approaches that may lead to a better understanding of the physics of the fatigue fracture process. [ABSTRACT FROM AUTHOR]

Highlights • The process-structure-property relationship is established by linking simulations. • The microstructure inhomogeneity of alloys is considered in the FEM simulations. • FEM simulations on various deformation conditions are conducted systematically. • Simulations capture the microstructural evolution and mechanical properties. Abstract To study process-structure-property relationships, the multiparticle diffusion simulation and the finite element method simulation are linked together in this paper. The mechanical properties of alloys during phase coarsening are analyzed with this linkage. The correlation between microstructural evolutions and the corresponding variations of mechanical properties during phase coarsening in alloys is investigated. We study how the resultant hardness, strength, ductility, and fracture toughness of the alloy depend on the microstructural evolution driven by phase coarsening in alloys. Related analysis demonstrates that considerable degradations occur for the mechanical properties of alloys during phase coarsening, which are sensitive to microstructures in the alloys. Our work shows that the linkage of multiparticle diffusion simulation to finite element method simulation provides a practical approach to investigate process-structure-property relationships. Our simulation results can predict the microstructural evolution, the main deformation and failure characteristics of alloys. [ABSTRACT FROM AUTHOR]

Abstract: Railway organizations are facing continuous increase in train frequency, running speed and axle load with ever limited financial resources. This is why methods broadening knowledge of external loads and internal rail stresses are of higher importance to address rail design or maintenance process. The following paper explains how the development and application of such methods has been conducted by a european partnership (called NOVUM) between railway organizations (SNCF, DB AG, RATP) and rail producer (CORUS) sharing their specific own competences, experience and material resources. Research institutes and universities (BAM, GKSS, INRETS, INSA, LMS) have been in charge of building sound numerical simulations or experimental tests and tools. Theoretical aspects of the method are described in independent paper “A global approach for modelling fatigue and fracture of rails”. A first task group of the program is dedicated to the determination of external forces coming from wheel/rail and from rail/support interactions. The second and third task groups are about material properties and internal stresses inside rail section. Laboratory and track validations are undertaken in the fourth task group. Two characteristic cases are then chosen to check the developed models. [Copyright &y& Elsevier]

This paper presents an improved local continuum damage model for quasi-brittle fracture analysis. A local damage model, as compared to its non-local damage counterpart, owns the advantages of simple implementation and low computational cost. However, it is in general suffered from the mesh-size dependency. In this work, this drawback is mitigated by incorporation of fracture energy and element characteristic length into the evaluation of damage parameter. For estimation of the equivalent strain, the concept of bi-energy norm, which allows the quantification of contribution from tension and compression parts of strain, is further enhanced by incorporation of the equivalent strain for cracking and crushing based on Mazars damage concept. The purpose of introducing this new incorporated bi-energy norm aims to improve the ability to simulate mixed-mode fracture behavior. The performance and accuracy of the developed local damage approach in modeling quasi-brittle fracture is illustrated through several numerical examples. The structural displacement–force curves and crack patterns are analyzed and compared with experimental data and reference numerical solutions derived from other numerical methods. In particular, as compared to the original bi-energy norm, numerical results indicate that our enhanced bi-energy norm based equivalent strain can predict better crack path of Nooru-Mohamed's test for double-edge notched concrete specimen. [Display omitted] • The bi-energy norm based equivalent strain is re-defined using the Mazars concept. • The ability of the developed local damage model in simulating mixed-mode fracture behavior is improved. • The mesh-size dependency in conventional local damage model is mitigated. • Only one parameter for calibration is needed in the developed approach. • The accuracy of the model is demonstrated by comparison with experimental results. [ABSTRACT FROM AUTHOR]

In this paper, a method to simulate ductile crack growth under very low-cycle fatigue loading condition is given and simulation results are compared with published test data of compact tension specimens and circumferential through-wall cracked pipes. The damage model in simulation is based on the multi-axial fracture strain energy. Two parameters in the damage model are determined from tensile and fracture toughness data under the monotonic loading condition. The determined damage model is then used to simulate ductile crack growth in compact tension specimens subjected to cyclic loading with large-amplitudes and in full-scale through-wall cracked pipes subjected to monotonic and cyclic loading with two different load ratios. Predicted results show a good agreement with experimental results. [ABSTRACT FROM AUTHOR]

The paper shows three-dimensional numerical results regarding concrete fracture at aggregate level in a notched concrete beam under bending using cohesive interface elements. Concrete heterogeneity was taken into account by considering a 3-phase material description: aggregate, cement matrix and interfacial transitional zones (ITZs). The real shape and location of aggregate particles in concrete were assumed in numerical analyses based on X-ray μCT scans. The 3D meso-scale finite element method (FEM) with cohesive elements embedded in the cement matrix and ITZs was used in simulations. The effect of different properties of ITZs and cement matrix was investigated in parametric studies. A satisfactory agreement in terms of the vertical force versus crack mouth opening displacement evolution and crack geometry was achieved between analyses and laboratory tests. [ABSTRACT FROM AUTHOR]

The designed fracture of laminated glass (LG) makes it useful for architectural, glazing, automotive safety, photovoltaic, ultraviolet ray protection, and decorative applications. The present review is divided into three sections: the first section includes a description and classification of the laminated plate (LP) theories that are used to explain fracture of LG plate, second section comprises explanation of fracture of LG samples during three-point bending, ring on ring and ball drop impact testing using linear elastic finite element (FE) model and the last section includes numerical simulations techniques used for explaining the impact fracture of LG. The outcome of the review highlights the requirement of quantitative work on crack propagation prediction during LG fracture and critical evaluation of the numerical algorithms available for modeling the glass-ply cracking and principal damage pattern in LG. This review paper is meant for the faster comprehensive understanding of this research area. [ABSTRACT FROM AUTHOR]

Zero thickness cohesive element approach for arbitrary crack propagation has a deficiency of introducing artificial compliance to the model, especially when cohesive elements are inserted into every element interfaces. For dynamic problems, the artificial compliance decreases the stress wave speed and makes the result less accurate. In this paper, the reason of the artificial compliance is examined, and the bilinear and exponential cohesive law are compared. The work shows that by choosing the right cohesive stiffness, element size and using bilinear cohesive law rather than exponential cohesive law, the artificial compliance issue can be limited to a negligible level without greatly increasing the computational time. Three numerical simulations are used to support the argument. The bilinear cohesive law also shows more robust behavior in terms of cyclic loading than exponential law, and a new cyclic loading formulation is proposed to help fix the discontinuity observed in exponential law. According to our finding, in order to limit the artificial compliance and computational time, large element size is recommended, however, in fracture problems, small element size around crack tip is essential to capture the cohesive zone behavior. To escape the dilemma, we modify the cohesive zone enlargement approach presented in the literature (Dugdale, 1960) and adopt it for arbitrary crack propagation. The modified methodology enlarges cohesive zone size by reducing the cohesive strength only around crack tips to allow more cohesive elements inside the cohesive zone. Two benchmark numerical simulations are carried out to verify the modified methodology. [ABSTRACT FROM AUTHOR]

In this paper, the gas tungsten-arc welding (GTAW) process of a thin cylinder made of Al6061-T6 alloy was simulated using 3-D finite element model in the ABAQUS code and the induced distribution of residual stress was obtained. Temperature dependent thermo-mechanical properties were considered for the aluminum alloy and for simulating the heat source of tungsten arc welding; Goldak's double ellipsoid model was employed. The numerical simulation method employed for the GTAW process of investigated aluminum material was validated experimentally using the hole drilling method as well. High residual stresses were found around the weld line and HAZ area which can increase the risk of crack initiation and propagation in this region of welded aluminum cylinder. Hence in the second part of this research, a longitudinal semi-elliptical crack was considered in the wall of aluminum cylinder subjected to combined internal pressure and torsional loads and its mixed mode I/II fracture parameters (i.e. K I , K II and T ) were determined numerically along the crack front and for different crack geometries. Finally the influence of obtained residual stress field on the computed fracture parameters was reanalyzed using the coupled residual stress/mechanical loading applied to the cylinder. The residual stress field had no effect on the mode II fracture component but the most influence of this factor was observed for mode I stress intensity factor ( K I ) and the deepest point of 3D elliptical crack. [ABSTRACT FROM AUTHOR]

In this paper, the constraint effect caused by a side-groove on creep crack growth behavior in P92 steel was studied using finite element analysis. Creep crack growth simulations were conducted on compact tension specimens for side-grooves with different depths and angles. The simulated outcome indicated that the creep crack growth rate increased as the depth and the angles of the side-grooves in the specimen increased. Next, the profile of the crack front for the different specimens was discussed. The distribution of the average stress triaxiality and the average equivalent stress on the crack front were studied to investigate the mechanical mechanism describing the constraint effect on creep crack growth behavior. Finally, the creep crack growth rate determined from numerical simulation results was determined to be consistent with existing experimental data. [ABSTRACT FROM AUTHOR]

The numerical simulation of two-dimensional fracture processes of quasi-brittle materials by means of the Embedded Finite Element Method is dealt with. Attention is paid to the coupling with the global crack-tracking strategy, which has been proposed in the literature in the form of a heat conduction-like problem. It turns out that the stiffness-like matrix associated with this formulation is singular and a numerical perturbation has to be introduced in order to overcome the ill-posedness of the problem. The dependence of the solution on this parameter may represent a limitation for the global tracking approach. Furthermore, it is found that if the root of each discontinuity is not updated during an incremental analysis, a loss of continuity of the crack path may appear when principal stress directions rotate. This paper aims to provide a solution to the aforementioned issues. An alternative mathematical formulation of the problem is thus given in terms of Navier-Stokes equations, linking the diffusive contribution to a characteristic mesh length. Additionally, a modified crack-tracking algorithm, considering the evolution of the root for the identification of the crack path, is proposed. The numerical assessment of the proposed tracking strategy is reported by means of benchmark tests at the structural level. [ABSTRACT FROM AUTHOR]

Crack propagation is not only influenced by the loading situation but also by a material gradation within the structure. Therefore, it has to be examined how the crack propagation behavior changes when a crack grows through regions which are characterized by different fracture mechanical material properties. Within the scope of this paper, especially the influence of a fracture mechanical material gradation on the beginning of stable crack propagation, the crack velocity, the crack propagation direction as well as on the occurrence of unstable crack growth for statically and cyclically loaded components is discussed. In this context, a developed concept for the prediction of crack propagation in fracture mechanical graded structures, experimental investigations as well as numerical simulations of crack growth are presented. The experimental considerations clarify the influence of the material gradation and confirm the predictions of the new concept. The numerical simulations of crack growth indicate the influence of the material gradation especially on the lifetime of graded components. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing of rocks has various engineering applications. However, there has been limited research into crack propagation prediction by three dimensional analytical techniques. This paper discusses such a technique for predicting the propagation surface of a pressurized circular crack subjected to various loading conditions. The propagation surfaces predicted from the proposed crack front propagation algorithm align well with published results. The suggested method consumes only a fraction of the time needed for a numerical simulation, and therefore it could be useful in assisting the design of hydraulic fracturing operations. [ABSTRACT FROM AUTHOR]

A new rock-like resin has been developed after extensive formula research. This resin is completely transparent and low temperature brittle. Its tension-compression ratio can reach 1/6.6 in the −10 to −15 °C temperature range. It can simulate many kinds of engineering rocks. Specimens are made with a single internal crack. The progressive failure processes of specimens under uniaxial and biaxial compressions are investigated. The uniaxial failure process of specimens is divided into four stages. Some forms of secondary cracks, like anti-wing cracks in biaxial test, have never been reported in previous studies. 3-D numerical simulation is carried out using FLAC3D. A new elastic-brittle constitutive model is developed in the simulation. Superfine element division is also required. The uniaxial and biaxial numerical results of the new method possess an excellent consistency with experiment results in this paper. [ABSTRACT FROM AUTHOR]

Understanding hydraulic fracture propagation behaviours is vital for optimizing fracturing design in oil and gas production. It has been observed that the stress and pore pressure distribution are much more complex during fracturing treatment as a result of long-term fluid injection and production in the reservoir. When rock is subjected to internal hydraulic pressure and external mechanical loading, the closing, opening, or other interactions of pre-existing weaknesses or induced new fractures will be altered. In this paper, a number of hydraulic simulation scenarios are performed to investigate the effect of pore pressure distribution on fracture initiation and propagation using the unified pipe-interface element method (UP-IEM). The proposed method for predicting the hydraulic fracture path in the permeable porous medium with non-uniform pore pressure field is validated with experimental results. Considering the arrangement of well patterns and natural fractures in the rock, the problems of hydraulic fracture propagation behaviours with wellbore interaction and pore pressure induced natural fracture activation are simulated. The influence of pore pressure saturation and the injection sequence of wellbores on hydraulic fracturing are researched. A sensitivity analysis is carried out to investigate the parameter effects on pre-existing fracture tortuosity, opening width and breakdown pressure under pore pressure. These numerical examples provide guidance to engineers to estimate the probability of danger or possibilities to improve the injection and production of wells. • A novel numerical method is proposed to simulate hydraulic fracturing in permeable porous medium. • Hydraulic fracturing with wellbore interaction under the influence of pore pressure saturation and level are investigated. • The behaviours of pore pressure induced natural fracture activation is simulated and analysed. [ABSTRACT FROM AUTHOR]

An example of dynamic crack propagation in a 2D plate is used to clearly describe a problem affecting regular peridynamic grids: the crack-path dependence on the grid orientation. The problem, potentially very damaging for a computational method devised to simulate in particular crack propagation conditions, is investigated and better understood. In order to solve it the paper proposes a strategy which involves an increase of the computational cost when applied to the whole discretized domain. The use of adaptive refinement techniques allows to apply such a strategy only where crack propagation is taking place and, in this way, drastically increases the computational efficiency. [ABSTRACT FROM AUTHOR]

The Split Hopkinson Pressure Bar (SHPB) technique is a widely used method for measuring mechanical properties of materials subjected to high-strain-rate loads, while it is difficult to simulate the whole testing process including high-rate deformation, local damage and failure of materials by the common numerical methods. In this paper, an improved numerical approach based on the non-local peridynamic (PD) theory is employed to study the elastic wave dispersion and propagation and the impact failure of concrete Brazilian discs in SHPB test. Meanwhile, an improved PMB (Prototype Microelastic Brittle) model and an implementation method of the contact-impact process are introduced. In PD, the nonlocal long-range force controls the numerical dispersion of wave through different material point sizes and horizon sizes. The numerical dispersion can result in a slight distortion of the wave speed and crack propagation speed, which is not conductive to failure analysis of solids. The improved PMB model can effectively lessen the numerical dispersion compared with the original PMB model. Furthermore, the PD simulation of concrete Brazilian disc SHPB test can reproduce damage accumulation and progressive failure of a specimen, and produce typical final failure pattern. The PD simulation method for SHPB test can be used to analyze the dynamic response of solids suffering impact load. [ABSTRACT FROM AUTHOR]

This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive–frictional damage on quasi-brittle materials. The mechanical behaviour is described by an isotropic damage model with a Mohr–Coulomb failure surface. The correct crack propagation among the two alternative fracture planes proposed by the Mohr–Coulomb theory is selected with the use of an energy criterion based on the total elastic strain energy. The simulation of three benchmark problems of mixed-mode fracture in concrete demonstrates that the proposed methodology can reproduce the material’s frictional characteristics, showing robustness, as well as mesh-size and mesh-bias independence. [ABSTRACT FROM AUTHOR]

In this paper we present an experimental and numerical approaches aimed to assess the hygrothermal aging effect on the mechanical properties and ductile tearing of polyamide 6 (PA6). Conditioning was conducted at different temperatures (24 ± 3, 70 and 90 °C) and diffusion coefficients were estimated. The behavior of PA6 is discussed before and after aging. Digital Image Correlation (DIC) method was used to precise the displacement field at different steps of loading. A numerical model based on the local approach to fracture mechanics was tested to predict ductile tearing of PA6. Excellent agreement was proved with experimental results in terms of the J – Δ a , load–displacement and CTOD–Δ a curves. [ABSTRACT FROM AUTHOR]

The paper deals with new experiments and corresponding numerical simulations to study the effect of stress state on damage and fracture behavior of ductile metals. Different branches of ductile damage criteria are considered corresponding to various mechanisms depending on stress intensity, stress triaxiality and the Lode parameter. New experiments with two-dimensionally loaded specimens have been developed covering a wide range of stress triaxialities and Lode parameters in the tension, shear and compression domains. Scanning electron microscope (SEM) analyses of the fracture surfaces show various failure modes corresponding to different stress states detected by numerical simulations of the experiments. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the fish-eye fatigue crack growth after crack nucleation for very high cycle fatigue. The crack growth rate is modeled by the Paris–Hertzberg law. An iterative procedure based on three dimensional finite element analyses is developed to conduct crack growth simulations. The virtual crack closure technique is used to calculate the stress intensity factor for each step of the crack growth process. These stress intensity factors are then used to estimate the fatigue crack growth by integrating the fatigue crack law between the initial and final crack lengths. Our objectives are twofold: first is to study the variation of the fish-eye shape when the crack tip approaches the edge of structure, second is to study the evolution of the fatigue crack growth life when analytical solutions are not available or not sufficiently reliable. [ABSTRACT FROM AUTHOR]

Computation cost is a key issue for finite element methods to simulate hydraulic fracturing. In this paper a coupled finite element method combined with a condensation technique is proposed to address this issue. Removing the node displacements that have no contribution to fracture widths from the coupled equations, the condensation technique reduces the size of the coupled equations in the proposed method. The numerical method with the condensation technique is verified. Simulations show that the condensation technique can reduce the computation cost effectively, in particular when the fracture propagation regime is viscosity-dominated or the simulation is on the early stage. The effects of the condensation technique on the simulation accuracy, stability, and convergence of the numerical method are discussed. The condensation technique is applicable to other finite element methods that are based on linear elastic fracture mechanics. [ABSTRACT FROM AUTHOR]

• Calibrating the K&C model and HJC model in LS-DYNA software for UHPC material. • Establishing the impact analysis methods of UHPC using SHPB technology under the typical dynamic damage models. • Evaluating the applicability of the calibrated K&C and HJC models used for UHPC based on SHPB technology. This paper focuses on evaluating the feasibility of typical dynamic damage models used for ultra-high performance concrete (UHPC) based on split Hopkinson pressure bar (SHPB) technology. The material characteristics of the UHPC are assigned by modifying the critical parameters of the Holmquist Johnson Cook (HJC) and the Karagozian and Case concrete (K&C) models in LS-DYNA software. The dynamic analysis methods of the UHPC using SHPB technique under the two typical dynamic damage models are established. The validations of the calibrated K&C and HJC models used in UHPC are evaluated by a comparison with the measured waveform. The results indicate that (1) the recommended strength parameter A in the HJC model is 1.54 for obtaining realistic dynamic damage behavior of UHPC at a compressive strength of 200 MPa; (2) based on the appropriate calibrated parameter values, the numerical simulation using the K&C or HJC models can predict the measured waveform of UHPC on the SHPB test with an acceptable accuracy; and (3) compared to the K&C model, the fluctuation of the calculated waveform based on the HJC model is more apparent, and the calculated residual transmitted waveform in the descending stage demonstrates a larger deviation from the measured waveform. [ABSTRACT FROM AUTHOR]

• 1. There is a competitive relationship between initiation and propagation of perforated cracks. Perforated cracks will eventually form a crack propagation mode dominated by several main cracks and supplemented by micro cracks. • 2. An obvious spatial form associated with asymmetric main cracks and micro cracks derived around them. Parallel perforation crack initiation presents four modes of competitive initiation. • 3. With the increase of perforation density, the fracture initiation rate of parallel perforation in the initial stage of fracturing decreases gradually, the number and the complexity of fractures also increase gradually; with the continuous increase of the stress difference, the initiation rate at the initial stage of hydraulic fracturing and the number of the main formed cracks and derived micro cracks all show a decreasing trend. Horizontal well perforation is one of the main factors affecting formation fractures around the wellbore and subsequent hydraulic fractures extending along the predetermined path. In this paper, the RFPA2D-Flow software is used to conduct a numerical simulation study on the initiation and propagation of parallel perforation fractures in the perforation cluster. Then influence of different perforation density and different stress on the initiation and propagation of perforation fractures are studied. The results show that there is a competitive relationship between initiation and propagation of perforated fractures. Three parameters, the initial initiation rate and the length of the hydraulic fracture, and the generated fracture number, are put forward as the indexes to measure the competitive relationship. Perforated fractures will eventually form a fracture propagation mode dominated by several main fractures and supplemented by micro fractures. Then it shows that an obvious spatial form associated with asymmetric main fractures and micro fractures derived around them. Parallel perforation fracture initiation presents four modes of competitive initiation. With the increase of perforation density, the fracture initiation rate of parallel perforation in the initial stage of fracturing decreases gradually, the number and the complexity of fractures also increase gradually; with the continuous increase of the stress difference, the initiation rate at the initial stage of hydraulic fracturing and the number of the main formed fractures and derived micro fractures all show a decreasing trend. [ABSTRACT FROM AUTHOR]

In this paper results of fatigue crack growth tests performed under both small and large scale yielding conditions on corner-crack specimens are presented for a turbine shaft steel. It can be shown, that the crack opening stress is the main factor influencing the fatigue crack growth rates. In order to account for plasticity effects numerical simulations are performed, which yield solutions for the J-integral. Those solutions are transferred to cyclic loading conditions by using the effective cyclic J-integral. Finally, all crack growth tests can be described within a single scatterband. [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper investigates the effect of stress singularities on the scaling of fracture of hybrid structures. [•] The scaling mechanism transits from energetic to statistical as the stress singularities get weaker. [•] The energetic-statistical scaling relation agrees well with the numerical simulations by a stochastic cohesive crack model. [Copyright &y& Elsevier]

This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated fracture processes including fracture initiation, propagation, coalescence, and branching by using only a scalar field, the phase field. In addition, fracture is a natural outcome of the simulation and obtained through the solution of an additional differential equation related to the phase field. No extra fracture criteria are needed and an explicit representation of a crack surface as well as complex track crack procedures are avoided in PFM for fracture, which in turn dramatically facilitates the implementation. The PFM is thermodynamically consistent and can be easily extended to multi-physics problem by 'changing' the energy functional accordingly. Besides an overview of different PFMs, we also present comparative numerical benchmark examples to show the capability of PFMs. • Development in phase field models and the computer implementation is reviewed. • The theories on phase field modeling are systematically summarized. • Representative numerical examples are presented for different fracture problems. [ABSTRACT FROM AUTHOR]

• Shear-modified GTN model has combined with the ductile phase-field fracture model. • The phase-field degradation function includes void volume fraction and shear damage. • The coupled model can reflect the crack propagation law of ductile materials. An appropriate failure model of ductile materials needs to consider complex phenomena at the microscopic level, such as the nucleation, growth, and coalescence of microvoids and the final fracture at the macroscopic level. A recent popular continuous phase-field method based on the regularization of sharp crack discontinuities can easily model macroscopic cracks. In this work, we developed a coupled model to predict the crack law when materials undergo ductile fracture. The coupling model combined the ductile phase-field fracture model of the material with the shear-modified GTN model to illustrate the microscopic damage accumulation caused by the growth of voids and the macroscopic crack initiation and propagation. In addition, a modified phase-field degradation function was established, combining phase field, void volume fraction, and shear damage. This paper also considers the crack propagation law when the materials undergo ductile fracture under different stress triaxialities. In this study, we used the subroutines UEL and UMAT in the commercial finite element software Abaqus to give the staggering solution algorithm for ductile phase-field fracture of the materials. The shear-modified GTN model was written by the subroutine UMAT, while the ductile phase-field fracture model was written by the subroutine UEL. The results of the numerical simulations showed good agreement with the experimental damage failure mechanisms and the load–displacement curves. [ABSTRACT FROM AUTHOR]

Abstract: Bones are the principal structural components of a skeleton; they play unique roles in the body providing its shape maintenance, protection of internal organs and transmission of forces. Ultimately, their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain loads until a certain limit, beyond which they fail. Understanding a fracture behaviour of bone is necessary for prevention and diagnosis of trauma; this can be achieved by studying mechanical properties of bone, such as its fracture toughness. Generally, most of bone fractures occur in long bones consisting mostly of cortical bone tissue. Therefore, in this paper, an experimental study and numerical simulations of fracture processes in a bovine femoral cortical bone tissue were considered. A set of experiments was conducted to characterise fracture toughness of the bone tissue in order to gain basic understanding of spatial variability and anisotropy of its resistance to fracture and its link to an underlying microstructure. The data was obtained using single-edge-notch-bending specimens of cortical bone tested in a three-point bending setup; fracture surfaces of specimens were studied using scanning electron microscopy. Based on the results of those experiments, a number of finite-element models were developed in order to analyse its deformation and fracture using the extended finite-element method (X-FEM). Experimental results of this study demonstrate both variability and anisotropy of fracture toughness of the cortical bone tissue; the developed models adequately reflected the experimental data. [Copyright &y& Elsevier]

Abstract: Moisture-induced cracking of wood is a well-known phenomenon. Nevertheless, until now, no numerical approaches are at hand to appropriately capture this feature. Hence, in the framework of this paper, a novel multiphysical hybrid interface-element and a respective interface material formulation are derived in order to be able to coincidentally simulate anisotropic moisture transfer through and along the crack plane and the mechanical response. Hygro-mechanical coupling is considered by means of moisture-dependent input quantities and swelling/shrinkage of the adjacent bulk material. The hybrid element is applied for a comprehensive numerical parameter study on the influence of wood species, material direction and initial moisture content on moisture-induced cracking. [Copyright &y& Elsevier]

Abstract: A detailed study of the propagation of bidimensional (2D) through-thickness cracks has been conducted on a 304L austenitic stainless steel used in nuclear industry in view of providing a detailed description of the effective driving force to be introduced in numerical simulation of thermal fatigue crack arrays in some critical components. To answer this problem, crack closure is precisely determined for long cracks and 2D short cracks artificially obtained in CT specimens, for different loading conditions. The present results will be used to validate numerical simulations of crack closure presented in a second part as a sister paper. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to characterize and predict numerically the limits of the hole-flanging process arising from material failure for two different aluminium sheets. Firstly, an analysis of the types of failure, i.e. necking and cracks, that appear under different process conditions has been performed. Then, a fracture criterion based on local strain measures in tension has been identified for both materials. A particular attention has been paid to the modelling and identification of the constitutive law in a large strain range, and then numerical predictions of the strain limits obtained from successful parts were compared to experimental results. The main conclusions are focused on the occurrence of damage in the conventional hole-flanging process from numerical simulations and experiments, depending on several process parameters. [Copyright &y& Elsevier]

Abstract: In this paper, the crack propagation in ductile materials is simulated under cyclic and dynamic loading. The adaptive finite element method is used to model the discontinuity due to crack propagation. The ductile fracture assumptions and continuum damage mechanics are utilized to model the material rupture behavior. Moreover both the rate-independent and rate-dependent constitutive equations are elaborated and the crack closure effect and combined hardening model are discussed in addition to some aspects of finite element implementation. Finally, a comparison is performed between the numerical simulation results and those of experiments to illustrate the robustness of proposed computational algorithm. [Copyright &y& Elsevier]

Abstract: The paper provides an advanced creep model which gives reasonable descriptions of the effects of damage and stress state from micromechanics viewpoint. A modified creep ductility exhaustion approach is employed to calculate the creep damage. Based on the proposed creep-damage model, numerical analyses of creep crack growth are conducted with a failure simulation technique. The simulated results are compared favorably with available experimental data for compact tension and thumbnail crack specimens for 316 stainless steel tested at 600°C. The comparisons show the excellent capability of the proposed model in predicting the crack growth rate and progressive crack profiles. [Copyright &y& Elsevier]

Abstract: In this paper, a modal analysis for computation of stress intensity factors under dynamic loading conditions at low frequency using eXtended Finite Element Method (X-FEM) is conducted. Modal stress intensity factors for a body with a stationary crack are first computed from the displacement fields associated with the deformed mode shapes. The modal approach based on the recombination of the modal stress intensity factors is then employed to compute the dynamic stress intensity factors. A convergence study on the first natural frequency for a plate with an edge crack is conducted to prove the correctness of the model implementation. Then, dynamic stress intensity factors obtained from the modal approach are compared with those obtained from full transient direct dynamic computations in order to validate the X-FEM computational results. The computational results show that the modal approach can be used to obtain accurate stress intensity factors for cracked structure under dynamic loads (at low and moderate frequency ranges) with a significant reduction of the computing time compared to a full transient dynamic computation. Finally, the validated modal analysis is used to investigate the change of the natural frequency due to crack propagation for a cracked turbine blade during operation in a power plant. [Copyright &y& Elsevier]

Abstract: The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. It has caused considerable confusion due to its in-depth subtleness and complex entanglement with different theories and numerical simulations. The present paper presents completely analytical theories based on Euler and Timoshenko beam theories using a brand new approach which reveals the hidden mechanics of the problem. Orthogonal pairs of pure modes are found and used to partition mixed modes. The developed theories are extensively validated against numerical simulations using finite element methods. Moreover, the fracture mode partition space is thoroughly investigated and crack tip running contact is found which results in a region of pure mode II. The theories are finally applied to general one-dimensional fracture in beams and axisymmetric plates. [Copyright &y& Elsevier]

Abstract: In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension. [Copyright &y& Elsevier]

Abstract: This paper deals with the numerical simulation of a stable crack propagation experiment at in a 16MND5 steel. At this temperature, the material is viscoplastic. A cohesive zone model is formulated in order to simulate the rupture of a CT specimen. A large displacement 3D cohesive element with eight nodes is implemented in the finite element code ABAQUS. The associated traction–separation law is of Tvergaard and Hutchinson type, in which an hardening slope has been added. This hardening simulates the material strengthening associated to the increasing strain rate in front of the crack tip when crack tip starts to propagate. We show that in this case the form of the cohesive law has great impact on the simulated propagation velocity. [Copyright &y& Elsevier]