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Shale anisotropy characteristics have great effects on the mechanical behaviour of the rock. Understanding shale anisotropic behaviour is one of the key interests to several geo-engineering fields, including tunnel, nuclear waste disposal and hydraulic fracturing. This research adopted the finite discrete element method (FDEM) to create anisotropic shale models in ABAQUS. The FDEM models were calibrated using the mechanical values obtained from published laboratory tests on Longmaxi shale. The results show that the anisotropic features of shale significantly affect the brittleness and fracturing mechanism at the micro-crack level. The total fracture number in shale under the Uniaxial Compressive Strength (UCS) test is not only related to the brittleness of shale. It is also strongly dependent on the structure of the shale, which is sensitive to shale anisotropy. Two new brittleness indices, BIf and BICD, have been proposed in this paper. The expression for BIf directly incorporates the number of fractures formed inside of the rock, which provides a more accurate frac-ability using this brittleness index. It can be used to calculate the frac-ability of rocks in projects where there are concerns about fractures after excavation. Meanwhile, BICD links brittleness to the CD/UCS ratio in shale for the first time. BICD is easy to obtain in comparison to other brittleness indices because it is based on the Uniaxial Compressive Strength test only. In addition, it has been shown there is a relationship between tensile strength and the crack damage strength in shale. Based on this, an empirical relationship has been proposed to predict the tensile strength based on the Uniaxial Compressive Strength test. Highlights: Through the use of FDEM simulations, the fracturing mechanics of shale, fracturing behaviour, and brittleness of shale have been investigated from a micro-scopic viewpoint taking shale anisotropy into account. Two new brittleness indices are proposed. One relies on the number of fractures in the shale to reflect the shale's frac-ability, and the other uses strength parameters that can be easily obtained from UCS tests. This paper proposes an empirical relationship to predict the tensile strength of rocks based on UCS tests. [ABSTRACT FROM AUTHOR]

This paper presents a forensic numerical study on hydro-fracturing at three locations within an excavation in a clayey till underlain by an aquifer in Ontario, Canada. The pioneering forensic studies were based on continuum mechanics using finite element method (FEM) combined with an effective medium approach, which did not explicitly simulate the physical process of fracture propagation. This has overestimated the size of the venting holes (i.e., model aperture approximately 8 m, observed approximately 0.1 m), hindering accurate assessment of the venting locations at the excavation base. For this reason, a coupled hydro-mechanical XFEM analysis, which explicitly models fracture propagation, was performed in this study to revisit the case history from the perspective of fracture mechanics. Parametric study is also performed to investigate the influence of flow rate on the direction of the fracture propagation, and thus location of venting holes. It is shown that the coupled hydro-mechanical XFEM analysis offers better predictions than previous FEM analysis for both, locations and sizes of the three observed venting holes. The parametric study reveals that an increase in the flow rate from 5 to 10 L/min (which is within the reported range) leads to a wider and less curved fracture, altering the predictions of the venting locations at the excavation base by around 8 m. This is because an increasing flow rate causes wider aperture and higher shear stress near the fracture tip, which intensifies the re-orientation of maximum principle stress that facilitates the re-direction of the propagating fractures. [ABSTRACT FROM AUTHOR]

Abstract: Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code. [Copyright &y& Elsevier]

This paper reviews the experimental and modeling work that has been carried out concerning the behavior of fiber-reinforced polymer (FRP) composites in fire since the 1980s. The first part focuses on the thermophysical properties and temperature responses, while the second considers thermomechanical properties and responses, which are significantly affected by the thermal exposure of the FRP material. Furthermore, the application of deformation-based or strength-based failure criteria enables the prediction of time-to-failure. If the fire exposure time is less than the time-to-failure, the post-fire behavior is of interest and the post-fire properties and their potential recovery after cooling are particularly addressed. This fundamental understanding obtained as a result of both modeling and experimental work makes a reliable endurance design for FRP structures in fire possible. [ABSTRACT FROM AUTHOR]

This paper proposes a linear elastic fracture mechanics approach for the prediction of plate end debonding in rectilinear and curved plated beams. The analytical model results in simple equations, suitable for immediate design use. The load-deflection curve of a plated beam, from the onset of debonding up to the complete separation of the plate, is obtained by controlling the length of the interfacial debonding crack. Its shape clearly shows that snap-back or snap-through instabilities may arise when the beam is loaded under displacement or force control. Analytical predictions are also compared with finite element results based on an interfacial cohesive crack model. It is shown that the predictions of the proposed analytical model match closely the numerical solution, provided that an effective crack length accounting for the size of the fracture process zone is used in the calculations. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Thin plates made of high–strength steel are frequently used both in civil and military ballistic protection systems. In order to choose an appropriate type of alloy, it is necessary to fulfil a number of criteria, such as the condition of use, the desired ballistic performance, weight, dimensions, and price. This paper presents a numerical analysis of the penetration of a 30mm armor-piercing projectile with a velocity of 750m/s into steel alloy Weldox 460 plates of different thicknesses at a distance of 1000m . Methods: The analysis has been performed using numerical methods and finite element modeling to calculate stresses and deformation caused by the penetration effect. For defining material characteristics, the Johnson- Cook material model and the fracture of materials model have been used. In this paper, the software packages FEMAP and LS Dyna have been used for defining models and performing numerical calculations. Results: The results of the performed numerical analysis as well as the obtained stress and displacement values are presented for four different armor plate thicknesses: 30mm, 33mm, 34mm, and 40mm. The results show a penetration effect and an interaction between the projectile and the armor plate. Conclusion: Modeling the impact on armor-piercing obstacles is very complex, extensive, and demanding, and the formed models approximate the real problem of projectile penetration in a very successful way (or with a certain deviation). In recent times, the analysis using the finite element method has proven to be one of effective approaches to solving such and similar problems. The material and the dimensions of the obstacle, as well as the material and the ballistic parameters of the projectile have the greatest influence on projectile penetration. Keeping all the input parameters at the same level and increasing the thickness of the target leads to its increased resistance to penetration. [ABSTRACT FROM AUTHOR]

The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm's attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm. [ABSTRACT FROM AUTHOR]

In this paper, a method of crack propagation analysis based on adaptive extension finite element is proposed. This method combines adaptive mesh reconstruction technology with the extended finite element method (XFEM). Firstly, the model of the engineering structure is discretized with the help of mesh generation software, and the initial mesh is divided. Secondly, the Construction of the XFEM model and the tip of the crack strengthening function are introduced to describe the physical field properties of the crack tip. The integral equation is solved to obtain the crack tip parameters. Then, the adaptive mesh reconstruction technology is built to refine the mesh of the crack tip area through the error estimation of the crack tip. Finally, the SIFs at the crack tip were calculated using the interaction integral, and the path direction of crack growth was determined using the maximum circumferential tensile stress criterion. Thus, the propagation path can be well traced. [ABSTRACT FROM AUTHOR]

Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated. [ABSTRACT FROM AUTHOR]

The paper investigates the interaction of a steel striker with a three-layer target barrier. The barrier had three layers: ceramic, orthotropic organoplastic, and aluminum. The interaction velocity was 841 m/s, and the initial interaction angles with the barrier surface were set normal and 45°. The study is carried out numerically by the finite element method in a three-dimensional setting using the computer complex EFES developed by the authors. An elastic-brittle model is proposed to describe the behavior of the composite. A tensor-polynomial criterion of the second degree is used for the composite fracture. To describe the fracture of the orthotropic material of the target barrier, a two-stage model is proposed. The model of the composite behavior takes into account different strength moduli in compression and tension. As a criterion for the ceramics fracture, the deformation criterion was used. The behavior of the striker material and the metal layer are described by an elastoplastic medium, for the fracture of which a deformation criterion is proposed based on the limiting value of plastic deformation. The influence of the layer arrangement and initial interaction angle on the fracture of the target barrier has been studied. [ABSTRACT FROM AUTHOR]

In this paper, the effect of thermal stress on crack-inclusion problem in inhomogeneous superconducting cylinder in the cooling process is investigated. By using the gradient finite element method, the thermodynamic coupling equation is solved numerically and the thermal stress is obtained during the drop from room temperature to operating temperature. Then the stress intensity factors for the cooling process are solved. The effects of thermal stress on crack growth are discussed, and the effects of the inclusion on crack growth under thermal stress are analyzed. According to the results, the crack length increases to promote the crack growth, then the effect of thermal stress on the crack growth increases as the crack length increases. In addition, the size and type of the inclusion, as well as the distance of the inclusion from the crack tip, can also affect the crack extension. [ABSTRACT FROM AUTHOR]

Residual stress is an important factor that affects the properties of cold spray coatings. The study performed 2D single-, 3D single-, and 3D multiple-particle finite element simulations based on the Eulerian method, and hole drilling measurements to study residual stress in cold-sprayed copper coatings. The study examined how the basic modeling parameters affect residual stress in the 2D system. It found that the mesh size, substrate dimension, and simulation duration change the residual stress; while material failure does not have much effect because failure is localized. It also found that thermal softening, which occurs when the initial temperature and/or plastic deformation increase, helps to reduce the residual stress. In addition, the residual stress along the axisymmetric axis of the particle changes from being compressive at first to being compressive-tensile-compressive along the through-depth thickness direction with the interfacial stress being tensile that mainly originates from friction shear of the interfacial layers. For the 3D single-particle simulations, the average residual stress to the through-depth thickness shows tension to compression transition and is similar to the 2D cases. For the 3D multiple-particle simulations, the residual stresses in the coatings/substrate are all compressive because of the repeated and strong impact of the particles, which agree with the experimental measurements. The study also found that the compressive stresses decrease when the coating thickness increases because of more plastic deformation-induced thermal softening. This paper clarifies the effects of Eulerian-based finite element parameters on simulating residual stress in cold spray and will serve as a valuable reference for future studies. [ABSTRACT FROM AUTHOR]

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

The tooth bending fatigue fracture is caused by the alternating loads for the heavy-duty transmission gears. The crack initiation and propagation are the two major parts in the failure process. The crack propagation behavior is mainly affected by initial crack position except for the load and material properties. In this paper, the crack propagation model of a gear is established under the considering of crack initiation location by using extended finite element method (XFEM). The model accuracy is verified by testing results of strain and fractography by conducting the single-tooth bending fatigue experiment. The influence of crack initiation locations on subsequent crack propagation behavior is analyzed. The crack length in the tooth width direction and depth direction is faster when the initial crack is located in the middle of root surface. The crack growth rate is lower for the initial crack located in the surface close to the end surface of the gear. [ABSTRACT FROM AUTHOR]

Cracking is a common failure mode in asphalt concrete (AC) pavements. Many tests have been developed to characterize the fracture behavior of AC. Accurate crack detection during testing is crucial to describe AC fracture behavior. This paper proposes a framework to detect surface cracks in AC specimens using two-dimensional digital image correlation (DIC). Two significant drawbacks in previous research in this field were addressed. First, a multiseed incremental reliability-guided DIC was proposed to solve the decorrelation issue due to large deformation and discontinuities. The method was validated using synthetic deformed images. A correctly implemented analysis could accurately measure strains up to 450%, even with significant discontinuities (cracks) present in the deformed image. Second, a robust method was developed to detect cracks based on displacement fields. The proposed method uses critical crack tip opening displacement (δc) to define the onset of cleavage fracture. The proposed method relies on well-developed fracture mechanics theory. The proposed threshold δc has a physical meaning and can be easily determined from DIC measurement. The method was validated using an extended finite-element model. The framework was implemented to measure the crack-propagation rate while conducting the Illinois-flexibility index test on two AC mixes. The calculated rates could distinguish mixes based on their cracking potential. The proposed framework could be applied to characterize AC cracking phenomenon, evaluate its fracture properties, assess asphalt mixture testing protocols, and develop theoretical models. [ABSTRACT FROM AUTHOR]

The explosion products, such as shock waves, fragments and heat energy formed by explosion, act on the plate structure, which may cause structural damage, material failure and even phase transformation of material. In this paper, the damage mechanism and protective effect of near-field blast load on sandwich structure based on foam-nickel core material were studied. Firstly, the near-field explosion test was conducted to investigate the blast response of the foam-nickel sandwich structure subjected to blast shock from 8701 explosive at near-field position. The deformation characteristics and stress history of the sandwich structure on the acting location of blast load were carefully investigated via experimental methods. A finite element model of near-field explosion was established for effective numerical modelling of the dynamic behaviour of the sandwich structure using the explicit dynamics software ANSYS/LS-DYNA for more comprehensive investigations of the blast shock response of the sandwich structure. The finite element model is reasonable and validated by mesh independence verification and comparing the simulated response behaviour to that from the experimental results for the sandwich structure subjected to near-field blast load. On this basis, the damage mechanism and protection effect of the near-field explosion impact on foam-nickel cores with different density and porosity are simulated more systematically. The investigated results from the experiments and a series of numerical simulations show the large deformation effect due to the extensive energy absorption, which suggests that the sandwich structure based on foam-nickel core material may be expected to become a new choice of protective structure under near-field blast load. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework combining the state-based peridynamics (SBPD) with the extended finite element method (XFEM) for crack propagation in two-dimensional solids. Numerical examination is conducted fulfilling both the quasi-static and time-dependent loading conditions. The computational domain is partitioned into two regions: (a) SPBD region: the vicinity of crack tips and potential region where the crack is likely to propagate, and (b) XFEM region: the area behind the crack tip and the rest of the body. The salient features of the developed framework include: (a) avoiding requirement of a priori knowledge of enrichment functions like the conventional XFEM; (b) without fracture criteria for crack propagation; (c) no restriction on the value of Poisson's ratio like the bond-based peridynamics; and (d) higher computational efficiency than the pure peridynamics. The efficiency and accuracy of the proposed framework are systematically demonstrated through benchmark examples involving quasi-static crack growth and dynamic crack branching problems. [ABSTRACT FROM AUTHOR]

Railway turnouts are essential in the train traffic route management for modern railways. Despite significant devotion to railway turnout research, one of their most common failures has not been thoroughly investigated, which is a fatigue over the turnout crossing nose. At the crossings, wheel-rail discontinuity imparts high-frequency high-magnitude forces, which are the source of fatigue failure over the crossing nose. In this study, a novel approach built on "Peridynamics" (PD) has been developed to obtain new insights into the fatigue cracks. A recent approach using "crack on mid-plane" has also been employed in this study to enhance the limited capability of Peridynamics. This paper is the world's first to investigate fatigue failures over a crossing nose from fracture mechanics perspective. This paper also introduces a novel adaptive time-mapping method as an alternative to earlier time-mapping methods for fatigue models proposed in the open literature. The new model has been verified against both Finite Element Method and experimental data. It reveals that our new approach can simulate fatigue damage, particularly in mode I crack propagation. The study has provided important insights on the fatigue crack development, which is not possible before by existing Peridynamics fatigue model. The new approach on the basis of "adaptive time-mapping" and "crack on mid-plane" is demonstrated to be effective and efficient in PD simulations. [ABSTRACT FROM AUTHOR]

• For blunt crack tips, as the radius increases, the specimens' compliance also increases. • For sharp crack tips, as the element size of the crack tip increases, the specimens' compliance decreases. • Similar compliance results are obtained for both meshes when the radius or element size of the crack tip are low enough. • Two models were created that show the crack tip radius or the element size impact on the elastic unloading compliance. • A parameter that normalizes the crack tip radius or the element size with the specimens' width is proposed. Elastic unloading compliance is a common technique to determine instantaneous crack size in fracture mechanics properties such as resistance curves (R-curves) and fatigue crack growth. This technique uses a polynomial, developed using finite elements models, to correlate compliance with crack depth. In these models, crack tip is usually modeled with a blunt mesh (with a crack tip radius ρ) or a sharp mesh (with element size in the width direction l) , and neither are standardized in the literature. This paper shows that both affect compliance, therefore potentially impacting results of fracture mechanics properties acquired from simulations. This paper focuses on how those parameters affects compliance in SE(B) models. Finally, a parameter φ that normalizes ρ or l with the width was developed and recommended values based on compliance convergence are suggested. Controlling φ may help to ensure reliable results in fracture mechanics models where compliance needs to be determined. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method for assessing fracture mechanics parameters such as Stress Intensity Factor (SIF), Energy Release Rate (J) and Crack Tip Opening Displacement (CTOD). An electromagnetic–mechanical coupling (EMC) approach is employed to evaluate and to measure these fracture parameters by monitoring the variation of impedance using eddy currents. This approach relies on the eddy current signal obtained from a sensor, which calculates and verifies SIF parameters along with the J-integral and CTOD through changing the sensor impedance. To ensure theoretical consistency, the magnetic field is theoretically used, formulated and verified. Additionally, a numerical simulation method employing the finite element method is used to analyze and identify cracks in structures and assess their propagation. The quantification of SIF and J-integral parameters is demonstrated using two sensors based on a differential probe. This research paper demonstrates that the proposed method is the most efficient approach for exploring and detecting cracks in materials, as well as understanding their propagation behavior. [ABSTRACT FROM AUTHOR]

The aim of this article is to review the application of the finite element method (FEM) to cross-wedge rolling (CWR) modeling. CWR is a manufacturing process which is used to produce stepped axles and shafts as well as forged parts for further processing on forging presses. Although the concept of CWR was developed 140 years ago, it was not used in industry until after World War 2. This was due to the limitations connected with wedge tool design and the high costs of their construction. As a result, until the end of the twentieth century, CWR tools were constructed by rolling mill manufacturers as they employed engineers with the most considerable experience in CWR process design. The situation has only changed recently when FEM became widely used in CWR analysis. A vast number of theoretical studies have been carried out in recent years, and their findings are described in this overview article. This paper describes nine research areas in which FEM is effectively applied, namely: the states of stress and strain; force parameters; failure modes in CWR; material fracture; microstructure modeling; the formation of concavities on the workpiece ends; CWR formation of hollow parts; CWR formation of parts made of non-ferrous materials; and new CWR methods. Finally, to show the potential of FEM on CWR modeling, a CWR process for manufacturing a stepped shaft used in car gearboxes is simulated numerically. This numerical simulation example shows that FEM can be used to model very complex cases of CWR, which should lead to a growing interest in this advanced manufacturing technique in the future. [ABSTRACT FROM AUTHOR]

Damage mechanics models exhibit favorable properties such as the intrinsic influence of stress triaxiality on damage evolution and the prediction of crack initiation as well as propagation leading to structural failure. However, their application requires advanced expertise hindering the transfer of these models into industrial practice, especially since the parameter calibration is a key obstacle. In this paper, a simplified procedure is proposed for a non-local extension of the Gurson–Tvergaard–Needleman model (GTN), which is a highly accepted model for ductile failure of metals. The procedure is iteration free and requires experimental input data from only two standardized tests. The parameters are determined using look-up diagrams created on the basis of systematic simulations and made available for different material behavior covering the majority of ductile metals. Benchmark tests for three different steels are conducted to evaluate the robustness of the proposed procedure. The reliability of the GTN model is validated for all investigated materials. [ABSTRACT FROM AUTHOR]

Understanding the formation of impact craters on planetary surfaces has fundamental importance in geology, impact dynamics, and planetary sciences. The finite element-smoothed particle hydrodynamics (FE-SPH) adaptive method combines the advantages of smoothed particle hydrodynamics (SPH) and finite element method (FEM) in solving hypervelocity impact (HVI) problems. Employing FE-SPH adaptive method is a new idea for the analysis of planetary impact cratering which is different from impact-simplified arbitrary Lagrangian Eulerian (iSALE). In this paper, we establish a complete numerical model of planetary impact cratering through the FE-SPH method, including material failure criterion, thermodynamic analysis, gravity preloading, etc. We reproduce the numerical results by Collins et al. (2012) and highly consistent results are obtained through comparative analysis. This study simulates the formation process of simple and complex impact craters, and the temperature, pressure, density, and geometric shape of the impact zone can be quantitatively obtained. We further analyze the distribution of polymorphs and rock fragmentations in the impact zone based on the theories of shock metamorphism. The proposed analysis method may assist geologists in conducting geological studies. • We establish a complete numerical model of planetary impact cratering different from iSALE. • We analyze the distribution of high-pressure polymorphs based on shock metamorphism. • The FE-SPH model has higher numerical precision for planetary cratering impacts. [ABSTRACT FROM AUTHOR]

A finite element model (FEM) of the bracket arm of wrecker is developed and the mechanical behavior under six representative conditions is studied in this paper. Stress test experiment is carried out to validate the presented FEM. Comparison analyses show that results predicted from the FEM are in good agreement with those obtained from the test experiment. Moreover, the mechanical behavior analyses also give the danger working conditions for each component of the bracket arm. Based on the stress distributions under the danger working condition, structural improvement is conducted for the component which is prone to material failure. Mechanical behavior analyses of the improved structures are also carried out in this paper. Numerical analysis results show that the maximum stresses of each improved component of the bracket arm are all reduced to close or below the allowable stress. This indicted that the load bearing capacities of each component are improved effectively and meet the requirements of engineering applications. [ABSTRACT FROM AUTHOR]

Many concrete structures, such as bridges and wind turbine towers, fail mostly due to the fatigue rapture and bending, where the cracks are initiated and propagate under cyclic loading. Modeling the fracture process zone (FPZ) is essential to understanding the cracking behavior of heterogeneous, quasi-brittle materials such as concrete under monotonic and cyclic actions. The paper aims to present a numerical modeling approach for simulating crack growth using a scaled boundary finite element model (SBFEM). The cohesive traction law is explored to model the stress field under monotonic and cyclic loading conditions. In doing so, a new constitutive law is applied within the cohesive response. The cyclic damage accumulation during loading and unloading is formulated within the thermodynamic framework of the constitutive concrete model. We consider two common problems of three-point bending of a single-edge-notched concrete beam subjected to different loading conditions to validate the developed method. The simulation results show good agreement with experimental test measurements from the literature. The presented analysis can provide a further understanding of crack growth and damage accumulation within the cohesive response, and the SBFEM makes it possible to identify the fracture behavior of cyclic crack propagation in concrete members. [ABSTRACT FROM AUTHOR]

Based on fracture mechanics theory, a finite element method was used to determine the stress intensity factors of the inclined crack on the inner surface of the pipe under axial compression load and external pressure. The effects of different influencing factors on the stress intensity factor along the crack front considering crack closure were systematically explored, which were different to those under internal pressure. The effects of high aspect ratio on KII, the crack inclination asymmetry caused by curvature and the effects of the friction coefficient on the stress intensity factors of the pipe with an inclined inner surface crack under axial compression load and external pressure were explored in this paper. To be fit for defect assessment, the solutions for stress intensity factors KII and KIII were derived, and new correction factors fθ and fμ were proposed in the empirical solutions to accommodate the crack inclination asymmetry and the friction coefficient, respectively. [ABSTRACT FROM AUTHOR]

Simulations of tunnel excavations have to take into account the natural occurrence of joints and faults in the surrounding rock mass, which dominantly control its mechanical response. In this paper, we present work in progress toward 3D finite element analysis of excavation using equivalent rock-mass properties derived from stochastically generated discrete fracture networks (DFNs). The equivalent stiffness is determined by volume averaging. Presently, we solve the problem linearly for an incremental change of the stress state. The fracture's stiffness is assumed to depend on the initial normal stress acting in direction normal to it. However, within the solved incremental step, we assume the fracture's stiffness to be constant. This assumption is acceptable for small stress changes. Since the fractures represented in the DFN model have preferred directions, the equivalent stiffness is anisotropic. [ABSTRACT FROM AUTHOR]

This paper presents a fully coupled thermo‐hydro‐mechanical (THM) model which simulates frost heave in fully saturated soils. The model is able to simulate the formation and growth of multiple distinct ice lenses. The basic equations of the system were derived using the continuum theory of mixtures, nonequilibrium thermodynamics, and fracture mechanics, considering skeleton deformation, water flow and heat transport. Central to this model is the coupled transport of mass due to the temperature gradient across the frozen fringe, which acts as the main driving force of the phenomenon. The model is formulated in terms of measurable physical properties and thus no ad hoc parametrization is required. In an ice‐lens‐free state, the system is solved as a continuum using the finite element method (FEM). It is then locally treated as a discontinuous system upon the formation of ice lens, by enriching the elements carrying the embedded ice lens(es) using the extended finite element method (X‐FEM). The accuracy and efficiency of the proposed model has been verified using several laboratory tests on Devon silt samples at different overburden pressures and thermal boundary conditions. Shut‐off pressures have been also estimated and compared with the experimental results. [ABSTRACT FROM AUTHOR]

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples. [ABSTRACT FROM AUTHOR]

Purpose: The fuselage riveted lap-joints are susceptible to multiple site damage (MSD) and should be considered in damage tolerance analysis. This paper aims to investigate the stress intensity factor (SIF) and crack growth simulation for lap-joints based on three-dimensional (3D) finite element analysis. Design/methodology/approach: The 3D finite element model of lap-joints is established by detailed representation of rivets and considering the rivet clamping force and friction. Numerical study is conducted to investigate the SIF distribution along the thickness direction and the effect of clamping force. A predictive method for the cracks propagation of MSD is then developed, in which an integral mean is adopted to quantify the SIF at crack tips, and the crack closure effect is considered. For comparison, a fatigue test of a lap-joint with MSD cracks is conducted to determine the cracks growth live and measure the cracks growth. Findings: The numerical study shows that the through-thickness crack at riveted hole in lap-joints can be treated as mode I crack. The distribution of SIF along the thickness direction is inconstant and nonmonotonic. Besides, the increase in clamping force will lead to more frictional load transfer at the faying surfaces. The multiple crack growth simulation results agreed well with the experimental data. Originality/value: The novelty of this work is that the SIF distribution along the thickness direction and the MSD cracks growth simulation for lap-joints are investigated by 3D finite element analysis, which can reflect the secondary bending, rivet clamping, contact and friction in lap-joints. [ABSTRACT FROM AUTHOR]

This paper presents the Finite Element (FE) analyses carried out with the aim to predict the tooth root fatigue and Rolling Contact Fatigue (RCF) behavior of spur gears, in terms of crack propagation maximum number of cycles. The combination of different materials, i.e. steel and titanium, and surface treatments, i.e. case-hardening and application of surface layers by Physical Vapor Deposition (PVD), are investigated. The residual stresses induced by the deposition of the coating are modelled. The stress intensity is described by linear elastic relations based on the crack tip opening displacement and the crack propagation in the case-hardened spur gears is described with the help of mathematical models. Experiments are carried out to evaluate tooth damage under RCF for different treated gears. The best solutions in terms of bulk material – treatment combination among the ones investigated are identified, also highlighting innovative possibilities which can guarantee appreciable performance. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufacturing processes. Ductile failure is accompanied by a significant amount of plastic deformation in metallic structural components. Finite element simulation of damage evolution in ductile solids is presented in this paper. Uncoupled models are implemented in a finite element model simulating deep drawing as well as cutting processes. Based on the Johnson–Cook model, the effect of deformation on the evolution of flow stress is described. The combined effect of strain, strain rate, and temperature on plasticity and damage behavior in cutting processes is considered. The accuracy of these models is verified when predicting ductile damage in forming and cutting processes. [ABSTRACT FROM AUTHOR]

Cracks are one of the major characteristics of soil structure failure. Successfully performed numerical simulation of the soil crack evolution process is conducive to the prediction of potential dangers. In recent years, crack evolution simulation has been greatly facilitated in the field of fracture mechanics by the development of the extended finite-element method (XFEM). However, it is rarely used to simulate crack evolution in earth structures, because in most cases soil cannot be regarded as a quasi-brittle material. Based on the characteristics of stress concentration and redistribution at the tip of a soil crack revealed by numerical tests, this paper proposes a discriminating method for crack propagation that can reflect the influence of the stress field at the soil crack tip on the crack propagation direction, which is then coded to an XFEM program. Compared with existing methods, this new method is found to be more accurate and effective. [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]

In this paper, crack growth in orthotropic materials subjected to dynamic loading is numerically studied using an adaptive phase-field method. The study starts with a coarse structured mesh and the adaptive refinement strategy based on a user-defined threshold on the phase-field variable is proposed for computational efficiency, and variable-node elements are employed to treat the hanging nodes as a result of local adaptive refinement. The Hughes-Hilbert-Taylor (HHT) time integration scheme is adopted for temporal discretization. The directionality of orthotropic materials is represented by a penalized second-order structural matrix, which is incorporated in the crack face energy density. Through numerical examples, the influence of the material orientation on the dynamic crack growth in orthotropic materials is studied and the reliability of the proposed framework is validated. • An adaptive PFM is proposed to simulate dynamic crack growth in orthotropic materials. • Time integration method HHT is combined with a staggered solving scheme. • A robust local adaptive refinement strategy is used based on a phase-field threshold. • Variable-node elements are used to overcome incompatibility in the refined mesh. • Performance of the proposed framework is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

This work presents a novel numerical methodology to model the degradation and failure of composite materials like GFRP submitted to monotonic and high cycle fatigue loads. This is done by using the Serial–Parallel Rule of Mixtures homogenisation technique together with a proper mechanical characterisation of the constituent materials of the composite. This paper also proposes an efficient way of estimating the fatigue properties of each of the material constituents (fibre or matrix) to comply with the experimental results obtained at composite level; this enables to estimate the fatigue strength of any stacking/orientation of fibres with only one mechanical characterisation of the material properties. A comparison of the results obtained analytically and experimentally for GFRP is presented. The results show the applicability and accuracy of the proposed methodology in this field. [ABSTRACT FROM AUTHOR]

Fracture toughness is an important parameter for measuring material properties in industry. In order to obtain data on the fracture toughness of a material it is often necessary to carry out a large number of fracture toughness experiments. The cost of the experiments is high and the experimental process is cumbersome. Moreover, in practice, there are often not a large number of materials that meet the requirements for the experiment. The relationship between different experimental ambient temperatures and fracture toughness can be determined by determining the reference temperature T 0 in the master curve method. In this paper the load-displacement curves of the specimens are obtained using finite element analysis. Determine the J integrals corresponding to the initiating load P int and the maximum load P c on the load-displacement curve using the Load Slope Compliance Changing Rate method. Determine the reference temperature T 0 in conjunction with the single temperature method. On the one hand, in order to validate the method, finite element analyses were performed on specimens of different thicknesses, temperatures, materials and types. This method was also applied to obtain fracture toughness data and to determine the reference temperature T 0. On the other hand, combining the master curve method and combining the experimental data of 16MnDR, 16MnR and 20MnMoNi55 ferritic steels were verified. The experimental results show that the results predicted by this method are in good agreement with the actual results. However, it has a certain conservative type. It provides a good solution for practical engineering. The accuracy of fracture toughness and reference temperature of ferritic steels of different thicknesses can be verified by few experiments. • The study found a Load Slope Compliance Changing Rate method for determining the specimen initiation load P int and critical load P c. • It is shown that φ in P int = P 0 + φ × (P c − P int) (0< φ <1) is not a fixed value. • The master curve for the predicted reference temperature works well and is able to include almost all experimental data for values less than K Jc(limit). • P int and Pc determined by CCR method have a quadratic relationship as the thickness changes. [ABSTRACT FROM AUTHOR]

The failure assessment diagram (FAD) is a widely used tool for evaluating the fracture acceptance of structural components. In addition to linear elastic fracture mechanics, elastic-plastic fracture mechanics, and limit load analysis, the ASME Code incorporated FAD as an alternative safety evaluation method for flaws in nuclear pipes starting from 2004 edition. This paper conducts a series of finite element elastic-plastic fracture mechanics analyses to establish the specific J –based FAD curves considering various loading and geometry conditions for ferritic pipes containing various circumferential flaws. By comparing with the suggested FAD of ASME Code Section XI - Appendix H, it is found that the radius-to-thickness ratio of pipes and the flaw depth influence the applicability of FAD, but with minor effects of crack length. In addition, the effects of material properties between base metal and weld materials on FAD are also discussed. The result of this work could be a reference when applying the FAD to evaluate the flawed piping for nuclear power plants. • The applicability of ASME FAD for ferritic piping has been investigated. • Specific FAD curves for various flawed piping conditions are calculated by conducting a series of elastic and elastic-plastic finite element analyses. • The ASME FAD is applicable for various loading combinations, pipe geometries and flaw sizes, but affected significantly by material properties. [ABSTRACT FROM AUTHOR]

Despite substantial advancements in optimizing structural designs for stiffness, the field of design against fracture is still in its early stages. This paper introduces a fundamental and standardized paradigm for structural design against brittle fracture, achieved through the minimization of the energy release rate G within the framework of linear elastic fracture mechanics (LEFM). By leveraging the Griffith criterion expression and the total potential energy in LEFM, we propose an efficient approach for structural optimization that enhances the toughness of architected materials. The energy release rate G is evaluated a synergistic application of finite element analysis and finite difference methods, yielding a precision of 0.6% compared to benchmarks in published handbooks. We demonstrate significantly reduced G values compared to standard stiffness and stress-oriented topology optimization, which directly contributes to increased toughness. To comprehensively analyze the fracture process encompassing damage, crack initiation, propagation, and failure, we employ post-processing phase field fracture modeling on the optimally designed architected materials. By performing multi-objective optimization of the stiffness and energy release rate G , the toughness and extreme load-bearing capacity can be simultaneously improved. The resulting perforated architecture effectively outperforms homogeneous structures in both toughness and peak load. Additionally, we extend our analysis to various configurations, such as non-center cracks, pure shear loading, and adherence to the standard 3D compact tension ASTM E-399-72. The designed structures are additively manufactured and experimentally validated, demonstrating a toughness increase of over 10 times compared to stress-based design. These contributions offer promising prospects for advancing the design of future engineering structures and materials with a favorable balance of critical fracture resistance characteristics. [ABSTRACT FROM AUTHOR]

• Shear bands' morphology in amorphous polymer under four-point bending is concerned. • Physical mechanisms of detour and strength decay of bands at intersections are analyzed. • Constitutive model can predict the morphology of shear bands under four-point bending. As a significant means of plastic deformation in polymers, shear bands play a crucial role in material failure and performance optimization. In this paper, the finite element method is utilized to numerically investigate the morphology of shear bands in an amorphous polymer plate under plane strain four-point bending. Amorphous polymers are characterized by the elastic-viscoplastic constitutive relationship that takes into account the effect of pressure on yielding, including intrinsic softening and subsequent orientation hardening. The impact of material parameters including intrinsic softening, orientation hardening, and initial imperfections on the evolution of shear bands and the undulations of the specimen's surface are explored in detail. In addition, the physical mechanisms responsible for the detour and strength decay of shear bands after passing the intersections are described. It appears that intrinsic softening is the driving force promoting the detour of shear bands at intersections, while orientation hardening is the driving force inhibiting the detour. By comparing the simulations with experimental observations, it is demonstrated that the model can qualitatively depict the morphology of the shear band during the four-point bending of amorphous glassy polymers. [Display omitted] [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to use numerical methods early in the airframe design process and access the structural performance of wing leading edge devices made of different materials and design details, under bird strike events. Design/methodology/approach: Explicit finite element analysis was used to numerically model bird strike events. Findings: Structural performance charts related to materials and general design details were drawn to explore the design space dictated by the current applicable airworthiness requirements. Practical implications: This paper makes use of the current capability in the numerical tools available for structural simulations and exposes the existing limitations in the terms of material modelling, material properties and fracture simulation using continuum damage mechanics. Such results will always be in the need of fine-tuning with experimental testing, yet the tools can shed some light very early in the design process in a relative inexpensive manner, especially for design details down selection like materials to use, structural thicknesses and even design arrangements. Originality/value: Bird strike simulations have been successfully used on aircraft design, mainly at the manufactured articles design validation, testing and certification. This paper presents a hypothetical early design case study of leading edge devices for appropriate material and skin thickness down selection. [ABSTRACT FROM AUTHOR]

This paper is a consecutive work based on the last paper "Finite element analysis of viscoelastic/damage behaviors of composite solid propellant for underwater intelligent equipment". This paper studies adhesive failure behaviors of multi-material structure in underwater intelligent equipment, which includes the propellant layer/lining layer/adiabatic layer/aluminum layer. First, the hyperelastic mechanical properties for ethylene–propylene–diene monomer for adiabatic layer are predicted by using the Mooney–Rivlin constitutive model, where the material parameters are fitted by combining with theoretical and experimental load curves. Second, the adhesive failure between the propellant layer and the lining layer is predicted for the designed multiple material layers under shear loads by combining with the bilinear cohesive model, the constitutive models for the propellant and adiabatic layer materials. Finally, the adhesive failure mechanisms and the load responses are studied for the shear specimens. [ABSTRACT FROM AUTHOR]

This paper conducted experiments and theoretic analysis of the fracture performance of pultruded GFRP (Glass Fiber Reinforced Polymers) laminates. The mode-I fracture toughness of pultruded GFRP laminates was evaluated by the eccentrically loaded, Extended Compact Tension (ECT) specimen. The geometry of specimen and experimental procedure refer to ASTM E1922. A total of 16 specimens were tested, which included 0° and 90° roving orientation. Finite element analysis with the Virtual Crack Closure Technique (VCCT) was implemented to calibrate the experimental results. A correction function for normalized notch length was proposed for pultruded GFRP translaminar fracture toughness. Carpet plot was designed to discuss the relationship between fiber volume ratio and fracture toughness, which demonstrated that the fracture toughness strongly correlated with the fiber volume ratio. Also, the effect of fraction of 0° layers on fracture toughness and material orthotropy was studied. The relationship of material orthotropy parameter and fracture toughness was discussed. [ABSTRACT FROM AUTHOR]

In the context of the eXtended Finite Element Method (X-FEM), the use of two level set functions allows the representation of the crack to be achieved regardless of the mesh. The initial crack geometry is represented by two distinct level set functions, and the crack propagation is simulated by an update of these two level set functions. In this paper, we propose a new approach, based on the Fast Marching Method (FMM), to update the level set functions. We also propose a new implementation of the FMM, designed for tetrahedral volume meshes. We then extend this method to all types of volume elements (tetrahedra, hexahedra, pentahedra, pyramids) available in a standard finite element library. The proposed approach allows one to use the same mesh to solve the mechanical problem and to update the level set functions. Non-planar quasi-static crack growth simulations are presented to demonstrate the robustness of the approach, compared to existing methods based on the integration of Hamilton-Jacobi equations or geometric approaches. [ABSTRACT FROM AUTHOR]