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In order to investigate the effects of stress triaxiality, Lode angle, temperature and strain rate on the fracture characteristics of 6061-T651 aluminum alloy materials, the mechanical property tests of materials are carried under different stress states, temperature and strain rate using universal material testing machine. Firstly, the mechanical property test results show that the fracture strain of 6061-T651 aluminum alloy material decreases with the increase of stress triaxiality. And also, the fracture strain of material related to the Lode angle parameter, especially the effect of the Lode angle more significantly at the range of lower stress triaxiality. When the temperature less than 250 ℃, the temperature of material has significant influence on its flow stress, while the influence of temperature on its fracture strain can be ignored. While the temperature more than 250℃, the temperature of material has greatly influence on its flow stress and fracture strain. Moreover, the strain rate has no significant effect on the fracture strain of 6061-T651 aluminum alloy. Subsequently, basing on the test results of mechanical properties, the Modified Johnson-Cook(MJC) criterion is obtained by modifying Johnson-Cook(J-C) fracture criterion, and the parameters of MJC and Modified Mohr-Coulomb(MMC) fracture criterion are calibrated. Finally, the impact test of sphere projectile penetrating the 6061-T651 aluminum alloy target plate is conducted on a one-stage gas gun, and also the ballistic limit velocity and failure mode of target are obtained. In order to verify the validity of the model and parameters, and the corresponding 3D model of projectile impact target is established by using ABAQUS/Explicit finite element software. The results showed that the prediction results of Lode angle dependent MMC fracture criterion is closer to the test compared with the Lode angle independent MJC fracture criterion. [ABSTRACT FROM AUTHOR]

We present a survey of the research into the problems of fracture mechanics of solid bodies with V-shaped notches. The methods used for the solution of plane problems of the theory of elasticity in the domains with corner points on the boundary contours are analyzed. Special attention is given to the unified approach to the solution of the problems of stress concentration near sharp and rounded V-shaped notches in elastic domains. The fracture criteria for solid bodies with V-shaped notches are analyzed. On the basis of the solution of plane elastoplastic problem within the framework of the model of plastic strips for a plane with infinite rounded V-shaped notch, we propose a new deformation fracture criterion for quasibrittle bodies with sharp and rounded V-shaped notches. [ABSTRACT FROM AUTHOR]

Abstract: This article deals with the calibration of a fracture criterion that has been implemented in a material model in LS-DYNA. The failure process in thin-walled metallic materials is complex and often due to interaction between plastic instability phenomena and ductile fracture. The material failure often occurs due to highly localized plastic deformation originating from plastic instability. The present work aims at establishing an in-plane shear test, which gives direct information about the phenomenon of ductile fracture, and a numerical scheme for identification of the fracture parameter. Shear tests of extruded plates in AA7108 temper T6 were carried out, and the fracture parameter was found through inverse modeling. AA7108 has previously been characterized and an anisotropic yield criterion has been calibrated with simple material tests including standard uniaxial tensile tests and through-thickness compression tests. It is discussed how the yield criterion calibration can be improved through in-plane shear tests and related numerical analyses. In order to evaluate the model and calibration, simple three-point bending tests of the same material were carried out. In these tests, the nose shape of the indenter was varied. Numerical analyses of the tests were then carried out with the implemented model and identified model parameters. [Copyright &y& Elsevier]

• Application of AENDB specimen for mixed mode I/II fracture toughness of PUR foam. • Relationship between mixed mode fracture toughness envelope and foam density. • Lower fracture toughness and fracture initiation angle compared to the other test samples. • Prediction of test data with the Maximum tangential stress/strain criteria. Rigid foam materials are among the low strength structural components that can be failed catastrophically under mechanical loads. Low fracture toughness is therefore a major failure mode in these materials and researchers try to find suitable testing methods for determining the fracture toughness of foam materials. In this research a suitable test specimen that is an edge notch disc bend specimen subjected to asymmetric three-point bending and called Asymmetric Edge Notch Disc Bend (AENDB) is proposed for conducting mixed mode I/II fracture experiments on polyurethane (PUR) foam with different cell densities. The geometry factors of the specimen that are required for determining the stress intensity factors were determined by means of the finite element analyses for different mode mixities. The mixed mode I/II fracture toughness envelope and fracture initiation angle were obtained for the (AENDB) specimen made of three foam densities ranging from 100 to 300 kg/m3. For example, K Ic and K IIc values were varied in the ranges 0.08–0.31 MPa.m0.5 and 0.09–0.34 MPa.m0.5, respectively. It was observed that the fracture toughness data are increased for all mode mixities by increasing the foam density. However, the mixed mode fracture curve and fracture initiation directions obtained from the AENDB specimen were lower than the corresponding curves of other mixed mode I/II test samples such as asymmetric semi-circular bend (ASCB) specimen. This can be attributed to the plane strain condition that is obtained at the mid-section of the AENDB specimen, since the crack front length in the AENDB specimen is significantly greater than the ASCB specimen. Finally, the experimental results obtained from the AENDB specimen were predicted using two fracture criterions. The results of this research indicate that the suggested AENDB specimen is a good candidate mixed mode I/II fracture configuration for investigating foam and other similar cellular materials. [ABSTRACT FROM AUTHOR]

The effect of the hole-edge condition on the hole-expansion ratio (HER) of ferrite-bainite (FB) dual-phase steel is analyzed by developing a dual-scale finite element (FE) approach. The proposed dual-scale approach consists of macroscale simulation of hole expansion test (HET) and microscale simulation for capturing localized inhomogeneous deformation at the microstructure level. The macroscale HET simulation considers the experimentally measured hole-edge geometry and hardness profile under different clearance conditions. The deformation history in the region of interest calculated from the macroscale simulation was transferred to the microscale simulation as boundary conditions. In the microscale simulation, the deformation inhomogeneity within the two-phase microstructure was calculated by considering the dislocation pile-up at the grain boundaries. In the experimental aspect, the geometry and surface roughness of the hole edge, which are factors for quantifying the damage from the punching process, were measured using a confocal microscope. The work hardening of the material was quantitatively analyzed by measuring the hardness profile in the radial direction from the hole edge. For the work hardening due to the punching process, the measured hardness is converted into an equivalent plastic strain, which is transferred to both macro-and microscale models in the form of pre-strain. The predicted HERs are compared with the experimentally measured HER values, and it is confirmed that the damage caused by punching is critical to the hole expansion formability of the dual-phase FB steel. [ABSTRACT FROM AUTHOR]

• The physical meanings of two incremental-J-integral-based fracture criteria are provided. • How to utilize tractions on crack surfaces to replace FPZ is given. According to a previous paper (Lu LK, Liu ZL, Zhuang Z. Eng Frac Mech. 2021, 254: 107907), the Rice J-integral can be generalized into two incremental J-integrals for crack growth in elastic-plastic materials: one is based on free energy density, and the other is based on internal energy density. This paper aims at providing the physical meanings of these two criteria. The fracture criterion of incremental-J-integral based on free energy corresponds to a direct generalization of the classic Griffith equilibrium condition. This fracture criterion means no net change in total energy during the quasi-static crack growth in an elastic-plastic solid. For a small crack extension, the body's potential energy is reduced by a value, which can be balanced by the increment of plastic dissipation work plus an extra energy term. The crack growth could happen if this extra energy term equals the energy required for forming these new crack surfaces. For the incremental-J-integral based on the internal energy density, its fracture criterion is a direct result of the first law of thermodynamics of a cracked body containing two independent thermodynamic systems: the volumetric and surface systems. In addition, the cases that a part of crack surfaces has tractions are discussed. If the loaded part of crack surfaces is stationary during crack growth, the results are identical to cases that crack surfaces are traction-free. If the loaded-part of crack surfaces moves with the growing crack tip, the derived fracture criteria become the incremental J-integral criteria in which the integral contour is a boundary of this loaded-part of crack surfaces. [ABSTRACT FROM AUTHOR]

The cracks formed in the hot deformation are typical defects caused by plastic capacity limitations. For tested steels, the fracture behavior is associated with temperature, strain rate, and stress state. In this study, a highly crack-sensitive steel with Nb micro-alloying is selected as the research material to establish the fracture criterion considering the above factors comprehensively. First, compression and tension experiments are performed, and various specimen geometries are designed to produce different stress states in the tests at different temperatures and strain rates. Second, the critical stroke of these tests is extracted, and corresponding calculations are completed using the finite element method (FEM). The loading paths of stress states are independent of temperature and strain rate; however, they differ when distinct specimen shapes are considered in the tests. Third, a high–temperature Mohr–Coulomb criterion, which is applicable at elevated temperatures, is established by considering the effects of temperature, strain rate, and stress states on fracture. Finally, some examples of compressive and tensile tests are employed for verifying the formulated fracture criterion. By comparing the FEM and experimental results, it is found that the fracture criterion could accurately describe the fracture behavior during hot deformation with distinct stress paths. • Various stress states and stress paths are used in the tests for modeling at elevated temperatures. • In-situ observation of fracture based on CLSM. • A modified Mohr–Coulomb criterion is established by considering the influences of stress state, temperature, and strain rate. • Fracture analysis and model validation are accomplished based on the combined experimental and FEM results. [ABSTRACT FROM AUTHOR]

To demonstrate the importance of incorporating Lode angle into fracture criterion in predicting the penetration resistance of high-strength steel plates, ballistic tests of blunt-nosed projectiles with a diameter of 5.95 mm impacted 4 mm thick Weldox 900 E steel plates were conducted. Impacting velocity range was 136.63~381.42 m/s. The fracture behavior and the ballistic limit velocities (BLVs) were obtained by fitting the initial-residual velocities of the projectiles. Subsequently, axisymmetric finite element (FE) models parallel to the tests were built by using Abaqus/Explicit software, and the Lode-independent Johnson–Cook (JC) and the Lode-dependent ASCE fracture criterion were incorporated into the finite element model for numerical simulation. Meanwhile, to verify the sensitivity of the mesh size in the numerical simulation, different mesh sizes were used in the shear plug area of the target. It can be found that Weldox 900 E steel has obvious mesh size sensitivity by comparing the experimental results and numerical simulation, and the JC fracture criterion and the ASCE fracture criterion predicted similar BLV for the same mesh size. [ABSTRACT FROM AUTHOR]

Fracture toughness is a critical input parameter for fracture-mechanics based fitness-for-service assessments, and it is preferable to determine this by experiment. In the present paper, fracture toughness of rock/concrete bimaterial interface was obtained by the tests which were performed on the universal material tester. A beam specimen with single-edge crack is used to form the different fracture mode mixity. The stress intensity factors of specimen per unit load with different combinations of K1 and K2 were calculated by the mixed hybrid finite element method on the principals of linear elastic interface fracture mechanics. By regressing the critical stress intensity factors of 7 specimen groups, two experiential fracture criterions of mixed crack interface were derived, and the fracture toughness($K_{1{\rm{C}}}^* $, $K_{2{\rm{C}}}^* $) of rock/concrete were obtained further. [ABSTRACT FROM AUTHOR]

The aim of this work is to assess the fracture risk prediction of the cancellous bone in the body of a lumbar vertebra when the mechanical parameters of the bone, i.e. stiffness, porosity, and strength anisotropy, of elderly and osteoporotic subjects are considered. For this purpose, a non-linear three-dimensional continuum-based finite element model of the lumbar functional spinal unit L4--L5 was created and strength analyses of the spongy tissue of the vertebral body were carried out. A fabric-dependent strength criterion, which accounts for the micro-architecture of the cancellous bone, based on histomorphometric analyses was used. The strength analyses have shown that the cancellous bone of none of the subject types undergoes failure under loading applied during normal daily life like axial compression; however, bone failure occurs for the osteoporotic segment, subjected to a combination of the compression preloading and moments in the sagittal or in the frontal plane, which are conditions that may not be considered to occur 'daily'. In particular, critical stress conditions are met because of the high porosity values in the horizontal direction within the cancellous bone. The computational approach presented in the paper can potentially predict the material fracture risk of the cancellous bone in the vertebral body and it may be usefully employed to draw failure maps representing, for a given micro-architecture of the spongy tissue, the critical loading conditions (forces and moments) that may lead to such a risk. This approach could be further developed in order to assess the effectiveness of biomedical devices within an engineering approach to the clinical problem of the spinal diseases. [ABSTRACT FROM AUTHOR]

In the present investigation, the Gmax criterion, which is based on the elastic strain energy principle, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the plastic strain energy and, hence, a new elasto-plastic energy-based model is presented. Subsequently, the proposed model is employed to predict fatigue crack growth in rectangular steel plates under complex stress states. The results obtained using the elasto-plastic energy model proposed are compared with those obtained using the commonly used Paris law and our experimental data. [ABSTRACT FROM AUTHOR]

A ring shaped specimen is used for studying mixed mode fracture in brittle materials. The ring specimen is subjected to a compressive diametral load and contains two angled central cracks. A series of fracture tests are conducted under various mode mixities using the ring specimen. It is shown that the obtained experimental results are in a very good agreement with theoretical predictions of the modified maximum tangential stress criterion. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the ballistic resistance of double-layered steel shields against projectile impact at the sub-ordnance velocity is evaluated using finite element simulations. Four types of projectiles of different weight and nose shapes are considered, while armor shields consist of two layers of different materials. In a previous study of the same authors, it was shown that a double-layered shield of the same metal was able to improve the ballistic limit by 7.0–25.0% under impact by a flat-nose projectile, compared to a monolithic plate of the same weight. Under impact by a conical-nose projectile, a double-layered shield is almost as capable as a monolithic plate. The present paper extends the analysis to double-layered shields with various metallic material combinations. The study reveals that the best configuration is the upper layer of high ductility and low strength material and the lower layer of low ductility and high strength material. This configuration results in some 25% gain in the ballistic limit under moderate detrimental impact. This research helps clarify the long standing issue of the ballistic resistance of the multi-layered armor configuration. [Copyright &y& Elsevier]

Abstract: Due to its close proximity to realistic conditions in engineering structures the angled crack problem has been given special attention in the recent years by fracture mechanics investigators. In this study, experimental and theoretical investigations were conducted to characterize the fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack. The inclined angle of the crack with respect to the axis of loading was varied between 0° and 90°. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a circular shape plastic zone with a constant radius. The commonly employed fracture criterion, the minimum strain energy density criterion, is modified by adopting the von Mises elasto-plastic boundary. The threshold condition of fracture is also established based on the experimental data. Finally, the influence of material microstructures on fatigue crack growth is assessed using the scanning electron microscope (SEM). [Copyright &y& Elsevier]

The critical fracture criterion of a cylinder with V-notches on the inner surface under explosive loading is studied. The functional expression of relationship between stress concentration factor and non-dimensional geometrical structure parameters is fitted through results of a series of calculation models using the numerical simulation method. The damage evolution equation is modified on the base of Feng jia-bo's study given the stress-strain field at the root of V-notch effected on the accelerating growth of holes or cracks. Assuming the natural expansion rate of the cylinder to be constant, the critical fracture criterion of the cylinder with notches on the inner surface is obtained. Results of theoretical analysis and the experimental results are consistent with each other. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the explicit solutions of free-edge stresses near circumferential cracks in surface coatings of circular torsion bars and their application in determining the progressive cracking density in the coating layers. The problem was formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses near crack tip and the shear stresses in the cross-section of the torsion bar were approached in explicit forms based on the variational principle of complementary strain energy. Criterion for progressive cracking in the coating layer was established in sense of strain energy conservation, and the crack density is thereby estimated. Effects of external torque, aspect ratio, and elastic properties on the density of progressive cracking were examined numerically. The present study shows that, in the sense of inducing a given crack density, compliant coating layer with lower modulus has much higher critical torque than that of a stiffer one with the same geometries and substrate material, i.e., compliant coating layer has greater cracking tolerance. Meanwhile, the study also indicates that thicker surface coating layer is more pliant to cracking than the thinner ones. The present model can be used for analyzing the damage mechanism and cracking tolerance of surface coatings of torsion shafts and for data reduction of torsional fracture test of brittle surface coatings, etc. [Copyright &y& Elsevier]

Abstract: Behaviour of an atomic structure in the vicinity of the crack tip is simulated. Buckling and postbuckling deformation of three- and four-atomic cells at generalized tension is studied. A discrete-integral fracture criterion is proposed for normal rupture cracks when stress fields have a singular component, vectors of fields of stresses and deformations being collinear. When formulating the proposed criterion, we used the new rank of solutions, which differ from solutions applied in formulating the classical sufficient fracture criterion, in conformity with Novozhilov’s hybrid model. The proposed criterion permits limiting passage to necessary criterion when energetic characteristics of postbuckling deformation of cells can be neglected within the limit. Values of critical loads obtained in conformity with the sufficient criterion essentially differ from those obtained in conformity with the necessary criterion. [Copyright &y& Elsevier]

In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used σc, the ultimate stress, and Gc, the critical energy release rate. The third parameter is the characteristic length l as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials. [ABSTRACT FROM AUTHOR]

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material. [ABSTRACT FROM AUTHOR]

Four-point-bending V-notched specimens of lead zirconate titanate (PZT) poled parallel to the long axis are fractured under conditions of controlled crack growth in a custom-made device. In addition to the mechanical loading electric fields, up to 500 V/mm are applied parallel and anti-parallel to the poling direction, i.e., perpendicular to the crack surface. To determine the different contributions to the total energy release rate, the mechanical and the piezoelectric compliance, as well as the electrical capacitance of the sample, are recorded continuously using small signal modulation/demodulation techniques. This allows for the calculation of the mechanical, the piezoelectric, and the electrical part of the total energy release rate due to linear processes. The sum of these linear contributions during controlled crack growth is attributed to the intrinsic toughness of the material. The nonlinear part of the total energy release rate is mostly associated to domain switching leading to a switching zone around the crack tip. The measured force-displacement curve, together with the modulation technique, enables us to determine this mechanical nonlinear contribution to the overall toughness of PZT. The intrinsic material toughness is only slightly dependent on the applied electric field (10% effect), which can be explained by screening charges or electrical breakdown in the crack interior. The part of the toughness due to inelastic processes increases from negative to positive electric fields by up to 100%. For the corresponding nonlinear electric energy change during crack growth, only a rough estimate is performed. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to propose a new fracture criterion of rubber-like materials under plane stress loading. Our experimental data already published [A. Hamdi, M. Naït Abdelaziz, N. Aït Hocine, P. Heuillet, N. Benseddiq, Fracture criteria of rubber like-materials under plane stress conditions. Polym. Test. 25(9) (2006) 994–1005] are herein completed by results obtained from pure shear tests and then further analysed. In this analysis, we used a theoretical approach based on a reference axis change principle, introduced earlier by Nevière et al. [A strain based design criterion for solid propellant rocket motors. Proceedings OTAN, Symposium on Combat Survivability of Air, Sea and Land Vehicles, Alborg, Denmark, 2002, pp. 23–26] for the case of solid propellant materials. Logarithmic extensions evaluated in a specific coordinates system were introduced in the analytical development, which leads to identifying a relevant rubber fracture criterion. The ultimate experimental extensions were compared with the predictions of this criterion and good agreement was observed. [Copyright &y& Elsevier]

Abstract: The brittle fracture criterion is developed for a blunted crack. The curvature radius of the blunt crack tip is suggested as a characteristic length for brittle materials, and then the fracture toughness of the brittle materials can be determined from the cohesion strength and the characteristic length of the materials. [Copyright &y& Elsevier]

Abstract: A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K I, K II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens. [Copyright &y& Elsevier]

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction. [ABSTRACT FROM AUTHOR]

Abstract: The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and/or kinking of an interface crack in a two-dimensional bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations are employed with respect to each region. However, when the crack kinks into the matrix material, the non-hypersingular traction boundary integral equations are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack-tip controlled by the fracture criterion. Kinking of the interface crack is controlled by a criterion developed from the quasi-static one. Once the crack kinks into the matrix, its propagation is modeled by adding new elements of constant length to the moving crack-tip controlled by a criterion extended from the quasi-static maximum circumferential stress. The numerical results of the crack growth trajectory for different material combinations are computed and compared with the corresponding experimental results. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic propagation and deflection of an interface crack. [Copyright &y& Elsevier]

Narrow notches often cause damage that can lead to the destruction of components. The stress field in the vicinity of such crack-like notches in two-dimensional (2D) structures is similar to the stress field around equivalent cracks. Therefore similar investigations are necessary to predict the fracture load for components with cracks or narrow notches. Thus, the asymptotical stress field for a narrow notch with a rounded notch root is deduced from an Airy’s stress function. Based on this stress field a fracture criterion is developed. Comparing the theoretical fracture limit curves derived from the fracture criterion with experimental results it can be shown that for brittle material the local stress state at the fracture initiation point is the same for mode I, mixed-mode and mode II loading. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we attempt to derive a fracture criterion for filled and unfilled elastomer vulcanizates and thermoplastics from a set of experimental data. Firstly, fracture criteria reported in the literature have been applied to experimental data obtained from tests including various loading modes (simple tension, equal biaxial tension and biaxial tension) and performed on four materials: a natural rubber (NR), a styrene butadiene rubber (SBR), a polyurethane (PU) and a thermoplastic elastomer (TPE). Then, a new failure criterion based on an equivalent elongation concept is proposed. This equivalent elongation seems to be linearly dependent on a given biaxiality ratio , which leads to expressing the principal elongations at break as functions of both the biaxiality n and two experimental parameters. Quite good agreement is highlighted when comparing the failure experimental data with the proposed criterion for the tested elastomers. [Copyright &y& Elsevier]

Abstract: Resistance to the brittle cracks of single damascene line patterns on silicon wafers is investigated through three points bending tests. After loading, samples are observed by atomic force microscopy or field emission gun scanning electron microscopy, in order to detect cracks. For given load and pattern period, an appropriate numerical procedure allows calculation of the characteristic parameters of all the stress singularities, which appear along the dihedral lines at interfaces between the various materials. The most critical singularity is determined in terms of crack initiation according to a criterion combining stress intensity and energy release rate conditions. In these interconnects, crack initiation appears to be intrinsically governed by energy release conditions, so that short cracks are very difficult to initiate or propagate. The absence of detectable cracks after bending is in good agreement with this prediction. [Copyright &y& Elsevier]

Abstract: In the note, a fracture criterion of mixed-mode cracks is presented by considering the fracture parameters on the Nadai elastic–plastic boundary around a crack tip. The fracture analysis of center-inclined crack plate shows that the effect of different yield strengths in tension and compression on mixed-mode crack fracture is basically the same as that of the scatter of the fracture experimental data of brittle material. [Copyright &y& Elsevier]

Abstract: In order to predict the fracture direction and fracture loadings of cracked materials under the general mixed-mode state, this paper presents a new general mixed-mode brittle fracture criterion based on the concept of maximum potential energy release rate (MPERR). This criterion can be easily degraded to the pure-mode fracture criterion, and can also be reduced to the commonly accepted fracture criteria for the mixed-mode I/II state. In order to validate the proposed criterion, we have carried out the experiments with aluminium alloy specimens under various mixed-mode loading conditions. The experimental results agree well with the predictions of the proposed criterion. [Copyright &y& Elsevier]

The paper presents a physico-mechanical model for predicting creep rupture in neutron-irradiated materials. The model is based on the approach whereby damage is described as voids on grain boundaries. The equations for void nucleation and growth which were proposed by the authors earlier are augmented to include neutron irradiation of material. Constitutive equations are derived to describe viscoplastic deformation of material including void propagation. A criterion for plastic stability of a unit cell is employed as a fracture criterion. [ABSTRACT FROM AUTHOR]

Abstract: Fracture loads of ceramic components with rounded notches cannot be computed by linear elastic fracture mechanics techniques because no stress singularity exists. We propose a procedure to estimate such fracture loads, which is based on the cohesive zone model and supported by experimental evidence with alumina, zirconia and silicon ceramics. Data from 18 ceramic materials and different notched geometries were used. The only material parameters needed were the tensile strength and the fracture toughness. [Copyright &y& Elsevier]

Abstract: The material body considered in this work consists of multiphases. Digital imaging data are taken as the input to specify the configuration and composition of the specimen. Meshless method is demonstrated as a superior numerical tool to analyze crack initiation and propagation in multiphase material. A fracture criterion, based on the ratio of the opening stress over the material toughness distributed in front of the crack tip, is proposed to determine the direction of crack propagation of mixed mode fracture problem in multiphase material. Numerical results are presented and discussed. [Copyright &y& Elsevier]

The topic of the paper is the extension of the Maximum Circumferential Tensile Stress Criterion to orthotropic materials, to obtain the crack initiation angle and the fracture loci. It includes the effects of orthotropy, load biaxiality and non-singular terms. It requires the solution of the elastostatic problem of an orthotropic plate having a central inclined crack and subjected at infinity to a uniform biaxial load. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. The original problem has been transformed by rotation into a system of coordinates with one axis along the crack. The effects of the rotation of the reference system on the stress–strain equations as well as on the equilibrium equations have been considered. The stress field is represented in terms of two potential functions and the crack problem is solved by means of the superposition principle. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides a large number of experimental results from the fracture of round-notched samples of a material that remains essentially in the linear elastic regime up to crack initiation. Loading of the samples ranged from pure tensile up to bending. Notch acuity was changed by changing the notch tip radii, notch angle and notch depth. All these experimental results have been used to analyze the predictive capability of the cohesive crack model. All tests were numerically simulated and several criteria justifying the adopted softening function are discussed. The agreement between numerical prediction and experimental results was very good. [Copyright &y& Elsevier]

Abstract: Over the past 5 years, there has been increasing interest of the automotive, aerospace, aluminum, and steel industries in numerical simulation of the fracture process of typical structural materials. Accordingly, there is a pressure on the developers of leading commercial codes, such as ABAQUS, LS-DYNA, and PAM-CRASH to implement reliable fracture criteria into those codes. Even though there are several options to address fracture in these and other commercial codes, no guidelines are given for the users as to which fracture criterion is suitable for a particular application and how to calibrate a given material for fracture. The objective of the present paper is to address the above issues and present a thorough comparative study of seven fracture criteria that are included in libraries of material models of non-linear finite element codes. A set of 15 tests recently conducted by the authors on 2024-T351 aluminum alloy is taken as a reference for the present study. The plane stress prevails in all these tests. These experiments are compared with the constant equivalent strain criterion, the Xue–Wierzbicki (X–W) fracture criterion, the Wilkins (W), the Johnson–Cook (J–C) and the CrachFEM fracture models. Additionally, the maximum shear (MS) stress model, and the fracture forming limit diagram (FFLD) are included in the present evaluation. All criteria are formulated in the general 3-D case for the power law hardening materials and then are specified for the plane stress condition. The advantage of working with plane stress is that there is one-to-one mapping from the stress to the strain space. Therefore, the fracture criteria formulated in the stress space can be compared with those expressed in the strain space and vice versa. Fracture loci for all seven cases were constructed in the space of the equivalent fracture strain and the stress triaxiality. Interesting observations were made regarding the range of applicability and expected errors of some of the most common fracture criteria. Besides evaluating the applicability of several fracture criteria, a detailed calibration procedure for each criterion is presented in the present paper. It was found rather unexpectedly that the MS stress fracture model closely follows the trend of all tests except the round bar tensile tests. The X–W criterion and the CrachFEM models predict correctly fracture in all types of experiments. The W criterion is working well in certain ranges of the stress triaxiality. [Copyright &y& Elsevier]

Experimental results of the compression fracture strength of ceramic notched elements are summarized and analyzed in the present paper. The fracture model of ceramic notched elements under compression can be put forward based on Griffith's theory of brittle fracture. It is shown that the fracture of Al2O3 ceramics under compression loading is a typical brittle one induced by tensile stress, irrespective of whether the specimens are with or without a notch. The test results show that the product of the compression notch strength and the stress concentration factor is equal to the compression fracture strength, and the validity of the above-mentioned fracture model is thus checked. Finally, the procedures for predicting the fracture criteria with given survivability for A1203 ceramic notched elements can be developed based on the test results and the analysis mentioned above. [ABSTRACT FROM AUTHOR]

Blanking operation is widely used to cut sheet or plates by a shearing process between punch and die. The process of shearing and the conditions of the sheared surface are influenced by the punch, the die, the speed of punching, the lubrication, the clearance between the punch and the die, and the properties of the workpiece material. This study investigates the blanking operation of very thin sheet metals like membranes, which are used for lithium-polymer battery containers of cellular phones. The punch–die clearance and radius for a given sheet material and thickness are examined, using the finite element technique and Cockroft and Latham’s fracture criterion. This criterion successfully applied to a variety of loading situations, is used in the present investigation to estimate fracture locations during the deformation process. The shearing mechanism is studied by simulating the blanking operation of an aluminum foil and a copper foil. The numerical predictions are compared with the experimental results. [Copyright &y& Elsevier]

Various grinding defects were produced on the surface of specimen dental low fusion porcelain in an attempt to establish the relationship between defect size and fracture strength. In addition, the applicability of the process zone size-fracture criterion in assessing the material properties of dental low fusion porcelain was examined.Super porcelain AAA E3 (Noritake Co., Japan) was used as dental low fusion porcelain. The bending strength and fracture toughness value were estimated by the three-point bending test. After glazing, grinding flaws were introduced by grinding the specimen with abrasive papers of various mesh sizes. In order to calculate the fracture toughness value of dental low fusion porcelain, we introduced a surface crack using a Vickers indenter. The results were discussed based on the process zone size-fracture criterion. The size of cracks caused by grinding was estimated with the process zone size-fracture criterion and Newman–Raju formula.As the defect size decreased, the fracture stress approached the strength for smooth specimen without defect. The Kc value showed a tendency to approach the Klc value when the defect size increased. The relationship between the fracture stress, σF, and the equivalent crack length, ae, was in good agreement with the theoretical relations deduced from the criterion in dental low fusion porcelain. [Copyright &y& Elsevier]

In this paper, based on a solution of an elliptic cavity in piezoelectric ceramics with uniform loading at infinity, we analyze the stress and electric fields in the limit cases of the solution when the elliptical cavity tends gradually to a crack. The result in the zone near the crack tip is different from the result in the zone far away from the crack tip. The calculation results of a PZT-4 material are presented. Two new fracture criteria are developed for piezoelectric fracture in this paper. One is based on a generalized stress intensity factor related to the stress field at the tip of the crack and another is based on the crack opening displacement (COD) related to the relative displacement of crack faces. PZT-5h ceramics with a center crack were subjected to the combined effect of mechanical load and electrical load in this experiment to analyze the effect of electric field on fracture. The measured fracture toughness of central crack specimens of poled soft lead zirconate titanate ceramics (PZT-5) is presented to compare with the theoretical results. Some existing fracture criteria are examined through the comparison of their calculation results and the experimental results. [Copyright &y& Elsevier]

Using a probabilistic fracture mechanics code, the importance of the choice of fracture criterion and the material fracture resistance characterization at the crack tip is elucidated in the failure probability analysis of an reactor pressure vessel. The paper describes the procedure to evaluate the crack extension based on R6, where an increase in fracture resistance by ductile crack extension is considered. Two standard J–resistance curves are prepared for applying the elasto-plastic fracture criterion by R6 tearing.Case studies concerning the effect of the tearing fracture criterion were carried out using a severe pressurized thermal Shock transient. Results are discussed with respect to the fracture criterion, the material J–resistance curve, the algorithm for evaluating the crack tip fracture toughness and the initial crack geometry.The introduction of the elasto-plastic fracture criterion significantly contributes to removal of over-conservatism in applying a linear elastic fracture criterion. It was also confirmed that the algorithm of the re-evaluation method for crack tip fracture toughness has to be correctly applied. [Copyright &y& Elsevier]

A piezoelectric material with a Griffith crack perpendicular to the poling axis is analyzed within the framework of the theory of linear piezoelectricity. Using exact electric boundary conditions at the crack surfaces, the nonlinear behavior between the electric displacement at the crack faces and applied loading is given, and it can be approximated by a linear relation on applied electric field. The Fourier transform technique is employed to reduce the mixed boundary value problem to dual integral equations. Solving resulting equations, expressions for the electroelastic field in the entire plane are obtained explicitly for a cracked piezoelectric material subjected to uniform combined electromechanical loading. The distribution of asymptotic field and the intensity factors of electroelastic field as well as the elastic T-stress are determined. Particularly, the maximum hoop strain sθθ is suggested as a fracture criterion for piezoelectric materials. Based on this criterion, relevant experimental results can be explained successfully. As an illustrative example, theoretical predictions for PZT-4 ceramic with a crack are in excellent agreement with existing experimental data, not only in qualitative behavior but also in quantitative results. [Copyright &y& Elsevier]

Steady-state intersonic propagation of a shear crack is considered, with the admission of cohesion across the crack faces. The asymptotic limit of "small-scale cohesion", which occurs when the magnitude of the cohesive stress far exceeds that of the applied stress, is developed explicitly, to obtain a criterion of "Barenblatt" type. The application of this criterion requires only the calculation of the "applied" stress in- tensity coefficient with cohesion disregarded; an equation of motion follows by equating this coefficient to a "modulus of cohesion" which depends on the cohesive model that is employed. An explicit formula for the "modulus of cohesion" is given for the special case of a cohesive zone of Dugdale type. [ABSTRACT FROM AUTHOR]

Forming limit curves at neck (FLCN) and forming limit curves at fracture (FLCF) for various steel sheets were determined from a hemispherical punch stretching. The measured FLCF of the sheets with higher ductility limit had approximately linear shape like one of the bulk forming process. Whereas, the FLCF of the sheets with relatively lower ductility limit had a rather complex shape approaching the FLCN towards the equi-biaxial strain paths. Some experimental FLCFs of aluminum sheets and steel sheets were compared with the fracture strains predicted from some ductile fracture criteria reported in the literature. To determine the constants in the various ductile fracture criteria, a numerical procedure, which is based on plane stress condition and Barlat’s nonquadratic anisotropic yield criterion, was used. To predict precisely the experimental FLCFs with both the linear shape and the complex shape approaching the FLCN towards the equi-biaxial strain paths, from a combination of the Cockroft–Latham ductile fracture criterion and the maximum shear stress criterion, an empirical ductile fracture criterion in sheet metal forming process was newly suggested. The empirical criterion could be used to predict the FLCFs with the rather complex shape as well as the linear shape. [Copyright &y& Elsevier]

The bonded area is largely affected by the surface morphology and mechanical properties of materials by surface activated bonding (SAB) process, because the room temperature bonding process is carried out under a low temperature and low pressure for short time. Accordingly, interfacial defects cause fatally harmful problems in many cases. For an application of this technique, it is important to know the effect of interfacial defects on fracture behavior. The fracture mechanism and its criterion for the growth of interfacial defects were investigated using the Al/sapphire joint. It became clear that the growth of interfacial defects is the dominant factor for crack propagation. An estimation of stress intensity factor for the growth of interfacial defects was tried in two ways, stress criterion and energy criterion. A critical stress intensity factor for the growth of interfacial defects was estimated as 0.3–0.5 MPa m[sup 1/2] by the analysis of FEM calculation and experimental observation. [ABSTRACT FROM AUTHOR]

Based on a large experimental sample, the influence of stress triaxiality and temperature have been studied on the growth of micro voids and the ductile/brittle transition (DBT) of 40 Cr steel. Ductile and brittle fractures have been investigated simultaneously. The experiments show that the ductile fracture is controlled by the micro void mechanism, and the critical void growth ratio can be used as the criterion of ductile fracture. The brittle fracture is modeled by an embedded penny crack, and a micro stress intensity with a characteristic length can be used as the criterion of the brittle fracture. The DBT is the result of the competition of the two mechanisms. Which exists in the fracture of all specimens simultaneously. The distributions of model parameters were measured experimentally. A random model and a random-fuzzy model for DBT were presented. The comparison between the calculated and experimental results shows that the random-fuzzy model can model the DBT satisfactorily. [ABSTRACT FROM AUTHOR]

The objective of this paper is to show the advantages of the cohesive crack model for predicting fracture of V-notched components. Critical values of the generalized stress intensity factor can be obtained from the knowledge of the material softening function and the elastic parameters, avoiding a cumbersome experimental work. The results were checked successfully against experimental ones, from other authors, in different materials: steel, aluminium, PMMA and PVC. A non dimensional formulation of the fracture criterion for sharp V-notched components was obtained and a simple approximate expression derived for easy appication. [ABSTRACT FROM AUTHOR]

In our previous experiments, the tensile net fracture stress of double-edge-notched carbon-carbon composite (C/C) specimens has been in some cases much higher than that of smooth specimens. To optimally utilize this phenomenon, the tensile fracture behaviour of multi-holed C/Cs with cross-ply lamination was examined. Multi-holed specimens with different numbers of holes and different distances between the holes were prepared and tensile fracture tests were conducted. FEM calculations were performed in order to study the stress distributions during the tensile tests. Higher tensile strength than that of smooth specimens was obtained in an optimal case on the basis of averaged net stress. The strength dependency on the specimen geometry could be explained mainly by the load sharing effect among the ligaments. [ABSTRACT FROM AUTHOR]