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• Enormous plasticity occurs under tension at –196 °C in a high-strength bcc steel that is brittle in toughness tests. • The transition of failure mechanisms at –196 °C shows significant stress state dependence. • A unified fracture criterion is proposed to describe cryogenic fracture covering a broad range of stress states. • A threshold triaxiality governing the transition of failure mechanisms depends on strain hardening capacity and fracture strength. The fracture properties of a high-strength steel with a body-centered cubic (bcc) crystal structure have been characterized at –196 °C by performing tensile tests with different specimen geometries, three-point bending tests using Charpy specimens, and fracture mechanics tests, covering a broad range of stress states under quasi-static conditions. Both strength and ductility of the bcc steel are significantly increased when the temperature is decreased from room temperature to –196 °C. Enormous plasticity occurs in the material during tensile tests using various specimens at –196 °C, while macroscopic brittle fracture takes place in high triaxiality scenarios. A stress state dependence of ductile to brittle transition properties is observed, as the failure mechanisms at –196 °C change from cleavage fracture to shear failure with decreasing stress triaxiality. A unified stress-state-dependent fracture criterion, which considers the transition of failure mechanisms, is proposed to describe the fracture properties of similar bcc materials at cryogenic temperatures. The threshold triaxiality at which the transition of failure mechanisms takes place is a material property that is determined by the strain hardening capacity and fracture strength. In addition, a probabilistic formulation relying on the extreme value distribution has been incorporated into the model to render the statistical nature of cleavage fracture. [ABSTRACT FROM AUTHOR]

A modified ductile fracture criterion is proposed based on the traditional Ayada criterion and coded into the finite element simulation platform of VUMAT/ABAQUS for prediction and analysis of ductile fracture in metal plastic strain processes. In this modified ductile fracture criterion, stress triaxiality is taken into account, and more importantly, the exponential effect of the equivalent plastic strain on the damage behavior, which is generally ignored in other ductile fracture criteria, is also considered. The material related constants in the modified ductile fracture criterion are determined by tensile tests together with finite element simulations. The applicability and reliability of the ductile fracture criterion in ductile fracture prediction in two types of classic stress states, viz. shear stress, tensile stress in sheet metal forming, are investigated based on the deformation behavior and fracture occurrence in two case studies with two typical types of materials, i.e. Al 6061 and T10A. The materials have a wide range of plasticity. The simulation and experimental results verify the applicability and reliability of the developed ductile fracture criterion in prediction of the ductile fracture with and without necking in different stress states of plastic strain. [ABSTRACT FROM PUBLISHER]

Few studies have focused on the interface fracture performance of zirconia/veneer bilayered structure, which plays an important role in dental all-ceramic restorations. The purpose of this study was to evaluate the fracture mechanics performance of zirconia/veneer interface in a wide range of mode-mixities (at phase angles ranging from 0° to 90°), and to examine the effect of mechanical properties of the materials and the interface on the fracture initiation and crack path of an interfacial crack. A modified sandwich test configuration with an oblique interfacial crack was proposed and calibrated to choose the appropriate geometry dimensions by means of finite element analysis. The specimens with different interface inclination angles were tested to failure under three-point bending configuration. Interface fracture parameters were obtained with finite element analyses. Based on the interfacial fracture mechanics, three fracture criteria for crack kinking were used to predict crack initiation and propagation. In addition, the effects of residual stresses due to coefficient of thermal expansion mismatch between zirconia and veneer on the crack behavior were evaluated. The crack initiation and propagation were well predicted by the three fracture criteria. For specimens at phase angle of 0, the cracks propagated in the interface; whereas for all the other specimens the cracks kinked into the veneer. Compressive residual stresses in the veneer can improve the toughness of the interface structure. The results suggest that, in zirconia/veneer bilayered structure the veneer is weaker than the interface, which can be used to explain the clinical phenomenon that veneer chipping rate is larger than interface delamination rate. Consequently, a veneer material with larger fracture toughness is needed to decrease the failure rate of all-ceramic restorations. And the coefficient of thermal expansion mismatch of the substrates can be larger to produce larger compressive stresses in the veneer. [ABSTRACT FROM AUTHOR]

The paper concentrates on in situ bending tests and analysis of the failure of materials exhibiting strong anisotropy. As a typical example, Ti 2 AlC microcantilevers (MCs) were scrutinized. The anisotropic flexural strength of Ti 2 AlC MCs was measured, and the strength of the strong orientation was found to be two and half times as high as that of the weak orientation. The transition of fracture strength and mechanisms could be evaluated. Our findings have generic implications for future study on the fracture behavior of layered materials. [ABSTRACT FROM AUTHOR]

In this investigation, ductile fracture in stiffened and unstiffened panels is simulated employing the fracture criterion, which depends on the mesh size, stress state and damage induced softening. The aim of the study is to show that employed fracture criterion removes mesh size effects more efficiently than traditional fracture criteria adjusted only on the basis of uniaxial tension. Fracture model is implemented into Finite Element software ABAQUS using user-defined material, VUMAT-subroutine, available for shell elements. Mesh size sensitivity analysis is carried out. Finite element simulation results are validated with experimental measurements available in literature. Comparison of numerical and experimental results shows that simulations effectively capture most of the experimentally observed features, especially when considering different mesh densities. In most cases, mesh size effects are considerably reduced compared with the fracture criteria adjusted on the basis of a uniaxial tension. [ABSTRACT FROM AUTHOR]

Abstract: A nonlocal fracture criterion with accounting of the work during bonds deformation at a fracture process zone has been implemented analytically for analysis of quasistatic cracks growth along a weak interface. The criterion consists of two clauses: (1) the necessary energy condition of the crack tip limit equilibrium which takes into account the energy release rate to the crack tip and the rate of the deformation energy consumed by bonds in the crack process zone; (2) the sufficient condition is the equality of the crack opening at the process zone trailing edge to the bond limit stretching. Subcritical and quasi-statical regimes of cracks growth are analyzed for the case of a homogeneous plate with internal straight bridged crack and bonds traction which is constant and independent of the external loading. The critical fracture stress and the crack bridged zone size in the limit equilibrium state have been determined and analyzed. The limit case of a crack which is filled with bonds is considered as a weak interface model. [Copyright &y& Elsevier]

We present the results of a large series of experiments aimed at the study of laws of damage accumulation and fracture in highly filled polymer materials under loading conditions of various types: monotone, repeated, low- and high-cycle, with varying type of stress state, dynamic (in general, more than 50 programs implemented on specimens from one lot of material). The data obtained in these test allow one to make conclusions about the constitutive role of the attained maximum of strain intensity when estimating the accumulated damage in the process of uniaxial tension by various programs (in particular, an additional cyclic deformation below the preliminary attained strain maximum does not affect the limit values of strain and stress in the subsequent active extension), about the strong influence of the stress state on the deformation and fracture, about the specific features of the nonlinear behavior of the material under the shock loading conditions and its influence on the repeated deformation. All tests are described (with an accuracy acceptable in practical calculations, both with respect to stresses and strains in the process of loading and at the moment of fracture) in the framework of the same model of nonlinear viscoelasticity with the same set of constants. The constants of the proposed model are calculated according to a relatively simple algorithm by using the results of standard uniaxial tension tests with constant values of the strain rate and hydrostatic pressure (each test for 2-3 levels of these parameters chosen from the ranges proposed in applications, each loading lasts until the fracture occurs, and one of the tests contains an intermediate interval of total loading and repeated loading) and one axial shock compression test if there are dynamic problems in the applications. The model is based on the use of the criterion fracture parameter which, in the class of proportional loading processes, is the sum of partial increments of the strain intensity on active segments of the process (where the strain intensity is at its historical maximum) with the form of the stress state and the intensity of strain rates taken into account. [ABSTRACT FROM AUTHOR]

Highlights: [•] Formulate a semi-analytic method for determining interfacial stresses of hard coatings. [•] Investigate the dependency of interfacial stresses upon structural and material parameters. [•] Determine the spacing of progressive cracking in hard coatings based on an energy criterion with refined stress field. [Copyright &y& Elsevier]

The basic results of establishing the foundations of the mechanics of fracture of homogeneous materials compressed along cracks and inhomogeneous (composite) materials compressed along interface cracks are analyzed. These results were obtained using elastic, plastic, and viscoelastic material models. This review consists of three parts. The first part discusses the basic concept that the start (onset) of fracture is the mechanism of local instability near the cracks located in a single plane or parallel planes. The fracture criterion and the basic problems arising in this division of fracture mechanics are also formulated. Two basic approaches to establishing the foundations of the mechanics of fracture of materials compressed along cracks are outlined. One approach, so-called beam approximation, is based on various applied theories of stability of thin-walled systems (including the Bernoulli, Kirchhoff-Love, Timoshenko-type hypotheses, etc.). This approach is essentially approximate and introduces an irreducible error into the calculated stresses. The other approach is based on the basic equations and methods of the three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains. This approach does not introduce major errors typical for the former approach and allows obtaining results with accuracy acceptable for mechanics. The second part offers a brief analysis of the basic results obtained with the first approach and a more detailed analysis of the basic results obtained with the second approach, including the consideration of the exact solutions for interacting cracks in a single plane and in parallel planes and results for some structural materials. The third part reports new results for interacting cracks in very closely spaced (or coinciding, as an asymptotic case) planes. These results may be considered a transition from the second approach (three-dimensional linearized theory of elastic stability) to the first approach (beam approximation). This is how the accuracy of results produced by the first approach is evaluated and the boundary conditions near the crack tip are established in the second approach. [ABSTRACT FROM AUTHOR]

As a result of growing safety-related requirements in shipbuilding the design of double hulls in respect to accidents and collisions is mainly orientated on damage stability calculations. In order to increase the collision resistance and thereby the damage stability of ships the concept of an alternative stiffening system (English: plates strengthened stiffeners, German: Plattenverstärkte Profilsteifen – PVPS) invented by Röhr et al. (2008) was investigated for practical use within the scope of the project SideColl, funded by the German Federal Ministry of Economics and Technology (BMWi). A collision experiment with a scaled double hull structure is performed with the alternative stiffening system. Beside the experimental investigations numerical simulations with the finite element software LS-Dyna are conducted. With the adaption of suitable discretizations and fracture criteria in the finite element model the structural response in terms of the force-displacement curve are well predicted. Furthermore, the crack initiation and the failure mechanism are captured in good agreement with the experiment. An equivalent model for weld joints is applied to the double hull structure to reproduce the different material behavior at plastic deformations and fracture in the numerical analysis. [ABSTRACT FROM AUTHOR]

• Several uncoupled fracture criteria were implemented into the CPFEM to predict the fracture behaviour of the cross-scaled components. • With the decrease of t/d (1.07∼24.26), the fracture strain and stress decrease generally, but there are abnormal phenomena in some areas due to random texture. • A reasonable fracture criterion with the less affected fracture threshold by random texture is obtained, viz., the equivalent stress fracture criterion. • The scattering distribution function of cross-scaled component fracture behaviour under different t/d is obtained. Product miniaturisation has increased the demand for cross-scaled components with various sized features covering the macroscale (mm-scale) and mesoscale (μm-scale). During the sheet metal forming process, the feature size of cross-scaled components, such as foil thickness, changes from macroscale to mesoscale. The fracture behavior of the cross-scaled components varies from that of the macroscale components due to the size effect, leading to a high scrap rate and unacceptable cost in manufacturing. To reveal size effect on fracture and predict the fracture occurring of the cross-scaled components is still a challenge urgently to be solved. Thus, taking Inconel 718 superalloy cross-scaled foils as the case material, firstly, the cross-scaled foils were prepared with the thicknesses from 0.05 to 1.5 mm, the ratio of thickness to grain size (t/d) from 1.07 to 24.26. Uniaxial tensile tests and in-situ tensile tests were performed to reveal the fracture mechanism of the superalloy cross-scaled foils. Then, several uncoupled fracture criteria were implemented into the crystal plasticity finite element modeling (CPFEM) with the cross-scaled geometric modeling and random texture to predict the fracture behavior of the cross-scaled components. The uncoupled fracture criteria include Freudenthal criterion, Cockcroft & Latham(C&L) criterion, Normalized C&L, Brozzo criterion, Ayada criterion, Rice & Tracy criterion, Tresca criterion, equivalent stress criterion, equivalent strain criterion and maximum principal strain criterion. The phenomenological crystal plasticity model and dislocation density-based crystal plasticity model were compared in terms of calculation accuracy and efficiency. Thirdly, the size effect related fracture mechanisms of the cross-scaled foils were revealed, and the relationship between the fracture strain, fracture stress and t/d were obtained. Generally, the fracture strain and stress drop with a decrease in t/d. Consequently, an abnormal phenomenon occurs where the plasticity and strength increase with the decrease of t/d in some areas. The random textures lead to fluctuations in the strength and plasticity of the cross-scaled foils. Finally, the equivalent stress fracture criterion (ESFC) was determined where the fracture threshold is less affected by random texture. The relationship between the fracture threshold of ESFC and t/d was found, and the CPFEM-ESFC model was established considering the random textures induced scattering of the fracture threshold due to random textures. The scattering distribution function of cross-scaled component fracture behavior under different t/d was obtained through CPFEM-ESFC model and hundreds of random textures designs. The study provides a statistical method to avoid the forming scattering and a theoretical basis for the process design of cross-scaled components. [ABSTRACT FROM AUTHOR]

Abstract: An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing. [Copyright &y& Elsevier]

Abstract: We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener–Hopf techniques and allows us to obtain an expression for an important constant (which may be used in a fracture criterion) that describes the leading order of tractions near the crack tip for the unperturbed problem. We present computations that demonstrate how varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion’s presence having an amplifying or shielding effect on the propagation of the main crack. [Copyright &y& Elsevier]

Mixed-mode fracture is a common failure phenomenon of materials, while its experiment requires at least a material test machine, test materials and special machining procedures. In this paper, a simple but effective mixed-mode fracture experiment using office paper is proposed, so one can easily conduct the mixed-mode fracture experiment and understand its fracture criteria such as the maximum tensile stress (MTS) criterion. [ABSTRACT FROM AUTHOR]

Abstract: The occurrence of adiabatic shear localized fracture (ASLF) which is the final stage of adiabatic shear evolution usually leads to discontinuously short serrated chip with only a few segments joined together or even isolated segment formation. To develop a deep study on ASLF, damage evolution mechanism of ASLF in chip formation is investigated under optical microscope and scanning electron microscope (SEM) through high speed machining experiment of hardened AISI 1045 steel at a relatively high cutting speed. Considering the energy convergence during damage evolution in shear band, the theory model of ASLF in which adiabatic shear saturation limit and saturation degree are proposed as the ASLF criterion is built and compared with the experimental results. The quantitative influences of shear band properties, material properties and loading conditions on ASLF are also analyzed numerically. The results presented here show that complete ASLF in isolated segment formation is found above cutting speed of 1300m/min. The mechanism of ASLF in isolated segment formation is a multi-damage evolution process (or ductile–brittle–ductile transition mechanism), including voids coalescence, crack propagation and even fusing. Thermal softening effect plays a significant role in the process of ASLF. A thinner shear band with larger specific heat and thermal conductivity under higher strain and strain rate more easily leads to ASLF. The proposed ASLF theory can effectively assess saturation limit and quantitatively in machining hardened AISI 1045 steel. [Copyright &y& Elsevier]

The main objective of this article is to present a new fracture criterion for predicting both crack growth initiation and crack propagation direction in wood specimens under mixed mode I/II loading. This criterion is based on distribution of the maximum shear stress in the crack tip vicinity. An accurate estimation of the damage zone effect in wood is the main advantage of this criterion in comparison with available ones. The variation compliance of damaged material due to growth of microcracks is considered by a suitable damage factor. This criterion is extended for specimens with arbitrarily oriented cracks with respect to the orthotropic axes. It is revealed that developed approach is more compatible with the nature of the fracture phenomena in wood. The superiority of proposed method has been shown by some verification cases for several available fracture test data. [ABSTRACT FROM AUTHOR]

Basing on the Asymmetric Continuum Theory, we develop the thermodynamics including fragmentation spin fracture processes; applications for the earthquake source processes are considered. The fracture band model is used to describe a dislocation and disclination superlattice. The Gibbs free energy of defect formation is specified. A dynamic spin fracture criterion was formulated. Consequently, a dynamic model of rock fracture employing dislocations, disclinations, and cracks was constructed to describe slip and fragmentation fracture processes in the earthquake sources. [ABSTRACT FROM AUTHOR]

Abstract: Iron ore pellets are sintered, centimetre-sized spheres of ore with high iron content. Together with carbonized coal, iron ore pellets are used in the production of steel. In the transportation from the pelletizing plants to the customers, the iron ore pellets are exposed to different stresses, resulting in degradation of strength and in some cases fragmentation. For future reliable numerical simulations of the handling and transportation of iron ore pellets, knowledge about their mechanical properties is needed. This paper describes the experimental and numerical work to investigate the mechanical properties of blast furnace iron ore pellets. To study the load deformation behavior and the fracture of iron ore pellets, a number of point load tests are carried out and analyzed. Material parameters for an elastic–plastic constitutive model with linear hardening for iron ore pellets are derived and expressed in terms of statistical means and standard deviations. Two finite element models are developed for different purposes. For the material parameter determination, a perfectly spherical model is used. The constitutive model is validated with a finite element model based on a representative optically scanned iron ore pellet. The proposed constitutive model is capturing the force displacement relation for iron ore pellets in a two-point load test. A stress based fracture criterion which takes the triaxiality into account is suggested and calculated as the maximum equivalent effective stress dependent on the three principal stresses at fracture. The results of this study show that the equivalent effective stress in the vicinity of the centre of an irregular model of an iron ore pellet is very close to the results of a model of a perfectly spherical iron ore pellet. The proposed fracture criterion indicates fracture in the representative iron ore pellet model coincident with the location of the crack developed during the test of the optically scanned iron ore pellet. [Copyright &y& Elsevier]

Abstract: In order to interpret the two different kinds of experimental results of the effect of applied electric fields on the critical load at present, a new fracture criterion, the mechanical crack tip opening displacement (MCOD), is proposed in this paper. The fracture criterion predicts that the effect of applied electric fields on the critical load is different in two cases. The two theoretical results are all in according with the two kinds of experimental observations. It is interesting that the existing contrary experiments can be fully interpreted by the MCOD fracture criterion based on the results in this paper. [Copyright &y& Elsevier]

Abstract: A new constitutive model describing the pressure dependence of plasticity and fracture in solder joints is proposed. The pressure dependence of the solders flow stress is obtained from the Peierls stress necessary to move mobile dislocations. Conservation of volume during plastic deformation is achieved through a deviatoric associated flow rule. Fracture is considered as a result of damage accumulation depending on the amount of plastic strain and triaxiality of stress the sample has experienced. The constitutive model was implemented in the FEM code Abaqus using the user subroutine UMAT. The model predictions were compared to experimental results of tensile tests performed with Sn-3.5Ag solder joints of various thicknesses. Ultimate tensile strength and ductility showed a strong dependency on the solder joints geometry. It is demonstrated that the model can nicely be fitted to experimental results. [Copyright &y& Elsevier]

Abstract: The newly proposed isotropic ductile fracture criterion (), based on the magnitude of stress vector (MSV), is further developed to include strain rate and temperature dependences. Based on new observed responses during quasi-static and dynamic shear experiments, an exponential term is included to simulate the strain rate effect on ductile fracture of Al2024-T351 alloy. The KHL hardening model type temperature dependent term is also included to correlate with the observed temperature sensitivity of the ductile fracture of Al2024-T351 alloy. These modifications allow the proposed MSV fracture criterion to simulate the ductile fracture of Al2024-T351 alloy over wide ranges of strain rate and temperature. Further, by demonstrating the influence of hydrostatic pressure on the anisotropic ductile fracture behavior of a HCP alloy (Ti–6Al–4V), a new uncoupled anisotropic ductile fracture criterion is proposed. To comprehensively consider the anisotropy and tension compression asymmetry in the Ti–6Al–4V alloy, the modified Hill anisotropic function proposed by , is used to describe the geometry of the anisotropic fracture loci in principal stress space. Moreover, the KHL hardening mode type strain rate and temperature terms, in power-law forms, are adopted in the new anisotropic fracture criterion to correlate the fracture strength of the Ti–6Al–4V alloy over wide ranges of strain rate and temperature. Based on measurements at different strain rates and temperatures, a systematic procedure is listed for the determination of the material constants involved in the proposed anisotropic ductile fracture criterion. Furthermore, a generalized form of the fracture criterion, which can comprehensively simulate quadratic, non-quadratic and intermediate type fracture behaviors, is proposed. Excellent correlation between proposed fracture loci and the corresponding fracture observations is demonstrated. [Copyright &y& Elsevier]

Abstract: Using the fracture mechanics framework, a fracture criterion based upon the intrinsic defect concept was developed to predict the failure of rubber parts under biaxial monotonic loading. This fracture criterion requires as input data the fracture toughness of the material in terms of critical value of the J integral, the constitutive law of the material and the breaking stretch of a smooth specimen under uniaxial tension. To develop this criterion a generalized expression of the J integral under biaxial loading is proposed on the basis of finite element calculations on a RVE containing a small circular defect. The estimated failure elongations were found in very nice agreement with experimental data on two kinds of rubber materials. Moreover, we have also shown that this criterion could be extended to the failure analysis of thermoplastic polymers. [Copyright &y& Elsevier]

Abstract: The aim of this investigation is to establish a universal, accurate and efficient fracture criterion for ductile metals. First, new experiments including pure torsion, uniaxial tension followed by torsion and non-proportional biaxial compression on the Al 2024-T351 alloy are presented. These experimental results, along with published data on same material by , are used to establish a phenomenological fracture criterion using the magnitude of stress vector and the first invariant of stress tensor. The results are compared to, and shown better than, the maximum shear stress fracture criterion proposed by Stoughton and Yoon, J 2 fracture criterion and the Xue–Wierzbicki fracture criterion. Moreover, the proposed fracture criterion is used to correlate the ductile fracture data of another aluminium alloy published by . [Copyright &y& Elsevier]

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61-72 ) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios. [ABSTRACT FROM AUTHOR]

Abstract: A novel method combining the experimental data at only two different mixed mode fractures and an empirical interface toughness function has been proposed to establish the interfacial toughness function of a bimaterial in submicron scale. The modified four-point bend specimen was used in experiment to evaluate the first type of mixed mode fracture, while the sandwiched cantilever specimen was employed to get the second one. An empirical interface toughness function reflecting quite accurately the delamination behavior was adopted as a typical one. The obtained results investigated that the proposed method could be used to calibrate not only the interfacial fracture criteria at pure modes but also at any mixed mode fracture of bimaterials in submicron scale. [Copyright &y& Elsevier]

This study focuses on the behavior of a crack in piezoelectric material in which the crack is parallel to the poling direction. Tests were carried out on four-point bend specimens made of PZT-5H (Morgan Electro Ceramics, Wrexham, UK). Cracks were introduced parallel to the poling direction. With an electric field induced perpendicular to the cracks, the load was increased until failure occurred. Using the load at fracture, the level of the electric field and the critical crack length, finite element analyses were carried out to determine the intensity factors. These included K, K and a small K component. The latter occurred because of the small asymmetry of the crack. The material within the crack (air) was modeled to be a dielectric material. A fracture criterion is implemented in which the test results show small scatter about the failure curve. These tests were carried out in order to improve on the scatter obtained from a previous set of tests presented in Motola et al. (Int J Fract 159:167-190, ). The scatter from those results will be explored. [ABSTRACT FROM AUTHOR]

Abstract: We extend Sih’s strain energy density criterion () for crack kinks and material failure by weighting differently the volumetric and distortional parts in the extended strain energy density factor. The work is inspired by the factor that failure by microscopic shearing governed by distortion and microscopic separation controlled by hydrostatic tension represent distinct deformation processes, and should be treated differently as we count their influences to material failure. With the weight parameter introduced to the extended strain energy density factor criterion, we explain satisfactorily several critical experiments which reported crack kink in samples subjected to mixed-mode loading. The extended strain energy density idea is also used to derive a generalized pressure-dependent yielding criterion, which supplies a theoretical basis for those novel strength criteria for materials like bulk metallic glasses. Corresponding methods to determine the two material parameters, the critical strain energy density factor and the weight parameter quantifying the relative contribution by distortion over volumetric deformation, are discussed. [Copyright &y& Elsevier]

Abstract: Although a crack is a typical detail of a real solid, the theory of cracks in surface science was reduced to studying flat-parallel slits for a long time. The last decade has brought a number of new results related to the thermodynamic and surface science fundamentals of wedge-shaped cracks including the crack line tension. These results, essentially correcting and developing the theory of cracks, could not yet be included in the previous reviews of the author [A.I. Rusanov, Surf. Sci. Rep. 23 (1996) 173–247 and A.I. Rusanov, Surf. Sci. Rep. 58 (2005) 111–239] and make a subject for reviewing in this paper. Surface characteristics of a crack are described including the crack line tension as a new property that can be important for nanocracks. General thermodynamic relationships are derived, and the calculation of the thermodynamic surface and line tensions for solids with dispersion forces is given as an example. The dependence of the crack line tension on the crack size is analyzed for the conformal change (when a crack changes its size with maintaining its geometrical similarity) and the depth growth (when the distance between the crack lips is fixed). The latter has been found to be more favorable energetically. Since the presence of a crack is more probable for a loaded body, a general and rigorous approach to the thermodynamic description of loaded solids is presented including correcting earlier mistakes and terminology. The thermodynamic consideration presented outputs a useful contribution to the theory of solid strength. A generalized brittle fracture criterion is deduced and the ultimate strength is calculated for both the above mechanisms of the crack growth. The influence of the line tension on the ultimate strength is estimated both for the 2d and 3d cases. [Copyright &y& Elsevier]

A comparative analysis of various double-lap assembly configurations was realized using a refined analytical model for the stress distribution. All the components of the stress field were defined function of the Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed stress in the first element and then introduced into the potential energy formulation. Using this analysis method allow to establish a Tsai-Hill type failure criterion. [ABSTRACT FROM AUTHOR]

A phenomenological model of dynamic fracture of solids and a two-level fracture criterion, which takes into account increase in the degree of damage of materials on loading, are proposed. Within the framework of a model of elastoplastic solid, solutions of a three-dimensional problem of the dynamic fracture of rock on its interaction with the cutting tool have been obtained by a numerical method. The effect of the criterion on the development of the fracture process and the dependence of cutting force on time are considered. [ABSTRACT FROM AUTHOR]

The process of ultrasonically-assisted turning (UAT) is a superposition of vibration of a cutting tool on its standard movement in conventional turning (CT). The former technique has several advantages compared with the latter, one of the main being a significant decrease in the level of cutting forces. In this paper the effects observed in UAT are analysed employing ideas of dynamic fracture mechanics. The active stage of loading duration depends heavily on ultrasonic frequency and the cutting speed; he application of the fracture criterion based on the notion of incubation time makes it possible to calculate a dependence of this duration on its threshold amplitude. An estimation of energy, necessary to create a threshold pulse in the material, is made by solving the contact Hertz problem. The obtained time dependence of energy has a marked minimum. Thus, the existence of energy-efficient loading duration is demonstrated. This explains the decrease in the cutting force resulting from superimposed ultrasonic vibration. The obtained results are in agreement with experiments on ultrasonic assisted machining of aluminium and Inconel 718 alloy. [ABSTRACT FROM AUTHOR]

Abstract: The fracture behavior of adhesively-bonded double- and stepped-lap joints composed of pultruded glass fiber-reinforced polymer composite laminates and subjected to axial tension was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance method and the virtual crack closure technique. Their results showed good agreement for stepped-lap joints, while significant deviations were observed for double-lap joints due to small stiffness changes. The experimental compliance method results were sensitive to these small changes and the virtual crack closure technique accuracy was affected by the inability of the finite element analysis to accurately model the behavior before visual crack initiation. The dominant fracture mode changed from Mode I to Mode II in the case of stepped-lap joints, while an almost constant mode ratio was retained for double-lap joints in the applied loading range. A non-convex mixed-mode fracture criterion was established for crack initiation and propagation based on the virtual crack closure technique results. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of the structural joints examined, provided that stiffness degradation can be accurately described. [ABSTRACT FROM AUTHOR]

In this paper, we advanced a new interval reliability analysis model for fracture reliability analysis. Based on the non-probabilistic stress intensity factor interference model and the ratio of the volume of the safe region to the total volume of the region associated with the variation of the standardized interval variables is suggested as the measure of structural non-probabilistic reliability. We use this theory to calculate the reliability of structure based on fracture criterion. This model needs less uncertain information, so it has less limitation for analysing an uncertain structure or system. Examples of practical application are given to explain the simplicity and practicability of this model by comparing the interval reliability analysis model with probabilistic reliability analysis model. [ABSTRACT FROM AUTHOR]

Abstract: A semi-circular specimen containing a vertical edge crack was used to assess mode I, mode II, and mixed mode fracture toughness of a marble rock. The specimen was subjected to three-point bending while the bottom supports were placed asymmetrically with respect to the crack position. Since the critical tangential stress should be the same in various fracture modes, it was shown that the first three terms of tangential stress infinite series in the vicinity of the crack tip should be used to satisfy this condition. Accordingly, a criterion was presented to predict the mixed mode fracture toughness of brittle materials which showed a good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

This article summarises the uniaxial tension tests for 20 notched bars fabricated from high strength steel Q345 specified in Chinese National Standards. The effects of the notch radius, r, and that of the notch depth ratio, , on the ductility and fracture resistance of this high strength steel are examined. The experimental data are further analyzed using a generalized yield model together with an elliptical fracture stress envelope originally proposed by the first author. The experimental results demonstrate that cracks initiate at the notched section, with the fracture surface filled with many dimples and shearing marks. Specimens with a sharper notch radius (a smaller r) and a larger notch depth (a smaller ratio) show poor ductility, but high fracture strength. The stress field computed from the numerical procedure including the generalized yield model indicates that the crack initiation occurs at the centre of the notched section which experiences the highest stress triaxiality ratio . As the stresses at the notched section reach the limiting values determined from the elliptical fracture criterion, macroscopic fracture failure in the notched bar occurs. [ABSTRACT FROM AUTHOR]

Flexural strengthening of reinforced concrete (RC) beams using externally bonded fiber reinforced polymer (FRP) sheet is a popular application nowadays. In this application, the FRP to concrete bond interface is typically exposed to a mixed-mode loading condition at the vicinity of a critical flexural/shear crack, which includes a pull-out action parallel to the interface and introduced by the opening displacement of the flexural/shear crack together with a push-off action perpendicular to the interface and introduced by the shear sliding displacement of the flexural/shear crack. This paper presents an experimental program to evaluate the fracture properties of the FRP to concrete interface under the coupled pull-out (mode II) and push-off (mode I) loading condition. An analytical model was developed to evaluate the mode I and mode II strain energy release rates and the corresponding fracture mechanisms of the FRP to concrete interface under a pure bending action, a pure dowel action, and the coupled action of both, respectively. The reliability of the proposed analytical model was verified in comparison with the experimental results. [ABSTRACT FROM AUTHOR]

Fracture tests carried out on unpoled and poled PZT-5H four-point bend specimens are presented in this paper. The crack faces were parallel to the poling direction. Both mechanical loads and electric fields were applied to the poled specimens. The experimental results were analyzed by means of the finite element method and a conservative M-integral including the crack face boundary conditions. Fracture tests on four-point bend PIC-151 specimens with the crack faces perpendicular to the poling directions were also analyzed here; the experimental results were taken from the literature. A mixed mode fracture criterion is proposed for piezoelectric ceramics. This criterion is based upon the energy release rate and two phase angles. This criterion was implemented with experimental results from the literature and from this investigation. Excellent agrement was found between the fracture curve and the experimental results of the specimens with the crack faces perpendicular to the poling direction. With some scatter, reasonable agreement was observed between the fracture curve and the experimental results of the specimens with crack faces parallel to the poling direction. [ABSTRACT FROM AUTHOR]

ABSTRACT: The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy''s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the in uence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line. [Copyright &y& Elsevier]

In the present paper, we continue to study the nonlinear constitutive relation (CR) between the stress and strain proposed in [1] to describe one-dimensional isothermal rheological processes in the case of monotone variation of the strain (in particular, relaxation, creep, plasticity, and superplasticity). We show that this CR together with the strain fracture criterion (FC) leads to theoretical long-term strength curves (LSC) with the same qualitative properties as the typical experimental LSC of viscoelastoplastic materials. We propose two parametric families of fracture criteria in the case of monotone uniaxial strain, which are related to the strain fracture criterion (SFC) but take into account the strain increase history and the dependence of the critical strain on the stress. Instead of the current strain, they use other measures of damage related to the strain history by time-dependent integral operators. For any values of the material parameters, analytic studies of these criteria allowed us to find several useful properties, which confirm that they can be used to describe the creep fracture of different materials. In particular, we prove that, together with the proposed constitutive relations, these FC lead to theoretical long-term strength curves (TLSC) with the same qualitative properties as the experimental LSC. It is important that each of the constructed families of FC forms a monotone and continuous scale of criteria (monotonously and continuously depending on a real parameter) that contains the SFC as the limit case. Moreover, the criteria in the first family always provide the fracture time greater than that given by the SFC, the criteria in the second family always provide a smaller fracture time, and the difference can be made arbitrarily small by choosing the values of the control parameter near the scale end. This property is very useful in finding a more accurate adjustment of the model to the existing experimental data describing the fracture time dependence on the stress, temperature, radiation, and other factors: if these data are poorly described by the SFC, then one can choose a more appropriate criterion from the constructed families by varying the value of the control parameter smoothly and monotonously. For any admissible values of the model determining parameters, we derive the TLSC corresponding to the proposed fracture criteria. Studying the dependence of their properties on the material function and on the material parameters of the CR and FC, we can state the requirements on the TLSC that follow from the general qualitative properties of experimental LSC of different viscoelastoplastic materials and obtain the corresponding restrictions on the material parameters and the model function. [ABSTRACT FROM AUTHOR]

The interaction between hydraulic fractures and natural fractures have significant influence on the geometry of hydraulic fracture network in fractured reservoirs. In previous mathematical model, the interaction relationship of non-intersecting fractures in propagation process were often been ignored, which resulted the inaccuracy of simulation results. Based on boundary element method and rock failure criterion, we established mathematical model to study the fracture interaction mechanisms and fracture network morphology under induced stress. Simulation results show that hydraulic fracture with incipient propagation superiority are more likely to have a rapid propagation and inhibit the continuous initiation of surrounding micro fractures. Under proper conditions, single natural fracture can deflect the propagation direction of hydraulic fracture by at least 22°. Firstly proposed that shielding and transmission efforts of induced stress by natural fracture are the fundamental reason that affect the complexity of fracture network, which can reduce the normal stress around natural fracture by 50% in this paper. When the inclination Angle of natural fractures is between 45 and 70°, it is more favorable to form complex fracture network. This study is of great significance for the control of fracture network morphology and the further improvement of fracturing effect. • Established a propagation model considering the interference between non-contact fractures. • The asymmetrical distribution of stress is likely to cause the coalescence of fracture. • The tip of hydraulic fracture will gradually deflect as it approaches natural fracture. • Natural fracture have both shielding and transferring effects on induced stress. • Simulated the plane fracture network morphology influenced by different parameters. [ABSTRACT FROM AUTHOR]