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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.

The mixed-mode brittle fracture of two types of commercial graphite is investigated focusing on strain-based fracture criteria. The previously published experiments using centrally-cracked Brazilian disk specimens subjected to mixed-mode loadings are simulated by two strain-based fracture criteria: the traditional maximum tangential strain (MTSN) criterion only considering the singular terms, and the extended maximum tangential strain (EMTSN) criterion, which considers the first nonsingular strain term as well as the singular terms. Numerical simulations on the centrally-cracked Brazilian disk specimen show that the first nonsingular tangential strain term significantly influences the tangential strain distribution around the crack tip. The comparison of the evaluations by the MTSN and EMTSN criteria with the experimental data shows that the EMTSN criterion is more capable of successfully estimating the fracture resistance of graphite materials rather than the traditional MTSN criterion. In addition, when the first nonsingular term is considered, the strain-based fracture criterion provides better predictions for near mode II loadings than the stress-based fracture criterion.

Предложена модель деформирования и разрушения слоистых горных пород, обладающих анизотропными прочностными свойствами. Проведено теоретическое и экспериментальное исследование влияния величины и ориентации главных напряжений относительно плоскостей напластования горных пород на их прочность и геометрию разрушения. В условиях сложного истинно трехосного напряженного состояния рассмотрены два возможных механизма разрушения: по плоскостям напластования, являющимся плоскостями ослабления, и по плоскостям, на которых достигается критическое значение комбинации напряжений типа Кулона-Мора с коэффициентом сцепления и углом внутреннего трения, характеризующими породу в целом. Для описания перехода деформирования горных пород в неупругое состояние были использованы критерий, учитывающий возможность реализации двух указанных механизмов, и полуэмпирический критерий, аналогичный критерию текучести Хилла для анизотропных сред, учитывающий влияние нормальных напряжений. Проведено экспериментальное изучение деформационных и прочностных свойств горных пород из продуктивных пластов двух нефтегазовых месторождений Федоровского и Талаканского. Исследования проводились с использованием испытательной системы трехосного независимого нагружения, разработанной в Институте проблем механики РАН. Горные породы испытывались по двум группам программ нагружения, соответствующим условиям сжатия с боковым поджатием (аналогично кармановской схеме) и условиям обобщенного сдвига (при неравенстве и немонотонности всех трех главных напряжений). Получены полные кривые деформирования. Результаты исследования показали хорошее качественное соответствие экспериментальных результатов и теоретических оценок. Показана возможность на основе испытаний конкретных горных пород определять значения параметров, входящих в предложенную модель., A deformation and fracture model has been put forward for stratified rocks with anisotropic strength properties. The effect of the principal stress magnitude and orientation relative to the rock bedding planes on the rock strength and fracture geometry is studied theoretically and experimentally. Two possible fracture mechanisms under true triaxial stress states are considered: along bedding planes of weakness, and along planes with a critical combination of Mohr-Coulomb stresses with the cohesion coefficient and internal friction angle typical of the whole rock. Rock transition to inelastic deformation is described using a criterion accounting for the occurrence of the two above mechanisms, and a semi-empirical criterion analogous to Hill's yield criterion for anisotropic media which accounts for the effect of normal stresses. The deformation and strength properties of rocks are studied in experiments on samples from productive strata of the Fedorovskoe and Talakanskoe oil and gas fields. The investigation was performed using an original triaxial independent loading test system. Rocks were tested in two groups of loading programs corresponding to compression with lateral confinement (similar to the Karman scheme), and to generalized shear (with all three principal stresses being unequal and nonmonotonic). Full stress-strain curves were obtained. The experimental and theoretical results are in good qualitative agreement. The possibility to determine the model parameter values is shown in tests on particular rocks.

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.

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.

We extend Sih’s strain energy density criterion (Sih, 1974) 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.

The correct choice of process parameters is important in predicting the cut surface and obtaining a fully-fine sheared surface in the fine blanking process. The researchers used the value of the critical fracture criterion obtained by long duration experiments to predict the conditions of cut surfaces in the fine blanking process. In this study, the clearance-dependent critical ductile fracture criteria obtained by the Cockcroft-Latham and Oyane criteria were used to reduce the time and cost of experiments to obtain the value of the critical fracture criterion. The Finite Element Method (FEM) was applied to fine blanking processes to study the influences of process parameters such as the initial compression, the punch and die corner radii and the shape and size of the V-ring indenter on the length of the sheared surface. The effects of stress triaxiality and punch diameters on the cut surface produced by the fine blanking process are also discussed. The verified process parameters and tool geometry for obtaining a fully-fine sheared SPCC surface are described. The results showed that the accurate and stable prediction of ductile fracture initiation can be achieved using the Oyane criterion.

Al-based metal matrix composites consisting of pure Al reinforced with different amounts of mechanically alloyed Zr57Ti8Nb2.5Cu13.9Ni11.1Al7.5 glassy powder were produced by powder metallurgy, and their mechanical properties were investigated by room temperature compression tests. The samples were consolidated into highly dense bulk specimens at temperatures within the supercooled liquid region in order to take advantage of the viscous flow behavior of the glassy powder. Compression tests show that the addition of the glass reinforcement increases the strength of pure Al from 155 to 250 MPa, while retaining appreciable plastic deformation with a fracture strain ranging between 70% and 40%. The yield strength and the elastoplastic deformation of such composites containing a high volume fraction of glassy particles were accurately modeled using a shear lag model and a self-consistent effective medium approach. Finally, the fracture characteristics of the reinforcing particles were rationalized using a proposed fracture criterion. � 2009 Acta Materialia Inc.

We have developed a new type of method of estimating fracture loads using stress intensity factors in IC ceramic packages under complicated load conditions. The right-angle corners in the cross sections of IC ceramic packages were assumed to be wedge cracks, and the fracture criterion was defined as curved surface in ModeⅠ(tensile opening)-ModeⅡ(in-plane shear)-ModeⅢ(tearing) coordinate space.

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.

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.

Among the bulk metal forming processes hot forging is often the only option if large reductions of the forging load are required or if the material formability needs to be significantly increased or even if specific thermally-induced microstructural changes are needed to take place during the deformation process. Moreover it still retains at some extent the positive features of the cold forging processes: high production rates, complex final shapes attainable and little to no material waste. Hot forging is therefore used for the production of large parts, with complex shapes and especially when using materials characterized by low formability and high toughness at room temperature or if particular microstructural characteristics are required. It is worth to be underlined that these are often the features of the innovative metal alloys that have been increasingly being used in the last decade and namely: Mg alloys, Al alloys, Ti alloys and superalloys. Finite Element metal forming numerical simulation has become an increasingly important process optimization tool, due to the growing computational power available at reduced costs, which spread it in the industrial world. Its use allows reducing process design time and prototyping costs as well as long and expensive plant downtimes for process variable tuning. For all these reasons hot forging has become a strategic process and its accurate numerical simulation is encountering great industrial interest. One of its main targets is the determination of the maximum strain that the material can undergo during the deformation process, since it is strictly related with both the final shape and the surface quality of the manufactured part. In this sense hot formability modelling provides a meaningful example of a topic which is both of great scientific and industrial interest. From the scientific point of view ductile damage modelling has been developed at first for cold processes, for which crack formation is usually a major issue. Last decade research efforts focused on the development of more advanced fracture criteria, keeping into account a complete characterization of the stress state dependency of formability. However the complex analytical formulation of these criteria and their expensive experimental calibration kept them de facto away from practical industrial use. On the other hand hot formability modelling was traditionally addressed by direct application of the conventional cold fracture criteria, under the implicit assumption of isothermal conditions. This approach has evident limits since it does not account for temperature influence on material formability and it does not even provide any physical insight on the different fracture mechanisms that can develop as temperature changes. In recent years some research efforts have been performed on a deeper investigation upon this point: experimental formability campaigns on different metal alloys were carried out in order to assess the temperature and strain rate influence, while some analytical models were proposed in order to describe the damage evolution at high temperature and in particular the onset of the so-called “hot shortness”. However these models are still quite simple and can describe only a limited variety of formability trends, losing in accuracy once complex microstructural phenomena take place. Moreover their validation has been done with simple laboratory tests and not with real processes industrial trials in which non-uniform thermo-mechanical conditions are present and the material can evolve through fracture mode-changing regimes. The objective of this work is the elaboration of a novel approach to hot ductile fracture modelling, capable to represent accurately the formability evolution of a metal alloy as a function of both the main thermo-mechanical variables and its physical and microstructural characteristics, yet providing a tool simple enough to be of industrial utility. To this aim the hot cross wedge rolling of a precipitation hardened aluminium alloy was taken as industrial reference case, since it is an innovative and non-standard forging process which entails variable and non-homogeneous thermo-mechanical conditions. The study case is of remarkable interest since it has a narrow process temperature window, being limited at the top by Mannesmann-type axial cracking onset and at the bottom by unwanted grain coarsening. Moreover the metal alloy used, the AA6082-T6, has the microstructural features, namely the intermetallic precipitates, that make it a good example of a metal alloy of wide industrial use, that during forming can undergo complex microstructural changes. A hot tensile test campaign was performed on a wide range of thermo-mechanical conditions and the results highlighted an unexpected negative strain rate influence on formability. Fractographic and micro-chemical analysis were then performed in order to assess the microstructural reasons of this behaviour and finally two approaches to the material formability modelling were proposed and calibrated extending to hot conditions the classic Oyane-Sato fracture criterion. The first one consists on the empirical calibration of the criterion by means of a bi-linear interpolation of the experimental data, while the second one entails a physically-based analytical formulation of the material fracture locus, which has also the advantage of being of easier calibration. These models were then validated on the cross wedge rolling process simulation by comparison with the industrial trials results and the outcomes were critically assessed.

В обзоре приводятся результаты исследований в рамках так называемой континуальной теории поврежденности, восходящей к работам Л.М. Качанова и Ю.Н. Работнова. В рамках таких моделей в структуру определяющих соотношений явным образом вводятся внутренние переменные (имеющие в общем случае различную математическую природу), описывающие неориентированное (при помощи скалярных параметров поврежденности) либо ориентированное (при помощи тензорных характеристик различного ранга) распределение повреждений в материале. Далее исходя из соображений механического или термодинамического характера вводится критерий разрушения. Следует отметить, что для ряда материалов (например композиционных) модели этого типа до сих пор являются наиболее часто используемыми при расчете конструкций на прочность. Поскольку возникновение и развитие поврежденности тесно связаны с локализацией деформации, рассматриваются постановки и методы исследования устойчивости процессов неупругого деформирования. Значительное внимание уделено анализу влияния на результаты исследования конечно-элементной сетки, особенностям алгоритмов, применяемых для решения подобных задач, возможностям использования нелокальных конститутивных моделей. К этому же классу работ отнесены исследования с применением градиентных моделей: для процессов формирования повреждений характерны резкие пространственные изменения кинематических и/или динамических характеристик, для описания которых требуется использование неклассических определяющих соотношений (градиентных, нелокальных, микроморфных континуумов)., This paper reports the results of research in the framework of the so-called continuum theory of damage which goes back to the works of Kachanov and Rabotnov. In these models, internal variables that generally have different mathematical structure are explicitly introduced to constitutive relations. The variables describe a non-oriented (using scalar damage parameters) or oriented (using different rank tensors) damage distribution in the material. Then, a fracture criterion is introduced based on mechanical or thermodynamic considerations. The models of this type are still most frequently used in the structural analysis of strength of some materials (e.g., composites). Since damage nucleation and growth are closely related to strain localization, consideration is given to formulations and methods for analyzing the stability of inelastic deformation processes. Special attention is given to the influence of finite element mesh on simulation results, to algorithms applied to solve such problems, and possibilities of using non-local constitutive models. This group of research works also includes studies that use gradient models, because damage formation is characterized by sharp spatial variations of kinematic and/or dynamic characteristics, which must be described using non-classical constitutive relations (gradient, non-local, micromorph continuum).

The bending and tensile strengths of timber can be reduced by the presence of heterogeneities. The knots and the local slope of grain in the surrounding area are the most relevant. Nowadays, the effect of knots reduces the stiffness and the strength of structural elements. The Timber grading is not optimized and does not promote the strongest beams for a timber engineering use. The goal of this study is to evaluate the influence of knots on the bending strength of beams in Maritime Pine, order to improve their timber grading. This work is focused on a database, which takes into account the mechanical and the physical properties of beams and specific geometrical parameters relative to knots detected in elements. Several statistical tools like neural networks are used to define the explanatory variables and their predictive powers of the bending strength. From these analyses, it is shown that some variables characterizing the knots are pertinent and allow the improvement of the prediction of the strength. To justify the presence of these variables in the predictive equations, finite element simulations of single knot are proposed. These numerical computations associated to a fracture criterion allow the establishment of strength performance curves due to the presence of knot in an elementary loaded volume (tension and bending configurations). These numerical data are compared to the experimental results in the aim to verify the reliability of the finite element approach., Dans le cas du bois massif, les résistances en flexion et en traction peuvent être altérées par la présence de défauts. Les nœuds et la distorsion du fil qui en découle, sont les causes de la diminution du rendement mécanique des sections de poutres de structure. A ce jour, l’effet de ces défauts sur la perte de résistance de l’élément de structure ne peut être quantifié avec exactitude. Le classement mécanique du bois de structure n’est alors pas optimal et ne permet pas de valoriser les éléments de fortes résistances. La présente étude a pour objectif d’étudier l’influence de la nodosité sur le rendement mécanique de poutres en Pin Maritime dans le but d’en améliorer son classement mécanique. Cette étude s’appuie sur une base de données recensant les propriétés mécaniques et physiques de poutres de grandes dimensions ainsi que les propriétés géométriques des nœuds présents sur ces éléments. Différents outils statistiques sont utilisés afin de définir les variables explicatives et leurs pouvoirs prédictifs sur la résistance mécanique de ces composants structurels. De ces analyses, il ressort que certaines caractéristiques propres aux nœuds sont significatives et permettent d’améliorer la prédiction de la résistance. Des modélisations éléments finis de tronçons de poutres présentant un nœud sont proposées pour justifier la présence de ces paramètres dans les modèles prédictifs et afin de compléter cette base de données par des propriétés mécaniques. Ces modélisations numériques, accompagnées d’un critère de ruine, permettent d’établir des courbes de performances mécaniques en présence d’un nœud. Ces données numériques sont comparées aux résultats expérimentaux afin de vérifier la fiabilité de l’approche proposée.

В рамках модифицированной модели Леонова-Панасюка-Дагдейла анализируется точность описания зоны предразрушения, расположенной на продолжении трещины в квазихрупком материале со структурой. Рассматривается материал, в котором под действием растяжения, приложенного на бесконечности, реализуется первая мода разрушения в условиях плоского напряженного состояния. Для более полного соответствия с известными численными результатами предложено уточнение структурных формул критической длины зоны предразрушения и критической нагрузки для квазихрупких материалов. Получено обобщение модифицированной модели Леонова-Панасюка-Дагдейла на случай квазивязких материалов., The paper analyzes a modified Leonov-Panasyuk-Dugdale model and its accuracy in describing a prefracture zone on crack extension in structured quasibrittle materials. The material under study is that in which a mode I crack develops under plane tensile stress conditions. For more complete agreement with available numerical data, the formulae for critical prefracture zone length and critical load in quasibrittle materials are refined. The model is generalized for quasiductile materials.

Nuclear power plants have the greatest potential for use in space ships, underwater vehicles, and so on. Because the space and the weight for those plants have limitation, it is very important to develop new radiation shielding materials which have excellent mechanical strength and heat-resistant characteristics. Chromium carbide ceramics (Cr_3C_2) is the neutron absorber which is more excellent than titanium boride ceramics and has been investigated as a radiation shielding material. This report presents an evaluation of thermal shock strength by the laser irradiation technique for chromium carbide ceramics. Their temperature and thermal stress distributions are analyzed by the finite element method (FEM), and critical fracture curves, which can specify a critical power density for a given laser beam spot diameter, are obtained from the relationships between the spot diameter of the laser beam and the maximum tensile thermal stress. And furthermore, size effects to the fracture criterion of chromium carbide ceramics are examined, and the laser irradiation experiments are performed on chromium carbide ceramics using a CO_2 laser. Finally, theoretical results are compared with experimental ones, and the thermal shock strength P_L of Cr_3C_2 ceramics with laser irradiation is ～3.4 W/mm^2 for tension by the FEM analyses