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The local conditions for void initiation are determined for individual MnS-inclusions near the crack tip in a mild steel St37. First, the crack tip opening displacement at the moment of void initiation, CODvi, is measured by quantitative fracture surface analysis; subsequently, the maximum interfacial stress, σmaxinterf, is calculated from models by Argon et al. [Metall Trans 1975;6:825] and Beremin [Metall Trans 1981;12:723]. A strong effect of the size of the MnS-inclusions on the CODvi- and the σmaxinterf-values is revealed.

This article deals with the homogenization of metal matrix composites (MMCs) with inhomogeneous particle distribution by severe plastic deformation. In this study, Al6061-10 pct SiC and Al6061-20 pct Al2O3 powder metallurgy (PM) MMCs with clustered particle distribution in the as-fabricated condition are subjected to high-pressure torsion (HPT) at room temperature. The evolution of the microstructure during HPT is investigated. It is shown that, in the two materials, two different types of particle clusters appear that behave differently during deformation. In MMCs with dense particle clusters, the process of declustering during HPT occurs through a mechanism of particle debonding from the surface of the clusters. On the contrary, in MMCs with diffuse particle clusters, the deformation of the clusters is mainly responsible for the homogenization; therefore, the strain necessary to obtain a homogeneous particle distribution can be predicted by the Tan and Zhang model (M.J. Tan and X. Zhang: Mater. Sci. Eng. A, 1998, vol. 244, pp. 80–85).

An Al6061-20%Al 2 O 3 powder metallurgy (PM) metal matrix composite (MMC) with a strongly clustered particle distribution is subjected to equal channel angular pressing (ECAP) at a temperature of 370 °C. The evolution of the homogeneity of the particle distribution in the material during ECAP is investigated by the quadrat method. The model proposed by Tan and Zhang [Mater Sci Eng 1998;244:80] for estimating the critical particle size which is required for a homogeneous particle distribution in PM MMCs is extended to the case of a combination of extrusion and ECAP. The applicability of the model to predict a homogeneity of the particle distribution after extrusion and ECAP is discussed. It is shown that ECAP leads to an increase of the uniformity of the particle distribution and the fracture toughness.

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T-max and the separation energy, Gamma) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality. (c) 2005 Elsevier Ltd. All rights reserved.

This paper describes a theoretical model and related computational methods for examining the influence of inhomogeneous material properties on the crack driving force in elastic and elastic-plastic materials. Following the configurational forces approach, the crack tip shielding or anti-shielding due to smooth (e.g. graded layer) and discontinuous (e.g. bimaterial interface) distributions in material properties are derived. Computational post-processing methods are described to evaluate these inhomogeneity effects. The utility of the theoretical model and computational methods is demonstrated by examining a bimaterial interface perpendicular to a crack in elastic and elastic-plastic compact tension specimens.

The local deformation behaviour of powder metallurgy metal matrix composites (MMCs) with two different SiC partacle sizes and aging conditions are investigated and compared to the behaviour of the un%reinforced matrix. In situ tensile loading experiments are carried out in a scanning electron microscope. Images taken at different deformation stages are analysed by a system for local deformation measurement. It is found that evef the pure matrix material deforms inhomogeneously, showing a shear-band pattern which is independent of the loading stage. The MMCs with coarse reinforcements deform mainly due to shear bands which are induced by fractured partacles. The MMCs with small particles exhibit a shear-band pattern which is controlled by the particle arrangement. The fracture of small particles does not induce far-reaching shear bands and, therefore, these materials have a higher strength and ductility.

Particle reinforced MMCs with a particle size of 100µm and an aluminium matrix (Al6061) are analyzed by the means of automatic local deformation analysis. Two different heat treatment conditions (under- and over-aged) are investigated. It is found that the local deformation behaviour is strongly determined by particle damage. While the under-aged material shows only particle fracture, the over-aged MMC shows also particle debonding as a relevant damage mechanism.

The relation between the local and global values of the fracture initiation toughness is investigated for a cast Al6061-based metal matrix composite with 10% of Al2O3 particles after different heat treatments. The global values of the fracture initiation toughness are determined by conventional fracture mechanics tests. The local values of the fracture initiation toughness are found by measuring the critical crack tip opening displacement (CODi) at different locations along the crack front. To do this, an automatic fracture surface analysis system is applied. Despite of the large scatter of the individual CODi-values, a good correlation to the global fracture initiation toughness values is found.

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.

A procedure is proposed to determine, for second-phase particles near a crack tip, the maximum particle stresses at the moment of void initiation by either particle fracture or particle/matrix interface separation. A digital image analysis system is applied to perform a quantitative analysis of corresponding fracture surface regions from stereo image pairs taken in the scanning electron microscope. The fracture surface analysis is used to measure, for individual particles, the crack tip opening displacement at the moment of void initiation and the particle location with respect to the crack tip. From these data, the stress tensor at the moment of void initiation is calculated from the Hutchinson–Rice–Rosengren (HRR) field theory. The corresponding average local stresses within the particle are evaluated by a non-linear Mori–Tanaka-type approach. These stresses are compared to estimates according to the models by Argon et al. [A.S. Argon, J. Im, R. Safoglu, Metall. Trans. 6 (1975) 825] and Beremin [F.M. Beremin, Metall. Trans. 12 (1981) 723]. The procedure is demonstrated on an Al6061–10% Al2O3 metal matrix composite.

This paper presents a case study, examining the influence of a sharp bimaterial interface on the effective crack driving force in a fracture mechanics specimen. The inhomogeneity of the elastic modulus in linear elastic and non-hardening and hardening elastic–plastic bimaterials is considered. The interface is perpendicular to the crack plane. The material properties and the distance between the crack tip and the interface are systematically varied. The effect of the material inhomogeneity is captured in form of a quantity called “material inhomogeneity term”, C inh . This term can be evaluated either by a simple post-processing procedure, following a conventional finite element stress analysis, or by computing the J -integral along a contour around the interface, J int . The effective crack driving force, J tip , can be determined as the sum of C inh and the nominally applied far-field crack driving force, J far . The results show that C inh can be accurately determined by both methods even in cases where J tip -values are inaccurate. When a crack approaches a stiff/compliant interface, C inh is positive and J tip becomes larger than J far . A compliant/stiff transition leads to a negative C inh , and J tip becomes smaller than J far . The material inhomogeneity term, C inh , can have the same order of magnitude as J far . Based on the numerical results, the dependencies of C inh on the material parameters and the geometry are derived. Simple expressions are obtained to estimate C inh .

The local deformation behaviour of powder metallurgy metal matrix composites (MMCs) with two different SiC particle sizes and aging conditions are investigated and compared to the behaviour of the un-reinforced matrix. In situ tensile loading experiments are carried out in a scanning electron microscope. Images taken at different deformation stages are analysed by a system for local deformation measurement. It is found that even the pure matrix material deforms inhomogeneously, showing a shear-band pattern which is independent of the loading stage. The MMCs with coarse reinforcements deform mainly due to shear bands which are induced by fractured particles. The MMCs with small particles exhibit a shear-band pattern which is controlled by the particle arrangement. The fracture of small particles does not induce far-reaching shear bands and, therefore, these materials have a higher strength and ductility.

Beim Fullen und Entleeren eines Silos kann es durch die Staubentwicklung des Lagerguts und das Vorhandensein einer Zundquelle zu einer Staubexplosion kommen, welche durch ihre Heftigkeit ein groses Risiko fur die Anlage darstellt. Dieser Beitrag beschaftigt sich mit der druckstosfesten Ausfuhrung von Silos, welche dem zu erwartenden Explosionsdruck mit bleibenden Verformungen widersteht. Das Grenztragverhalten der einzelnen Schalenanteile des Silos, wie Zylinder, Kegel, Torus und Kugelkalotte, wird mit Hilfe der Plastizitatstheorie und dem Kriterium nach Considere bestimmt. Das Tragverhalten der Schalenubergange wird mittels einer nichtlinearen Berechnung mit dem Finite-Element-Programm ABAQUS untersucht. Weiter werden die plastischen Grenzdrucke aufgrund von fehlerbehafteten Schweisnahten (Kerben und Risse) an den Schalenverbindungen mittels der Schadigungs- und Bruchmechanik bestimmt, wobei die Materialkennwerte aus den durchgefuhrten Versuchen verwendet wurden. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An experimental procedure has been developed to systematically investigate the local deformation behavior of polycrystalline materials at the micrometer scale. The procedure consists of a combination of the measurement of the local in-plane strains and the local crystal orientation during an in-situ deformation test in the scanning electron microscope. The local in-plane strains are determined from micrographs that are taken before and after a considered deformation step. By means of a digital image analysis system, homologue points are found on the two micrographs. The homologue points form a deformation field that can be derived to determine the local strain fields. The local crystal orientation is measured by orientation image microscopy analyses, again taken before and after the deformation step. From these measurements, the local rotation of the crystal lattice during the deformation step and the Miller indices of the rotational axis are determined. The combination of the data of the local crystal orientation and the local in-plane strains is used to estimate, with a simple kinematic model, the slip systems that are locally active at arbitrary positions within a grain. A polycrystalline copper specimen was loaded in two deformation steps to 7.4 and 14% global tensile strain. A region of ≈250×200 μm was analyzed. The experiment shows that very strong heterogeneities in the in-plane strain and in the local lattice rotation exist within the single grains. At some grain boundaries, very high lattice rotations are observed. Even far from the boundary, the activation of slip systems can be quite different in different regions of a grain. On the specimen surface, more than three independent slip systems must be activated in some grain boundary regions to accommodate the influence of the neighboring grain. In most regions of the grain interior, three slip systems seem to be enough. With the developed procedure, we have generated a tool for a very comprehensive experimental characterization of crystal plasticity in polycrystals.

An experimental procedure has been developed to systematically investigate the local deformation behavior of polycrystalline materials at the micrometer scale. The procedure consists of a combination of the measurement of the local in-plane strains and the local crystal orientation during an in-situ deformation test in the scanning electron microscope. The local in-plane strains are determined from micrographs that are taken before and after a considered deformation step. By means of a digital image analysis system, homologue points are found on the two micrographs. The homologue points form a deformation field that can be derived to determine the local strain fields. The local crystal orientation is measured by orientation image microscopy analyses, again taken before and after the deformation step. From these measurements, the local rotation of the crystal lattice during the deformation step and the Miller indices of the rotational axis are determined. The combination of the data of the local crystal orientation and the local in-plane strains is used to estimate, with a simple kinematic model, the slip systems that are locally active at arbitrary positions within a grain. A polycrystalline copper specimen was loaded in two deformation steps to 7.4 and 14% global tensile strain. A region of ≈250×200 μm was analyzed. The experiment shows that very strong heterogeneities in the in-plane strain and in the local lattice rotation exist within the single grains. At some grain boundaries, very high lattice rotations are observed. Even far from the boundary, the activation of slip systems can be quite different in different regions of a grain. On the specimen surface, more than three independent slip systems must be activated in some grain boundary regions to accommodate the influence of the neighboring grain. In most regions of the grain interior, three slip systems seem to be enough. With the developed procedure, we have generated a tool for a very comprehensive experimental characterization of crystal plasticity in polycrystals.

In-situ tensile tests were carried out in a scanning electron microscope on an Al-6061 aluminum alloy reinforced with 10 vol pct SiC particles with a mean diameter of 100 μm. High resolution strain maps were generated by analyzing the scanning electron micrographs of different deformation stages by a digital image analysis system. The methodology is called automatic local deformation analysis. An area of about 670 x 540 μm was analyzed during four deformation steps. Global tensile strains up to 1 pet were measured; the local strains were found to be up to five times larger than the global ones. Local anisotropy is quantified on the analyzed surface concerning the orientation and aspect ratio of the particles, and taken into account as parameters determining particle fracture. The development of particle failure in the bulk and at the surface is determined for the deformed and undeformed material.

The paper deals with the determination of the cohesive zone parameters (separation energy, Gamma, and cohesive strength, T-max) for the 3D finite element modeling of the micro-ductile crack growth in thick, smooth-sided compact tension specimens made of a low-strength steel. Since the cohesive zone parameters depend, in general, on the local constraint conditions around the crack tip, their values will vary along the crack front and with crack extension. The experimental determination of the separation energy via automated fracture surface analysis is not accurate enough. The basic idea is, therefore, to estimate the cohesive zone parameters, Gamma and T-max, by fitting the simulated distribution of the local crack extension values along the crack front to the experimental data of a multi-specimen J(I C)-test. Furthermore, the influence of the cohesive zone parameters on the crack growth behavior is investigated. The point of crack growth initiation is determined only by the magnitude of Gamma. Both Gamma and T-max affect the crack growth rate (or the crack growth resistance), but the influence of the cohesive strength is much stronger than that of the separation energy. It turns out that T-max as well as Gamma vary along the crack front. In the center of the specimen, where plane strain conditions prevail, the separation energy is lower and the cohesive strength is higher than at the side-surface.

This article evaluates the effect of material inhomogeneities on the crack-tip driving force in general inhomogeneous bodies and reports results for bimaterial composites. The theoretical model, based on Eshelby material forces, makes no assumptions about the distribution of the inhomogeneities or the constitutive properties of the materials. Inhomogeneities are modeled by making the stored energy have an explicit dependence on the reference coordinates. Then the material inhomogeneity effect on the crack-tip driving force is quantified by the term Cinh, which is the integral of the gradient of the stored energy in the direction of crack growth. The model is demonstrated by two model problems: (i) bimaterial elastic composite using asymptotic solutions and (ii) graded elastic and elastic–plastic compact tension specimen using numerical methods for stress analysis.

The aim of this study is to provide a tool, which is capable of studying, at a sub-grain level, the formation and evolution of strain inhomogeneities at the surface of polycrystalline materials. The capabilities of the tool are demonstrated on an oxygen free high conductivity copper (OFHC) specimen which is plastically deformed in an in-situ tensile test in the scanning electron microscope (SEM). At different deformation stages, SEM micrographs are captured which are processed by a new system for local deformation analysis. The key part of the system is a matching procedure for the determination of homologue points in two deformation micrographs. The homologue points form a deformation field, which can be numerically derived to evaluate the local in-plane strains. Due to the high matching accuracy and the high density of the homologue points, it is possible to determine the in-plane strain fields with an accuracy and lateral resolution that has not been possible so far. The system allows us to conduct local deformation analyses in a wide range of magnifications. As an example, a region of about 180×130 μm is analyzed on the copper specimen in deformation steps of about 1% global strain. The in-plane components of the local strain field are characterized by incremental or cumulative strain maps. The exact distribution of the local strains near grain and twin boundaries is obtained by means of local displacement and strain profiles.

The fracture behaviour of near-γ (NG) and fully lamellar (DFL) intermetallic TiAl alloys with and without warm pre-stressing (WPS) is investigated by testing three point bending specimens with fatigue pre-cracks at room temperature and at 700 °C. Detailed fractographic observations and FEM calculations are carried out to find the critical step of cleavage fracture. The results show that the cleavage fracture is induced by direct propagation of the pre-crack and that the stress at the crack tip is the decisive controlling factor. The WPS process improves the fracture initiation toughness of both the NG and the DFL microstructure, but deteriorates slightly the increase of the K-resistance curves, especially for the DFL microstructure. The compressive residual stress induced by WPS plays the main role in improving the fracture initiation toughness.

Crystallographic fractometry is a new method for analysing fracture surfaces. It is based on linking crystal orientation measurements and three dimensional reconstruction of fracture surfaces by means of EBSD technique and computer aided stereo-photogrammetry, respectively. This allows to characterise the crystallographic orientation of fracture surfaces and fractographic features down to sub-micrometer scale. The possibilities of this method are demonstrated on examples of TiAl - fracture surfaces.

In materials with local variations in yield stress, such as functionally graded materials or materials with interfaces or interlayers, the local near-tip crack driving force can become different from the nominally applied far-field value. The near-tip crack driving force is enhanced, if the yield stress increases in the crack growth direction, and vice versa. This effect is termed as the yield stress gradient effect. A model is developed that allows us to derive analytical expressions to quantify the effect and to evaluate the effective crack driving force for smooth and abrupt variations in yield stress. These expressions can be used to optimize graded materials and interface and interlayer transitions so that the fracture resistance increases. The predictions of the model agree well with the results of previously reported finite element computations for cracks near bimaterial interfaces. Available experimental observations of the fatigue crack growth normal to interfaces and interlayers can be qualitatively explained. The yield stress gradient effect plays an important role for the fracture behavior in multiphase or composite materials, in functionally graded materials, in materials with special surface treatments like nitrided or case hardened steels, as well as in brazed and welded components.

The total plastic strain energy which is consumed during fracture of a plain-sided CT specimen is separated into several components. These are the energies required for deforming the specimen until the point of fracture initiation, for forming the flat-fracture surfaces, for forming the shear-lip fracture surfaces, and for the lateral contraction and the blunting at the side-surfaces, W lat. Characteristic crack growth resistance terms, R flat and R slant, are determined describing the energies dissipated in a unit area of flat-fracture and slant-fracture surface, respectively. R flat is further subdivided into the term R surf, to form the micro-ductile fracture surface, and into the subsurface term, R sub, which produces the global crack opening angle. Two different approaches are used to determine the fracture energy components. The first approach is a single-specimen technique for recording the total crack growth resistance (also called energy dissipation rate). Plain-sided and side-grooved specimens are tested. The second approach rests on the fact that the local plastic deformation energy can be evaluated from the shape of the fracture surfaces. A digital image analysis system is used to generate height models from stereophotograms of corresponding fracture surface regions on the two specimen halves. Two materials are investigated: a solution annealed maraging steel V 720 and a nitrogen alloyed ferritic-austenitic duplex steel A 905. For the steel V 720 the following values are measured: J i=65 kJ/m2, R surf=20 kJ/m2, R flat=280 kJ/m2, R slant=1000 kJ/m2, W lat=30 J. For the steel A 905 which has no shear lips, the measured values are: J i=190 kJ/m2, R flat=1000 kJ/m2, and W lat=45 J. Apart from materials characterization, these values could be useful for predicting the influence of specimen geometry and size on the crack growth resistance curves. Key words: Elastic-plastic fracture mechanics, fracture energy, energy dissipation rate, fracture surface analysis.

In materials with local changes in yield strength, the near-tip crack driving force becomes different from the applied far-field value. This effect is termed here as the plasticity gradient effect. A model is developed that allows us to derive analytical expressions to quantify the plasticity gradient effect for smooth and abrupt variations in yield strength. The predictions of the model agree well with previons finite element computations and available experimental observations. The model can be used to optimize the fracture properties of FGMs, as well as interface and interlayer transitions.

— A new tool is presented to investigate cleavage fracture surfaces. It is based on the combined techniques of crystal orientation measurements using the Electron Back-Scatter Diffraction (EBSD)-technique and 3-dimensional surfaces reconstruction by an Automatic Surface Reconstruction System (ASRS). With this tool we can perform crystallographic fractometry of cleavage fracture facets of polycrystals within the limits of the resolution of a Scanning Electron Microscope (SEM), e.g. we can determine the crystallographic indices of cleavage planes and of directions on such planes.

Stereoscopic scanning electron micrographs can be used to reconstruct the microscopic topography of material surfaces. By applying a system for automatic image processing we can obtain Digital Elevation Models (DEMs) of the investigated surface. These DEMs are used to measure the degree of deformation on metallic fracture surfaces. By modelling the deformation the amount of plastic energy that is necessary to shape the microductile fracture surface can be calculated. These values are compared with experimentally obtained results.

For a nitrogen alloyed ferritic-austenitic duplex steel X3CrMnNiMoN 25 6 4 the crack growth resistance is recorded in terms of the J -integral, J , and the energy dissipation rate, D . Due to the anisotropic microstructure of elongated ferrite and austenite domains, very different resistance curves appear for three different crack plane orientations. Metallographic and stereophotogrammetric studies lead to a model which is able to explain these curves. It is found that the geometrical arrangement of the (brittle) ferrite and the (ductile) austenite domains is the main influence factor on the crack growth resistance (and not the volumetric fraction of ferrite and austenite). Since no standard J IC -values can be determined, a procedure is proposed to evaluate an alternative measure of the fracture initiation toughness, i.e. “quasi-initiation” J -integral values.

We determine the fracture toughness of a duplex stainless steel using the COD-concept (crack tip opening displacement). The CODi values are obtained by stereophotogrammetric reconstruction of fracture surfaces. This is done by analyzing stereoscopic scanning electron microscope (SEM) images of the surfaces with an automatic image processing system. This system allows the automatic generation of a digital elevation model (DEM) with approximately 50000 points for each fracture surface image. Height-profiles at the point of crack initiation can be obtained from this DEM. The examination of corresponding profiles from both specimen-halves leads to CODi.

Purpose of this work is to investigate the effects of reverted and retained austenite on the fracture toughness of high Co–Ni steels. Different cryogenic and tempering treatments are applied to a high Co–Ni steel in order to alter the austenite content, its chemical composition and hence its stability against transformation to martensite. Austenite stability is analyzed by applying thermal cycles in the dilatometerand by X-ray diffraction. For each heat treatment, the fracture toughness is characterized by J-integral and fractographic crack growth resistance measurements. The results indicate that cryogenic and two-step tempering treatments lead to a higher austenite stability and impede austenite transformation during cooling after tempering. Consequently, the toughness is considerably improved.

After a review of the literature on the prognosis of ductile fracture, a damage indicator is developed which is based on micromechanical results and adapted to experiments. A calibration of this damage indicator is possible by inspecting in detail a load displacement curve for a long and smooth specimen. Relation to currently published damage indicators is discussed. The damage indicators can be used to indicate the onset of a local crack in a ductile structure

A numerical simulation of the stable crack growth in a thick smooth compact tension specimen with two-dimensional elastic-plastic finite element analyses is presented. The different fracture behaviors in the center and near the side surfaces of the specimen were accounted for by using plane strain analysis for the center part and plane stress analysis for the surface part. The input data to control the fracture initiation and the crack growth, i.e. CTOD i , and CTOA C , were directly measured from the center and the side surfaces of specimens. The calculated results were compared with the experimental ones. A satisfactory agreement was achieved.

A model is presented to simulate a 3D elastic-plastic FE analysis of a fracture mechanics specimen with 2D analyses. Its application for CT specimens is thoroughly investigated. It is shown that the model can easily be used and the result is very satisfactory.

The influences of the specimen thickness, the ligament length and the overall size on the J R -curves are numerically investigated for CT specimens. The thickness effect is taken into account with 2D analyses by dividing aplain sided specimen into a plane stress part and a plane strain part. For a given geometry the overall out-of-plane constraint of the specimen is determined by the relative thickness of the plane stress and the plane strain part which can be estimated with the help of a simple tridimensional analysis. It is found that the variation of the out-of-plane constraint with the geometries of the specimens is one of the main reasons for the complicated geometry effects on J R -curves. Different patterns of geometry effects are observed for one material in our numerical analyses. Similar patterns have been reported in experimental studies found in the literature. It is also shown that different classes of material may lead to different patterns of geometry effects.

The paper deals with the assessment of the fracture resistance of an inhomogeneous welded joint. The material inhomogeneities create a difference between the near-tip crack driving force, J tip, and the nominally applied far-field crack driving force, J far. This difference is quantified by the socalled material inhomogeneity term, Cinh, which can be evaluated by a post-processing procedure to a conventional finite element stress analysis. Figure 1 shows a welded joint, where the weld metal is in half overmatched (OM) and half undermatched (UM) configuration. Such welds are commonly used for repair welding or for welded joints where the possibility of hydrogen assisted cracking exists. The crack is perpendicular to the mismatch interface. The material properties have a jump at the mismatch interface, but are assumed constant in the regions above and below. In a preliminary study it has been shown that the slant interfaces to the HAZ have no noticeable effect. For this reason, the geometry is simplified to that of a CT specimen with a biomaterial interface between the OM and UM weld metal. The material inhomogeneity term is given by $$ C_{inh} = - e \cdot \int_\Sigma {\left( {\left[\kern-0.15em\left[ \phi \right]\kern-0.15em\right]I - \left\langle \sigma \right\rangle \cdot \left[\kern-0.15em\left[ {grad{\text{ }}u} \right]\kern-0.15em\right]} \right) \cdot n{\text{ }}ds} $$ (1) where σ is the Cauchy stress, u the displacement, I the identity matrix, e the unit vector in the direction of crack growth, and n the unit normal to the mismatch interface Σ.

The aim of this contribution is to compare three different methodologies that can be apply to solve an engineering problem as is the assessment of apparent toughness in a residual stresses-containing material.

International audience; The application of crystal plasticity in finite element codes provides a virtual copy of a real grain structure, including stress–strain state and slip system activity. This paper presents, first, finite element computations of an oxygen-free, high-conductivity copper multicrystal under monotonic tension. A series of polishing operations are used to reveal the real three-dimensional (3-D) microstructure, so that the mesh is a full 3-D mesh. A single crystal plasticity model is used to represent the elasto-plastic behavior for each of the approximately 100 grains. The results obtained with a full 3-D mesh and an extended 2-D mesh with columnar grains are compared in order to check the bias introduced by a simplified mesh generation. The paper goes on to compare the computational results to experimental data obtained by orientation image microscopy and local strain field measurements. Local strain and lattice rotation fields are shown. Finally, the numerical results for the slip system activity are analyzed.

International audience; Two damage indicators for ductile failure, as proposed by Hancok-Mackenzie-Gunawardena and Atkins, are compared with experimental results from literature for the upsetting process of cylindrical specimens. It is shown, for this specific example, that quite similar results can be obtained from highly different damage indicators as long as they allow for the accumulation of damage proportional both to the equivalent strain and to the stress triaxiality; the specific mathematical structure of the indicator seems to be of minor importance. These findings give some guidelines for the practical choice of a damage indicator for the stimulation of industrial forming processes, and suggest the use of the void growth based Hancock-Mackenzie-Gunawardena indicator even for a certain class of bulk forming processes. In addition, a slight geometry dependence of the failure lines obtained by the Hancock-Mackenzie-Gunawardena indicator is obtained that has so far neither been reported by experimentalists, nor can it be reproduced in a comparable manner by the Atkins indicator. A surprising correlation is found between these results and those obtained from an entirely different micromechanical analysis proposed recently by one of the authors.

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.

Ductile fracture occurs through growth and coalescence of micro-voids that originate at the location of inclusions and precipitates. The plastic work dissipated in these micro-separation processes leading to the creation of a unit fracture surface area is a measure of the micro-toughness of the material. Furthermore, void growth and coalescence processes are accompanied by plastic deformation of the material surrounding the voids. The energy dissipated by the micro-separation processes of void growth and coalescence, and the plastic deformation in the bulk material surrounding the voids together contribute to the overall fracture toughness of the material. Conventional fracture toughness tests fail to individually measure these two very different contributions. As a result, there is limited transferability of fracture toughness test data from the laboratory to an actual structure.