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Dust explosions are among the most hazardous accidents affecting industrial facilities processing particulate solids. Describing the severity parameters of dust clouds is critical to the safety management and risk assessment of dust explosions. These parameters are determined experimentally in a 20 L spherical vessel, following the ASTM E1226 or UNE 14034 standards. Since their reproducibility depends on the levels of turbulence associated with the dust cloud, a computational model of the multi-phase (gas-solid) flow is used to simulate the dispersion process with the open-source CFD code OpenFOAM. The model is successfully validated against experimental measurements from the literature and numerical results of a commercial CFD code. In addition, this study considers the impact of particle size on the turbulence of the carrier phase, suggesting that particles attenuate its turbulence intensity. Moreover, the model predicts well the formation of a two-vortex flow pattern, which has a negative impact on the distribution of the particle-laden flows with dp≤ 100 μm, as most of the particles concentrate at the near-wall region. Contrarily, an improved homogeneity of dust cloud is observed for a case fed with larger particles (dp= 200 μm), as the increased inertia of these particles allows them to enter into the re-circulation regions.

INTRODUCTION The number of variables that influence the success of an ACL reconstruction is such that, the use of numerical tools becomes increasingly necessary. In this work, a finite element model is developed to simulate the ACL reconstruction in its tibial insertion. MATERIAL AND METHODS Tibiae and ligaments porcine samples were used in this work. As the tibial fixation, an interference screw with a nominal diameter of 7mm and a length of 25mm is used. The plasty which replace the injured ligament was characterize using tensile tests. Uniaxial and confined compression tests, as well as indentation tests, were used for characterizing trabecular bone. Finite element methods were used for the implementation of the ACL reconstruction simulation, which studies the effect in the knee joint of all the elements involved (plasty, bone and interference screw). RESULTS None of the models available for the description of the trabecular bone behavior (von Mises, Hill and Crushable Foam), is capable of doing it in a completely proper manner. The use of one or the other constitutive model does not greatly influence the numerical simulation results. CONCLUSIONS As trabecular bone has a strongly anisotropic and non-symmetric mechanical behavior, none of the constitutive models available in the finite element code used is capable of fully describing it. Thus, the use of von Mises criterion is recommended, as it is the easiest to define and the one that requires the least numerical resources (lower computational cost).

The phase field fracture method is attracting significant interest. Phase field approaches have enabled predicting - on arbitrary geometries and dimensions - complex fracture phenomena such as crack branching, coalescence, deflection and nucleation. In this work, we present a simple and robust implementation of the phase field fracture method in the commercial finite element package Abaqus. The implementation exploits the analogy between the phase field evolution law and the heat transfer equation, enabling the use of Abaqus’ in-built features and circumventing the need for defining user elements. The framework is general, and is shown to accommodate different solution schemes (staggered and monolithic), as well as various constitutive choices for preventing damage under compression. The robustness and applicability of the numerical framework presented is demonstrated by addressing several 2D and 3D boundary value problems of particular interest. Focus is on the solution of paradigmatic case studies that are known to be particularly demanding from a convergence perspective. The results reveal that our phase field fracture implementation can be readily combined with other advanced computational features, such as contact, and deliver robust and precise solutions. The code developed can be downloaded from www.empaneda.com/codes .

We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus' in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed can be downloaded from www.empaneda.com/codes.

We investigate the influence of microstructural traps on hydrogen diffusion and embrittlement in the presence of cyclic loads. A mechanistic, multi-trap model for hydrogen transport is developed, implemented into a finite element framework, and used to capture the variation of crack tip lattice and trapped hydrogen concentrations as a function of the loading frequency, the trap binding energies and the trap densities. We show that the maximum value attained by the lattice hydrogen concentration during the cyclic analysis exhibits a notable sensitivity to the ratio between the loading frequency and the effective diffusion coefficient. This is observed for both hydrogen pre-charged samples (closed-systems) and samples exposed to a permanent source of hydrogen (open-systems). Experiments are used to determine the critical concentration for embrittlement, by mapping the range of frequencies where the output is the same as testing in inert environments. We then quantitatively investigate and discuss the implications of developing materials with higher trap densities in mitigating embrittlement in the presence of cyclic loads. It is shown that, unlike the static case, increasing the density of “beneficial traps” is a viable strategy in designing alloys resistant to hydrogen assisted fatigue for both closed- and open-systems.

We present a probabilistic framework for brittle fracture that builds upon Weibull statistics and strain gradient plasticity . The constitutive response is given by the mechanism-based strain gradient plasticity theory, aiming to accurately characterize crack tip stresses by accounting for the role of plastic strain gradients in elevating local strengthening ahead of cracks. It is shown that gradients of plastic strain elevate the Weibull stress and the probability of failure for a given choice of the threshold stress and the Weibull parameters. The statistical framework presented is used to estimate failure probabilities across temperatures in ferritic steels . The framework has the capability to estimate the three statistical parameters present in the Weibull-type model without any prior assumptions. The calibration against experimental data shows important differences in the values obtained for strain gradient plasticity and conventional J2 plasticity. Moreover, local probability maps show that potential damage initiation sites are much closer to the crack tip in the case of gradient-enhanced plasticity. Finally, the fracture response across the ductile-to-brittle regime is investigated by computing the cleavage resistance curves with increasing temperature. Gradient plasticity predictions appear to show a better agreement with the experiments.

We investigate the influence of gradient-enhanced dislocation hardening on the mechanics of notch-induced failure. The role of geometrically necessary dislocations (GNDs) in enhancing cracking is assessed by means of a mechanism-based strain gradient plasticity theory. Both stationary and propagating cracks from notch-like defects are investigated through the finite element method. A cohesive zone formulation incorporating monotonic and cyclic damage contributions is employed to address both loading conditions. Computations are performed for a very wide range of length scale parameters and numerous geometries are addressed, covering the main types of notches. Results reveal a strong influence of the plastic strain gradients in all the scenarios considered. Transitional combinations of notch angle, radius and length scale parameter are identified that establish the regimes of GNDs-relevance, laying the foundations for the rational application of gradient plasticity models in damage assessment of notched components.

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large deformations generally occur in the vicinity of a crack, the numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature.

Aluminium based nanostructured materials with additions of 0.5, 1 and 1.5 wt.% of zirconium have been produced and sintered using the spark plasma sintering technique in order to promote the nucleation of ZrAl3 platelets. The mechanical behaviour of all these nanocomposites was determined by means of the Small Punch Test. Zirconium additions significantly decrease the mechanical properties of these products when sintering time at the sintering temperature (625 °C) is short (3 min). Nevertheless, when the sintering time increases to 1 h (intermetallic crystallization), the zirconium additions show the expected effect: the stiffness and the yield strength increase while ductility and toughness decrease. The maximum load increases until a 0.5 wt.% Zr is attained and suddenly drops when the Zr content surpasses 1 wt.%. © 2012 Elsevier B.V. All rights reserved., The authors want to acknowledge the financial support of the Ministerio de Educación y Ciencia (Plan Nacional I+D+i), through the project numbers MEC-04-MAT2004-06992-C02-01 and MAT2008-06879-C03-00.

We present a compelling finite element framework to model hydrogen assisted fatigue by means of a hydrogen- and cycle-dependent cohesive zone formulation. The model builds upon: (i) appropriate environmental boundary conditions, (ii) a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, (iii) a mechanical behavior characterized by finite deformation J2 plasticity, (iv) a phenomenological trapping model, (v) an irreversible cohesive zone formulation for fatigue, grounded on continuum damage mechanics, and (vi) a traction-separation law dependent on hydrogen coverage calculated from first principles. The computations show that the present scheme appropriately captures the main experimental trends; namely, the sensitivity of fatigue crack growth rates to the loading frequency and the environment. The role of yield strength, work hardening, and constraint conditions in enhancing crack growth rates as a function of the frequency is thoroughly investigated. The results reveal the need to incorporate additional sources of stress elevation, such as gradient-enhanced dislocation hardening, to attain a quantitative agreement with the experiments.

A hot rolled API X-70 steel plate and its heat-affected zone (the region with the maximum hardness and lowest toughness of the welded joint made using this steel) were employed to obtain the material’s room temperature elasto-plastic fracture toughness, JIc, by means of small punch tests (SPTs) using both conventional un-notched samples and longitudinally-notched SPT specimens. In the latter case, the notches were manufactured by micromachining different notch depth-to-thickness ratios (a/t = 0.3 and 0.4). The representative toughness parameter used with the conventional SPT tests was the maximum strain measured directly in the failed region, while in the case of the notched samples, the consumed energy until the initiation of a crack from the tip of the notch was considered the most useful parameter of choice. The onset of crack initiation was determined directly from the load-displacement plot of each test with the aid of scanning electron microscope observations performed on different samples over which interrupted tests had been conducted. These tests were interrupted at different percentages of the maximum registered load. A simple correlation between the energy consumed until the initiation of crack growth in the notched SPT sample and the critical J value obtained using standard tests (J-R curves) was determined, defining an easy and promising way to derive fracture toughness from miniature SPT tests.

A new methodology to determine the elasto-plastic fracture toughness, JIc, by means of notched small punch tests (SPT) samples is reported. Standard SPT samples were used after being longitudinally notched machined from the centre of one side of the sample to the centre of the opposite side, producing a notch depth-to-thickness ratio a/t= 0.4. The onset of crack initiation was experimentally determined directly from the experimental load-displacement plot of the test and also with the aid of scanning electron microscope observations performed on different samples, with tests being interrupted at different percentages of the maximum registered load. The test was also modelled using finite element analysis and the J-integral was evaluated as a contour integral in ABAQUS. The obtained results were compared with the critical J values of the steel determined using standard tests (J–R curves) and the differences found were duly justified.

The typical heat-affected zone developed in an X-70 steel, usually used in pipeline manufacture, has been simulated via thermal treatment. A non-equilibrium microstructure consisting of bainite, with ferrite and some martensite, has been produced and mechanically characterised, resulting in much greater hardness and strength and a lower ductility and toughness than the corresponding base metal. This also has a lower ductility. Different single-edge notched bending specimens with different crack lengths (a/W between 0.1 and 0.5) were experimentally tested to assess the fracture behaviour of this product under different degrees of constraint. The J–a resistance curves at room temperature were determined, and the obtained results were explained by the effect of constraint on ductile crack growth.

The aim of this paper is to present the developed procedure for the simulation of the hot rolling process also referring to some patents. Rolling is a 3D process but using the generalized plane strain method, the real 3D problem can be solved using 2D Finite Element Model (FEM), saving an important computing time. Thus, this procedure is really useful to give assistance in the roll design and to obtain the stock cross-section temperature distribution in the whole rolling process. On the other hand, it is also presented the thermo-mechanical characterization of the R260 quality steel, 0.7% C pearlitic steel, commonly used in rail rolling. Finally, the procedure is applied to simulate the UIC-60 rail hot rolling. A good agreement between FEM results and the sample shapes was obtained in the ArcelorMittal, S.A. rail mill facility in Asturias (Spain). The thermo-mechanical properties of the steel were obtained by means of an extensive testing program and the adjustment of the Peirce model was performed and verified to take into account the viscoplastic behavior of the steel. Finally, the simulation results were compared with sample geometries of the rolling rail after every pass given into all the different shape grooves. These samples were obtained in the ArcelorMittal, S.A. rail mill facility in Asturias (Spain), and the agreement between both simulation and sample geometry was evaluated.

The small punch test (SPT) is very useful in those situations where it is necessary to use small volumes of material. The aim of this paper is to create and validate a methodology for the determination of the mechanical and damage properties of steels from the load-displacement curve obtained by means of SPTs. This methodology is based on the inverse method, the design of experiments, the polynomial curve adjustment and the evolutionary multi-objective optimization, and also allows simulating the SPTs. In order to validate the proposed methodology, the numerical results have been compared with experimental results obtained by means of normalized tests. Two dimensional axisymmetric and three-dimensional simulations have been performed in order to allow the analysis of isotropic and anisotropic materials, respectively.

The aim of this paper is to study the residual stresses in an UIC-60 rail and their reduction by means of roller straightening. Both experimental and numerical investigations have been carried out in the past to reveal the formation of dominant longitudinal residual stresses. However, the agreement between both investigations was not particularly good. The finite element method (FEM) has also been used to simulate one, two and three-dimensional analyses of a rail during roller straightening processes. The present model considers the longitudinal movement of a rail through the straightening machine, contact conditions between rail and rollers and kinematic hardening so as to take into account the plastic behaviour of the rail material (steel). These results were compared with the experimental investigations and good agreement was observed. In this respect, this paper presents a novel, more realistic numerical simulation by FEM for the roller straightening process. Finally, an improvement of the straightening process in order to obtain smaller residual stress in the rail section is proposed.

In this paper finite element simulations of mismatched welded joints at different temperatures have been performed in order to analyse the influence of temperature on their fracture behaviour and to obtain their transition curves. Cleavage is described by means of the Beremin micromechanical model. The ductile failure model is based on the so-called complete Gurson model. Both fracture mechanisms have been implemented in FORTRAN and introduced in ABAQUS by two user subroutines. The weld configuration significantly affects the stress and strain fields and different transition curves are obtained for the different configurations. The highest transition curve is obtained for the narrowest overmatched weld, being its transition temperature the lowest.

A mathematical algorithm which integrates the constitutive equations for the ductile fracture process in viscoplastic materials is described. The algorithm has been implemented in the finite-element commercial code ABAQUS by means of a constitutive USER subroutine. Based on the computational cell methodology proposed by Xia and Shih, the R-curves for pre-cracked Charpy specimens under different dynamic load conditions are obtained. In all cases it is observed that the mathematical algorithm is able to reproduce the increase in the material resistance to ductile tearing as the impact speed increases.

In this work, an analysis and numerical study have been carried out in order to determine the best candidate brick from the thermal point of view by the finite element method. With respect to the ecological design and the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviours, which fulfils all thermal requirements of the new CTE Spanish rule for further energy savings. The conduction, convection and radiation phenomena are taking into account in this study for four different types of bricks varying the material conductivity obtained from the experimental tests. Based on the previous thermal analysis, the best candidate was chosen and then a full 1.05 × 0.35 × 1.0 m. wall made of these bricks was simulated for fifteen different compositions and temperature distribution is also provided for some typical configurations. The major variables influencing the thermal conductivity of these walls are illustrated in this work for different concrete and mortar properties. The finite element method (FEM) is used for finding accurate solutions of the heat transfer equation for light concrete hollow brick walls. Mathematically, the nonlinearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of four hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. In order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given. Finally, conclusions of this work are exposed.

The application of design methods based on finite element analysis “Design by Analysis – Direct Route” as an alternative to the recommendations based on the experience and formulas “Design by Formula” allows removing the unnecessary conservatism of the current design codes. A finite element analysis (FEM) was used to calculate the behaviour of a pressure vessel (PV) made of high strength steel (P500) subject to the design loads and assuming the existence of the “worst case” crack allowed by the European standards in order to demonstrate the safe use of these steels and the too conservative design rules currently applied by the PV manufacture codes. It was demonstrated that the presence of cracks on pressure vessels made of high strength P500 steel non-detected during non-destructive tests, do not endanger the safety of the vessel, so its application can be fully successful and safe even under the worst allowed conditions, given way to significant reductions of wall thicknesses, weights and costs.

The aim of this work is to study the structural behavior of prefabricated thin-walled wood-based loadbearing stressed skin panels for use in roofs. These stressed skin panels are composed of double thin skins, made of waterproof agglomerate and oriented strandboard, with a rigid insulating core made of extruded polystyrene without a vapor control layer or breather membrane. Current design criteria for these panels are often governed by calculating shear strength rather than bending strength. However, bending is often observed as the controlling factor in real structures and experimental studies. This work describes a design procedure based on predicting whether bending or shear will control their structural behavior. In order to get this purpose, we have studied both experimentally and theoretically the different elements that constitute this construction system to determine accurately its response in the presence of the external loads. The numerical analysis of the different variables using the finite element method (FEM) was validated by means of real tests on prototypes. The biggest difficulties in the simulation were found in the supports, due to the contacts between the different elements that compose them, and in the orthotropic material properties. Finally, the conclusions and suggested simplified procedures of calculation to be applied in similar structures are given. Comparisons with experimental data and with predictions using the quasi-analytic formulas are provided in order to support the validity of the proposed models.

In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental measurements of crack tip deformation and high levels of lattice hydrogen concentration are predicted within microns to the crack tip. The important implications of the results in the understanding of hydrogen embrittlement mechanisms are thoroughly discussed. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Department of Public Works, owners and building proprietors are demanding high-capacity heat-insulating exterior masonry components specifically for further energy savings. For housing and industrial structures there is also a great interest in light building materials with good physical material behaviour, with respect to an energy conscious and ecological design, which fulfils all strength and serviceability requirements. The major variables influencing the thermal conductivity of masonry materials are illustrated in this work by taking blocks made from no-fine lightweight concrete and different mortar properties. The finite element method (FEM) is used for finding accurate solutions of the heat transfer equation for five different light concrete hollow brick walls. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the mortar conductivity and three different values for the bricks. Optimization of the walls is carried out from the finite element analysis of five hollow brick geometries by means of the mass overall thermal efficiency and the equivalent thermal conductivity. Finally, conclusions of this work are exposed.

A ductile-failure model for analysing the fracture behaviour of welded joints has been implemented. Finite element analyses of mismatched welded joints have been performed using the computational cell methodology applied to SE(B) specimens. Different crack lengths, material mismatching, and widths of weld metal have been considered. Ductile parameters have been experimentally and numerically obtained. The influence of geometry and material mismatching on the fracture behaviour of cracked welded joints has been validated by means of a testing program. In addition, the experimental results have been explained through the crack tip constraint, which has been numerically determined.

Constitutive relations and numerical integration algorithms for elastic–viscoplastic ductile materials are investigated. The Gurson yield function is considered, together with a coalescence criterion from Thomason. The constitutive equations are reformulated using the assumption of constant strain rate within an increment. A consistency condition is incorporated into the traditional viscoplastic rate format, and the tangential material operator expression is derived. The algorithm is used to investigate the influence of triaxiality in the critical coalescence values of porosity.

By means of finite element analyses of plane strain crack tip stress fields from homogeneous and heterogeneous modified boundary layer formulations, as well as homogeneous and mismatched full field solutions, a new constraint parameter β m has been established for overmatched welded joints, allowing the material mismatching effect on the crack tip stress fields to be quantified. In the case of complete specimens, both geometry and material mismatching affect the crack tip stress fields, and a total constraint parameter β T can be defined. This approach allows to quantify the stress fields directly from the values of the remote applied load.

The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.

Unbolted base plates are often used in civil engineering as structural connections in storage racks construction. The aim of this work is to describe the development of a numerical model to simulate accurately the connection between columns and foundation in metallic structures, which constitute any frame in automated storage systems. In this way, the bending stiffness of the column can be modeled in the analysis of these structures, in order to approach the real behavior in service, and these values can be included in linear beams of structural analysis programs, such as ESCAL3D [del Coz Diaz JJ, Ordieres Mere B, Siare Dominguez FJ, Bello Garcia A, Felgueros Fernandez D. J Constr Res 1998; 46:273–5]. In this study, a non-linear structural behavior of the model occurs due to the changing status of the contact surfaces and point-to-point contacts, the geometric non-linearities of the model and the material non-linearities, such as plasticity and surface friction. The finite element method is a general technique for numerical solution of differential and integral equations in science and engineering. Thus the finite element approach has been carried out in two phases. Firstly, a pre-buckling analysis has been accomplished and secondly, the above-mentioned non-linear analysis has been performed, updating the geometry of the finite element model to the deformed configuration for the first mode buckling. A total of four load cases were analyzed, with different compressive load and imposed lateral displacement. In order to validate the results some experimental models were tested to compare with the numerical model, so that a good agreement and better correlations were obtained between both.

— A ductile medium strength steel has been modelled by means of the Gurson model, and been used to investigate the effect of crack tip constraint in several fracture mechanics specimens. Both numerical and experimental results have been obtained, in the course of the crack extension process, for single edge notch bending specimens with different crack length-to-width ratios. The geometries with the shorter cracks always exhibited higher J values at initiation and steeper J crack growth resistance curves, and these results have been explained in terms of the stress and strain fields and damage development in the region ahead of the crack tip.

The characterization of the mechanical behaviour of structural materials, with the exception of material hardness, is a destructive procedure which requires direct extraction of test specimens from the component to analyse. Because this component needs to be operative, these specimens have to be as small as possible, in order not to affect the behaviour of the component and in order to allow easy reparation of the ‘damaged’ component. However, tests with miniaturized specimens are not defined in standards. Thus, the results obtained with these tests have to be interpreted in order to obtain the actual properties of the components from which the specimens have been extracted (Lucas et al., 2002). The small punch test (SPT) is very useful in all applications that require the characterization of the mechanical behaviour of structural materials or operational components without compromising their service (Lucon, 2001), as in the case of nuclear or thermal plants. Another application is the study of small testing zones. Thus, this test has been recently applied to the mechanical characterization of metallic coatings (Penuelas et al, 2009) or the heat affected zone of welds (Rodriguez et al, 2009), which are practically impossible to characterize by means of the conventional mechanical tests. Advance constitutive models frequently include parameters that have to be identified through numerical simulation of tests and mathematical optimization of variables, because they cannot often be directly measured in laboratory. In this paper, an inverse methodology for the identification of the mechanical and damage properties of structural steels has been developed. Thus, from the load-displacement curves obtained during the non-standard SPT, the mechanical and damage properties will be obtained. Moreover, this methodology also allows simulating the SP test with numerical methods. Structural steels may exhibit creep behaviour and behave according to the Hollomon’s law (σ = K·epn). Besides, ductile fracture of metallic materials involves micro-void nucleation and growth, and final coalescence of neighbouring voids to create new surfaces of a macro-crack. The ductile failure process for porous materials is often modelled by means of the Gurson model (Gurson, 1977), which is one of the most widely known micro-mechanical models for ductile fracture, and describes the progressive degradation of material stress capacity. In this model, which is a modification of the von Mises one, an elastic–plastic matrix material is considered and a new internal variable, the void volume fraction, f, is introduced. Although the original Gurson model was later modified by many authors, particularly by Tvergaard and Needleman (Tvergaard, 1981; Tvergaard, 1982; Tvergaard & Needleman, 1984), the resultant model is not intrinsically able to predict coalescence, and is only capable of

Elastic-plastic plane-strain crack problems subject to combined mode I and mode II loadings have been analysed with modified boundary layer formulations using the first two terms, K and T of the asymptotic elastic field. Corresponding full field calculations have been performed on geometries in which the mode I component arises largely from bending or tension and in which the T stress varies from tensile to compressive. The conditions for J dominance have been considered in terms of the effect of the T stress on the asymptotic field. As in related work on the pure mode I problem, positive T stresses are shown to favour J dominance, while compressive T stresses cause the stresses to fall from the HRR field.

Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.

The critical J integral and crack tip opening displacement, CTOD, at cleavage instability of a low carbon high strength steel were obtained from three point bending specimens with different crack to width ratios (0.04 < a/W < 0.48). The geometry dependence of the elastoplastic toughness parameters has been correlated with the T stress. The obtained results have been explained by means of a local cleavage fracture criterion applied to the brittle to ductile transition behaviour of the steel., Support for this work was provided by CICYT (Spain), Project Reference Number PB92-1084-C02.