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Glued-in rods (GiR) represent a very successful type of adhesively bonded joints in timber engineering. Despite their apparent geometrical simplicity, their dimensioning still challenges practitioners. A major source of mechanical complexity resides in the orthotropic nature of the wood, or engineered wood products, as laminated veneer lumber (LVL). This paper presents a relatively simple design approach based upon fracture mechanics (FM) and associated double-cantilever beam (DCB) tests that complemented tensile tests for material characterisation. In comparison with the state-of-the-art related to FM in timber engineering, the paper presents a practitioner oriented approach of a yet complex set of GiR geometries involving beech LVL (M16-8.8 threaded rods embedded in cross sections of 120 × 120 mm2 and embedment lengths of 96mm, 128mm and 160mm). The developed numerical model resulted in a good description of the load-displacement of a series of full scale, including very good estimates of their load capacities. Additionally, it allowed for significant insights regarding the complicated relationship between geometry, orthotropy, strength of the component and failure of the GiR, as for examples the complex fracture process, and the importance of transverse tensile stresses, which play a preponderant role, equal in importance to shear stresses. [ABSTRACT FROM AUTHOR]

Summary: This paper describes a particular formulation of the extended finite element method (XFEM) specifically conceived for application to existing discontinuities of fixed location, for instance, in geological media. The formulation is based on two nonstandard assumptions: (1) the use of sub‐interpolation functions for each subdomain and (2) the use of fictitious displacement variables on the nodes across the discontinuity (instead of the more traditional jump variables). Thanks to the first of those assumptions, the proposed XFEM formulation may be shown to be equivalent to the standard finite element method with zero‐thickness interface elements for the discontinuities (FEM+z). The said equivalence is theoretically proven for the case of quadrangular elements cut in two quadrangles by the discontinuity, and only approximate for other types of intersections of quadrangular or triangular elements, in which the XFEM formulation corresponds to a kinematically restricted version of the corresponding interface plus continuum scheme. The proposed XFEM formulation with sub‐interpolation, also helps improving spurious oscillations of the results obtained with natural interpolation functions when the discontinuity runs skew to the mesh. A possible explanation for these oscillations is provided, which also explains the improvement observed with sub‐interpolation. The paper also discusses the oscillations observed in the numerical results when some nodes are too close to the discontinuity and proposes the remedy of moving those nodes onto the discontinuity itself. All the aspects discussed are illustrated with some examples of application, the results of which are compared with closed‐form analytical solutions or to existing XFEM results from the literature. [ABSTRACT FROM AUTHOR]

The objective of this paper is to derive goal-oriented a posteriori error estimators for the error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the finite element method. Such error estimators are based on the well-established technique of solving an auxiliary dual problem. In a straightforward fashion, the solution to the discretized dual problem is sought in the same FE-space as the solution to the original (primal) problem, i.e. on the same mesh, although it merely acts as a weight of the discretization error only. In this paper, we follow the strategy recently proposed by Korotov et al. [J Numer Math 11:33–59, 2003; Comp Lett (in press)] and derive goal-oriented error estimators of the averaging type, where the discrete dual solution is computed on a different mesh than the primal solution. On doing so, the FE-solutions to the primal and the dual problems need to be transferred from one mesh to the other. The necessary algorithms are briefly explained and finally some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

Cohesive zone model (CZM) is commonly used to deal with the nonlinear zone ahead ofcrack tips in materials with elastoplastic deformation behavior. This model is capable of predicting the behavior of crack initiation and growth. In this paper, CZM-based finite element analysis(FEA) is performed to examine the effects of processing parameters (i.e., the clay nanoparticle volume fraction and aspect ratio) in the mechanical behaviors of a polymeric matrix reinforced with aligned clay nanoparticles. The polymeric matrix is treated as an ideal elastoplastic solid with isotropic hardening behavior, whereas the clay nanoparticles are simplified as stiff, linearly elastic platelets. Representative volume elements (RVEs) of the resulting polymer nanoclay composites(PNCs) are adopted for FEA with the clay nanoparticle distributions to follow both stack and stagger configurations, respectively. In the study, four volume fractions (Vf = 2.5%, 5%, 7.5% and 10%)and four aspect ratios (ρ= 5, 7.5, 10, and 20) of the clay nanoparticles in the PNCs are considered.Detailed computational results show that either increasing volume fraction or aspect ratio of the clay nanoparticles enhances the effective tensile strength and stiffness of the PNCs. The progressive debonding process of the clay nanoparticles in the polymeric resin was predicted, and the debonding was initiated in the linearly elastic loading range. The numerical results also show that PNCs with stagger nanoparticle configuration demonstrate slightly higher values of the engineering stress than those based on the stack nanoparticle configuration at both varying volume fractions and aspectratios of the clay nanoparticles. In addition, CZM-based FEA predicts a slightly lower stress field around the clay particles in PNCs than that without integration of CZM. The present computational studies are applicable for processing PNCs with controllable mechanical properties, especially the control of the key processing parameters of PNCs, i.e., the volume fraction and aspect ratio of the clay nanoparticles. [ABSTRACT FROM AUTHOR]

Using an analogy between dielectric breakdown and fracture of solids, this paper develops a phase field model for the electric damage initiation and propagation in dielectric solids during breakdown. Instead of explicitly tracing the growth of a conductive channel, the model introduces a continuous phase field to characterize the degree of damage, and the conductive channel is represented by a localized region of fully damaged material. Similar as in the classic theory of fracture mechanics, an energetic criterion is taken: The conductive channel will grow only if the electrostatic energy released per unit length of the channel is greater than that dissipated through damage. Such an approach circumvents the detailed analysis on the complex microscopic processes near the tip of a conductive channel and provides a means of quantitatively predicting breakdown phenomena in materials, composites, and devices. This model is implemented into a finite-element code, and several numerical examples are solved. With randomly distributed defects, the model recovers the inverse power relation between breakdown strength and sample thickness. Finally, the effect of the layered structure in a breakdown-resistant laminate is demonstrated through a numerical example. [ABSTRACT FROM AUTHOR]

The effect of support spans on single-hit ballistic limit and the effect of pre-existing ballistic damage on multi-hit ballistic limit for two S-2 glass/SC15 composite laminate thicknesses (i.e. 13.6 mm and 20.5 mm) using 0.50cal fragment simulating projectiles have been experimentally investigated in a companion paper. The main objective of this paper is to simulate and correlate the multi-hit ballistic experiments using finite element analyses. One multi-hit ballistic impact scenario on two different composite laminate thicknesses is considered in the present analyses. Finite element model of the impact scenario is developed using three-dimensional solid elements and are solved using LS-DYNA and the progressive composite damage model MAT162. The MAT162 properties and parameters of plain-weave S-2 glass/SC15 composites used in the present simulations were validated in our previous work. Multi-hit impact cases are simulated by sequentially impacting the composite laminate with five different fragment simulating projectiles at five different impact locations at an interval of 200 micro-seconds. Good correlations of ballistic limit velocities between experiments and finite element analyses are obtained. In addition, finite element analyses provided time histories of projectile and laminate dynamics, and damage evolution and interactions for the multi-hit impact cases. Detailed simulation results and comparison with the experiments are presented. [ABSTRACT FROM PUBLISHER]

This paper deals with energy based r-adaptivity in finite hyperelastostatics. The focus lies on the development of a numerical solution strategy. Although the concept of improving the accuracy of a finite element solution by minimizing the discrete potential energy with respect to the material node point positions is well-known, the numerical implementation of the underlying minimization problem is difficult. In this paper, energy based r-adaptivity is defined as a minimization problem with inequality constraints. The constraints are introduced to restrict the maximum distortion of the finite element mesh. As a solution strategy for the constrained problem, we use a classical barrier method. Beside the theoretical aspects and the implementation, a numerical experiment is presented. We illustrate the performance of the proposed r-adaptivity in the case of a cracked specimen. [ABSTRACT FROM AUTHOR]

Devices in modern technologies often have complex architectures, dissimilar materials, and small features. Their long-term reliability relates to inelastic, time-dependent mechanical behavior of such structures. This paper analyzes a three-layer structure consisting of, from top to bottom, an elastic film, a power-law creep underlayer, and a rigid substrate. The layers are bonded. Initially, the film is subject to a uniform biaxial tensile stress. A channel crack is introduced in the elastic film. As the underlayer creeps, the stress field in the film relaxes in the crack wake, but intensifies around the crack tip. We formulate nonlinear diffusion-like equations that evolve the displacement field. When the crack is stationary, the region in which the stress field relaxes increases with time. We identify the length scale of the region as a function of time. The stress intensity factor is proportional to the square-root of the length scale. For the power-law creep underlayer, this newly identified length depends on the film stress, and corrects an error in a previous paper by Huang, Prévost and Suo (Acta Materialia50, 4137, 2002). When the crack advances, its velocity can reach a steady state. We identify the scaling law for the steady velocity. An extended finite element method (X-FEM) is used to simultaneously evolve the creep strain and crack length. Numerical results are presented for the stress intensity factors of stationary cracks, and the steady velocities of advancing cracks. [ABSTRACT FROM AUTHOR]

Damage models are widely used to describe the ductile damage and fracture of metals. This paper proposes a new approach to determine the damage parameters of the Gurson-Tveergard-Needleman model, which uses a load-displacement curve coupled with finite element method. The load-displacement curve was obtained from a tensile test of a smooth tensile specimen and contained information about the damage and fracture behavior of the tested material. The principle of damage parameters identification is to minimize the deviation between experimental and simulated load-displacement curves by a hybrid particle swarm optimization. As a combination of particle swarm optimization and simulated annealing, the hybrid particle swarm optimization is an economical and effective algorithm to identify damage parameters. The identified damage parameters are also verified by testing and simulating deformation shapes of the smooth tensile specimen which is used for parameters determination. Tests and simulations of notched tensile specimens were carried out to discuss the transformability of the identified damage parameters. It is observed that the value of critical void volume fraction of the Gurson-Tveergard-Needleman model decreases with the increase of stress triaxiality. [ABSTRACT FROM AUTHOR]

Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh-generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, nine inter-relationships linking the stiffness matrix components of symmetrical or unsymmetrical laminates having transverse matrix cracks in some of the off-axis plies is presented. The crack closure condition under membrane and bending deformations is established and used to obtain the inter-relationships. The derived crack closure conditions and inter-relationships are validated using a numerical model based on previous work by the authors. These inter-relationships include the eighteen stiffness matrix components and are exact within the assumptions made in the classical lamination theory. When using a two-scale finite element-based model, six loading cases would be needed to obtain the complete stiffness matrix. With the obtained inter-relationships, only four loading cases would be needed, thus saving a third of the total amount of information and computing time. [ABSTRACT FROM AUTHOR]

A theoretical study has been carried out to solve the problem of four circular-arc cracks (located on the circumference of a circle) with coalesced yield zones in an infinite elastic perfectly plastic plate. The most significant part of the crack configuration is the coalesced yield zones between pairs of cracks. A well known complex variable method is used to derive closed form expressions for stress intensity factor, displacement components and crack opening displacement. A numerical study is also carried out in this paper to investigate the effect of coalesced yield zones on the load bearing capacity of the plate when the boundary of the plate is subjected to different types of stress profiles. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to propose a simple but robust three-node triangular membrane element with rational drilling DOFs for efficiently analyzing plane problems.Design/methodology/approach This new element is developed within the general framework of unsymmetric FEM. The element test functions are determined by using a conforming displacement field which is slightly different with the classical Allman’s interpolations, while a self-equilibrated stress field formulated based on the analytical airy stress solutions is adopted as the trial functions. To ensure the correctness between the drilling DOFs and the true rotations in elasticity, reasonable constraints are introduced through the penalty function method. Moreover, the special quadrature strategy is used for operating related integrations for future enrichment of element behavior.Findings Numerical benchmark tests reveal that this new triangular membrane element has exceptional prediction capabilities. In particular, this element can correctly reproduce a rigid body rotation motion and correctly undertake the external in-plane twisting moments; thus, it is a reasonable choice for being used to formulate flat shell elements or to be connected with other kind of elements with physical rotational DOFs.Originality/value This work provides a new approach for developing high-performance lower-order elements with simple formulations and good numerical accuracies. [ABSTRACT FROM AUTHOR]

The effect of shear displacement on the directivity of permeability in fractures is studied in this paper. The studied fracture surface has 3D self-affine fractal characteristics that are created using the modified successive random addition (SRA) method. Fluid flow through the fracture is simulated using the COMSOL Multiphysics code based on the finite element method (FEM) by changing the angle between the shear direction and macroscopic flow direction. The evolutions of the aperture distribution and flow paths with changes in shear displacement are investigated, and the change in the equivalent permeability is evaluated. The results show that the mean aperture and its deviation for rough fractures increase as the shear displacement increases, and this change is accompanied by an increase in void spaces and decreasing contact areas between the upper and lower fracture surfaces. The flow paths become more tortuous, and the channeling flow effect occurs during the shear process. The equivalent permeability of the fractures varies as the inclination between the shear direction and macroscopic flow direction changes. The permeability with the largest magnitude exists in the direction perpendicular to the shear direction, and the permeability with the smallest magnitude exists in the direction parallel to the shear direction. The equivalent permeability of the fractures at other inclinations varies between the smallest and greatest values. Notably, larger inclinations correspond to higher permeability magnitudes. The ratio of the directional permeability to the permeability in the direction parallel to the shear direction varies between 1.03 and 2.71. This ratio tends to decrease as the shear displacement and JRC increase, which indicates that the directivity of the permeability is more obvious for fractures with smaller JRCs and smaller shear displacement. [ABSTRACT FROM AUTHOR]

The finite element (FE) predictions of single-bolt connections shear-out failure in the literature were conducted with only elastic-plastic material models without any fracture model. This paper presents the FE single-bolt connection shear-out fracture (SBCSOF) prediction and failure analysis using the phenomenological shear fracture model. It is established that FE simulations without any fracture model employed in the literature cannot predict SBCSOF and thus cannot be employed for FE SBCSOF failure analysis. Consequently, it is essential to incorporate fracture model(s) for FE SBCSOF prediction and failure analysis. Analyses of the experimental and predicted SBCSOF shapes reveal that the shear fracture consists of a long main shear fracture which occurs under combined shear and compressive bending deformations, and a short shear lip that is oppositely inclined to the main shear fracture which occurs under combined shear and tensile bending deformations. The work thus presents the appropriate FE SBCSOF failure analysis technique that serves as a useful tool for in-service failure analysis when fractographic analysis is impracticable. The FE SBCSOF failure analysis technique could also serves as a tool for the parametric studies of connection parameters on the fracture behavior of single-bolt shear connections that exhibit the shear-out fracture mode. [ABSTRACT FROM AUTHOR]

As a main defect in pipeline, dents have brought great challenge to the integrity of oil and gas pipelines. Numerical study was presented in this paper to investigate the stress and strain state of dented X60 pipe. Suitable failure criteria is adopted and validated by full scale experimental results. And the failure process of dented X60 pipe is elucidated in detail. Based on the established model, effects of dent depth, indenter diameter, initial internal pressure, ratio of diameter to ratio thickness on limit pressure of dented pipe was discussed. Finally, a regression based prediction equation for dented X60 pipe was proposed. Results show this equation predicts accurate results with much less effort and time with regard of 3D finite element models. [ABSTRACT FROM AUTHOR]

Asymmetric four point bend specimens are often used for determination mode II fracture toughness. Different corrections were proposed to classical solution of Stress Intensity Factors for this specimen. This paper provides a solution for a bi-material four point specimen with sub-interface crack. The solutions were obtained using Finite Element Analysis, and the effect of crack distance to interface, crack length and materials combination were investigated. [ABSTRACT FROM AUTHOR]

Abstract: The mechanical behavior of fibrous networks is governed by complex multiple mechanisms. This study examines the effect of microstructure on the macroscopic deformation and fracture of two-dimensional random fiber networks and its practical implications for understanding the material failure in paper materials by using finite element models. Remote load is a pure mode I opening field, applied via a boundary layer. Characteristic networks, consisting of the union of solutions of several unique networks, are interpolated on a rectangular grid covering the whole problem domain. The interpolated solutions are interpreted as network-equivalent continuums representing the mechanical behavior, on average, for a specific set of structural properties. A regularization routine is included in a variational procedure in order to minimize potential energy in the body and produce continuous strains at cell borders in the grid. It is shown that using a classical continuum linear elastic fracture mechanics (LEFM) approach to describe macroscopic singular-dominated fields in fiber networks, can lead to erroneous results especially in networks having a low degree of bonds per fiber. The classical continuum description is too simple to capture the essential mechanical behavior for this class of material since a structural effect, that alters the displacement field, becomes pronounced. It is necessary to include a nonlocal theory to describe the mechanical behavior at a continuum level. By using an appropriate characteristic length in a nonlocal continuum formulation, strain energies, in the neighborhood of a dominant macroscopic singularity, are calculated that agree well with characteristic network models and hence produce fairly good agreements between the networks and the nonlocal continuum models. A key conclusion found is that, only for networks with a high degree of bonding, can the mechanical behavior around a macroscopic singularity be captured by the classical local continuum theory. In networks with a low degree of bonds per fiber, there are regions far away from the macroscopic singularity that have relatively higher magnitudes of strain energy than predicted by the classical theory. A relation between an internal length scale parameter, used in the nonlocal continuum model, and the structural properties of the network is approximated by a simple function. [Copyright &y& Elsevier]

Web holes are often made in wood I-joists to allow passage of services. Design properties of wood I-joists with a web hole are commonly developed through testing which leads to empirical design information. This paper describes a mechanics-based method to predict the strengths of wood I-joists with a circular web hole that is suitable for implementation as a design tool. Curved beam theory is used to compute stresses around a hole. Peak tensile stresses obtained from curved beam analysis agree well with those predicted using the finite-element method. Failure load is attained by the application of fracture mechanics based finite area method. The method developed is used to predict failure loads of wood I-joists of different depths with different web hole sizes. Simplification of the method leads to the development of a simple expression that can be used for engineering design. It is found that the predicted strengths are in a good agreement with the corresponding test results. The calculation method developed can potentially replace the testing approach generally adopted by the wood I-joist industry. [ABSTRACT FROM AUTHOR]

Asphalt paving layers, particularly the surface course, exhibit vertically graded material properties. This grading is caused primarily by temperature gradients and aging related stiffness gradients. Most conventional existing analysis models do not directly account for the continuous grading of properties in flexible pavement layers. As a result, conventional analysis methods may lead to inaccurate prediction of pavement responses and distress under traffic and environmental loading. In this paper, a theoretical formulation for the graded finite element method is provided followed by an implementation using the user material subroutine (UMAT) capability of the finite element software ABAQUS. Numerical examples using the UMAT are provided to illustrate the benefits of using graded elements in pavement analysis. [ABSTRACT FROM AUTHOR]

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/δ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from `complete slip before opening' to `opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings. [ABSTRACT FROM AUTHOR]

This paper presents a micromechanical analysis of the influence of fiber–matrix interface fracture properties on the transverse tensile response of fiber-reinforced composite. The method combines three-dimensional (3D) computational micromechanics and augmented finite element method to provide high-fidelity results of damage initiation and propagation. Random arrangement of fibers and normal distribution of interface toughness and strength are considered in representative volume elements to capture the stochastic behavior of the composite under loading. Sensitivity analysis with respect to the interface properties distribution, and shape and size of fibers on the representative volume element’s strength are performed. The effect of fiber volume fractions on the strength and elastic modulus of the composite is investigated. Failure path in different representative volume elements are compared. The results show that the response of a representative volume element with identical interface properties overestimates the composite’s transverse strength. It is also shown that the damage initiation and propagation locations are affected by the distributions of fracture properties, and the shape and size of fibers within the representative volume element. [ABSTRACT FROM AUTHOR]

Based on the finite element simulation and experimental analysis, this paper mainly studies the deformation damage and fracture of 7050-H112 aluminum alloy during double shear based on the elastic strain energy density. The analyses of deformation damage and fracture for ends-free and ends-constrained specimens in complex stress and strain states have been carried out. The different stress and strain states which are characterized by stress triaxiality and strain Lode parameter have important effects on damage and fracture according to the simulation and experimental results. The final fracture is mainly caused by tensile stress both for specimens with ends free and ends constraint. Meanwhile, the shear planes are mainly in a state of shear strain when fracture occurs according to the analysis of stress triaxiality and strain Lode parameter. Three characteristic areas (radiation area, fiber area and shear lips) are observed from fracture morphology and account for different proportions on fracture surface for ends-free and ends-constrained specimens. The simulated results on the damage evolution and fracture from finite element method (FEM) are in good agreement with the experimental ones. Besides, there are competitive relations between ductile fracture and brittle fracture during the process of fracture in this paper. [ABSTRACT FROM AUTHOR]

Defects in composite materials are created during manufacture to a large extent. To avoid them as much as possible, it is important that process simulations model the onset and the development of these defects. It is then possible to determine the manufacturing conditions that lead to the absence or to the controlled presence of such defects. Three types of defects that may appear during textile composite reinforcement or prepreg forming are analysed and modelled in this paper. Wrinkling is one of the most common flaws that occur during textile composite reinforcement forming processes. The influence of the different rigidities of the textile reinforcement is studied. The concept of 'locking angle' is questioned. A second type of unusual behaviour of fibrous composite reinforcements that can be seen as a flaw during their forming process is the onset of peculiar 'transition zones' that are directly related to the bending stiffness of the fibres. The 'transition zones' are due to the bending stiffness of fibres. The standard continuum mechanics of Cauchy is not sufficient to model these defects. A second gradient approach is presented that allows one to account for such unusual behaviours and to master their onset and development during forming process simulations. Finally, the large slippages that may occur during a preform forming are discussed and simulated with meso finite-element models used for macroscopic forming. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'. [ABSTRACT FROM AUTHOR]

Internal cracks often appear in cast slabs, and their evolution during hot deformation directly affects the product quality. In this paper, the authors investigate the closure behavior of internal cracks during plate rolling using a finite element (FE) model that takes into account the roughness of the crack surface. Influences of the roughness and reduction ratio on the closure of cracks are analyzed. The simulated results show that the models with consideration of the initial crack roughness can be used to investigate the formation of residual voids around the crack after rolling. The simulation results are validated by experimental observations. Finally, we propose an explanation of the crack closure mechanism during rolling. [ABSTRACT FROM AUTHOR]

An important concern in metal forming is whether the desired deformation can be accomplished without any failure of the material, even at elevated temperatures. This paper describes the utilization of ductile fracture criteria in conjunction with the finite element (FE) method for predicting the onset of fracture in warm metal working processes of magnesium alloy sheets. The uniaxial tensile tests of AZ31 alloy sheets with a thickness of 3 mm and FE simulations were performed to calculate the critical damage values for three kinds of ductile fracture criteria. The critical damage values for each criterion were expressed as the function of strain rate at various temperatures. In order to find out the best criterion for failure prediction, Erichsen cupping tests under isothermal conditions were carried out at various temperatures and punch velocities. Based on the plastic deformation histories obtained from FE analysis of the Erichsen cupping tests and the critical damage value curves, the initiation time and location of fracture were predicted under bi-axial tensile conditions. As a result, Cockcroft-Latham's criterion showed good agreement with the experiments. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM-XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum-based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved. [ABSTRACT FROM AUTHOR]

Abstract: Parts composed of two ceramic–metal composite layers have been fabricated by co-sintering of two powder blends. The major constituent was the ceramic powder in one blend and the metal powder in the second one. This paper focuses on the mechanical analysis of the co-sintering process. This process has been observed thanks to an original optical dilatometry set up that provided images of the component in the course of sintering cycle. These images allowed following component shape changes throughout the thermal cycle and also evidenced the formation of cracks at the edges of a part at particular stages of the sintering cycle. These phenomena are interpreted from the mismatch between the densification kinetics of each powder blend sintered alone. In a companion paper the results of a finite element simulation of cosintering are compared to the experimental data displayed in the present paper. [Copyright &y& Elsevier]

The objective of this paper is to evaluate the deformation behavior of clay-based landfill covers subjected to differential settlements through centrifuge model studies and finite-element analyses (FEA). A series of centrifuge tests were performed on model soil barriers subjected to continuous differential settlements through a motor-based differential settlement simulator by varying the thickness of the soil barrier with and without overburden equivalent to that of landfill coves at 40 gravities. In addition, a parametric study was carried out numerically by varying the thickness of the soil barrier and overburden pressure by using PLAXIS, a geotechnical finite-element code. The modeling considerations adopted in FEA were developed such that they are close to the centrifuge model tests in prototype dimensions. Differential settlements in FEA were assigned by using predefined displacement profiles. Results from centrifuge model tests deduce that both 0.6 and 1.2 m thick soil barriers were observed to experience full-depth cracks at the zone of maximum curvature and fail to serve the basic purpose of an effective hydraulic barrier. The results from FEA indicate the development of higher values of tensile stresses and strain extending throughout the thickness of the soil barrier at the zone of maximum curvature, which indirectly advocate the possibility of formation of tension cracking when the generated tensile stresses caused by deformation exceed the permissible tensile strength of the soil barrier material. The magnitude of the horizontal tensile stress along the top surface of the soil barrier at the zone of maximum curvature was found to be suppressed with an increase in the value of overburden pressure. When the soil barrier was subjected to an overburden pressure in the range of 50-75 kPa, there exists a complete transformation of tensile stresses to compressive stresses, which indirectly suggests that there can be no prospects of development of tension cracks even at a distortion level of 0.125. [ABSTRACT FROM AUTHOR]

This paper presents recent advances in the design of steel and composite beams with web openings for full integration with building services. The conventional design approaches, such as 'Tee Section Approach' and 'Perforated Section Approach', are provided as an introduction to the topic. The key findings of a comprehensive finite element investigation into the structural behaviour of steel beams with web openings of various shapes and sizes are presented, and a generalized design rule with a set of moment-shear interaction curves based on the finite element results is also developed for practical applications. It should be noted that based on three structural parameters, namely, the shear utilisation ratio, v, the coupled moment capacity ratio, m, and the coupled shear capacity ratio, v, the load carrying capacities of steel beams with web openings of various shapes and sizes are obtained readily through the use of the proposed moment-shear interaction curves.Moreover, an advanced finite element study on a composite beam with a pair of large rectangular web openings is also presented, and the structural behaviour of the perforated composite beam with deformable shear connectors of different deformation characteristics is examined. It is found that both the stiffnesses and the resistances of shear connectors are very important to the load carrying capacities of the perforated composite beams. The maximum difference in the load carrying capacities of the perforated composite beams with different types of shear connectors is shown to be around 15%, reflecting the different deformation states of the composite beams at failure. Moreover, large pull-out forces are also induced in those shear connectors in the vicinity of the web openings which have been neglected in the past. As the values of these pull-out forces are found to be comparable to the shear resistances of the shear connectors adopted in the models in some cases, such forces should be considered properly in design. [ABSTRACT FROM AUTHOR]

This paper developed 3D elastoplastic finite element analysis (FEA) models to investigate non-axisymmetric tubes neck spinning. The three-roller mandreless neck spinning process was simulated by commercial FEA software, MSC. Marc. The distribution of the transient von Mises stresses in the contact zone between the roller and the blank, and the equivalent plastic strains after spinning were obtained. The locations and causes of fractures were analyzed. The thickness distribution of the spun workpiece was investigated numerically and experimentally. It shows that during 3D non-axisymmetric tubes spinning, diametral elongation and fractures mostly occur at the opening end of workpiece, which considered as the primary location of defects. Fractures may also occur easily at the initial spinning area, which may be considered a secondary location of defects. The distributions of equivalent stresses and strains are non-uniform during both offset and oblique 3D non-axisymmetric tubes spinning. The maximum stress and strain values occur at the location where the biggest offset or inclination is induced, while the minimum values occur at the opposite location of 180° away from the maximum values. For the oblique tube, however, the strain distribution changes gradually along the axial direction, which is different from that of the offset tube. Thinning occurs during forward path spinning and thickening occurs during backward path spinning. Therefore, for multipath neck spinning processes, forward and backward paths should be applied alternately to avoid excessive thinning or thickening of workpiece. [ABSTRACT FROM AUTHOR]

The porous plasticity model (usually referred to as the Gurson-Tvergaard-Needleman model or modified Gurson model) has been widely used in the study of microvoid-induced ductile fracture. In this paper, we studied the effects of random voids on the porous plasticity model. Finite-element simulations were conducted to study a copper/tin/copper joint bar under uniaxial tension using the commercial finite-element package ABAQUS. A randomly distributed initial void volume fraction with different types of distribution was introduced, and the effects of this randomness on the crack path and macroscopic stress-strain behavior were studied. It was found that consideration of the random voids is able to capture more detailed and localized deformation features, such as different crack paths and different ultimate tensile strengths, and meanwhile does not change the macroscopic stress-strain behavior. It seems that the random voids are able to qualitatively explain the scattered observations in experiments while keeping the macroscopic measurements consistent. [ABSTRACT FROM AUTHOR]

Highlights • A XPFEM is proposed for solving large deformation fracture problems. • Modeling the discontinuities is based on a coupling scheme of polygonal and quadrilateral meshes. • The presence of hanging nodes are resolved as conforming polygonal elements. • Excellent performance of the present approach is confirmed by numerical testes. Abstract The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements. [ABSTRACT FROM AUTHOR]

ABSTRACT Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E-glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode-mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode-mixity at the crack tip, face sheet properties and core density. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to shed light on the effect of strain rate and viscoplastic deformation of bulk solder on the interfacial failure of lead-free solder joints. For this purpose, interfacial damage evolution and mode I fracture behavior of the joint were evaluated experimentally by performing stable fracture tests at different strain rates employing an optimized tapered double cantilever beam (TDCB) design. The viscoplastic behavior of the solder was characterized in shear, and the constitutive parameters related to the Anand model were determined. A rate-independent cohesive zone damage model was identified to best simulate the interfacial damage progression in the TDCB tests by developing a three-dimensional (3D) finite-element (FE) model and considering the viscoplastic response of the bulk solder. The influence of strain rate on the load capability and failure mode of the joint was clarified by analyzing the experimental and simulation results. It was shown how, at the lower strain rates, the normal stress generated at the interface is limited by the significant creep relaxation developed in the bulk solder and thus is not sufficiently high to initiate interfacial damage, whereas at higher rates, a large amount of the external energy is dissipated into interfacial damage development. [ABSTRACT FROM AUTHOR]

Abstract: This paper explores the specimen-dependence of the resistance (R-) curve for fracture of materials showing a pronounced R-curve effect. Using a cohesive zone framework, this paper demonstrates how to effectively predict the R-curve for a specimen type whose deformation is shear-dominated (compact tension, CT) from the R-curve of a specimen type whose deformation is bending-dominated (double cantilever beam, DCB). The mathematical relationships between crack extension and crack opening displacements for both CT and DCB specimens are first derived and related to a tri-linear cohesive law. Experimental tests for intralaminar fracture of CFRP are carried out and analysed. Using, as input, the experimental results from the DCB specimen, the cohesive law is shown analytically and using Finite Element (FE) to reproduce accurately the R-curve for the DCB and also to predict accurately the R-curve for the CT specimens. [Copyright &y& Elsevier]

This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1 m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5 m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1 m (39.4 in.), the size effect cannot be neglected. [ABSTRACT FROM AUTHOR]

Highlights • An average weight whole-process method is proposed across various structural steels. • The effect of temperature on ductile fracture property is not reflected by the toughness parameter. • The analytical results using the proposed method agree well with test results by an average parameter. • The predictive equations of ductile fracture parameters are proposed. Abstract An average weight whole-process method is proposed to evaluate the force-displacement curve, ultimate capacity, ductile fracture displacement and fracture force of high strength steel (HSS) Q690. Finite element analyses of 26 specimens are carried out to demonstrate the accuracy and application of the average weight whole-process method to predict the mechanical and ductile fracture performance of the HSS Q690. Modeling concepts and procedures for characterizing the material parameters of the average weight whole-process method are described using tensile tests conducted on the specimens after cooling down from various temperatures ranging from 20 °C to 900 °C as presented in a previous paper. In this method, four important parameters (including the equivalent plastic strain at the neck, true stress at the neck, weight parameter and toughness parameter) can be obtained through combining test result and finite element analysis. Finite element analytical results reveal that the effect of temperature experienced on the ductile fracture performance of the HSS Q690 is reflected by the equivalent plastic strain at the neck, the true stress at the neck and the weight parameter, and not by the toughness parameter. It is concluded that the proposed method in this study can predict the post-fire force-displacement curve, ultimate bearing capacity and ductile fracture performance with good accuracy across various temperatures experienced. Finally, the predictive equations of ductile fracture parameters based on all of the test and simulated results in this study are proposed. [ABSTRACT FROM AUTHOR]

In this paper, we develop and implement high-resolution, computationally efficient multi-cell finite-element (FE) models of metallic foams in order to more accurately investigate the collapse behaviour of these emerging materials. The main objective is to investigate the effect of morphological imperfections at the cellular scale on the global response of the cellular material. Attention was therefore devoted to three related aspects of the work. The first is concerned with the development of FE models of metallic foams accounting for morphological imperfections at the cellular level. The second is concerned with conducting parametric studies of different model parameters and examining their effect on the instantaneous load-deformation history, peak collapse loads and energy absorption levels of the foam. The third is devoted to a thorough comparison of the numerical simulations with experimental results. Results revealed the influence of these imperfections on low-density foams, and to a much lesser extent on high-density ones. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of interacting cracks using a generalized finite element method (GFEM) enriched with so-called global-local functions. In this approach, solutions of local boundary value problems computed in a global-local analysis are used to enrich the global approximation space through the partition of unity framework used in the GFEM. This approach is related to the global-local procedure in the FEM, which is broadly used in industry to analyze fracture mechanics problems in complex three- dimensional geometries. In this paper we compare the effectiveness of the global-local FEM with the GFEM with global-local enrichment functions. Numerical experiments demonstrate that the latter is much more robust than the former. In particular, the GFEM is less sensitive to the quality of boundary conditions applied to local problems than the global-local FEM. Stress intensity factors, computed with the conventional global-local approach showed errors of up to one order of magnitude larger than in the case of the GFEM. The numerical experiments also demonstrate that the GFEM can account for interactions among cracks with different scale sizes, even when not all cracks are modeled in the global domain. [ABSTRACT FROM AUTHOR]

Abstract: The active repair performance of the piezoelectric actuator for the cracked structure is studied in this paper. As an extension of the author’s previous study, this paper discusses a special repair case and new results by using two repair criteria: the slope continuity criterion and fracture mechanics criterion. Crack contact analyses and fracture mechanics in the crack tip field are considered in the plane strain finite element analyses. From numerical results, it is concluded that the fracture mechanics criterion is better for defining the repair voltage. The crack tip field and crack contact condition must be considered to obtain correct results. However, it is not a good idea for the active repair to use higher applied voltage on the piezoelectric actuator. [Copyright &y& Elsevier]

Abstract: The paper presents the results obtained from investigations of the “squat” type crack serving as an example of the rolling contact fatigue crack that appears in rail heads. Some geometrical parameters of the crack can be defined. The work is devoted mainly to the problem of crack thickness, i.e. the gap between crack faces. The observation of crack faces allowed us to formulate a concept of how this gap is forming. The crack thickness distribution over the whole crack face was measured. The results obtained were introduced into 3D FEM models. The paper also describes the changes in crack thickness distribution in the course of wheel rolling over the crack and the resulting crack volume changes. [Copyright &y& Elsevier]

This paper addresses mixed-mode crack growth in two-dimensional functionally graded materials, and assesses the predictive capability of some fracture criteria on both crack growth direction and crack initiation condition. Automatic simulation of mixed-mode crack propagation in homogeneous and functionally graded materials is performed by means of the finite element method in conjunction with a remeshing algorithm. Crack growth simulation consists of iterative procedures for the calculation of mixed-mode stress intensity factors by means of the interaction integral method, determination of crack growth direction and crack initiation, and local automatic remeshing along the crack path. The present approach requires a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present simulation are compared with available experimental results. [ABSTRACT FROM AUTHOR]

This paper investigates the effectiveness of theoretical failure criteria in the estimation of workability limits in cold forging through Finite Element Analysis (FEA), by incorporating them into the commercial software ABAQUS 6.3.1. Universal applicability of the threshold values of these criteria functions, at the location and instant of fracture, represents their overall performance. FEA of various cold working processes involving typical materials was carried out up to the experimentally observed limit for fracture. Threshold values of all failure criteria depended on the stress-state resulting from geometry and loading conditions of the process. Poor scalability of the failure criteria across stress-states is attributed to the transition in modes of fracture, from global ductile - local brittle to shear depending upon the level of hydrostatic stress at fracture sites. There exists a race between the types of fracture in the deformation zone and failure occurs by the mechanism reaching the threshold first. Among the existing failure models, Kuhn's fracture locus successfully delineates the safe and unsafe regions in plastic strain-space, irrespective of the mode of fracture. [ABSTRACT FROM AUTHOR]

Defects that form by mechanisms such as fatigue and stress corrosion cracking are influenced both by external loads on engineering structures and internal, residual stresses that are generated during the manufacture and operation. This paper describes a programme of experimental and analytical work on a high-strength, low-toughness aluminium alloy (AL2024-T351) to assess the influence of residual stress on crack opening displacement (COD) and crack-driving force (CDF) for a range of fatigue crack lengths in compact tension (CT) specimens containing a mechanically induced residual stress field. Comparison of experimentally measured and numerically predicted CODs, at the mid-plane and surface of CT specimens, show generally good agreement for cracks introduced into the finite-element model in a progressive, element-by-element manner. Cracks introduced in a simultaneous manner give larger than observed CODs. The CDFs for the progressively introduced crack are always smaller than for simultaneously introduced. These results have implications for the assessment of initiation for slowly growing cracks. [ABSTRACT FROM AUTHOR]