Modelling brittle impact failure of disc particles using material point method

Understanding the impact failure of particles made of brittle materials such as glasses, ceramics and rocks is an important issue for many engineering applications. During the impact, a solid particle is turned into a discrete assembly of many fragments through the development of multiple cracks. The finite element method is fundamentally ill-equipped to model this transition. Recently a so-called material point method (MPM) has been used to study a wide range of problems of material and structural failures. In this paper we propose a new material point model for the brittle failure which incorporates a statistical failure criterion. The capability of the method for modelling multiple cracks is demonstrated using disc particles. Three impact failure patterns observed experimentally are captured by the model: Hertzian ring cracks, meridian cracks, and multi-fragment cracks. Detailed stress analysis is carried out to interpret the experimental observations. In particular it is shown that the experimentally observed dependence of a threshold velocity for the initiation of meridian cracks on the particle size can be explained by the proposed model. The material point based scheme requires a relatively modest programming effort and avoids node splitting which makes it very attractive over the traditional finite element method.     

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm² with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model.The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie-Knott-Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.     

Finite element modelling of two phase Fe–Cu polycrystals

The plastic deformation of two-phase iron–copper polycrystals was studied experimentally and modelled by a FEM model calculation, taking into account anisotropic elasticity and crystal plasticity. The two-phase materials in experiment had microstructures ranging between interpenetrating network and matrix/inclusion type and were deformed by compression at room temperature. The measured quantities (macroscopic stress and strain, elastic strains and texture) were compared with the results from the FEM model calculation. The stress vs. strain dependence as obtained from the FEM-model appears to be in good accordance with experimental results. Good predictions of the texture evolution were found in cases only, where local micromechanical interactions are not too much influenced by the heterogeneity of the microstructure. The implications of these results for the development and use of FEM schemes for modelling heterogeneous polycrystal plasticity are discussed.     

Finite element prediction of thermal stresses and deformations in layered manufacturing of metallic parts

Summary Residual stress induced deformations are a major cause of loss in tolerances in Solid Freeform Fabrication processes employing direct metal deposition. In this paper, a 2D finite element thermo-mechanical model is presented to predict the residual stress induced deformations with application to processes where material is added using a distributed, moving heat source. A sequentially coupled thermo-mechanical analysis is performed using a kinematic thermal model and plane strain structural model. Temperature dependent material properties are used with the material modeled as elastic perfectly plastic. An interpass cooling between successive depositions is employed in accordance to the requirement of experiment. The simulation results are compared with experimental data for successive sections along deposition and it is found that, with the exception of deposition center and plate edges, the two are in very good agreement. The error at plate edges can be as high as 45%, and the reason is that a 2D model cannot capture the effect of plate bolting accurately. A case of continuous deposition, without interpass cooling, has been compared with the base case of employing interpass cooling. It has been found that continuous deposition results in higher preheating of the substrate which consequently reduces the deformation.     

Finite element modelling of hardening concrete: application to the prediction of early age cracking for massive reinforced structures

This article presents finite element modelling to predict the early age cracking risk of concrete structures. It is a tool to help practitioners choose materials and construction techniques to reduce the risk of cracking. The proposed model uses original hydration modelling (allowing composed binder to be modelled and hydric consumption to be controlled) followed by a non-linear mechanical model of concrete at early ages involving creep and damage coupling. The article considers hydration effects on this mechanical model, which is based on a non-linear viscoelastic formulation combined with an anisotropic, regularized damage model. Details of the numerical implementation are given in the article and the model is applied successively to a laboratory structure and to a massive structure in situ (experimental wall of a nuclear power plant studied in the framework of the French national research project CEOS.fr).     

Finite cover method for progressive failure with cohesive zone fracture in heterogeneous solids and structures

The finite cover method (FCM), which is a cover-based generalized finite element method, is extended for analyses of progressive failure processes involving cohesive zone fracture, starting from an interface debonding and evolving toward one of the constituents of heterogeneous solids and structures. Assuming that the constituents fail according to the maximum principal stress, we are able to represent the evolution of the resulting failure surfaces of discontinuity independent of mesh alignment owing to the distinctive features of the FCM. Also, interface elements with Lagrange multipliers are introduced to impose compatibility conditions on the material interface so that debonding is judged by the multipliers. Representative numerical examples demonstrate the capability of the proposed method in tracing the smooth transition of crack paths from interfacial to internal failure, and vice versa.     

Fast failure prediction of adhesively bonded structures using a coupled stress‐energetic failure criterion

The use of adhesively bonded joints in industrial structures requires reliable tools for the estimation of the failure load. The necessary and sufficient condition to predict the strength of such joints involves the implementation of a coupled stress and energetic criteria. However, its application necessitates the identification of the stress distribution along the adhesive layer, which has been approximated in this paper by a previously published closed‐form solution. This analysis along with finite element modelling results are compared with experimental data issued from a double‐notched sample tested with the Arcan fixture at various load ratios. The results show good agreement; the use of the closed‐form solution permitted to predict the failure load more rapidly and in a conservative manner compared with the experimental results. The application of the methodology is also extended to a wider range of joint geometries by means of spatial interpolation using the Kriging model.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

Finite element analysis of contact induced adhesion failure in multilayer coatings with weak interfaces

Experimental work reveals that the Ag/ZnO interface in the multilayer solar control coatings is weakest and most likely to fail during contact. In this study, a cohesive zone model embedded in a finite element code was used to model delamination in multilayer stack consisting of ZnO/Ag/ZnO on glass during contact. It shows that delamination occurs at the upper ZnO/Ag interface during loading when penetration exceeds a critical value, while, the double pinned buckling delamination failure occurs at the lower Ag/ZnO interface during the unloading cycle. Furthermore, it reveals the model based on mechanism of lateral crack at interface yields reasonably accurate values of interfacial toughness when tensile stress induced delamination occurs during unloading.     

Finite element modelling of core thickness effects in aluminium foam/composite sandwich structures under flexural loading

This paper models the flexural behaviour of a composite sandwich structure with an aluminium foam core using the finite element (FE) code LS-DYNA. Two core thicknesses, 5 and 20 mm, were investigated. The FE results were compared with results from previous experimental work that measured full-field strain directly from the sample during testing. The deformation and failure behaviour predicted by the FE model compared well with the behaviour observed experimentally. The strain predicted by the FE model also agreed reasonably well with the distribution and magnitude of strain obtained experimentally. However, the FE model predicted lower peak load, which is most likely due to a size effect exhibited by aluminium foam. A simple modification of the FE model input parameters for the foam core subsequently produced good agreement between the model and experimental results.     

Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system

A micromechanical model that provides explicit accounts for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on a cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of continuum fracture criteria which assume, for example, the existence of K-fields. Numerical analyses carried out concern failure in the forms of crack propagation and microcrack formation. Actual microstructures of brittle alumina/titanium diboride (Al₂O₃/TiB₂) composites are used. The results demonstrate the effects of microstructure and material inhomogeneities on the selection of failure modes in this material system. For example, the strength of interfaces between the phases is found to significantly influence the failure characteristics. When weak interfacial strength exists, interfacial debonding and microcrack initiation and growth are the principal mode of failure. When strong interfacial strength is derived from material processing, advancement of a dominant crack and crack branching are observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulations of dynamic crack propagation in brittle materials using nodal cohesive forces and continuum damage mechanics in the distinct element code LDEC

Experimental data indicates that the limiting crack speed in brittle materials is less than the Rayleigh wave speed. One reason for this is that dynamic instabilities produce surface roughness and microcracks that branch from the main crack. These processes increase dissipation near the crack tip over a range of crack speeds. When the scale of observation (or mesh resolution) becomes much larger than the typical sizes of these features, effective-medium theories are required to predict the coarse-grained fracture dynamics. Two approaches to modeling these phenomena are described and used in numerical simulations. The first approach is based on cohesive elements that utilize a rate-dependent weakening law for the nodal cohesive forces. The second approach uses a continuum damage model which has a weakening effect that lowers the effective Rayleigh wave speed in the material surrounding the crack tip. Simulations in this paper show that while both models are capable of increasing the energy dissipated during fracture when the mesh size is larger than the process zone size, only the continuum damage model is able to limit the crack speed over a range of applied loads. Numerical simulations of straight-running cracks demonstrate good agreement between the theoretical predictions of the combined models and experimental data on dynamic crack propagation in brittle materials. Simulations that model crack branching are also presented.     

Influences of complex loading and margin geometry: failure of curved brittle layer structures

This study investigates the influences of off-axis loading and of margin geometry on “margins failure” observed in loaded curved bi-layer structures, away from the contact loading point. Specimens of hemispherical bi-layer model consist of glass shells with varying margins geometry, and filled with epoxy resin substrate are prepared. These specimens are loaded with compliant PTFE Teflon cylindrical indenters, with a modulus of several orders of magnitude lower than the indented materials. Load is applied normally; axisymmetric to the dome apex, and at 45° from the axis of symmetry. In this fashion, the effect of off-axis loading and the influence of margin geometry on “margins failure” are studied. The onset of fracture is observed in situ using a video camera system. Finite element analysis is applied to determine basic stress distribution within the dome structures, and to confirm a shift in maximum tensile stress from the near-contact area to the dome sides with the use of more compliant indenters. Critical loads to initiate radial cracks and damage evolution are presented, and interpreted with the results of FEA.     

Finite element modelling of cracked inelastic shells with large deflections: two‐dimensional and three‐dimensional approaches

Higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances, both material and geometrical non‐linearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. The present study addresses the performance of surface‐cracked inelastic shells with out‐of‐plane displacements not negligible compared to shell thickness. This situation leads to non‐linear membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a non‐proportional history of bending moment and membrane force. An important point in the discretization of the problem is whether a two‐dimensional model describes the structural performance sufficiently, or a three‐dimensional model is required. Herein, the two‐dimensional modelling is performed by means of a Mindlin shell finite element. The cracked parts are accounted for by means of inelastic line spring elements. The three‐dimensional models employ eight‐noded solid elements. These models also account for ductile crack growth due to void coalescence by means of a modified Gurson–Tvergaard constitutive model, hence providing detailed solutions that the two‐dimensional simulations can be tested against. Using this, the accuracy of the two‐dimensional approach is checked thoroughly. The analyses show that the two‐dimensional modelling is sufficient as long as the cracks do not grow. Hence, using fracture initiation as a capacity criterion, shell elements and line springs provide acceptable predictions. If significant ductile tearing occurs before final failure, the line spring ligaments have to be updated due to crack growth.     

Finite element computational modelling and experimental investigation of perforated NiTi plates under tension

This paper explores the pseudoelastic deformation behaviour of perforated near-equiatomic NiTi plates by means of finite element modelling and tensile experimentation. The numerical modelling is based on an elastohysteresis model, which takes into account the hysteretic and hyperelastic contributions of material response in the global deformation. The effects of hole size, shape and number on stress–strain behaviour are discussed. The numerical results are compared and validated with experimental data.     

Fracture and fatigue failure in the Spanish codes for design of steel structures

This work describes from a Fracture Mechanics view the failure prevention approaches recently embodied in the European and Spanish codes for the design of steel structures. The codes formulate the design rules to prevent fatigue and fracture failures in terms of engineering practice, with the Fracture Mechanics foundations underlying them not being apparent. The design simplifications assumed are presented in the framework of Fracture Mechanics.     

Evaluation of geometrically nonlinear effects due to large cross-sectional deformations of compact and shell-like structures

Abstract

This paper investigates geometrically nonlinear effects due to large deformations over the cross sections of beam-like and shell-like structures. Finite elements are used to provide numerical solutions along with the Newton–Raphson technique and the arc-length method. Refined theories able to capture cross-sectional deformation are constructed by referring to the Carrera unified formulation. Full nonlinear Green-Lagrange strains and second Piola-Kirchoff stresses are employed in a total Lagrangian scenario. The numerical results demonstrate that geometrical nonlinearities play a fundamental role when cross-sectional deformations become significant and theories of structures with nonlinear kinematics are utilized. In other words, this means that the use of refined beam models may be ineffective if geometrical nonlinear relations are not employed. These phenomena become particularly evident in thin-walled/shell-like type structures.     

Finite element crash simulations of the human body: Passive and active muscle modelling

Conventional dummy based testing procedures suffer from known limitations. This report addresses issues in finite element human body models in evaluating pedestrian and occupant crash safety measures. A review of material properties of soft tissues and characterization methods show a scarcity of material properties for characterizing soft tissues in dynamic loading. Experiments imparting impacts to tissues and subsequent inverse finite element mapping to extract material properties are described. The effect of muscle activation due to voluntary and non-voluntary reflexes on injuries has been investigated through finite element modelling.     

A finite element approach to anisotropic damage of ductile materials in large deformations Part II: finite element formulation and applications

A finite element analysis model for material and geometrical non-linearities due to large plastic deformations of ductile materials is presented using the continuum damage mechanics approach. To overcome limitations of the conventional plastic analysis, a fourth-order tensor damage, defined in Part I of this paper to represent the stiffness degradation in the finite strain regime, is incorporated. General forms of an updated Lagrangian (U.L.) finite element procedure are formulated to solve the governing equations of the coupled elastic–plastic-damage analysis, and a computer program is developed for two-dimensional plane stress/strain problems. A numerical algorithm to treat the anisotropic damage is proposed in addition to the non-linear incremental solution algorithm of the U.L. formulation. Selected examples, compared with published results, show the validity of the presented finite element approach. Finally, the necking phenomenon of a plate with a hole is studied to explore plastic damage in large strain deformations. This revised version was published online in August 2006 with corrections to the Cover Date.