A 3-D finite element analysis of a chevron-notched,three-point bend fracture specimen for ceramic materials

A 3-D finite element analysis of a chevron-notched, three-point bend specimen was used to determine the load point displacement (LPD) and the crack mouth opening displacement (CMOD) for four initial crack-depth-to-width ratios of the chevron notch. Relations between the LPD and CMOD specimen compliances, as functions of crack length, were developed and the LPD compliance versus crack length relations were compared with previous analyses. In addition, the LPD compliance versus crack length relations are used to modify previously developed geometry correction factors for the stress intensity factor.The LPD/CMOD relations are then applied to calculate the LPD from the CMOD measured during the fracture testing of silicon nitride and silicon carbide chevron-notched, three-point bend specimens. The work-of-fracture values for the two ceramic materials are compared using the calculated and the measured LPD. The fracture toughness values are compared as calculated from the modified and the unmodified geometry correction factors for the stress intensity factor. Finally, the crack growth resistance curves are determined from the fracture test data.

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Résumé Sur une éprouvette de flexion sur trois points entaillée en chevron, on a fait usage de l'analyse par éléments finis à trois dimensions pour déterminer le déplacement au point d'application de la charge (LPD) et le déplacement d'ouverture des bords de la fissure (CMOD) correspondant à quatre rapports de profondeur sur largeur de fissure pour l'entaille en chevron. On a établi les relations de compliance entre le LPD et le CMOD en fonction de la longueur de fissure et on a comparé les relations de compliance entre le LPD et la longueur de fissuration avec celles résultant d'analyses antérieures. En outre, ces dernières relations ont été utilisées en vue de modifier les coefficients de correction géométrique précédemment établis pour le facteur d'intensité de contrainte.On applique ensuite les relations LPD/CMOD au cacul du LPD à partir du CMOD mesuré au cours d'essais de rupture en flexion sur trois points d'éprouvettes en nitrure de silicium et en carbure de silicium entaillées en chevron. On compare les valeurs du travail de rupture des deux matériaux céramiques en utilisant les valeurs de LPD calculées et mesurées. On compare les valeurs de la ténacité à la rupture obtenues par le calcul à partir des coefficients de correction de la géométrie modifiés ou non modifiés. Enfin, on détermine les courbes de résistance à la croissance des fissures à partir des données de rupture.

     

Stress analysis around crack tips in finite strain problems using the eXtended finite element method

Fracture of rubber‐like materials is still an open problem. Indeed, it deals with modelling issues (crack growth law, bulk behaviour) and computational issues (robust crack growth in 2D and 3D, incompressibility). The present study focuses on the application of the eXtended Finite Element Method (X‐FEM) to large strain fracture mechanics for plane stress problems. Two important issues are investigated: the choice of the formulation used to solve the problem and the determination of suitable enrichment functions. It is demonstrated that the results obtained with the method are in good agreement with previously published works. Copyright © 2005 John Wiley & Sons, Ltd.     

Stress intensity factor calculation for a modified round bend bar by 3-D finite element analysis

Stress intensity factors were calculated for a modified round bend bar (MRBB) using 3-D finite element analysis. The results were compared with published solutions for a rectangular and round bend bars. The stress intensity values for the MRBB are between those for the two other geometries as expected. The stress intensity solutions were non-dimensionalized utilizing limit solution for short and long cracks.     

Hybrid and mixed-penalty finite elements for 3-D analysis of soft hydrated tissue

Solution of biomechanics problems involving three-dimensional (3-D) behaviour of soft tissue on geometries representative of such tissue in vivo will require the use of numerical methods. Toward this end, a pair of tetrahedral finite elements has been developed. The equations which are used to model the tissue behaviour for both elements are those commonly known as the linear biphasic equations. This model assumes that hydrated soft tissue is a mixture of two incompressible, immiscible phases, and employs mixture theory to derive governing equations for its mechanical behaviour. The finite element techniques applied to these equations for the two elements are the mixed-penalty method and the hybrid method. Both elements are described here, and the special requirements for 3-D analysis are discussed. Results obtained by solving canonical problems in two and three dimensions using both elements are presented and compared. Both elements are found to produce excellent results. The hybrid element is also noted to have advantages for non-linear analyses involving finite deformation which will require solution in the future.     

The eXtended finite element method for cracked hyperelastic materials: A convergence study

The present work aims to look into the contribution of the extended finite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sufficient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, because it serves as an eXtended finite element method enrichment basis. Finally, a convergence study is carried out to show the contribution of the exploitation of such method. Copyright © 2014 John Wiley & Sons, Ltd.     

Hyperbolic constitutive model to study cast iron pipes in 3-D nonlinear finite element analyses

Cast iron (CI) pipes were widely installed as water mains and service connections in the last century and still large numbers of CI pipes remain in service. However, many CI pipes are becoming aged and severely corroded, causing frequent pipe leaks and breaks. To better understand the failure mechanism of CI pipes, this paper provides an efficient numerical approach to analyse the behaviour of CI pipes under various loading conditions. The numerical investigation was realised by implementing a hyperbolic constitutive model (a simplified nonlinear stress-strain analysis) for CI materials into finite element analysis (FEA) in ABAQUS. Three-dimensional (3-D) FEAs were carried out for a series of uniaxial tensile and compressive tests, 3-point beam bending tests and ring bending tests on various CI pipe coupons. The stress-strain characteristics and load-deflection responses obtained from these numerical examples were validated by experimental results. The numerical results obtained from the proposed method are in good agreement with the measured data, which indicates that the mechanical performance of deteriorated CI pipes can be adequately modelled using the relatively simple nonlinear constitutive model implemented in 3-D FEA. As nonlinear behaviour has proven to be intrinsic to the widely used CI pipes, it is expected that the proposed 3-D FEA modelling technique will be of importance to the evaluation of the mechanical performance of CI pipes and, possibly, other CI structures.     

A new 3-D finite element model to evaluate added mass for analysis of fluid-structure interaction problems

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted. A new 8-noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.     

Theoretical development and numerical verification of a geometrically non-linear, 3-D based finite element for composite materials

A geometrically non-linear thin shell element made from classical laminated materials is developed from three dimensional continuum concepts that admits arbitrarily large displacements and rotations. The development shows how explicit integration through the thickness of the element can be accomplished without sacrificing significant accuracy of the element. Computations obtained via the present formulation are compared with four test problems for which numerical data are available. All computations were carried out using the Crisfield–Riks arc length continuation algorithm with a full Newton–Raphson iterative scheme. Excellent agreement is observed for each test problem.     

Elastic-plastic analysis of stress state and spread of plastic zone around single edge-cracked plate by finite element method

A two-dimensional finite element model for estimating elastic-plastic displacements and stresses near a crack for the elastic-plastic situation of loadings is presented. Singularity effects near the crack tip are solved by introducing 12-node cubic isoparametric elements in the crack tip region and collapsing them into triangular elements. The proposed finite element model is used to determine the spread of the plastic zone and mouth opening displacements of an edge-cracked structural steel plate. The spread of the plastic zone is obtained by successive increments of applied nominal tensile stress transverse to the crack length. The mouth opening displacement values obtained by this model are also compared with those measured experimentally.     

Determination of creep parameters from indentation creep experiments: a parametric finite element study for single phase materials

Abstract

This paper explores the possibilities of determining creep parameters for a simple Norton law material from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analysed in terms of indentation rates at constant loads. Emphasis is placed on the evolving stress distribution in front of the indenter during indentation creep. Moreover the role of indenter geometry, size effects and of macroscopic constraints is explicitly considered. A simple procedure is proposed to translate indentation creep results into constitutive creep equations for cases where the dimensions of the tested material are significantly larger than the indenter. The influence of macroscopic constraints becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. As a striking example for size effects and for macroscopic constraints the indentation creep process in a thin film is analyzed. The results contribute to a better mechanical understanding of indentation creep testing.     

Static and dynamic finite element analysis of transformation toughening in ceramic materials

Computational studies have been conducted for the phenomenon of ‘transformation toughening’ which is observed in zirconia-containing ceramics such as PSZ (partially stabilized zirconia). The new constitutive modeling for transformation plasticity in which a stress history-dependent internal state variable is employed has been applied to the finite element analysis of stationary and growing macro-cracks under static and dynamic loading. The transformation toughening effect is discussed, along with the influence on it of the size of the transformed damage zone and the various parameters in the equations to be solved, through the observation of the behavior of the general crack tip energy release parameter, the T^*-integral.     

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.     

Stress analysis in continuous media with an edge dislocation by finite element dislocation model

In this paper, a finite element dislocation model is proposed, based on well‐known mathematical dislocation model. As application examples, the stress distributions around an edge dislocation in infinite homogeneous and inhomogeneous regions are calculated and compared with the analytical results. The FEM results coincide well with the exact solutions. The results show an applicability and a usefulness of finite element dislocation model, and further, a possibility of analysing a dislocation problem in finite region with complicated shapes and boundary conditions. Copyright © 2002 John Wiley & Sons, Ltd.     

3-D finite element analysis of stress concentration factor in spot-welded joints of steel: The effect of process-induced porosity

The work presented in this paper utilises a numerical analysis for the computation of stress concentration factor generated by the presence in the weld nugget of a pore formed during the welding process. Welded structure containing porosity is subjected to uniaxial tensile stress. The effects of geometrical parameters of the pore and the interaction pore-defect on the stress concentration factor variation have been analyzed.     

液-管耦合空间管路系统振动噪声的有限元分析方法

以包含设备和辅件在内、可具有分支结构的实际管路系统为研究对象,考虑内部流体介质和管路结构的相互作用,建立了液-管耦合振动噪声动力学分析的一体化有限元模型。给出了管路系统有限元模型的理论基础和典型有限元刚度矩阵单元的解析表达式,以及将管路隔振和消声器件阻抗试验数据引入有限元分析的转换方法。通过较为复杂的算例,分别对消声压力筒和管路挠性元件的噪声、振动衰减作用进行了研究。     

Stabilized finite element approximations for heat conduction in a 3-D plate with dominant thermal source

The present work studies the finite element approximation for the heat transfer process in an opaque three-dimensional plate with a temperature-dependent source dominating the conductive operator. The adopted mechanical model assumes the existence of a heat transfer from/to the plate following Newton's law of cooling. The numerical simulations performed have attested the instability of the classical Galerkin method when subjected to very high source-dominated regimen. Usual strategies in the Engineering practice of dealing with this shortcoming proved to be inefficient. A Gradient-Galerkin/Least-Squares formulation was adopted in the numerical simulations as a remedy for the Galerkin's instability when subjected to those regimen. Received 25 May 1998     

Numerical treatment of finite part integrals in 2-D boundary element analysis with application infracture mechanics

For the solution of problems in fracture mechanics by the boundary element method usually the subregion technique is employed to decouple the crack surfaces. In this paper a different procedure is presented. By using the displacement boundary integral equation on one side of the crack surface and the hypersingular traction boundary integral equation on the opposite side, one can renounce the subregion technique.An essential point when applying the traction boundary integral equation is the treatment of the thus arising hypersingular integrals. Two methods for their numerical computation are presented, both based on the finite part concept. One may either scale the integrals properly and use a specific quadrature rule, or one may apply the definition formula for finite part integrals and transform the resulting regular integrals into the usual element coordinate system afterwards. While the former method is restricted to linear or circular approximations of the boundary geometry, the latter one allows for arbitrary curved (e.g. isoparametric) elements. Two numerical examples are enclosed to demonstrate the accuracy of the two boundary integral equations technique compared with the subregion technique.     

A finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear

A finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading. The displacement field of the sectorial element is quadratic in the angular co-ordinate direction and asymptotic in the radial direction measured from the singular point. The formulation of Yamada and Okumura¹⁴ for in-plane problems is adapted for this purpose. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi-material wedges and junctions with and without disbonds. The nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries.     

2D finite element analysis of thermally bonded nonwoven materials: Continuous and discontinuous models

Due to a random structure of nonwoven materials, their non-uniform local material properties and nonlinear properties of single fibres, it is difficult to develop a numerical model that adequately accounts for these features and properly describes their performance. Two different finite element (FE) models – continuous and discontinuous – are developed here to describe the tensile behaviour of nonwoven materials. A macro-level continuum finite element model is developed based on the classic composite theory by treating the fibrous network as orthotropic material. This model is used to analyse the effect of thermally bonding points on the deformational behaviour and deformation mechanisms of thermally bonded nonwoven materials at macro-scale. To describe the effects of discontinuous microstructure of the fabric and implement the properties of polypropylene fibres, a micro-level discontinuous finite element model is developed. Applicability of both models to describe various deformational features observed in experiments with a real thermally bonded nonwoven is discussed.