Micromechanical response of fibre-reinforced materials using the boundary element technique

The boundary element method (BEM) and the embedded cell approach (ECA) have been used to analyse the effects of constituent material properties and fibre spatial distribution on the localised behaviour of a transversely loaded, unidirectional fibre-reinforced composite. The geometrical structures examined were perfectly periodic, uniformly spaced fibre arrangements in square and hexagonal embedded cells and 10 cells in which 60 fibres were randomly placed within the matrix. The models involve both elastic fibres and matrix, with the interfaces between the different phases being fully bonded. The results indicate that both the fibre packing and the material properties of the constituent phases have a significant effect on the overall stress distribution and the magnitude of localised stress concentrations within a composite. Non-periodic arrangements give rise to higher local stresses, and the magnitudes of these stress concentrations have a strong dependence on the ligament length (distance between the two neighbouring fibres that have a common high-stress region), and to a lesser extent on the angle relative to the applied load (angle between a plane containing the two fibre centres and the applied load). Furthermore, analysis of a three-phase composite, comprised of a mixture of both stiff and compliant fibres, had higher stress concentrations than the equivalent two-phase composites.     

A general Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics

This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading can be of in-plane or anti-plane, and can be applied along the no-crack boundary or crack surface. Furthermore, the body-force case can also be analyzed. The present BEM analysis is an extension of the work by Pan and Amadei (1996a) and is such that the displacement and traction integral equations are collocated, respectively, on the no-crack boundary and on one side of the crack surface. Since in this formulation the displacement and/or traction are used as unknowns on the no-crack boundary and the relative crack displacement (i.e. displacement discontinuity) as unknown on the crack surface, it possesses the advantages of both the traditional displacement BEM and the displacement discontinuity method (DDM) and yet gets rid of the disadvantages associated with these methods when modeling fracture mechanics problems. Numerical examples of calculation of stress intensity factors (SIFs) for various benchmark problems were conducted and excellent agreement with previously published results was obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

Snap-back Analysis of Fracture Evolution in Multi-Cracked Solids Using Boundary Element Method

According to the Linear Elastic Fracture Mechanics criteria, a numerical model is developed to simulate the failure evolution of multi-cracked finite plates by means of an incremental loading procedure. A modified crack length control scheme is used in order to analyse such problems depending on one or more independent parameters. The aim is to provide information about a discontinuous response, such as the snap-back instability, which can be highlighted only by a deformation controlled process. The load vs. displacement curve, included possible snap-back branches, is numerically traced by means of a procedure based on the Displacement Discontinuity Boundary Element Method. With reference to finite plates with ordered crack distributions in plane strain loading conditions, the model is applied in order to analyse the effects of the crack interaction on the fracture evolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

A study of microcrack formation in multiphase steel using representative volume element and damage mechanics

Multiphase steels have become a favoured material for car bodies due to their high strength and good formability. Concerning the modelling of mechanical properties and failure behaviour of multiphase steels, representative volume elements (RVE) have been proved to be an applicable approach for describing heterogeneous microstructures. However, many multiphase steels exhibit inhomogeneous microstructures which result from segregation processes during continuous casting. These segregations lead to a formation of martensite bands in the microstructure causing undesirable inhomogeneities of material properties. The aim of this work is to develop an FE evaluation procedure for predicting a microcrack formation provoked by banded martensitic structures. A micromechanism based damage curve was applied as a failure criterion for the softer ferritic matrix in the microstructure in order to simulate the propagation of cracks resulting from the failure of martensitic bands. The parameters of the damage curve were determined by in situ miniature bending tests and tensile tests with notched samples. The presented approach provides the basis for an assessment criterion of the component safety risk of multiphase steels with inhomogeneous microstructures.     

Fracture and fatigue of a Nicalon/CAS continuous fibre-reinforced glass-ceramic matrix composite

The fracture and fatigue behaviour of Nicalon/CAS continuous fibre-reinforced glass-ceramic matrix composite was studied at temperatures of up to 1000°C in both air and vacuum. Using chevron-notched test-pieces in bending, high nominal toughness values are measured at ambient temperature and at 1000°C in vacuum. In contrast, toughness values obtained in air decrease progressively with test temperature increase from 600 to 1000°C, and at 1000°C they are reduced by a factor of three from their values at ambient temperature. Marked changes in micromechanisms of crack growth under cyclic loading are also observed in air as the test temperature is increased: multiple cracking occurs at ambient temperature, while dominant Mode I cracks can be produced at 1000°C. A further study has been carried out in air on plane-sided test-pieces at a temperature at 1000°C, under both monotonic and cyclic loading. At ambient temperature, effects of cyclic loading have been deduced, while crack growth at 1000°C in air appears to be dominated by static loading with little effect of cyclic loading. These subcritical crack growth and toughness observations are consistent with changes that occur in the fibre/matrix interfaces at elevated temperatures in air reported in the literature.     

Solution of viscoelastic scattering problems in linear acoustics using hp Boundary/Finite Element Method

The interaction of acoustic waves with submerged structures remains one of the most difficult and challenging problems in underwater acoustics. Many techniques such as coupled Boundary Element (BE)/Finite Element (FE) or coupled Infinite Element (IE)/Finite Element approximations have evolved. In the present work, we focus on the steady‐state formulation only, and study a general coupled hp‐adaptive BE/FE method. A particular emphasis is placed on an a posteriori error estimation for the viscoelastic scattering problems. The highlights of the proposed methodology are as follows: (1) The exterior Helmholtz equation and the Sommerfeld radiation condition are replaced with an equivalent Burton–Miller (BM) boundary integral equation on the surface of the scatterer. (2) The BM equation is coupled to the steady‐state form of viscoelasticity equations modelling the behaviour of the structure. (3) The viscoelasticity equations are approximated using hp‐adaptive FE isoparametric discretizations with order of approximation p⩾5 in order to avoid the ‘locking’ phenomenon. (4) A compatible hp superparametric discretization is used to approximate the BM integral equation. (5) Both the FE and BE approximations are based on a weak form of the equations, and the Galerkin method, allowing for a full convergence analysis. (6) An a posteriori error estimate for the coupled problem of a residual type is derived, allowing for estimating the error in pressure on the wet surface of the scatterer. (7) An adaptive scheme, an extension of the Texas Three Step Adaptive Strategy is used to manipulate the mesh size h and the order of approximation p so as to approximately minimize the number of degrees of freedom required to produce a solution with a specified accuracy. The use of this hp‐scheme may exhibit exponential convergence rates. Several numerical experiments illustrate the methodology. These include detailed convergence studies for the problem of scattering of a plane acoustic wave on a viscoelastic sphere, and adaptive solutions of viscoelastic scattering problems for a series of MOCK0 models. Copyright © 1999 John Wiley & Sons, Ltd.     

Fracture in magnetoelectroelastic materials using the extended finite element method

Static fracture analyses in two‐dimensional linear magnetoelectroelastic (MEE) solids is studied by means of the extended finite element method (X‐FEM). In the X‐FEM, crack modeling is facilitated by adding a discontinuous function and the crack‐tip asymptotic functions to the standard finite element approximation using the framework of partition of unity. In this study, media possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered. New enrichment functions for cracks in transversely isotropic MEE materials are derived, and the computation of fracture parameters using the domain form of the contour interaction integral is presented. The convergence rates in energy for topological and geometric enrichments are studied. Excellent accuracy of the proposed formulation is demonstrated on benchmark crack problems through comparisons with both analytical solutions and numerical results obtained by the dual boundary element method. Copyright © 2011 John Wiley & Sons, Ltd.     

The Development of a Hybrid Technique Employing the Boundary Element Method for Thermoelastic Stress Separation

Abstract: This paper presents a development of a hybrid technique employing a boundary element method for determining individual stress components in two-dimensional arbitrarily shaped domains from experimental isopachics only. The procedure consists of a numerical solution of two Poisson equations representing equilibrium for two-dimensional plane-stressed solids with zero body forces. An existing technique is employed for smoothing interior thermoelastic data and enhancing boundary information. The algorithm of stress separation has been implemented with the help of commercial codes. The whole procedure has been tested through a complete post-processing example of thermoelastic stress analysis data.     

Fracture behavior and damage mechanisms identification of SiC/glass ceramic composites using AE monitoring

Large Scale Bridging in SiC/MAS-L (ceramic glass matrix) composites was investigated by using DEN specimens under tensile loading conditions with in situ Acoustic Emission monitoring. The AE data were successfully classified using Unsupervised Pattern Recognition Algorithms and the resulted clusters were correlated to the dominant damage mechanisms of the material. The evolution in time of the different damage mechanisms is feasible after the pattern recognition classification. Microscopic examination was used to correlate the clusters to the damage mechanism they correspond and thus to provide the failure mode identification based on AE data.     

Harmonic analysis of shear deformable orthotropic cracked plates using the Boundary Element Method

In this work, the modal and harmonic analysis of orthotropic shear deformable cracked plates using a direct time-domain Boundary Element Method formulation based on the elastostatic fundamental solution of the problem is presented. The Radial Integration Method was used for the treatment of domain integrals involving distributed domain applied loads and those related with inertial mass forces. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation.     

Fracture analysis of anisotropic materials using enriched crack tip elements

Enriched finite element methodology, which employs special crack tip elements, is extended for cracks in anisotropic materials. Enrichment formulation is described briefly and three validation examples using single crystal, directionally solidified, and orthotropic material properties are presented to demonstrate the accuracy and effectiveness of the methodology. In addition to validation examples, the effect of material anisotropy on stress intensity factors is investigated using the common compact tension specimen and the results are compared to the ASTM solution for isotropic materials. It is shown that the effect of anisotropy on the computed stress intensity factors can be significant, depending on the degree of anisotropy, material orientation, and a/W ratio in the compact tension specimen geometry.     

Dynamic and static analysis of cracks using the hypersingular formulation of the Boundary Element Method

A new methodology for computing dynamic stress intensity factors in the frequency domain based on the mixed boundary element method, a combination of the equations corresponding to the integral representations of displacements and tractions, is proposed and analysed. The expressions of hypersingular fundamental solution are presented and their singular parts extracted. Also, a discontinuous Singular-Quarter-Point element is constructed. Finally, various parametric computations and applications are described in order to illustrate the simplicity and accuracy of the proposed method as applied to both static and dynamic problems. © 1998 John Wiley & Sons, Ltd.     

Elasto-plastic Analysis of Two-dimensional Orthotropic Bodies with the Boundary Element Method

The Boundary Element Method (BEM) is introduced to analyze the elasto-plastic problems of 2-D orthotropic bodies. With the help of known boundary integral equations and fundamental solutions, a numerical scheme for elasto-plastic analysis of 2-D orthotropic problems with the BEM is developed. The Hill orthotropic yield criterion is adopted in the plastic analysis. The initial stress method and tangent predictor-radial return algorithm are used to determine the stress state in solving the nonlinear equation with the incremental iteration method. Finally, numerical examples show that the BEM is effective and reliable in analyzing elasto-plastic problems of orthotropic bodies.     

A parallel-supercomputing investigation of the stiffness of aligned,short-fiber-reinforced composites using the Boundary Element Method

Computational experiments are carried out in three-dimensional, multi-fibre specimens with the objective of determining the influence of fibre volume fraction (ϕ) and aspect ratio (a_r) on the effective tensile modulus of aligned, discontinuous fibre-reinforced composites. The Boundary Element Method (BEM), implemented on a 1840-node Intel Paragon parallel supercomputer using a torus-wrap mapping, enables the prediction of the tensile behaviour of composite specimens consisting of up to 200 discrete aligned short fibres, randomly dispersed in an elastic matrix. Statistical averages of the computed effective longitudinal moduli are compared with the predictions of the Halpin–Tsai equation and are found to be in good agreement for low values of a_r and ϕ. However, as a_r and/or ϕ increase, the predictions of the Halpin–Tsai equation fall below the computed moduli. Consideration of the finite packing efficiency of the fibres as proposed by Lewis and Nielsen results in a generalized form of the Halpin–Tsai equation whose predictions are in very good agreement with the BEM calculations for the entire range of ϕ and a_r examined. The scatter in the computed moduli decreases with increasing number of fibres, reflecting the ‘homogenization’ of the specimen brought about by consideration of larger numbers of smaller fibres. This scatter grows with increasing ϕ and a_r, reflecting an increase in the magnitude and complexity of inter-fibre interactions. © 1997 by John Wiley & Sons, Ltd.     

Fracture statistics of brittle materials with surface cracks

Several different statistical fracture theories are developed for materials with cracks confined to the surface. All assume that crack planes are normal to the surface, but are otherwise randomly oriented. The simplest theory assumes that only the component of stress normal to the crack plane contributes to fracture. This theory is in fair agreement with biaxial fracture data on Pyrex glass obtained by Oh. When the contribution of shear is included in the analysis, the crack shape has to be considered. Several shapes are examined and the corresponding fracture statistics are derived. Two failure criteria are employed. In one the fracture occurs when the maximum tensile stress on some part of the crack surface reaches the intrinsic strength of the material. The other is based on a critical strain energy release rate. The assumption of shear-sensitive cracks leads to improved agreement with experiment, but really good agreement appears to require the assumption that the cracks have a preferred orientation.     

Modelling the pressure die casting process using a hybrid Finite‐Boundary Element model

In this paper an efficient three‐dimensional hybrid thermal model for the pressure die casting process is described. The Finite Element Method (FEM) is used for modelling heat transfer in the casting, and the Boundary Element Method (BEM) for the die. The FEM can efficiently account for the non‐linearity introduced by the release of latent heat on solidification, whereas the BEM is ideally suited for modelling linear heat conduction in the die, as surface temperatures are of principal importance. The FE formulation for the casting is based on the modified effective capacitance method, which provides high accuracy and unconditional stability. This is essential for accurate modelling of the pressure die casting process and efficient coupling to the BEM. The BE model caters for surface phenomena such as boiling in the cooling channels, which is important, as this effectively controls the manner in which energy is extracted. The die temperature is decomposed into two components, one a steady‐state part and the other a time‐dependent perturbation. This approach enables the transient die temperatures to be calculated in an efficient way, since only die surfaces close to the die cavity are considered in the perturbation analysis. A multiplicative Schwarz method for non‐overlapping domains is used to couple the individual die blocks and casting. The method adopted makes use of the weak coupling between the domains, which is a result of the relatively high interfacial thermal resistance that is present. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted die and casting temperatures are compared with thermocouple measurements and good agreement is indicated. Copyright © 1999 John Wiley & Sons, Ltd.     

Fracture toughness determination of brittle materials using small to extremely small specimens

Diametral compression of a grooved, disc shaped specimen is used to determine fracture toughness. This method's most important features are that extremely small specimens can be used and no knowledge of material properties is needed. It is suitable for many brittle materials, e.g. glass, cemented carbides, ceramics, many geological, mining and building materials, perspex-like plastics, etc.