Computational assessment of the influence of load ratio on fatigue crack growth in fibre-reinforced metal matrix composites

A three-dimensional finite element model of a composite tensile specimen consisting of a Ti–6Al–4V matrix reinforced with unidirectional, continuous SiC fibres under cyclic loading has been developed. The model includes the fibre/matrix morphology, with the interface interaction being governed by the Coulomb friction law. The influence of the applied load ratio on the true crack-tip load ratio has been investigated for three different applied load ratios. The results from the model show that due to a combination of thermal residual stresses from processing and fibre bridging, the crack-tip load ratio becomes independent of the applied load ratio after a small amount of crack growth. With the fatigue threshold depending strongly on the load ratio, crack arrest occurs at a later stage than would be predicted from the applied load ratio.     

Development of a finite element micromodel for metal matrix composites

A finite element micromodel has been developed based on real microstructures. The method of modelling is unique in that displacements calculated from large-specimen models are used as boundary conditions to model more accurately at the microstructural level. The development was centred around determining the response of the matrix, near a crack tip, to the constraint imposed by the particles. The process of developing the model is given and the final result is compared with experimentally measured values of constraint from the stereoimaging analysis of the photographs the model was based on. Good agreement was found and both techniques, stereoimaging and FEM, verified each other.     

A material model for the finite element analysis of metal matrix composites

A finite element based procedure is presented which accounts for micromechanical nonlinear behavior of the matrix material in continuous fiber reinforced composites. The micromechanical model is a periodic hexagonal array of elastic fibers embedded in an elastic-plastic matrix material. This model is used to calculate the overall instantaneous material matrix at material points of a macromechanical finite element model of the structure being analyzed. The procedure is applied to a number of metal matrix composite systems subjected to thermomechanical loads.     

Mixed-mode delamination growth of laminar composites by using three-dimensional finite element modeling

ABSTRACT Delamination is one of the most frequent failure modes in laminated composites. Its importance is crucial, because a delamination can occur in the interior of a panel without any noticeable damage on the surface, drastically reducing its strength and stiffness. A study has to be made on critical dimensions of delaminations and their shape, through the calculation of the strain energy release rate (SERR), G. This study was performed numerically, for a given geometry, with varying loads and shapes of delamination, in pure and mixed‐mode propagation. All numerical values were obtained with three‐dimensional finite element (FE) analyses from a commercial package. The use of three‐dimensional analyses in simple geometries helps establish the basis for the more complex ones, and the correspondence with the usual analytical or numerical bi‐dimensional plane‐strain analysis. The conclusions were (a) G is not constant along the crack tip, even for mode I propagation and straight crack tip; (b) the mean value of G obtained from a three‐dimensional analysis equals the value obtained in bi‐dimensional plane‐strain analysis; (c) in mixed‐mode propagation, the method exhibits a good correlation with experimental results and (d) the shape and mode partitioning of the SERR depend not only on the loading, but also on the shape of the crack front.     

Finite element micromechanical modelling of unidirectional fibre-reinforced metal-matrix composites

Typical finite element formulations and models for unidirectional composite materials are reviewed. The application of micromechanical finite element analysis to the modelling of unidirectional fibre-reinforced metal-matrix composites is demonstrated by presenting some studies from recent publications. It is shown that while analytical models offer a simple tool for obtaining the overall response of composites, finite element analysis provides more accurate and detailed characterisation of composite properties for complicated geometries and constituent property variations. Various effects that influence the stress/strain response and fibre/matrix deformation of composites are studied through modelling. These effects include the fibre coating and reaction layer, fibre shape and distribution, metallurgical and environmental factors, stress distributions and damage. It is demonstrated that the properties and constituent phase interaction of metal-matrix composites are best modelled by finite element analysis. It is emphasized that in order to obtain good predictions, the models must be coupled with first-hand characterisations of the constituent phases and their interactions, including the thermal history of the specimens.     

Finite element modelling of creep deformation in fibre-reinforced ceramic composites

The tensile creep and creep-recovery behaviour of a unidirectional SiC fibre-Si₃N₄ matrix composite was analysed using finite element techniques. The analysis, based on the elastic and creep properties of each constituent, considered the influence of fibre-matrix bonding and processing-related residual stresses on creep and creep-recovery behaviour. Both two- and three-dimensional finite element models were used. Although both analyses predicted similar overall creep rates, three-dimensional stress analysis was required to obtain detailed information about the stress state in the vicinity of the fibre-matrix interface. The results of the analysis indicate that the tensile radial stress, which develops in the vicinity of the fibre-matrix interface after processing, rapidly decreases during the initial stages of creep. Both the predicted and experimental results for the composite show that 50% of the total creep strain which accumulated after 200 h at a stress of 200 MPa and temperature of 1200°C is recovered within 25 h of unloading.     

Conditions for matrix crack deflection at an interface in ceramic matrix composites

This paper describes a numerical approach developed to simulate the mechanism of matrix crack deflection at the fibre/matrix interface in brittle matrix composites. For this purpose, the fracture behaviour of a unit cell (microcomposite) consisting of a single fibre surrounded by a cylindrical tube of matrix was studied with the help of a finite element model. A fracture mechanics approach was used to design a criterion for deflection at the fibre/matrix interface of an annular crack present in the matrix. The analysis of the fracture behaviour of SiC/SiC and SiC/glass ceramics microcomposites shows that the introduction of a low modulus and low toughness interfacial layer at the fibre/matrix interface (e.g. a carbon coating) greatly favours matrix crack deflection at the interphase/fibre interface.     

Numerical aspects of finite element simulations of residual stresses in metal matrix composites

When a metal matrix composite (MMC) is cooled down from the fabrication or annealing temperature to room temperature, residual stresses are induced in the composite due to the mismatch of the thermal expansion coefficients of the matrix and reinforcement. A thermomechanical model describing these processes is presented considering that the reinforcement component has a thermo‐elastic behaviour and that the matrix material exhibits a thermo‐elastoviscoplastic behaviour. The model is implemented with a semi‐implicit forward gradient finite element method algorithm and the resulting code is used to perform numerical simulations and calculate thermally induced residual stress fields in MMCs. Several tests are performed on a continuously reinforced MMC and a short cylindrical particle MMC in order to optimize the algorithm and define its governing parameters. Good agreement was obtained with results from other authors. Copyright © 2001 John Wiley & Sons, Ltd.     

Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method

This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for fully-automatic modelling of cohesive crack growth in quasi-brittle materials. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. The constitutive law of these elements is modelled by the cohesive/fictitious crack model to simulate the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K_I vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating K_I using a “shadow subdomain”, are also described. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the new method. The results show that this SBFEM-FEM coupled method is capable of fully-automatically predicting both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for problems with strong snap-back. Parametric studies were carried out on the crack incremental length, the concrete tensile strength, and the mode-I and mode-II fracture energies. It is found that the K_I ? 0 criterion is objective with respect to the crack incremental length.     

A mixed hybrid finite element for three-dimensional elastic crack analysis

A new three-dimensional crack tip element is proposed, which is based on a mixed hybrid stress/displacement model. A truncated series expansion of eigenfunctions for the straight semi-infinite crack is deduced and assumed for the internal stress and displacement fields in the element. The basic approach of constructing these hybrid elements is outlined. Their good capability, efficiency and accuracy for analyzing three-dimensional elastic crack problems are demonstrated by first numerical examples.

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Résumé On propose un nouveau type d'élément tridimensionnel pour l'extrémité d'une fissure, basé sur un modèle mixte contraintes hybrides/déplacements. On en tire un développement en séries tronquées des eigenfonctions relatives à une fissure droite semi-infinie, et on suppose qu'elle est représentative des champs de contraintes internes et de déplacements dans l'élément. L'approche de base utilisée pour construire ces éléments hybrides est soulignée. On démontre par de premiers exemples numériques qu'ils ont la capacité, l'efficacité et la précision nécessaires à l'analyse des problèmes élastiques et tridimensionnels de fissuration.

     

A finite element algorithm for creep crack growth

A finite element algorithm involving the “Breakable element” concept is proposed for the prediction of the growth of a crack in a solid subject to combined thennoelastic-plastio-creep load. The unique advantage of this algorithm is its ability to provide detail stress and strain distributions, the kinematics of the inelastic zones, as well as the profiles of the growing crack. A numerical example with three assigned effective rupture strains as fracture criteria, is included to illustrate these special features.     

Extended finite element method for cohesive crack growth

The extended finite element method allows one to model displacement discontinuities which do not conform to interelement surfaces. This method is applied to modeling growth of arbitrary cohesive cracks. The growth of the cohesive zone is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish. This energetic approach avoids the evaluation of stresses at the mathematical tip of the crack. The effectiveness of the proposed approach is demonstrated by simulations of cohesive crack growth in concrete.     

Tensile strength of fibre-reinforced metal matrix composites with non-uniform fibre spacing

The influence of non-uniform fibre spacing on the strength of unidirectional fibre-reinforced metal matrix composites was studied by means of a Monte-Carlo computer simulation experiment. The influence of yield stress of the matrix and scatter of the fibre strength on the strength of composites were also studied for both uniform and non-uniform fibre spacings. It was demonstrated that (1) the strength of composites with non-uniform fibre spacing is lower than that with uniform spacing due to the high stress concentration arising from the breakage of fibres, and (2) the reduction in strength of composites due to the non-uniformity increases with increasing scatter of fibre strength. For both cases of uniform and non-uniform spacings, the following tendencies were observed : (a) the strength of composites increases but then decreases with increasing yield stress of matrix, (b) it is very sensitive to yield stress of the matrix when the scatter of fibre strength is large but not when it is small, and (c) it decreases but then increases with increasing scatter of fibre strength when the yield stress of the matrix is high, while it decreases monotonically with increasing scatter of fibre strength when the yield stress is low.     

On the three-dimensional interface crack problems in periodic two-layered composites

Within the framework of the linear thermoelasticity with microlocal parameters the solutions of some three-dimensional interface crack problems in a two-layered periodic space are obtained. Effective results have been achieved through the use of similarity in governing equations of the homogenized model for the laminated body and transversely isotropic elastic solid. Some specific examples concerning interface crack problems have been considered and discussed from the point of view of fracture theory.     

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

In this work, steady, dynamic crack growth under plane strain, small-scale yielding conditions along a ductile-brittle interface is analysed using a finite element procedure. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behaviour. The objectives of this work are to establish the validity of an asymptotic solution for this problem which has been derived recently [12], and to examine the effect of changing the remote (elastic) mode-mixity on the near-tip fields. Also, the influence of crack speed on the stress fields and crack opening profiles near the propagating interface crack tip is assessed for various bi-material combinations. Finally, theoretical predictions are made for the variation of the dynamic fracture toughness with crack speed for crack growth under a predominantly tensile mode along ductile-brittle interfaces. Attention is focused on the effect of mismatch in stiffness and density of the constituent phases on the above aspects.     

Extended finite element method for three‐dimensional crack modelling

An extended finite element method (X‐FEM) for three‐dimensional crack modelling is described. A discontinuous function and the two‐dimensional asymptotic crack‐tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three‐dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.     

Crack tip damage development and crack growth resistance in particulate reinforced metal matrix composites

A study of crack tip damage development and crack growth resistance of aluminium 359/20% V_f silicon carbide and aluminium 6061/20% V_f Micral^Tm particulate reinforced metal matrix composites has been conducted. Observations of crack tip process zone development at the specimen surface have been compared with the results of fractographic examination of the centre of the specimen. Both materials were found to fracture by a process of void nucleation, growth and coalescence. Void nucleation was found to be by fracture or debonding of reinforcement particles, and/or fracture or debonding of secondary matrix particles. The preferred mode of void nucleation was found to vary depending on the constituents of the PR MMC and even the heat treatment state of the material. It was found that in these materials fractured particles identified on the fracture surface fractured during loading rather than being pre-cracked during fabrication. It was further found that observations of damage development from the specimen surface did not necessarily reflect the mechanisms prevailing in the specimen bulk. Under plane strain conditions, both materials were found to exhibit decreasing crack growth resistance as crack extension proceeded, due to the “anti-shielding” effect of damage accumulated in the process zone ahead of the crack tip. In thin specimens of the Comral-85 composite, however, dramatically improved toughness was obtained, and K_R curves have been obtained for such specimens. The method of measuring crack length was found to have a profound effect on the K_R curve; it was concluded that the K_R curve determined using the crack length measured at the specimen surface best reflected the true crack growth resistance of these materials.     

A new enriched finite element for fatigue crack growth

This paper presents a numerical method for fatigue crack growth in the framework of finite element method, i.e. a new enriched element is presented in which only the analytical solutions around crack tips are used to describe the displacements and stresses fields. A special variational principle is introduced to simplify the mathematical derivations for discrete equation, and the stiffness matrix of the new enriched element is given in a compact form. Moreover, the stiffness matrix is found to be independent on the element size. Numerical examples on fatigue crack growth are given to illustrate the validity of the present method.     

A finite element method for crack growth without remeshing

An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement‐based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright © 1999 John Wiley & Sons, Ltd.