An energy release rate criterion for crack growth in unidirectional composite materials

A criterion for crack initiation in unidirectional composite materials is presented. It includes two assumptions:

1. (1) crack initiation occurs in the direction of fibers;

2. (2) rapid crack growth occurs when the energy release rate reaches a critical value, the resistance to crack growth in the direction of fibers.

Then a model of energy release rate for crack growth in unidirectional composites is presented. The model is applied to characterize the fracture of off-axis, unidirectional glass-epoxy and graphite-epoxy composites. The results indicate that the loads corresponding to crack growth predicted by the present model agree well with the experimental results.     

Energy release rate and bifurcation angles of piezoelectric materials with antiplane moving crack

The dynamic fracture problems of the piezoelectric materials with antiplane moving crack are analysed by using function of complex variable in the paper. The results show that the coupled elastic and electric fields inside piezoelectric media depend on the speed of the crack propagation, and have singularity at the crack tip. The stress intensity factor is independent of the speed of the crack propagation, which is identical to the conclusion of purely elasticity. Moreover, independent of the electric loading, the dynamic energy release rate can be expressed by the stress intensity factor and enlarge with the increase of crack speed. High speed of the crack moving could impede the crack growth. At the same time, the crack can be propagated into either curve or bifurcation if the crack speed is higher than the critical speed.     

An analysis of the energy release rate for non-coplanar crack growth in fiber reinforced composite materials

In view of the fact that non-coplaner crack growth is a common characteristic of crack propagation in fiber reinforced composite materials, an attempt is made to derive the equation of the energy release rateG for non-coplaner crack extension in orthotropic linear elastic solids. Combining the idea developed in our previous paper and the analysis by Sihet al., the equation ofG is obtained for the cases of plane symmetric loading, plane skew-symmetric loading, antiplane shear loading, and a combination of these. The result will serve as a basic tool for developing a fracture mechanics approach to composites.     

Energy release rate along a three-dimensional crack front in a thermally stressed body

Based on a line-integral expression for the energy release rate in terms of crack tip fields, which is valid for general material response, a (area/volume) domain integral expression for the energetic force in a thermally stressed body is derived. The general three-dimensional finite domain integral expression and the two-dimensional and axisymmetric specializations for the energy release rate are given. The domain expression is naturally compatible with the finite element formulation of the field equations. As such it is ideally suited for efficient and accurate calculation of the pointwise values of the energy release rate along a three-dimensional crack front. The finite element implementation of the domain integral corresponds to the virtual crack extension technique. Procedures for calculating the energy release rate using the numerically determined field solutions are discussed. For illustrative purposes several numerical examples are presented.

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Résumé En sa basant sur une intégrale simple exprimant le taux de relaxation d'énergie afférant aux champs de contrainte à l'extrémité d'une fissure, expression applicable à la réponse d'un matériau quelconque, on a déduit une intégrale de domaine (superficielle ou volumique) décrivant l'énergie dans un corps soumis à contraintes thermiques.On fournit l'intégrale générale relative à un domaine fini tridimensionnel et á des cas particuliers bidimensionnels et axisymétriques, exprimant le taux de relaxation d'énergie. L'intégrale de domaine est naturellement compatible avec une formulation par éléments finis des équations de champ. Comme telle, elle convient idéalement pour un calcul facile et précis des valeurs ponctuelles du taux de relaxation de l'énergie le long du front d'une fissure tridimensionnelle. L'implantation d'éléments finis dans l'intégrale de domaine correspond à une technique d'extension virtuelle de la fissure. On discute des procédures de calculs du taux de relaxation de l'énergie, qui utilisent les solutions relatives au champ déterminées par voie numérique. A titre d'illustration, on présente plusieurs exemples numériques.

     

Energy release rate calculations for the compact tension specimen using brittle orthotropic materials

An energy release rate calculation is performed using the modified crack closure integral (MCCI) method applied to the compact tension (CT) specimen. Mechanical properties used are typical of short-fiber sheet molding compound (SMC) materials. Using orthotropic linear constant strain finite elements, the classical solution is closely approximated with a relatively coarse grid. The wedge opening of the CT specimen is shown to lower the expected energy release rate by 6·1%, introducing a systematic error. Orientation of the SMC material near the load application point perpendicular to the applied load will raise the energy release rate by 12·0%. The CT specimen results are shown to be insensitive to the distribution of the applied load around the hole periphery. A probabilistic method is developed for converting the distribution of applied failure load to the distribution of critical energy release rate. This method is applied to predict the distribution of failure load for other geometries.     

Off-axis fatigue crack growth and the associated energy release rate in composite laminates

Stable matrix crack growth behaviour under mechanical fatigue loading has been studied in a quasi-isotropic (0/90/-45/+45)_s GFRP laminate. Detailed experimental observations were made on the accumulation of cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finite element model of the damaged laminate has been constructed. This model has been used to relate the energy release rate of growing cracks to the crack growth rate via a Paris relation.     

Energy release rate calculations for an interface mode III edge crack based on a conservation integral

The M-integral is applied to the calculation of energy release races for interface edge cracks of the Mode III type. Specifically, for an edge crack along the interface between two elastic wedges of different opening angles and dissimilar elastic properties, and that is subjected to point loads at the apex, a relation is derived among the length of the crack, the energy release race of the crack, the applied loads, the wedge angles and the material parameters.     

Creep crack growth in brittle materials

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack tip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r ^–1/2 singularity is now attenuated to r ^{–1/2 +} (0<<1/2) singularity. The singularity attenuation parameter is a function of the crack velocity and material parameters. The crack growth rate is related to the mode I stress intensity factor K by K ² at relatively high load, K ⁿ at intermediate load, and approaches zero at small load near K _th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load. Key words: Creep crack growth, brittle material, diffusive cavity growth, sintering stress, crack tip stress field.     

Simulation of crack growth in ductile materials

During crack growth of real materials, the total energy released can be partitioned into elastic and dissipative terms. By analyzing material models with mechanisms for dissipating energy and tracking all energy terms during crack growth, it is proposed that computer simulations of fracture can model crack growth by a total energy balance condition. One approach for developing fracture simulations is illustrated by analysis of elastic-plastic fracture. General equations were derived to predict crack growth and crack stability in terms of global energy release rate and irreversible energy effects. To distinguish plastic fracture from non-linear elastic fracture, it was necessary to imply an extra irreversible energy term. A key component of fracture simulations is to model this extra work. A model used here was to assume that the extra irreversible energy is proportional to the plastic work in a plastic-flow analysis. This idea was used to develop a virtual material based on Dugdale yield zones at the crack tips. A Dugdale virtual material was subjected to computer fracture experiments that showed it has many fracture properties in common with real ductile materials. A Dugdale material can serve as a model material for new simulations with the goal of studying the role of structure in the fracture properties of composites. One sample calculation showed that the toughness of a Dugdale material in an adhesive joint mimics the effect of joint thickness on the toughness of real adhesives. It is expected, however, that better virtual materials will be required before fracture simulations will be a viable approach to studying composite fracture. The approach of this paper is extensible to more advanced plasticity models and therefore to the development of better virtual materials.     

Creep crack growth in power plant materials

Economic considerations have made it desirable to extend the 30 to 40 year operating life of power plants by another 10 to 20 years. Crack growth at elevated temperatures is an important consideration in estimating the remaining life, determining operating conditions and deciding inspection criteria and intervals for power plant materials. This paper presents an overview of high-temperature crack growth phenomenon in such materials. The focus is on various techniques used for characterizing creep crack growth (CCG) and creep-fatigue crack growth (CFCG) in high-temperature materials. The collection of data, their analysis and the interpretation of results is discussed in detail, especially for CFCG laboratory testing. The discussion is primarily focussed on creep-ductile materials such as those used in power plant applications. Special considerations for elevated temperature crack growth in weldments are also presented. Finally, the application of these concepts to the life prediction of power plant components is also discussed.     

Fatigue crack growth rate model for metallic alloys

A model has been created to allow the quantitative estimation of the fatigue crack growth rate in steels as a function of mechanical properties, test-specimen characteristics, stress-intensity range and test-frequency. With this design, the remarkable result is that the method which is based on steels, can be used without modification, and without any prior fatigue test, to estimate the crack growth rates in nickel, titanium and aluminium alloys. It appears therefore that a large proportion of the differences in the fatigue crack growth rate of metallic alloys can be explained in terms of the macroscopic tensile properties of the material rather than the details of the microstructure and chemical composition.     

Steady state crack growth in elastic-viscoplastic materials

A recent theory of Hart for the steady state propagation of a mode III crack in a ductile material is extended to modes I and II. When a crack is moving at non-zero velocity v, it is shown that for a broad class of materials the stress state at the crack tip is characterized by a r ^1/2 singularity and by a local stress intensity factor K. The local K is the sum of the apparent stress intensity factor K _A and a plastic contribution K _P. The value of K _A is calculated from the remote loading and the crack geometry under the assumption of linear elastic response alone. The quantity K _P characterizes stress relief of non-elastic flow. Numerical calculations are made to determine K as a function of K _A and v for elastic-viscoplastic materials. A dependence of v on K _A is obtained by imposing a kinetic law for v as a function of K. The plots of v vs. K _A show that below some critical values of K _A, steady state conditions cannot be sustained. Corresponding to the threshold value of K _A there is a definite value for the velocity.     

Suppression of crack growth in hybrid fibre composites

A theoretical analysis based on the assumed form of the strain field surrounding a crack bridged by reinforcing elements has been used to examine the growth of a crack propagating transversely to the fibres in hybrid fibre composites. An intermingled carbon fibre/glass fibre polymer matrix system has been considered. Two situations have been investigated. In the first of these the effect of the addition of carbon fibres on the development of cracks resulting from the failure of the glass fibres by stress corrosion has been studied. The analysis indicates that crack growth can be severely inhibited by a 5% volume fraction of type III carbon fibres. The analysis has been used also to investigate the process by which strong high failing strain glass fibres inhibit the growth of cracks caused by the fracture of localized clusters of low failing strain carbon fibres. The predictions of this analysis agree with existing experimental data on glass fibre/carbon fibre hybrids.