Local approach to fracture for cleavage crack arrest prediction

Crack arrest can complement the crack initiation concept to assess integrity of structures. This paper deals with the application of a local approach model derived from the RKR model to predict cleavage crack propagation and arrest in thermal shock experiments performed on pre-cracked discs made of a low alloy bainitic steel. The numerical procedure takes into account dynamic effects and an accurate behavior law for the material. Simulations with a crack speed criterion help the identification of the critical stress criterion. The results show a good prediction of the crack jump when a 3D modeling is used.     

A model of fatigue crack growth based on Dugdale model and damage accumulation

The modified Dugdale model given by Budiansky-Hutchinson and a Coffin-Manson type damage law are used to calculate the cumulative fatigue damage of material elements at the tip of a fatigue crack. From this analysis a fatigue crack growth equation is obtained which gives predicted crack growth rates in reasonable agreement with experimental data for two aluminium alloys 7075-T6 and 2024-T81, two titanium alloys Ti-8A1-1Mo-1V and Ti-6A1-6V and a PH13-8Mo stainless steel. Limitations of this new fatigue crack growth model are also discussed.     

Crack arrest model for a piezoelectric plate — A generalised Dugdale model

The constant search for new materials has provided impetus to research in piezoelectric materials. An anti-plane problem for a cracked unbounded two-dimensional poled piezoelectric plate has been investigated. The crack rims open on account of shear mechanical forces applied at the remote boundary and in-plane electric displacement field prescribed at the infinite boundary. Thus the crack yields both mechanically and electrically. Consequently, a plastic zone and a saturation zone protrude ahead of each tip of the crack. These developed zones are in turn closed by applying yield point shear stress at the rims of plastic zone and normal closing saturation limit displacement on the rims of saturation zones. Two cases are investigated when (i) the developed saturation zone length exceeds that of the developed plastic zone, and (ii) saturation zone length is smaller than that of the plastic zone. Fourier integral transform method is used in each case to obtain the length of plastic zone and saturation zone. Closed form analytic expressions are obtained in each case. Crack opening displacement and potential drop across the rims of the crack are also obtained. The effect of mechanical loads on crack closure in the presence of electric field is investigated and vice-versa. Also energy release rate expressions are obtained for both the cases.     

About the mode II Dugdale crack solution

The plane problem of a Dugdale crack under pure mode II loading is investigated. The exact closed form solution is given and an overlapping phenomenon is discussed.

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Résumé On étudie le problème plan d'une fissure de Dugdale soumise à une sollicitation pure en mode II. On fournit la solution exacte sous une forme fermée et on discute d'un phénomène de recouvrement afférent aux faces de la fissure.

     

Weight function based Dugdale model for mixed-mode crack problems with arbitrary crack surface tractions

Weight function theory states crack surface displacements can be found for any arbitrary distribution of mode I, or mixed-mode crack face tractions via that geometry’s weight functions. This statement is validated via finite element analysis of the infinite center-cracked plate for various mixed mode loadings. An elastic-perfectly plastic material is considered using a Dugdale approach and compared to elastic-plastic finite element simulations. The weight function method in all cases agrees well with the finite element simulations for small scale yielding at the crack tip. As the maximum traction value approaches one-half the yield strength discrepancies become larger due to violation of small scale yielding.     

A model for the evaluation of indentation crack arrest fracture toughness of supported films

A simple model is proposed for the evaluation of crack-arrest fracture toughness K _Ic0 of thin films by Vickers indentation. This approach applies to films thinner than the penetration depth of the Vickers indenter. The model equations are provided in closed form, even though they are so complex that they must be integrated numerically in practical applications. The problem of the evaluation of K _Ic0 for thin films and substrates is derived in general form and applied to three cases: (i) evaluation of K _Ic0 for the film in the case that the depth of the crack in the film is smaller than the film thickness, (ii) evaluation of K _Ic0 for the film in the case that the crack emanating from the film either crosses the film/substrate interface or is stopped by it, (iii) evaluation of K _Ic0 for the substrate in the case that the crack emanating from the film crosses the film/substrate interface. The model was tested with original and literature experimental data: (i) revision K _Ic0 values of electroless Ni-P thin films were re-evaluated, (ii) K _Ic0 of electroless Ni-P thin films of various thickness with various loads were measured (original data) and computed, (iii) K _Ic0 of electroless Ni-P substrates coated with electrodeposited Au-Cu were measured (original data) and computed.     

About the Dugdale crack under mixed mode loading

The plane problem of a Dugdale crack under mixed mode loading is investigated. An exact closed form solution is given and the corresponding crack displacements are discussed.

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Résumé On étudie le problème plan d'une fissure de Dugdale soumise à une sollicitation selcn un mode mixte. Une solution exacte de forme fermée est fournie et les déplacementsde fissure correspondants sont discutés.

     

Analysis of fast fracture and crack arrest by finite differences

A finite difference scheme, recently proposed and mainly concerned with the DCB static solution under plane strain conditions, is here further extended to provide more information on fast crack propagation and arrest. The analysis is shown to predict crack lengths at arrest and crack velocities as well as dynamic stress intensity factors which are very close to those reported in the literature. This good agreement with experimental findings was obtained for steel and epoxy resin which, while in different classes of material, nevertheless as far as the analysis is concerned are distinguished only by their Poisson's ratios.

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Résumé Un schéma par différence finie proposé récemment et relatif principalement à la solution statique d'une éprouvette double cantilever sous conditions d'état plan de déformation, est étendu à l'obtention d'informations complémentaires sur les conditions de propagation instable et d'arrêt d'une fissure.L'analyse prédit des longueurs de fissure à l'arrêt et des vitesses de fissuration, ainsi que les facteurs d'intensité de contrainte dynamique qui sont très proches de ceux que l'on trouve dans la littérature. Ce bon accord avec les observations expérimentales a été obtenu pour de l'acier et pour une résine époxy, deux matériaux qui, bien que de classes différentes, ne se distinguent néanmoins dans le cadre de l'analyse que par leur modules de poisson.

     

On the validity of the Dugdale model for craze zones at crack tips in PMMA

Journal of Materials Science -     

Crack tip opening displacement of a Dugdale crack in a three-phase cylindrical model composite material

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.     

The generalised Frost–Dugdale approach to modelling fatigue crack growth

This paper summarises recent developments in the formulation and application of the generalised Frost–Dugdale crack growth law. We first reveal the relationship between the generalised Frost–Dugdale crack growth law, dislocation based crack growth laws, the two parameter crack growth model, and fractal fatigue concepts. We then show that a range of aircraft materials characterisation test data are consistent with this law and how it can be used to predict crack growth in a range of full-scale aircraft fatigue tests, and coupon tests including crack growth in aircraft fuselage lap joints.     

Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials

In this paper, the concept of Dugdale crack model and Yoffe model is extended to propose a moving Dugdale interfacial crack model, and the interfacial crack between dissimilar magnetoelectroelastic materials under anti-plane shear and in-plane electric and magnetic loadings is investigated considering the magneto-electro-mechanical nonlinearity. It is assumed that the constant moving crack is magneto-electrically permeable and the length of the crack keeps constant. Fourier transform is applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. The explicit expression of the size of the yield zone is derived, and the crack sliding displacement (CSD) is explicitly expressed. The result shows that the stress, electric and magnetic fields in the cracked magnetoelectroelastic material are no longer singular and the CSD is dependent on the loading, material properties and crack moving velocity. The current model can be reduced to the static interfacial crack case when the crack moving velocity is zero.     

Bridging crack model for fracture of spruce

An analysis is presented of how cracking in wood can be predicted using fracture mechanics. In situ, real-time, scanning electron microscopy was used as a tool to estimate the physical mechanism of fracture in softwoods using end-tapered double cantilever beam specimens. It was found that bridging behind the crack tip is the main toughening mechanism, which contributes to non-linear wood behavior in the presence of stress concentrations. A new bridging crack model is presented that mimics the observed cracking mechanism. Intrinsic flaw size is found to correspond to the fiber length of spruce.     

The DFZ model of fracture at crack tip and crack initiation criterion

Direct observation by transmission electron microscopy (TEM) has been made on the distribution of dislocations in front of the crack tip during tensile deformation of aluminum. A microfracture model has been established to describe the equilibrium configuration of the dislocations in the presence of a dislocation-free zone (DFZ). The site of void nucleation observed from TEM experiments was found to be at about the place of maximum dislocation density predicted from the model. The relationship between the size of crack, DFZ and crack opening displacement (COD) was obtained as a function for a crack initiation criterion.     

Evaluation of statistical fracture toughness parameters on the basis of crack arrest experiment

The crack diffusion theory addresses the origins of the observed scatter, in brittle fracture, of macroscopic fracture parameters under seemingly identical test conditions. An essential question of experimental evaluation of the nonconventional fracture parameters introduced there appears to be buried in the formalism. In this paper we report a pilot crack arrest experiment, in which a methodology of evaluating some of the new fracture parameters is demonstrated. Experimental observations are found to not disprove the theory.     

A cohesive crack model to study the fracture behaviour of fiber-reinforced brittle-matrix composites

A cohesive crack model analysis of the fracture resistance and ductility of fiber-reinforced brittle-matrix composites was performed. The bulk material is assumed to behave as a linear elastic solid. The constitutive equation for the cohesive crack is obtained through micromechanical considerations based on the shear lag model of fiber-matrix interaction and on the statistical nature of fiber failure. A parametrical study of the influence of fiber volume fraction, fiber strength and flaw distribution, interfacial shear stress and specimen geometry on the fracture resistance of these composites was carried out. The results illustrate the role of each of these factors in overall composite toughening, and suggest various strategies to improve the composites' performance.     

Applications of dynamic fracture mechanics for the prediction of crack arrest in engineering structures

The compatibility of the static and dynamic approaches to crack propagation and arrest is investigated. For clarity, the term kinetic is introduced for analyses that focus on the entire crack initiation/propagation/arrest process — as opposed to static analyses which consider only the end points — as dynamic effects are not always significant in a crack run/arrest event. The importance of integrating experimental and computational work in this field is also discussed and a differentiation is given between the ways in which this can be done. An example computation on a thermal shock problem where dynamic effects are minimal, i.e., where the static and kinetic approaches are nearly the same, and a computation for a DCB specimen where significant differences occur between the two approaches are described. It is concluded that the static and kinetic approaches are entirely compatible as long as reflected stress waves do not reach the crack tip prior to crack arrest. But, when this is not the case, it is the kinetic approach that must be used. Similarly, when inelastic effects are important, only the kinetic approach can properly admit them.

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Résumé On étudie la compatibilité des approches statiques et dynamiques pour la propagation et l'arrêt d'une fissure. Pour des raisons de clarification, le terme cinétique est introduit dans une analyse qui couvre l'entièreté du processus d'amorçage, propagation et arrêt d'une fissure, par opposition à l'analyse statique qui ne considère que les points terminals et dans la mesure où les effets dynamiques ne sont pas toujours appréciables dans un processus de course et d'arrêt d'une fissure. On discute également l'importance d'intéger le travail expérimental et le travail par calculs dans ce domaine et l'on établit une différence entre les différentes voies qui peuvent être suivies. A titre d'exemple, on établit le calcul pour un problème de choc termique où les effets dynamiques sont minimes, c'est-à-dire où les approches statiques et cinétiques sont à peu près les mêmes et un calcul pour une éprouvette Cantilever où des différences significatives surviennent entre les deux approches. On conclut que les approches statiques et cinétiques sont entièrement compatibles pour autant que les ondes de contrainte réfléchies n'atteignent pas l'extrémité de la fissure avant que ne se produisent son arrêt. Cependant, comme lorsque cela n'est pas le cas, c'est l'approche cinétique qui doit être utilisée. De même, lorsque les effets inélastiques sont importants, seule l'approche cinétique peut les prendre en compte.

     

Dynamic fracture toughness at crack initiation, propagation and arrest for two pipe-line steels

The influences of temperature and loading rate on fracture toughness of two pipe-line steels at initiation, K_1d, and at arrest, K_1a, and on stretch zone height were measured using specific techniques. Particular attention was given to the mechanism of delamination, typical for the gas internal pressure pipe fracture.