The kinked interface crack

The integral equation of the kinked interface crack is solved numerically. The values of K _I, K _II and G for an interface crack with an infinitesimal kink are used to predict the kinking angle for two different material combinations under uniaxial tension.     

The interface penny-shaped crack reconsidered

The penny-shaped crack at the interface between two bonded dissimilar media is reconsidered on the basis of recent developments on the elimination of oscillatory singularities. This is accomplished by assuming an annular frictionless contact zone at the crack circumference and reducing the problem to a Fredholm integral equation. Expressions for the strain energy, crack opening force and bond stresses are obtained and numerical results given for specific material combinations.     

Rectangular tensile sheet with single edge crack or edge half-circular-hole crack

By using the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author, this note presents the stress intensity factors (SIFs) of a rectangular tensile plate with single edge crack. Further this note studies the SIFs of crack emanating from an edge half-circular hole. By comparing the calculated SIFs of the single edge half-circular-hole crack with those of the single edge crack, a shielding effect of the half-circular hole on the SIFs of the single edge crack is discussed. It is found that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems in finite plate.     

Creep crack initiation at a free edge of an interface between submicron thick elements

To clarify the mechanics of time-dependent crack initiation at an interface edge in submicron thick elements due to creep, delamination experiments are conducted using a micro-cantilever bend specimen with a tin/silicon interface edge. After the specimen time-dependently deforms under a constant load, a delamination crack is initiated at the Sn/Si interface edge. In addition, the steady state creep property of Sn is estimated by performing an inverse analysis using a finite element method based on creep deformation experiments conducted for different specimens. Stress analysis using the obtained creep property reveals that stress and strain rate singularities exist at the Sn/Si interface edge under creep deformation. The intensity of the singular field time-dependently increases as the creep region expands, and eventually it becomes a steady state. The stress and strain rate intensities at the steady state correlate well with the crack initiation life, which indicates that the singular stress field near the interface edge governs the creep crack initiation.     

Dominant stress region for crack initiation at interface edge of microdot on a substrate

In order to examine the mechanics of crack initiation at the free interface edge of a microcomponent on a substrate, delamination tests are carried out for two specimen shapes of Cr microdots on a SiO₂ substrate. The microdots of the first specimen are shaped like the frustum of a round cone. The Cr microdots are successfully delaminated from the SiO₂ substrate in a brittle manner and the critical load is measured by atomic force microscopy (AFM) with a lateral loading apparatus. Stress analysis reveals that a singular stress field exists near the interface edge and the strength for the crack initiation is governed by the intensified normal stress field. The critical stress intensity parameter is evaluated as K_σC ≈ 0.24 MPa m^0.39. Similar delamination tests are conducted for microdots shaped like the frustum of an oval cone. The stress distributions at the crack initiation of this specimen shape show a higher normal stress than the first specimen shape in the region near the interface edge of about x < 40 nm, while it is lower in the region of about x > 50 nm (x: distance from the edge). This suggests a limitation of conventional fracture mechanics: namely, the crack initiation in these specimens is not uniquely governed by the intensity of the singular field. It is found that the delamination crack is initiated when the averaged stress σ_ya in the region of 90-130 nm reaches 190-270 MPa, regardless of the specimen shape. This indicates that the dominant stress region of crack initiation is roughly estimated as 90-130 nm and the criterion is given in terms of the averaged stress in the region.     

Initiation of interface crack at free edge between thin films with weak stress singularity

Delamination tests using sandwich type specimens are conducted for eight combinations of materials: thin films formed on silicon substrates which are relatively popular in micro-electronic industry, to develop a method for quantitative evaluation and comparison of crack initiation strength at the free edge. The difficulty stems from the difference of stress singularity, K_ij/r^λ (K_ij: stress intensity, r: distance from free edge and λ: order of stress singularity), where λ is depending on the combination of materials. Thus, the critical K_ij has different dimensions, MPa m^λ, in each interface. Using the experimentally observed delamination load, the stress distribution along the interface is analyzed by boundary element method. Since the orders of stress singularity, λ, in the materials are less than 0.07 (weak singularity), the stress field near the interface edge is almost constant in atomic (nanometer) level. Then, the critical strength for the interface cracking is quantitatively represented by the concentrated stress near the edge. The effects of the several factors such as species of thin films, oxidized interlayers and deposition processes of thin films on the interface strength are evaluated on the basis of this critical stress as well.     

A cohesive edge crack

The nucleation and growth of a cohesive edge crack is studied. This topic is germane to the initiation and early stage of crack growth during unnotched beam testing, the growth of short edge cracks in finite test pieces, and the formation of tension cracks of geological origin. This paper focuses on an edge crack in a semi-infinite plane, under a uniform far-field tensile stress acting parallel to the plane boundary. Expressions for the Mode I stress-intensity-factor and crack-opening-displacement for an edge crack subjected to arbitrary crack face loading are determined via the weight function method. All of the constants needed to define the weight function and associated integrals are themselves explicit functions of just two constants: f_r and ψ. Two types of softening behavior in the cohesive zone are examined: rectangular softening, and linear softening. In each case the process zone size, energy-release-rate, crack-opening displacement and load-ratio are examined. The different test behavior exhibited under load-control versus fixed-grip displacement control is explored. The test control conditions alter the fracture behavior significantly. For a linear softening cohesive edge crack, it is found out that under fixed-grip control (load-control), the process zone size decreases (increases) steadily with increasing traction-free crack length, approaching the semi-infinite crack asymptote from above (below). The differences between load-control versus fixed-grip control decrease rapidly with increasing traction-free crack length.     

The interface crack with a contact zone

An analytical method is applied to the contact zone model of the finite length interface crack problem. The results are valid for small contact zone lengths due to interpenetration of the crack faces. Qualitative results obtained in [1] are confirmed. Also where possible numerical comparisons are made with the work of Comninou et al. [2, 3, 4, 5] and reasonable agreement is obtained.

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Résumé On a appliqué une méthode analytique au modèle de zône de contact dans le cas d'un problème de fissure d'interface de longueur finie. Les résultats sont valables pour des longueurs de la zône de contact faibles, dues à une interpénétration des faces de la fissure. Des résultats qualitatifs obtenus dans la référence [1] sont confirmés. En outre, il a été possible de procéder à des comparaisons numériques avec les travaux de Comninou et al. [Réf. 2 à 5] et un accord raisonnable a été obtenu.

     

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.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

The competition between the crack kinking away from the interface and crack propagation along the interface in elastic bicrystals

The problem analyzed is of the crack kinking away from the interface between the two different anisotropic materials. The attention is concentrated on the initiation of the crack kinking and the condition that the length of the crack segment that is leaving the interface is small in comparison to the crack segment that remains along the interface. The emphasis is placed to the application of the fracture mechanics concept for the interfacial crack that propagates dynamically between the two orthotropic materials. The simulations and calculations were done by application of the Mathematica ^® programming routine. The stress intensity factors and the energy release rate are obtained for the kinked crack, as functions of the corresponding values for the interfacial crack prior to kinking. The analysis was performed of the influence of anisotropy on the crack kinking versus crack propagating along the interface competition. Due to anisotropy the kinking is easier, i.e., it is easier for the crack to kink away from the interface into the “softer” of the two materials. The oscillatory index for the case of the dynamic crack growth along the interface between the two orthotropic materials increases with crack tip speed v and with increase of the difference in stiffnesses. The practical application of this analysis could be for the interface in the glued joints and protective coatings.     

Orthogonal crack approaching an interface

We consider the problem of a tensile crack approaching a sliding interface in the direction normal to it in an attempt to find the mechanisms that control the crack offset. The crack in a plane free of loading is driven by uniform load applied to its faces. The interface is assumed to have no resistance to opening. The common conception is that as the crack approaches the interface it creates a zone of opening. When the crack touches the interface this opening zone eventually arrests the crack such that the continuation of the crack growth through the interface is only possible from an offset position. Our computer simulations conducted for frictionless interface and supported by a simple analytical model show that the situation is more complex. As the crack tip gets close, the zone of opening shrinks and the opening displacement increases. After the crack tip touches the interface, the opening zone disappears. Frictionless interface produces concentration of this stress only at the ends of the interface which physically corresponds to the points where sliding is artificially arrested.     

The use of interlayers in modeling interface crack propagation

Delaminations are a common mode of failure at interfaces between two material layers which have dissimilar elastic constants. There is a well-known oscillatory nature to the singularity in the stress fields at the crack tips in these bimaterial delaminations, which creates a lack of convergence in the modewise energy release rates. This makes constructing fracture criteria somewhat difficult. An approach used to overcome this is to artificially insert a thin, homogeneous, isotropic layer (the interlayer) at the interface. The crack is positioned in the middle of this homogeneous interlayer, thus modifying the original ‘bare’ interface crack problem into a companion ‘interlayer’ crack problem. Individual modes I and II energy release rates are convergent and calculable for the companion problem and can be used in the construction of a fracture criterion or locus. However, the choices of interlayer elastic and geometric properties are not obvious. Moreover, a sound, consistent, and comprehensive methodology does not exist for utilizing interlayers in the construction and application of mixed-mode fracture criteria in interface fracture mechanics. These issues are addressed here. The role of interlayer elastic modulus and thickness is examined in the context of a standard interface fracture test specimen. With the help of a previously published analytical relation that relates the bare interface crack stress intensity factor to the corresponding interlayer crack stress intensity factor, a suitable thickness and elastic modulus are identified for the interlayer in a bimaterial four-point bend test specimen geometry. Interlayer properties are chosen to make the interlayer fracture problem equivalent to the bare interface fracture problem. A suitable mixed-mode phase angle and a form for the fracture criterion for interlayer-based interface fracture are defined. A scheme is outlined for the use of interlayers for predicting interface fracture in bimaterial systems such as laminated composites. Finally, a simple procedure is presented for converting existing bare interface crack fracture loci/criteria into corresponding interlayer crack fracture loci.     

Nonradial edge crack in a circular disk

We deduce a singular integral equation of the problem of stress-strain state of a circular disk weakened by a rectilinear nonradial edge crack whose lips are subjected to the action of an arbitrary self-balanced load. For the case of a pressure uniformly distributed over the crack lips, we compute the stress intensity factors as functions of the orientation and crack length.     

Interaction between an interface crack and a parallel subinterface crack

In this paper, the pseudo-traction method addressed thoroughly in homogeneous cases is combined with the edge dislocation method to solve the interaction problem of an interface crack with a parallel subinterface crack. After deriving the fundamental solutions for a typical interface crack loaded by the normal and tangential concentrated tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is reduced to a system of singular integral equations which can be solved numerically with the aid of the Chebyshev polynomial technique. Numerical results for the stress intensity factors are shown in the figures in which six kinds of material combinations presented by Hutchinson et al. [1] are considered.     

The short single edge crack specimen with linearly varying end displacements

The quantitative effect of the loading non-symmetry introduced by a single edge crack in a short length specimen loaded in tension along the center line is determined. For deep cracks, the effect of the induced moment can be substantial. Stress intensity factor is plotted as a function of sheet geometry and crack length.

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Zusammenfassung Der quantitative Einfluss der Belastungsunsymmetrie, hervorgebracht durch einen ein zelrändigen Riss in einem kurzen der Mittellinie längs in Zugspannung belasteten Musterexemplar wird ge-, funden. Für tiefe Risse kann der Einfluss des verursachten Moments beträchtlich sein. Der Spannungsintensitätsfaktor wird als Funktion der Plattengeometrie and Risslänge graphisch aufgezeichnet.

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Résumé On détermine quantitativement l'effet de la dissymétrie de la charge qu'enttaine, dans une éprouvette courte soumise à traction axiale, une fissuration d'un de ses bords.Lorsque la fissure est profonde, le moment induit peut avoir des effets appréciables. On foumit, sous forme d'abaque, les valeurs de coefficient de concentration de tension en fonction de la géométrie de la tóle et de la longueur de la fissure.

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Formerly with U.S. Army Materials Research . Agency, Watertown, Massachusetts.     

The green's function for a slant edge crack

The Green's functions are determined for plane edge cracks which meet the free surface at an arbitrary angle. Modes I and II stress intensification factors are found for both normal and shear loading of the crack, since coupling is found to occur between each type of loading and the two possible modes of crack-tip response.