Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle

For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) − θ_o is predicted by using opening and sliding mate stress intensity factors, k₁ and k₂. These theoretical predictions are consistent with experimental fracture angles.

For the S theory, the crack spreads in the negative θ_o-direction in a plane for which S is a minimum, S_min. This quantity was obtained analytically. The experimental data of the critical S (S_cr) on plexiglass fracture specimens remains essentially constant.     

Stress distribution near a crack crossing an interface

The stress distribution around a crack lying normally across the boundary between two media is calculated. It is assumed that the elastic properties vary continuously, but rapidly, across the interface, and that methods employed for homogeneous materials are applicable. It is shown that the stresses behave as r ^–1 in the vicinity of the junctions of the crack and the interface, and that an appropriate interfacial stress intensity factor can be defined.

---

Résumé La distribution des tensions au voisinage d'une fissure se trouvant normalement à la zône de liaison entre deux milieux est calculée. On suppose que les propriétés élastiques varient de manière continue, encore que rapidement suivant l'interface, et que les méthodes utilisés pour les matériaux homogènes sont applicables. On montre que les contraintes varient en raison inverse du rayon au voisinage des jonctions de la fissure et de l'interface et qu'un facteur d'intensité des contraintes interfaciales approprié peut être défini.

     

Stress intensity factor for a crack normal to an interface between two orthotropic materials

In this paper, the problem of a crack normal to an interface in two joined orthotropic plates is studied as a plane problem. Body force method is used to investigate dependence of the stress intensity factor on the elastic constants: E _x1, E _y1, G _xy1, V _xy1 for material 1 and E _x2, E _y2, G _xy2, V _xy2 for material 2. A particular attention is paid to simplifying kernel functions, which is used in the body force method, so that all the elastic constants involved can be represented by three new parameters: H ₁, H _2I, H ₃ for the mode I deformation and H ₁, H _2II, H ₃ for the mode II deformation. From the kernel function so obtained it is found that the effects of the eight elastic constants on the stress intensity factors can be expressed by the three material parameters, H ₁, H _2I, H ₃ and H ₁, H _2II, H ₃, respectively for K _I and K _II. Furthermore, it is also found that the dependence of K _I on H ₁, H _2I, H ₃ is exactly the same as the dependence of K _II on H ₁, H _2II, H ₃. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stress intensity factors for an interface crack along an elliptical inclusion

The problem of a crack along the interface of an elliptical elastic inclusion embedded in an infinite plate subjected to uniform stresses at infinity is analyzed by the body force method. The crack tip stress intensity factors are calculated for various inclusion geometries and material combinations. Based on numerical results, the effect of the inclusion geometry on the stress intensity factors is investigated. It is found that for small interface cracks the stress intensity factors are mainly determined by the stresses, occurring at the crack center point before the crack initiation, and interface curvature radius alone.     

Stress distribution due to a griffith crack at the interface of an elastic half plane and a rigid foundation

The stress field in a semi-infinite elastic media bonded to a rigid foundation and containing a crack at its interface is determined. Two specific problems are discussed-first when the elastic half space is under shear such that σ_xv ~ P as √(x² + y²) → ∞ and next when the crack is opened by equal and opposite pressure on each of its sides. The solution is obtained via Fourier transforms which lead to a simultaneous set of dual integral equations containing a trigonometric kernel. It is observed that in a small region near the ends of the crack, violent oscillations occur in both the stress and displacement components.     

Stress intensity factor for an embedded elliptical crack under arbitrary normal loading

In this paper we introduce the boundary value problem of three-dimensional classical elasticity for an infinite body containing an elliptical crack. Using the method of simultaneous dual integral equations, the problem is transformed to the system of linear algebraic equations. Stress intensity factor is obtained in the form of the Fourier series expansion. Several solutions for specific cases of applied polynomial stress fields are derived and compared with existing results. Eligibility of the method for more complicated stress fields is demonstrated on the example of partially loaded elliptical crack.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

Stress intensity factors of a surface crack near an interface end

Due to the singular behavior of the stress field near the interface edge of bonded dissimilar materials, fracture generally initiates near the interface edge, or just from the interface edge point. In this paper, an edge crack near the interface, which can be considered as being induced by the edge singularity and satisfying two conditions, is analyzed theoretically, based on the singular stress field near the interface edge and the superposition principle. It is found that the stress intensity factor can be expressed by the stress intensity coefficient of the edge singular stress field, the crack length, the distance between the interface and the crack, as well as the material combination. Boundary element method analysis is also carried out. It is found that the theoretical result coincides well with the numerical result when the crack length is small. Therefore, the theoretical representation obtained by this study can be used to simply evaluate the stress intensity factor of an edge singularity induced crack for this case. However, when the crack length becomes larger than a certain value, a significant difference appears, especially for the case with large edge singularity.     

Stress singularities for crack normal to and terminating at bimaterial interface on orthotropic half-plates

The problem of a crack normal to and terminating at an interface in two joined orthotropic plates is considered and the eigenequation for the asymptotic behavior of stresses at the crack tip on the interface is given in an explicit form. It is found that the singular stress field around the crack tip can be separated into two independent fields, respectively of the mode I and II. Also it is found that for both the mode I and II deformations the effects of elastic constants on the stress singularity order can be respectively expressed by three material parameters, two of which are the same for both the mode I and mode II deformations.     

A limit load solution for a highly weld strength undermatched tensile panel with an arbitrary crack

A new plane strain upper bound solution for highly undermatched welded tensile panels with a crack is proposed. A distinguished feature of this solution is that the crack is arbitrarily located within the weld and its shape is also arbitrary, though some restrictions do apply. The latter are explained in detail such that the class of structures for which the solution is applicable is precisely specified. The solution is given in a very simple closed form.     

Stress intensity factors of an inclined elliptical crack near a bimaterial interface

In this paper the stress intensity factors are discussed for an inclined elliptical crack near a bimaterial interface. The solution utilizes the body force method and requires Green’s functions for perfectly bonded semi-infinite bodies. The formulation leads to a system of hypersingular integral equation whose unknowns are three modes of crack opening displacements. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of stress intensity factors along the crack front accurately. Distributions of stress intensity factors are presented in tables and figures with varying the shape of crack, distance from the interface, and elastic modulus ratio. It is found that the inclined crack can be evaluated by the models of vertical and parallel cracks within the error of 24% even for the cracks very close to the interface.     

Strain fields at an interface crack in a sandwich composite

Interface damage characterization and interlaminar failure of sandwich specimens with an initial interlaminar delamination in between the face sheet and the core is done by using the digital image correlation method (DIC). Virtual strain gages are emulated at the interface and beneath it, in the polyurethane core and opening strains are measured. Peel tests reveal interesting particularities on damage localization and strain variation while damage is completed. After analyzing the experimentally obtained results, four characteristic domains which describe the opening strain variations in the core are established together with the corresponding variation of the opening strain at the interface. The critical strain at damage initiation, as well as the critical displacement when damage is finalized, is established by DIC in the cohesive zone. After the calibration of the finite element model through experimental results, the use of the cohesive elements together with a linear softening law give in the core a pattern of strain variation similar to the one obtained experimentally.     

Rotating disk containing an internal crack located at an arbitrary position

A rotating disk containing an internal crack at an arbitrary position is treated by using the eigen function expansions of the complex stress potentials, and determining the unknown coefficients from the boundary conditions expressed in terms of the resultant forces. Numerical calculations are done for various configurations and convenient formulae for the stress intensity factors are presented.     

Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings.     

Stress intensity factor solution for a semi-elliptical crack in an arbitrarily distributed stress field

An equation for the stress intensity factor (SIF) for semi-elliptical crack has been developed. It is based on the Newman-Raju's solution for the crack in a plate under bending or tension. The equation can be applied when a stress distribution is described by a power function. Using the approach outlined, the SIF for a surface crack in a T-butt welded connection has been estimated. The results obtained can be used in a fracture-mechanics-based fatigue analysis.     

On the stress singularity at an interface crack

The plane elastostatic stress field near an interface crack is considered and a model developed for the interface crack tip which is free from the inter-penetration of the crack flanks present in some earlier investigations, yet permits propagation in a crack opening mode along or near the interface. The basis of the model lies in taking, as the configuration to which the loads are applied, a crack tip which subtends an opening angle. By means of an asymptotic eigen-analysis, the main features of this departure from the norm in LEFM are identified and some examples presented which demonstrates its potential usefulness.

---

Résumé Le champ de contrainte plane élastostatique au voisinage d'une fissure d'interface est prise en considération, et on développe un modéle pour l'extrémité de la fissure d'interface qui ne dépend pas de l'interpénétration des bords de la fissure telle qu'on l'avait envisagée dans des études précédentes, mais qui permet une propagation selon un mode d'ouverture de fissure le long ou au voisinage de cet interface. La base du modèle consiste à prendre comme configuration à laquelle les charges sont appliquées une extémité de fissure sous-tendant un angle d'ouverture. Au moyen d'une eigen-analysis asymptotique, les caractéristiques principales de cette déviation des normes de la mécanique de rupture linéaire élastique sont identifiées, et quelques exemples sont présentés qui démontrent son utilité potentielle.

     

A limit load solution for a highly undermatched scarf‐joint specimen with an arbitrary crack

A new plane strain upper bound solution for highly undermatched scarf‐joined specimens with a crack is proposed. A distinguished feature of this solution is that the crack is arbitrarily located within the weld and its shape is also arbitrary, though some restrictions do apply. The latter are explained in detail such that the class of structures for which the solution is applicable is precisely specified. The solution is given in a form of several ordinary integrals.     

Stress distribution ahead of an interface crack tip in a ductile adhesive layer

ABSTRACT In an adhesive layer sandwiched by stiff substrates, if the plastic zone size r_p reaches several layer thicknesses ahead of the crack tip, the maximum stress develops around the region of x₁=r_p, and the stress level is even higher than the one predicted by the remote K‐field. The unusual high stress is due to the restraint of the plastic flow by adhesion with the substrates, which is similar to the ‘friction hill’ occurring in plane strain compression or tension. As a theoretical approach, a slip line field model is proposed, which provides a fairly good approximation of the stress distribution σ₂₂ ? x₁ within the plastic zone. Using the slip line field approach, a new model is proposed to estimate the plastic zone size.     

Stress in the vicinity of a griffith crack at the interface of a layer bonded to a half plane—an approximate method

Approximations to the stress field in the vicinity of a Griffith crack located at the interface of a layer bonded to a dissimilar half plane are determined. A systematic use of Fourier transforms reduces the problem to that of solving a set of simultaneous dual integral equations with trigonometric kernels and weighting functions. This latter problem is reduced to the solution of an uncoupled pair of singular integral equations. An approximate technique using Legendre polynomial expansions is discussed. The analysis shows that when a constant pressure is applied to the faces of the crack, the stress components have the distinctive oscillatory singularities at the crack tip. Expressions up to the order of $\text{h}{}^{\mathrm{?4}}$, where $\text{h}$ is the thickness of the layer and is much greater than 1, are derived for the stress components.