Stress distribution near a crack tip in an anisotropic plate

The anisotropy of elastic properties of various materials was analyzed and its influence on the stress field near a crack tip under plane stress conditions was investigated. It was shown that this influence is substantial only in the case of sharply pronounced anisotropy.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 5, No. 6, pp. 714–719, November–December, 1969.     

Stress distribution,crack shape and energy for a penny-shaped crack in a plate of finite thickness

The shape of a penny-shaped crack located at the center of an elastic plate of finite thickness is related to the arbitrary axisymmetrical internal pressures applied to the crack surfaces in the form of a Fredholm integral equation, without using the methods of dual-integral equations. General expressions for the stresses in the plane containing the crack are written as the sums of the associated infinite solid stresses and the integrals accounting for the effect of plate thickness. The crack shape due to uniform crack pressures and the fracture criterion for brittle plates subjected to uniform stresses are obtained for various plate thicknesses.     

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.

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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 distribution around a surface crack a scattered-light photoelastic investigation

Stress distribution around a surface crack in a polyurethane rubber model subjected to axial pull are explored in a completely non-destructive manner using scattered-light photoelasticity.     

Stress intensity factor for a three-layered plate with a crack in the center layer

The objective of this study is to model the laminated composite as a multilayered plate each layer being made of a different material. With a crack in the mid-layer of the laminate, the stresses can vary in all three space coordinate directions and the problem is recognized as a three-dimensional one. A laminate plate theory is developed by application of the minimum complementary energy theorem in variational calculus such that the qualitative three-dimensional character of the crack edge stresses is retained while approximations are made in a quantitative sense on the stress intensity factor.Numerical values of the stress intensity factors for different construction of the laminate are reported and compared with the same size plate made of a single homogeneous material. When the modulus of elasticity of the middle layer which contains the crack is lower than that of the outer layers, the load transmission to the crack site as measured by the stress intensity factor can be reduced significantly. The present model assumes failure by crack propagation in only one layer of the laminate. Other possible modes of failure such as cohesive and/or adhesive fracture in laminated structures have yet to be explored.     

Stress distribution due to a crack opened by a semi-infinite wedge

Dislocation layers have been exploited in this paper to determine stresses in the neighbourhood of a crack opened by a semi-infinite rigid wedge when the equilibrium boundary of the crack surface is not known in advance. Some particular cases have been considered for illustration.

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Résumé Dans le mémoire, on a exploité les couches de dislocation en vue de déterminer la contrainte au voisinage d'une fissure ouverte par un coin rigide semi-infini, pour des conditions d'équilibre des frontières de la surface de la fissure inconnues à l'avance. A titre d'illustration, on a considéré certains cas particuliers.

     

Temperature distribution at a thermally insulated crack in a plate at various boundary conditions

Integral characteristics are defined for the temperature field of a plate with an open and thermally insulated crack and with boundary conditions of the first, the second, or the third kind at the lateral surfaces.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol, 23, No. 3, pp. 528–532, September, 1972.     

Stress intensity factors for an embedded elliptical crack in a plate of finite thickness

Summary This paper deals with the three-dimensional analysis of the stress distribution in a plate of finite thickness containing an embedded elliptical crack subjected to a constant pressure. By using the douboe Fourier transform, the problem is reduced to the solution of the integro-differential equation which is solved iteratively. A numerical solution of the integro-differential equation is also obtained. These solutions are compared with the results in the published accounts.     

Stress intensity factor at a bilaterally-bent crack in the bending problem of thin plate

An infinite plate with an asymmetric bilaterally-bent crack is analyzed as a bending problem of a thin plate. Stress distributions and stress intensity factors are obtained for some angles and length of bent crack. These are obtained for the some Poisson's ratio. Influence of the initial crack width on the stress intensity factor are also investigated. Three loading conditions are taken into consideration: uniform out of plane bending at infinity in the $\text{x}$ and $\text{y}$ directions and uniform out of plane twist. The rational mapping function in the form of a sum of fractional expressions and the complex variable method are used for the analysis.     

Stress distribution experienced under a portable light-weight deflectometer loading plate

In the field of pavement engineering, the need to rapidly and economically obtain properties of soils and materials has given rise to the development of many non-destructive techniques. Portable light-weight deflectometers (PLWD) are relatively new deflection-based tools. As a consequence, the main factors influencing the quality of the results obtained using such a tool are still being investigated. Therefore, through finite element modelling and experimental measurements, this research focussed on the stress distribution and stress variability under a PLWD loading plate and how it is influenced by stress level, plate diameter, rubber mat use and rubber hardness. It was shown that the stress distribution factor used for the calculation of elastic modulus from deflection testing is significantly influenced by the loading plate diameter. Moreover, the use of a harder rubber mat was found to be better, but no significant effect was observed for bonded rubber mat conditions.     

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.     

Stress intensity factors in anisotropic sandwich plate with a part-through crack under mixed mode deformation

An adhesively bonded anisotropic plate containing a part-through crack under mixed mode deformation is investigated. The problem is reduced to a pair of Fredholm integral equations of the second kind by mathematical analysis. By solving these equations numerically shear stresses of the adhesive and stress intensity factors in the cracked plate are obtained. Numerical results are presented for tension loading and shear loading, respectively, for various fiber orientations of the laminated composite. The results indicate a fairly strong dependence of the stress intensity factor on the fiber orientation of plate.     

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.     

Kinked crack in a bending trapezoidal plate

The interaction problem of a kinked crack and the edges of a bending trapezoidal plate which takes the effects of transverse shear deformation into account is presented. The research method is based upon the complex potential technique of Muskhelishvili using conformal mapping. Furthermore, for the analysis of the moment intensities at the tips of the kinked crack, the concept of dislocation distribution is applied. The integral equations for the stress disturbance problem along the line that is the presumed location of the kinked crack are then obtained as a system of singular integral equations with simple Cauchy kernels. As a consequence, the variation of moment intensity factors at the crack-tips is also illustrated.