Stress intensity factors in cracked cylindrical shells under tension

The singular stress field at the tip of a circumferential crack in a cylindrical shell under axial tension was studied by the optical method of caustics. The material of the shell was considered as linearly elastic and optically anisotropic. A complete study of the influence of the optical anisotropy of the material of the shell, the shell curvature and the characteristics of the optical set-up, on the shape and size of the caustics formed by illuminating the shell by a divergent or parallel light beam was undertaken. The stress intensity factor for the crack tip was evaluated by interrelating this quantity with the geometric characteristics of the caustics. Stress intensity factors evaluated experimentally on shells made either of an optically inert material (plexiglas) or of an optically active material (polycarbonate) compared favorably with the already existing theoretical solutions.

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Résumé On étudie la singularité du champ de tensions à l'extrémité d'une fissure circulaire dans une enveloppe cylindrique sous tension axiale par la méthode optique des caustiques. On considère que le matériau de l'enveloppe est linéaire élastique et anisotrope du point de vue optique. On entreprend une étude complète de l'influence de l'anisotropie optique du matériau, de la courbure de l'enveloppe et des caractéristiques de l'installation optique sur la forme et de la dimension des caustiques qui se forment lorsqu'on éclaire l'enveloppe par un rayon lumineux divergent ou parallèle. Le facteur d'intensité des contraintes relatif à l'extrémité de la fissure est évalué en le mettant en relation avec les caractéristiques géométriques des caustiques. On constate que les facteurs d'intensité des contraintes qui sont évalués par voie expérimentale sur des enveloppes en matériau optiquement inerte (plexiglas) ou en matériau optiquement actif (polycarbonate) soutiennent la comparaison avec les solutions existantes établies par voie théorique.

     

Stress concentration of a strip with double edge notches under tension or in-plane bending

The stress concentration analysis of 60° V-shaped or partially-circular double edge notches in an infinite strip under tension or in-plane bending is discussed. The stress field induced by a point force in an infinite plate is used to solve these problems. The present results for semicircular notch are in close agreement with other reports. The results calculated on the 60° V-shaped notches show that the Neuber formula gives an underestimated stress concentration factor of about 11% for tension case and in about 9% for bending case. These errors exist for a wide range of notch depth. However, in the case of blunt notches, the Neuber solution of deep hyperbolic notches still gives a sufficient accuracy in engineering use. In addition, the stress concentration factors of 60° V-shaped notches are also represented by diagrams for wide use.     

An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole

A magneto-thermo-visco-elastic problem of an infinite isotropic medium is considered in this problem. The analysis encompasses Lord–Shulman and Green–Lindsay theories of generalized thermo-elasticity to account for the finite velocity of heat equation. The problem is solved by taking Laplace transform techniques and the inversion of the Laplace transform is carried out using a numerical approach.     

Exact solution of shear problem for inclined cracked bending reinforced concrete elements

In spite of a wide experimental and theoretical data on shear that forms a basis for modern design approaches, exact solution of shear problem for inclined cracked bending reinforced concrete elements is still not found. It yields high dispersion in the bearing capacity of concrete according to the main compression stresses. A similar problem appears with the internal forces carried by shear reinforcement. The above mentioned problem is related to two parameters: the angle of the main compression stresses and that of the inclined links. Corresponding internal forces together with the force in the tensile reinforcement form a commonly used design model (truss model), therefore each force depends on the other. This fact is practically not considered in modern design provisions hence there are no tools to express the shear capacity accurately. The two angles should be considered simultaneously in every case, when the links section is taken according to the calculated value (but not to the minimum one). The present study is one of the first attempts, focused on considering the interaction between the internal forces in concrete and inks according to the design model. It allows calculation of an exact angle, defining the inclined cracks and forces in links within the known experimentally investigated limits of this angle.     

Finite element plastic loads for circumferential cracked pipe bends under in-plane bending

This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic-perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.     

Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating

A solution is given for the induced temperature and stress fields in an infinite transversely isotropic solid continuum with a cylindrical hole. The solid medium is considered to be exposed to a magnetic field and the cavity surface is assumed to be subjected to a ramp-type heating. Green and Lindsay model has been used to account for finite velocity of heat conduction. Magnetic field induced within the cavity is also determined. The problem is solved analytically by using integral transform technique.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)_2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)_2s, (45/−45)_4s and (0/90)_4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate.     

Electroelastic properties of cracked piezoelectric materials under longitudinal shear

Analytical solutions are obtained to quantify the influence of cracks on electroelastic properties of piezoelectric materials containing doubly-periodic arrays of cracks. Both the rectangular and diamond-shaped arrays of cracks are considered. Solutions are obtained for the case of an antiplane shear load coupled with an in-plane electrical load. This study makes it possible to understand the multicrack interactions in piezoelectric solids and their effects on the fracture and electroelastic properties. The crack tip field intensity factors and the change in stored electroelastic energy due to the presence of many microcracks are calculated. These calculations enable the prediction of the effective elastic, piezoelectric and dielectric constants of a damaged piezoelectric material. The results of this work can be useful in developing a technique to determine the state of mechanical and electrical damage in piezoelectric materials.     

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.     

Limiting state of a thin cracked plate under biaxial tension

The results of investigation of the limiting state of cracked plates formed from aluminum alloy D16AT under biaxial tension are presented. The ratio of the corresponding displacements of the plate's boundary and the ratio of nominal stresses at the crack tip are adopted as parameters characterizing the stress-strain state of the plate's material. A relation is established between these parameters and the limiting state of the plate.Translated from Problemy Prochnosti, No. 12, pp. 21–26, December, 1992.     

Buckling behavior of a central cracked thin plate under tension

The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.     

Stress concentration of a cylindrical bar with a V-shaped circumferential groove under torsion, tension or bending

The stress concentration of a cylindrical bar with a V-shaped circumferential groove is analyzed by the body force method. The stress field due to a ring force in an infinite body is used to solve this problem. The solution is obtained by superposing the stress fields of ring forces in order to satisfy the given boundary conditions. The present results for semi-circular notches are in close agreement with Hasegawa's results. As a result of the systematic calculation of a 60° V-shaped notch, it is found that the stress concentration factors obtained by Neuber's trigonometric rule used currently have non-conservative errors of about 10% for a wide range of notch depths. The stress concentration factors are illustrated in charts so they can be used easily in design or research.     

Effects of a viscoelastic substrate on a cracked body under in-plane concentrated loading

Summary The effect of a viscoelastic substrate on an anisotropic elastic cracked body under in-plane concentrated loading is studied in this paper. Based on the correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The fundamental elastic solution is solved as three complex potentials via the property of analytical continuation to satisfy the continuity condition along the interface between dissimilar media. A singular integral technique in association with the dual coordinate transformation is applied to obtain the stress intensity factors for various crack orientations. Using the standard solid model to formulate the viscoelastic constitutive equation, some numerical examples are considered to demonstrate the use of the present approach.     

Postbuckling response and failure of symmetric laminates under in-plane shear

This paper summarizes a study aimed at understanding the postbuckling behaviour and progressive failure of thin, simply supported symmetric rectangular laminates with various possible in-plane boundary conditions and under the action of in-plane shear loads. First-order shear deformation theory and geometric non-linearity, in the von-Karman sense, is used with a finite-element procedure. The 3D Tsai–Hill criterion is used to predict failure of lamina and the maximum stress criterion is used to predict the onset of delamination at the interface of two adjacent layers. The effect of in-plane boundary conditions, plate lay-ups, plate aspect ratio, fiber orientations and lamina material properties on the load deflection response, buckling load, first-ply failure load, ultimate load and the maximum transverse displacement associated with failure loads is presented.     

Fatigue behavior of laminated composites with a circular hole under in-plane uniaxial random loading

A modified fiber failure fatigue model is presented to evaluate the behavior of laminated composites with a central circular hole under in-plane uniaxial random/block loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane uniaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Degradation of material strength as a function of applied number of cycles is considered in the model presented. Random loading case is analyzed based on rainflow counting technique. Analytical predictions are compared with the experimental results for uniaxial block loading.     

The solution of a rectangular orthotropic sheet with a central crack under anti-plane shear

Making use of the basic theorem of the Fourier transform and series, the solution of the stress intensity factor of a rectangular orthotropic plate containing a central crack under anti-plane shear, is obtained in this study. The result to the mixed boundary value problem is expressed in terms of a Fredholm integral equation of the second kind. It is easily proved that the problem of a strip with a central crack of mode III, are the special cases of the solution in this article.