Fracture analysis of surface- and through-cracked sheets and plates

The Neuber stress-concentration relation for notches in an elastic-plastic material subjected to shear loading was generalized for a crack in a finite plate subjected to tensile loading, similar to the way in which Kuhn modified the Hardrath-Ohman notch equation for a cracked plate. An equation was derived which related the linear elastic stress-intensity factor, the applied stress, and two material parameters. The equation was then used as a two-parameter fracture criterion for surface- and through-cracked specimens.Fracture data from the literature on surface- and through-cracked sheet and plate specimens of steel, titanium alloy, titanium weldment, and aluminum alloy tested at room and cryogenic temperature were analyzed according to the proposed equation. For surface cracks, wide ranges of crack-depth to crack-length ratio and crack-depth to specimen-thickness ratio were considered. For through cracks, wide ranges of crack length and specimen width were also considered. An empirical equation for the elastic magnification factors on stress intensity for a surface crack in a finite-thickness plate was also developed. The fracture stress predictions computed from the two-parameter fracture criterion for both surface- and through-cracked sheet and plate specimens are consistent with experimental failure stresses.     

Fracture mechanics analysis of geometrically nonlinear shear deformable plates

This paper presents boundary integral equations for fracture mechanics analysis of geometrically nonlinear shear deformable plates. A radial basis function and dual reciprocity method are utilized to evaluate the derivative terms and the domain integrals that appear in the formulations, respectively. Numerical examples of the clamped and simply supported plates containing a center crack subjected to uniform transversal loadings are presented. Displacement extrapolation technique is used to compute the stress intensity factors (SIFs). Stress intensity factors of mode I for plate bending and membrane problems are presented. The normalized stress intensity factors in membrane significantly increase after few increments of the load while the normalized stress intensity factors in bending decrease. Less displacement and rotational constraints in cracked plates under uniform transversal loadings will raise the stress intensity factors. The bending stress intensity factors of a central crack in clamped square plate were found to be the highest values compared to those for clamped non-square plates.     

Fracture analysis of center cracked infinite plates of linearly softening materials

A crack in an infinite plate is described as a mixed boundary value problem based on the Damage Zone Model. The boundary value problem is treated by means of Fourier transformation. The resulting integral equations are solved numerically to give stresses and displacements. It is shown that the maximum applied stress before failure can be found by an eigenvalue calculation. The dependence of the maximum applied stress on the crack length and the material parameters is given.     

Fracture mechanical analysis of self-fatigue in surface compression strengthened glass plates

This paper presents a fracture mechanical analysis of the static fatigue and spontaneous fragmentation of surface compression-strengthened glass plates in the absence of applied load. It is suggested that if an initial surface crack which is sufficiently deep to penetrate into the tensile zone within the plate interior is introduced into the plate, then static fatigue, and eventually spontaneous fracture may follow. The crack problem for glass plates under various internal stress fields is solved and the stress intensity factor is obtained as a function of the crack depth. Using the fracture toughness and the slow crack growth characterization of the material, the conditions for no crack propagation, crack propagation leading to crack arrest, and that leading to catastrophic failure are established and discussed. The general results obtained are illustrated by means of a numerical example based on a 2 mm thick surface compression-strengthened glass plate exposed to water at 25° C.Such a problem was encountered in relation to an eye-lens during a consulting case by one of the authors (DPHH).     

Fracture mechanics analysis of anisotropic plates by the boundary element method

This paper presents an analysis of mixed mode fracture mechanics problems arising in anisotropic composite laminates. The boundary element method (BEM) and the J _k integral are presented as accurate techniques to compute the stress intensity factors K _I and K _II of two dimensional anisotropic bodies. Using function of a complex variable a decoupling procedure is derived to obtain the stress intensity factors. The procedure is based on the computation of the J ₁-integral and of the ratio of relative displacements at the crack faces, near the crack tip. Applications are presented for unidirectional and symmetric laminates of glass, boron and graphite-epoxy materials. Numerical examples of problems of pure mode I and mixed mode deformations are given, in order to demonstrate the accuracy of the method.     

Fracture of plates with variable thickness

We study the mechanics of fracture of plates with variable thickness weakened by rectilinear through cracks and propose a method for the solution of problems of the theory of elasticity for plates of this kind. We also generalize theoretical results of the investigation of crack propagation in deformable elastoplastic plates to plates with variable thickness and present solutions of new problems in the mechanics of structural arrest of propagating through cracks by local changes in the thickness of platelike structural members near the crack tip. Azerbaijan Technical University, Baku, Azerbaijan. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 46–54, May–June, 1996.     

Fracture of composite plates with periodical edge cracks

The elastostatic properties of two sets of periodically arranged and perfectly bonded strips are investigated under the assumption that every set of strips has edge cracks perpendicular to the interfaces, and that the external loads are applied parallel to the interfaces far away from the crack region. The problem is formulated in terms of a system of singular integral equations and solved numerically to obtain the stress intensity factors.

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Résumé On étudie les propriétés élasto-statiques de deux séries de feuillards arrangés de manière périodique et parfaitement collés, sous l'hypothèse que chaque série de feuillards présente des fissures de bord perpendiculaires à l'interface et que les charges externes sont appliquées parallèlement à ces interfaces et suffisamment loin de la zône de fissuration. Le problème est formulé en terme d'un système d'équations intégrales singulières et résolu numériquement en vue d'obtenir les facteurs d'intensité de contrainte.

     

Fracture of plates which consist of periodic dissimilar strips

In this paper the fracture problem of a composite plate which consists of perfectly bonded parallel load carrying laminates and buffer strips is considered. It is assumed that the fatigue cracks may appear and spread in main laminates or in buffer strips or in both perpendicular to the interfaces. The external load is applied to the plate parallel to the strips and away from the crack region. The problem is solved for fully imbedded cracks and for broken laminates or strips and the corresponding stress intensity factors are calculated.

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Résumé Dans ce mémoire, on considère le problème de la rupture d'une tôle composite constituée de plaques portantes parfaitement collées et soumises à une charge ainsi que de feuillard-amortisseurs.On suppose qu'une fissure de fatigue peut apparaître et se développer dans les plaques principales ou dans le feuillard-amortisseur ou dans les deux et ce perpendiculairement à leur interface. La charge extérieure est appliquée à la tôle parallèlement au feuillard et suffisamment loin de la zône fissurée. Le problème est solutionné dans le cas de fissures complètement noyées et pour des plaques ou des feuillards rompus.Les facteurs d'intensité des contraintes correspondants sont par ailleurs calculés.

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This work was supported by the National Aeronautics and Space Administration under the Grant NGR 39-007-011 and by the National Science Foundation under the Grant GK-42771X.     

Fracture of coated plates and shells under thermal shock

The main interest in this study is in the subcritical crack propagation and fracture of coated materials, specifically of cylindrical shells under repeated thermal shock. First it is shown that the circumferential crack problem in a cylindrical shell may be approximated by a plate on an elastic foundation under plane strain conditions. The thermal shock problem for a layered plate supported by an elastic foundation containing a crack in each layer of arbitrary sizes and locations is then considered. An additional factor studied is the influence of the cooling rate of the plate surface on the stress intensity factors at the crack tips. The problem is formulated in terms of a pair of singular integral equations which are solved for a number of typical crack geometries such as an edge crack, a crack terminating at the interface, an undercoat crack, and a crack crossing the interface. The main results of this paper are the stress intensity factors.     

低温下高强钢缺口板断裂试验

为研究低温下结构钢断裂机理及抗断设防,在冷脆转换温度下(-45 ±2℃)对的个16mm厚Q345钢材缺口板进行了单向拉伸断裂试验,研究了缺口尺寸(a、2b)对结构钢断裂模式的影响.结果表明:试件断裂于刻痕心部,断口心部有一条清晰的起裂棱,宏观断面大致垂直于加载方向;试件缺口愈尖锐或缺口比率(2b/a)愈小,断裂延性愈差...     

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

Adhesively bonded composite patch repair is efficient means to regain load carrying capacity, alleviate the crack growth, and improve the service life of the damaged structure. In this paper, three dimensional finite element models are developed to examine the fracture behavior of a single edge V-notched Aluminum plate repaired with Kevlar-49/epoxy or e-glass/epoxy pre-preg patches on both sides. Contour integral method was used for evaluating the stress intensity factor (SIF), an indicator of the crack stability. The load transfer mechanisms, stress distribution, damage variable (D), and crack mouth opening displacement (CMOD), were also presented to estimate the effectiveness of composite patch repair. The influence of the patch material, crack length and the adhesive thickness has been investigated. Results have shown that the crack induced damage increased nonlinearly with a larger crack size. With the composite patch repairs, SIF is reduced to 1/7–1/10 of that of the bare plate and CMOD decreased by 79%. The damage variable is reduced significantly and the load capacity is increased. A thinner adhesive layer results in a higher percentage of load shared by the composite patch.     

Fracture behavior of cracks in ductile plates under monotonic mixed-mode loading

An experimental study of the early stages of ductile fracture was undertaken by using scanning electromicroscopy (SEM). The variation of several parameters influencing this type of fracture was introduced during the study of the preliminary blunting phase followed by the creation of the damaged ligament in front of the crack which resulted in the initiation of the slow propagation phase. This was achieved by changing the angle of obliqueness, , of the edge cracks made in thin or thick plates of polycarbonate which exemplified cases where predominantly plane stress or plane strain conditions prevailed. The change of the angle influenced drastically the value of the mixed-mode factor = K ₁₁/K ₁. The parameters studied were the crack-tip opening angle (CTOA), the damaged ligament in front of the crack face, the direction and orientation of the subsequent crack initiation and propagation and finally the variation of crack propagation and velocity at the early stage of slow crack propagation. Important results were derived from this experimental study which clarified various aspects of ductile fracture during the initiation of a new step of propagation of the crack.     

Eigen analysis of fiber-reinforced composite plates

Composites plates of various orientation and thickness with fiber-reinforced plastics (FRP) find increasing applications in aerospace and automotive structures (due to their high strength, stiffness to weight ratios, and high damping characteristics). Determination of the dynamic characteristics and the investigation of such structures are essential not only in the design but also in manufacture development.

In the present paper, the eigen analysis of laminated square plates with various fiber orientations, various boundary fixations, and different stacking sequences has been presented and discussed. The experimental analysis and finite element techniques are utilized to study the effect of fiber orientation and boundary conditions on the dynamic characteristics of frequency and mode shapes. The vibrational system technique is utilized for experimental measurements. The results show agreement between experimental and theoretical investigations. Also, these results show a close connection between damping and stiffness characteristics in glass-fiber composites.     

Plane elastostatic analysis of V-notched plates

Solutions are given for several plane elastostatic problems of plates having a V-notch on one edge, and subjected to a variety of boundary conditions. The effect of the magnitude of the V-notch angle and specimen geometry on stress intensity factors K _I and K _II are obtained for unloaded notch surfaces. There is less than one percent difference in opening mode I stress intensity factor in going from a zero degree notch angle to a 30 degree notch angle. Notch opening displacements at the plate edge were measured experimentally and the results obtained were in excellent agreement with the computed results.     

Failure analysis of steel bearing plates

Steel bearing plates appeared to have failed during service due to wear damage. The subsequent failure analysis revealed that the observed surface damage was the result of widespread plastic deformation and smearing associated with a network of surface crazing, rather than wear. Additionally, the majority of the bearing plates examined met microstructural specifications, although both the carbon and manganese contents were below the specified limits. The deficiencies in carbon and manganese lowered the hardenability of the alloy and may have contributed to the need for an overly severe quench during the heat treatment processing employed during manufacture.     

Aerothermoelastic analysis of composite laminated plates

The flutter behavior of a thermally buckled composite laminated plate is investigated in the frequency and time domains using the finite element method. Von Karman large deformation assumptions and quasi-steady aerodynamic theory are employed for the analysis. The effects of temperature gradient, panel length-to-width ratio, fiber orientation, and stacking sequence on aerothermoelastic behavior of the plate are studied in detail. The flutter boundary, buckling boundary, time history response, and phase plane plots of cross-ply and angle-ply laminates are presented. The numerical results show that temperature gradient induces thermal moments and increases the overall stiffness of the plate, and thus may increase the flutter boundary significantly. When the buckle pattern of the plate changes, the eigenvalues of the natural modes are changed suddenly and the sequence of the natural modes may be altered. Therefore, the change in the buckle pattern postpones the coalescence and the flutter boundary may increase. The change in the coalescence pair may also postpone the coalescence and increase the flutter boundary.