Computation of membrane and bending stress intensity factors for thin,cracked plates

The crack tip stress fields for plate bending and membrane loading problems are reviewed and the four stress intensity factors that determine these fields are defined. These four stress intensity factors arise from use of Kirchhoff plate theory to account for the bending loads and two dimensional plane stress elasticity to account for the membrane loads. The energy release rate is related to the stress intensity factors and to the stress resultants of plate theory. Virtual crack extension, nodal release and modified crack closure integral methods are discussed for computing components of the energy release rate from finite element analyses of cracked plates. Sample computations of stress intensity factors for single and mixed mode cases are presented for a crack in an infinite plate. Sample computations of stress intensity factors for a double edge notched tension-torsion test specimen are given as well.School of Civil and Environmental Engineering, Cornell University     

A Mohr-circle graphical method for stress intensity factors in cracked plates under different loadings

The concept of the stress intensity factor circles (SIF circles) was introduced in this paper, as well as the correlation of these circles with Mohr's circles. The main advantage of this graphical representation is the facility in establishing a one-to-one correlation between the values of the angle of a slant crack in a cracked plate submitted to a biaxial normal loading at infinity and different loading modes at infinity. Moreover, the definition of a general transformation of any biaxial state to another equivalent one, such that the stress intensity factors remain invariant in both states, was also established and discussed. The special cases where the reduction of any biaxial state to that of equal tension-tension at infinity, or uniaxial tension, or equal tension-compression, are also investigated. The method yields the possibility of replacing biaxial tests in cracked plates, which are difficult to be executed with the appropriate accuracy and convenience, with uniaxial ones, which are much easier and accurate than the biaxial ones. Examples indicate the validity and the simplicity of the method.     

Determination of stress intensity factors in cracked plates by the finite element method

Stress fields near crack tips in an elastic body can be specified by the stress intensity factors which are closely related to the stress singularities arising from the crack tips. These singularities, however, cannot be represented exactly by conventional finite element models. A new method for the analysis of stresses around cracks is proposed in this paper on the basis of the superposition of analytical and finite element solutions. This method is applied to several two-dimensional problems whose solutions are obtained analytically, and it is shown that their numerical results are in excellent agreement with analytical ones. Sufficiently accurate results can be obtained by the conventional finite element analysis with rather coarse mesh subdivision. Computational efforts are then considerably reduced compared with other methods.     

The stress intensity factor for a double edge cracked plate by boundary collocation method

A set of complex functions for the double edge cracked plate is proposed. The boundary collocation method is used for estimating the stress intensity factors and the results obtained by this method compare very favorably with existing solutions for many cases.

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Résumé On propose un jeu de fonctions complexes pour représenter une plaque fissurée sur ses deux bords. On utilise la méthode de collocation des limites pour estimer les facteurs d'intensité de contraintes. Dans de nombreux cas, les résultats obtenus par cette méthode supportent très favorablement la comparaison avec les solutions existantes.

     

Photoelastic determination of stress intensity factors in patched cracked plates

In this paper, the influence of patch parameters on stress intensity factors in edge cracked plates is studied by employing transmission photoelasticity. Edge cracked plates made of photo-elastic material are patched on one side only by $\text{E}$ glass-epoxy and carbon-epoxy unidirectional composites. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of magnification 50, converted into a polariscope. Irwin's method is used to compute stress intensity factors from photoelastic data. The reduction in stress intensity factors is presented in graphical form as a function of patch parameters, namely stiffness, location and length. An empirical equation connecting reduction in stress intensity factor and these patch parameters is presented.     

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.     

Assessment of stress intensity factor and aspect ratio variability of surface cracks in bending plates

In this paper, a closed-form solution for the stress intensity factor (K) of semielliptical surface cracks in plates subjected to pure bending, obtained by Newman and Raju using 3D finite elements, is critically evaluated. This solution is compared to a recommended solution by the Society of Experimental Stress Analysis (SESA). It is also compared to photoelastic K measurements. In addition, in this study the aspect-ratio variability of surface cracks under fatigue loading is predicted and compared with experimental data and also with the predictions of other empirical equations proposed by Porten, Kawahara and Kurihara, and lida. Finally, the usefulness of this equation for the prediction of fatigue life of surface cracks is evaluated by a comparison with experimental results.     

Analytical calculation of the stress intensity factor in a surface cracked plate submitted to thermal fatigue loading

A stainless steel specimen with a pre-existing surface notch is exposed to a convective medium of cyclic temperature. The history of stress intensity factor of the cracked body for different crack lengths is obtained by a closed-form integration of the stress field, using Duhamel’s theory with principle of superposition and appropriate weight functions. The obtained results are compared with numerical simulations performed with ABAQUS and they appear to be in very good agreement. The stress intensity factor history shows that fatigue behavior does not depend only on temperature amplitude ΔT=T_max-T_min, quenching rate, and duration of thermal shock but also on heating rate and duration.     

Evaluation of stress intensity factor and fatigue growth of surface cracks in tension plates

A closed form solution for the stress intensity factor (K) of semielliptical surface cracks in tension plates, obtained by Newman and Raju using 3D finite elements, is critically evaluated. This solution is compared to a recommended solution by the Society of Experimental Stress Analysis (SESA). It is also compared to photoelastic K-measurements. In addition, the aspect ratio variability of surface cracks under fatigue loading is predicted and compared with experimental data and also with the predictions of other empirical equations proposed by Portch, Kawahara et al. and Iida. Finally, the usefulness of this equation for the prediction of fatigue life of surface cracks is evaluated by a comparison with experimental results.     

Stress intensity solutions for cracked plates by the dual boundary method

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved. __________ Translated from Problemy Prochnosti, No. 5, pp. 81–93, September–October, 2007.     

Edge function analysis of stress intensity factors in cracked anisotropic plates

The edge function method, which involves the use of analytic solutions to model field behavior in the various parts of an elastic region, is applied to the analysis of a finite anisotropic plate with a single crack. Analytical solutions for the stress singularities at each crack tip facilitate the inexpensive calculation of accurate values of the stress intensity factors. A boundary Galerkin variational principle is used to match the boundary conditions. The method is applicable to isotropic and anisotropic materials and is demonstrated for a number of fracture problems involving variation of the crack position, crack orientation and material orientation. For the range of geometries examined in this paper, the calculated values of the stress intensity factors do not show a major dependence on the material anisotropy. The formulation of the method makes it easily applicable to the study of the interaction of several cracks and also to a limited study of crack propagation or damage development in a composite laminate.     

Stress intensity factor for a cracked specimen under compression

For a cracked specimen under compression, a set of complex stress functions is proposed and by using the boundary collocation method, the unknown coefficients of these complex stress functions are determined. Based on the calculation results of the boundary collocation method, the formulas of the stress intensity factor for a cracked specimen under compression are obtained, and by using these formulas, the influence of confining stress on stress intensity factor is analyzed.     

An investigation of the stress intensity factor for a finite internally cracked plate by using variational method

The eigenfunction expansion variational method (EEVM) is proposed to determine the stress intensity factors for two-dimensional cracked bodies. In the new method, the undetermined coefficients in the truncated eigenfunction expansion form are determined by using the variational method. It is expected that the uncertainty initiated in boundary collocation scheme can be avoided. Several numerical examples are given, which can prove the efficiency of the EEVM method.     

Method of determining bending stress intensity coefficients for cracked ferroconcrete components

Summary A method is proposed for calculating the stress intensity coefficient in a ferroconcrete element containing a crack in bending with reinforcement by rods. A three-dimensional solution has been obtained. The attachment of the reinforcement to the concrete is incorporated.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 3, pp. 98–104, May–June, 1992.     

Three-dimensional stress intensity factor calibration for a stiffened cracked plate

Three-dimensional finite element analyses are used in this paper to calibrate the stress intensity factor in a cracked stiffened plate subjected to remote uniform traction. An accurate numerical determination of the stress field and stress intensity variation through the thickness of a central cracked plate was first carried out in order to evaluate three-dimensional effects. A stiffened cracked plate was then analysed, taking into account the results and the conclusions obtained in the previous study. Such a structure was chosen due to the growing interest for large integral metallic structures for aircraft applications, following the continuous need for low cost and the emergence of new technologies. The J-Integral technique was used to calculate the values of the stress intensity factor along the plate thickness. The plane strain behaviour near the crack front and the variation of the opening stress are discussed.     

Eigenfunction expansion variational method for stress intensity factor and T-stress evaluation of a circular cracked plate

Summary In this paper, the eigenfunction expansion variational method (Abbreviated as EEVM) is developed to solve the T-stress problem of the circular cracked plate. In the traction boundary value problem, EEVM is equivalent to the theorem of least potential energy in elasticity. Therefore, EEVM possesses a clear physical meaning. EEVM does not need any boundary collocation scheme. For the circular cracked plate, the following boundary value problems are solved: (a) with a uniform normal loading on the boundary, (b) with a partial loading on the boundary, (c) under mixed boundary condition. For the circular cracked plate with applied concentrated forces, after using the superposition principle and EEVM, the boundary value problem is solved. In the numerical examples, many computed results for stress intensity factor (SIF) and T-stress are presented. Some of computed results for T-stress are first presented in this paper.     

Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions

This paper is concerned with the analysis of stress intensity factors of a strip with a longitudinal crack subject to tension and bending along its edges, and the tension of rectangular plates with a central crack. For both problems three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered.Analysis is based on Laurent expansions of the complex potentials satisfying the stress free relations along the crack.The expansion coefficients are determined from boundary conditions along outer edges, by using a perturbation technique in the first problem and a boundary collocation procedure based on resultant forces and mean displacements in the second problem. Numerical calculations are performed for various plate configurations, and the results are summarized in forms ready for practical use. The accuracy of numerical results are also examined, and they are regarded as correct up to four figures.