Boundary-integral equation analysis of twisted internally cracked axisymmetric bimaterial elastic solids

 Green's function is obtained for the infinite bimaterial elastic solid, containing an internal circular interface crack, loaded by a unit tangential co-axial circular source. An axisymmetric direct boundary integral equation (BIE) is used for the analysis of a finite bimaterial axisymmetric body containing an internal circular interface crack and a finite homogeneous cracked cylinder, both under torsional loading. Using the proposed technique, no discretization of the crack surface is necessary. Numerical results for both examples as obtained by the proposed method are presented and discussed. Received: 29 October 2001 / Accepted: 29 May 2002     

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.     

Analysis of cracked anisotropic plates using the hybrid finite element method

This paper presents a convenient and efficient method to obtain accurate stress intensity factors for cracked anisotropic plates. In this method, a complex variable formulation in conjunction with a hybrid displacement finite element scheme is used to carry out the stiffness and stress calculations of finite cracked plates subjected to general boundary and loading conditions. Unlike other numerical methods used for local analysis such as the boundary element method, the present method results in a symmetric stiffness matrix, which can be directly incorporated into the stiffness matrix representing other structural parts modeled by conventional finite elements. Therefore, the present method is ideally suited for modeling cracked plates in a large complex structure.     

Finite element analysis of anisotropic plates

Two aspects of the finite element analysis of mid-plane symmetrically laminated anisotropic plates are considered in this paper. The first pertains to exploiting the symmetries exhibited by anisotropic plates in their analysis. The second aspect pertains to the effects of anisotropy and shear deformation on the accuracy and convergence of shear-flexible displacement finite element models. Numerical results are presented which show the effects of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.     

A new boundary integral equation method for cracked 2-D anisotropic bodies

By using integration by parts to the traditional boundary integral formulation, a traction boundary integral equation for cracked 2-D anisotropic bodies is derived. The new traction integral equation involves only singularity of order 1/r and no hypersingular term appears. The dislocation densities on the crack surface are introduced and the relations between stress intensity factors and dislocation densities near the crack tip are induced to calculate the stress intensity factors. The boundary element method based on the new equation is established and the singular interpolation functions are introduced to model the singularity of the dislocation density (in the order of ) for crack tip elements. The proposed method can be directly used for the 2-D anisotropic body containing cracks of arbitrary geometric shapes. Several numerical examples demonstrate the validity and accuracy of BEM based on the new boundary integral equation.     

On invariant integrals in the analysis of cracked plates

Bending of cracked plates is considered within a formulation in which transverse shear deformation is taken into account. Path-domain-independent (or invariant) integrals are constructed by separating the strain energies of bending and shear. This separation permits the expression of the three stress intensity factors, which can occur simultaneously under certain loadings, in terms of the integrals mentioned. A numerical implementation is proposed and illustrated by means of a known example. Future applications are discussed in order to solve more complicated configurations.

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Résumé On considère la flexion de tôles fissurées selon une formulation où la déformation par cisaillement transversal est prise en considération. On construit des intégrales indépendantes du domaine ou du parcours (ou intégrales invariantes) en séparant les énergies de déformation en flexion et le cisaillement. Cette séparation permet d'identifier trois facteurs d'intensité de contraintes qui peuvent se présenter simultanément sous certaines charges et qui s'expriment selon les intégrales mentionnées. On propose une présentation numérique et on l'illustre au moyen d'un exemple connu. On discute les applications futures en vue de résoudre des configurations plus complexes.

     

Stiffened cracked plates analysis by dual boundary element method

In this paper a boundary element formulation for analysis of shear deformable stiffened cracked plates is presented. By coupling boundary element formulation of shear deformable plate and two dimensional plane stress elasticity, dual boundary integral equations are presented. The interaction forces between stiffeners and the plate are treated as line distributed body forces along the attachment. Both concentric and eccentric stiffeners have been considered. Rectangular stiffened plate containing a single crack and double cracks subjected to uniform distributed moment on the crack surface and uniform shear load on the plate are analysed by the proposed method. Good agreement has been achieved compared with analytical solutions.     

A generalized collocation method for stress analysis of cracked plates

A generalized collocation method for stress analysis of cracked plates is developed in this paper. The Papkovich-Neuber general solution has been used instead of the Williams stress function. The expressions obtained are very suitable for computer programming. The trial functions can be used for force-boundary conditions as well as displacement-boundary conditions. In this method the conditions on all boundaries are satisfied approximately. As more trial functions are used, more complicated boundary value problems may be analysed. The accuracy and versatility of the method are demonstrated by several interesting examples.     

Three-dimensional finite element analysis of cracked thick plates in bending

By using the finite element technique, stress intensity factors have been obtained for finite rectangular plates and the results have been given for various h/a, W/a and L/W ratios. By using a three-dimensional isoparametric element, the problem has been considered as a three-dimensional one and the variation of stress intensity factor across the plate thickness has been found to be nonlinear.     

Boundary-integral equation method for elastodynamic scattering by a compact inhomogeneity

The set of singular integral equations which relates unknown fields on the surface of the scatterer to a time-harmonic incident wave is solved by the boundary element method. The general method of solution is discussed in some detail for scattering by an inclusion. Results are presented for a spherical cavity, and for a soft and a stiff spherical inclusion. Fields on the surface of the scatterer are compared with previous results obtained by different methods. Back-scattered and forward-scattered displacement fields are presented, both as a function of position at fixed frequency, and as a function of frequency at fixed position. The quasi-static approximation is briefly discussed.     

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.     

Dual boundary element analysis of cracked plates: singularity subtraction technique

The present paper is concerned with the formulation of the singularity subtraction technique in the dual boundary element analysis of the mixed-mode deformation of general homogeneous cracked plates.The equations of the dual boundary element method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation is applied on the other, general mixed-mode crack problems can be solved in a single region boundary element formulation, with both crack surfaces discretized with discontinuous quadratic boundary elements.The singularity subtraction technique is a regularization procedure that uses a singular particular solution of the crack problem to introduce the stress intensity factors as additional problem unknowns. The single-region boundary element analysis of a general crack problem restricts the availability of singular particular solutions, valid in the global domain of the problem. A modelling strategy, that considers an automatic partition of the problem domain in near-tip and far-tip field regions, is proposed to overcome this difficulty. After the application of the singularity subtraction technique in the near-tip field regions, regularized locally with the singular term of the Williams' eigenexpansion, continuity is restored with equilibrium and compatibility conditions imposed along the interface boundaries. The accuracy and efficiency of the singularity subtraction technique make this formulation ideal for the study of crack growth problems under mixed-mode conditions.     

Stress-strain state of microinhomogeneous cracked plates

For the model of a microinhomogeneous body, we determine the distribution of efficient (averaged over microvolumes) components of the stress tensor and study the effects of the parameters of rigidity of the material in micro- and macrovolumes, the dimensions of the selected volume, and the angle of application of the external load on the value of critical (ultimate) stresses in the vicinity of the crack tip and the direction of crack propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 50–56, March – April, 1995.     

Plastic intensity factors for cracked plates

An elastic-plastic analysis is performed for two problems relevant to fracture mechanics: a semiinfinite body with an edge crack in a far out-of-plane shearing field and an infinite plate under plane stress conditions containing a finite line crack in a remote tensile field. Amplitudes of the dominant singularity in the plastic region at the crack tip, the plastic stress and strain intensity factors, are calculated for applied stress levels approaching the yield stress. A technique is developed for using the dominant singular solution in conjunction with the finite element method to make accurate calculations for the near-tip fields. Additionally, a comparative study of deformation theory with flow theory is performed for cracks in an anti-plane shear field. Elastic fracture mechanics is extended to high levels of applied stress for which the plastic zone is no longer small compared to the crack length by relating the critical stress for fracture initiation to the plastic intensity factors.     

Elasto-plastic cracked plates in plane strain

The plane strain behavior of an clasto-plastic cracked plate in tension is examined at two levels of work-hardening. The results are compared to similar data for the case of plane stress

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Zusammenfassung Das Flächenanspannungsverhalten einer elastisch-plastisch gespaltenen Platte unter Spannung wurde in zwei Verfertigungsvorgängen untersucht. Die Ergebnisse warden mit ähnlichen Daten im Bereich von Flächenanspannung verglichen.

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Résumé Le comportement en état plan de déformation d'une tô1e comportant une fissure et soumise à tension dans le domaine é1asto-plastique est examiné pour deux niveaux de taux d'écrouissage. Les résultats sont comparés à ceux que l'on obtient, dans des conditions similaires, en état plan de tension.

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This work was supported by the National Aeronautics and Space Administration Research Grant NGR-39-002-023.     

Elastic-plastic analysis of cracked plates in plane stress: An experimental study

Summary An experimental method is presented for the complete solution of the elastic-plastic plane stress problem of an edge-cracked plate obeying the Mises yield criterion and the Prandtl-Reuss incremental stress-strain flow rule. The material of the plate is assumed as a strain-hardened one with different degrees of hardening. The elastic and plastic components of strain were determined by using the method of birefringent coatings cemented on the surface of the metallic specimens made of the material under study. Normal incidence of circularly polarized light yielded the isolinics and isochromatics of the coating which provided the principal elastic strain differences and strain-directions at the interface. Evaluation of the stress intensity factor at the crack tip, by using the Griffith-Irwin definition, gave the sum of principal stresses at the crack tip. These data were sufficient to separate the components of strain at the coating-plate interface by using the classical shear-difference method.The stress components on the partially plastically deformed cracked plate were determined by using the Prandtl-Reuss stress-strain relationships in a step-by-step process following the whole history of loading of the plate. Thus, a radial distribution law for the equivalent stress and strain in all directions of the plate was established which gave the instantaneous position of the elastic-plastic boundary and its evolution during loading, as well as the distribution of elastic and plastic components of stresses allover the plate.Four cases were solved for various amounts of strain-hardening from a quasi perfectly plastic material to an almost brittle strain hardened one. The values of the characteristic parameters defining each type of material were established.The results derived compare excellently with existing ones based either on experimental or numerical solutions and since they are based on both the theory of elasticity and the incremental theory of plasticity they constitute a sound basis for comparison. Moreover, the algorithm based on this hybrid method is fast and stable requiring a minimum computer time, memory and data preparation.     

General criterion of fracture of cracked plates

International Journal of Fracture -     

Fatigue life prediction of cracked padded plates

The fatigue crack propagation analyses of padded plates are conducted to predict the crack growth behaviour under various loading conditions. The fatigue life of a padded plate with a single edge crack originating from the weld toe is calculated using the weight function approach. The fatigue strength of padded plates with different pad thickness under remote loading conditions was investigated and compared to the T-plate joint. The improvement of the fatigue strength of the pad design is verified.
  The thickness effect of the padded plate was investigated using the fracture mechanics approach. The geometrically similar model pairs with different initial crack sizes were investigated under remote loading conditions. It was shown that the thickness effect depends on both stress concentration and initial crack size.