A precise computation of stress intensity factor on the front of a convex planar crack (original) (raw)
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Computing stress intensity factors for curvilinear cracks
International Journal for Numerical Methods in Engineering, 2015
The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. We formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles the one of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates, and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method on the size of the domain of integration.
Effect of curvature at the crack tip on the stress intensity factor for curved cracks
International Journal of Fracture, 1993
In this paper, the numerical solution of the hypersingular integral equation using the body force method in cucved crack problems is presented. In the body force method, the stress fields induced by two kinds of standard set of force doublets are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form r-2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density functions and power series. The calculation shows that the present method gives rapidly converging numerical results for curved cracks under various geometrical conditions, In addition, a method of evaluation of the stress intensity factors for arbitrary shaped curved cracks is proposed using the approximate replacement to a simple straight crack.
The Effect of the Size and Position of the Crack on the Normalized Stress Intensity Factor
Algerian Journal of Renewable Energy and Sustainable Development
In this work, finite element method was used to determine the normalized stress intensity factors for different configurations. For this, a 2-D numerical analysis with elastic behavior was undertaken in pure I mode. This simulation was carried out using a numerical calculation code. On the basis of the numerical results obtained from the different models treated, there is a good correlation between the nodal displacement extrapolation method (DEM) and the energy method based on the Rice integral (J) to evaluate the normalized stress intensity factors and this for different crack lengths. For each configuration, the increase in the crack size causes an amplification of normalized intensity stresses fators.
Stress Intensity Formulas for Three-dimensional Cracks in the Vicinity of an Interface
Journal of Testing and Evaluation, 2007
In this study, stress intensity formulas are considered in terms of the square root of area parameter to evaluate arbitrary shaped defects or cracks in lhe vicinity of an interface. Here "area" is the projected area of the defect or crack. Stress fatens ity factors for an elliptical crack parallel to a bimaterial interface are considered with varying the distance, aspect ratio of the crack, and combinations of materia l's elastic constants. Also, stress intensity factors of an interface crack and a crack in a functionally graded material are investigated. Then, it is found that the maximum stress intensity factors normalized by the square root of area are always insensitive to the crack aspect ratio. They are given in a form offonnulas useful for engineering applications.
The three-dimensional stress intensity factor due to the motion of a load on the faces of a crack
Quarterly of Applied Mathematics
The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of a pair of point loads that move in a direction perpendicular to the crack edge, is considered. The exact expression for the mode I stress intensity factor as a function of time for any point along the crack edge is obtained by extending a procedure recently introduced by Freund [1], The method of solution is based on integral transform methods and the theory of analytic functions of a complex variable. Some features of the solution are discussed and graphical results for various point load speeds are presented.
International Journal of Solids and Structures, 2006
The present work deals with an evaluation of stress intensity factors (SIFs) along straight crack fronts and edges in three-dimensional isotropic elastic solids. A new numerical approach is developed for extraction, from a solution obtained by the boundary element method (BEM), of those SIFs, which are relevant for a failure assessment of mechanical components. In particular, the generalized SIFs associated to eigensolutions characterized by unbounded stresses at a neighbourhood of the crack front or a reentrant edge and also that associated to T-stress at the crack front can be extracted. The method introduced is based on a conservation integral, called H-integral, which leads to a new domain-independent integral represented by a scalar product of the SIF times some element shape function defined along the crack front or edge. For sufficiently small element lengths these weighted averages of SIFs give reasonable pointwise estimation of the SIFs. A proof of the domain integral independency, based on the bi-orthogonality of the classical two-dimensional eigensolutions associated to a corner problem, is presented. Numerical solutions of two three-dimensional problems, a crack problem and a reentrant edge problem, are presented, the accuracy and convergence of the new approach for SIF extraction being analysed.
Numerical estimation of stress intensity factors in patched cracked plates
Engineering Fracture Mechanics, 1987
The fatigue and fracture performance of a cracked plate can be substantially improved, by providing patches as reinforcements. The effectivenessof 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 crack, patchand adhesive parameters. In this investigation a finite element technique to compute the SIF through the J-integral for patched cracked plates is presented. TRIM6 and TRUMPL elements of ASKA are employed to model cracked sheet and cracked sheet-adhesives-patch regions, respectively. Path independency of J-integral for unpatched plates is shown by considering many contours. For patched plates, the contours chosen do not enclose the patch-cracked sheet region. The values of SIF's are obtained for unpatched edgecracked, un patched centre-cracked and patched centre-cracked plates. These values are compared with the analytical and numerical results existing in the literature. This study shows that conventional finite elements can be used to model patched cracks and reasonable estimate of SIF can be made via the i-integral. NOTATION IJ" CTy,a,y G" G,., GX>' E'. i-integral Contour surrounding the crack tip Traction vector defined according to the outward normal along r, Fig. I Displacement vector at a point on contour, ii = iu+jv Arc length along the contour Crack length and semi crack length for edge crack and centre-crack plates respectively Width and semi witith for edge-crack and centre-crack plates respectively Length of plates State of stress at a point (x, y) State of strain at a point (x, y) Young's modulus of the cracked plate Strain energy density, 1/2 (atGt +CTyEy +ax).Ex)'
Stress Intensity Factors of an Interface Crack under Polynomial Distribution of Stress
Journal of Solid Mechanics and Materials Engineering, 2010
In this paper, stress intensity factors for a two-dimensional interface crack under polynomial distribution of stress are considered. The problem is formulated as a system of hypersingular integral equations on the idea of the body force method. In this analysis, unknown body force densities are approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack under constant distribution of stress exactly. The stress intensity factors of a 2D interfacial crack under polynomial distribution of stress are expressed as formulas for the reader's convenience with the varying polynomial exponent n. The exact expressions of crack opening displacements are also indicated.