Stress Intensity Factors In Plates Research Articles

Development of Stress Intensity Factors for Cracks With Large Aspect Ratios in Pipes and Plates

The stress intensity factors (SIFs) for pipes containing semi-elliptical surface cracks with large aspect ratios were calculated by finite-element analysis (FEA). The cracks were circumferential and axial surface cracks inside the pipes. The parameters of the SIFs are crack aspect ratio, crack depth, and the ratio of pipe radius to wall thickness. In comparing SIFs for plates and pipes, it can be clarified that SIFs for both plates and thin pipes with t/Ri ≤ 1/10 are almost the same, and the SIFs for plates can be used as a substitute for pipes with t/Ri ≤ 1/10, where t is the pipe wall thickness, and Ri is the inner radius of the pipe. This means that it is not necessary to provide SIF solutions for pipes with t/Ri ≤ 1/10, and it is suggested that the number of tables for influence coefficient values for pipes can be significantly reduced.

Crack Front Shapes and Stress Intensity Factors in Plates under a Pure Bending Loading that Induces Partial Closure of the Crack Faces

This paper investigates, both experimentally and numerically, stress intensity factors and evolving geometry of through edge cracks in plates loaded under pure transverse bending; the loading induces partial closure of the crack faces. After performing experiments on steel specimens, it was found that a kink in the crack front forms as the crack grows, changing the initial straight front into an L-shape. To understand the distribution of stress intensity factors along such crack fronts, the observed crack shapes were reproduced in a three-dimensional fracture code (FRANC3D) coupled with a finite element analysis program (ABAQUS). With this coupled system, linear elastic stress analyses were performed considering the nonlinear effects caused by the crack face contact in the compressed region. The proposed methodology computes stress intensity factors along the crack front based on observed crack front shapes obtained from the experimental tests. A method is proposed to treat numerical noise around the crack front kink and at crack front end. In addition, normalized empirical expressions for stress intensity factors are proposed.

Computation of stress intensity factors for through cracks in plates using p‐version finite element method

AbstractThe present study concerns the analysis of bending of plates and shells subjected to various boundary conditions and load. Bending stress intensity factors for plates containing through‐thickness crack under edge bending load are evaluated. To accomplish this task, hierarchical degenerated plate/shell and crack‐tip singular plate/shell elements were developed.The hierarchical degenerated plate shell element has four corner nodes, four mid‐side nodes and one central node on the mid‐surface of the shell geometry with five degrees of freedom at each node. p‐Version shape functions up to order seven were used for defining the displacement field. Enriching the displacement field with the asymptotic displacement field near the crack tip, a crack‐tip singular plate/shell element was developed. Some benchmark problems were analyzed and compared. Analyses were performed to obtain the stress intensity factors of plate with through‐thickness crack using singular hierarchical degenerated plate/shell element around the crack tip. Numerical results obtained from the present element formulations are compared with analytical/numerical solutions available from literature. It is inferred that numerical results are in good agreement with the benchmark plate and shell problems. Copyright © 2007 John Wiley & Sons, Ltd.

Computation of stress intensity factor in cracked plates under bending in static and fatigue by a hybrid method

A hybrid weight-function technique is presented. It consists of dividing an elliptical crack into two zones, then using the appropriate weight function in the area where it is more efficient. The proportion between zones is determined by optimizing two crack parameters (axis ratio and curvature radius). Stress intensity factors for plates containing elliptical and semi-elliptical cracks are hence computed by a self developed computer code. Static and fatigue loadings of bending are considered. The results found by the present approach are in good correlation with the analytical solutions (when available) as well as with those of other researchers.

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress- or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

ANALYTICAL DETERMINATION OF STRESS INTENSITY FACTOR FOR PLATE BENDING PROBLEMS

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 109-119 (2003) No AccessANALYTICAL DETERMINATION OF STRESS INTENSITY FACTOR FOR PLATE BENDING PROBLEMSLALITHA CHATTOPADHYAYLALITHA CHATTOPADHYAYAdvanced Research Group, Structures Division, National Aerospace Laboratories, P.O. Box 1779, Kodhihalli, Bangalore 560 017, India Search for more papers by this author https://doi.org/10.1142/S1465876303000776Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an isotropic elastic plate of constant thickness is examined. The plate containing cracks is infinite and its boundary is subjected to bending moment or twisting moment. Using classical plate theory and integral transform techniques, the general formulae for the bending moment, twisting moment and bending stress distribution in an elastic plate acted upon by moment forces and containing cracks located on a single line are derived. The solution is obtained in detail, for the case in which there is a single crack in an infinite plate and the bending stress intensity factor is determined in a closed form and the results are compared with those obtained from finite element analysis. Close agreements between the analytical solution, numerical solution and reference solution were found in all cases.Keywords:Stress intensity factorplatecrackbendingintegral transform References M. L. Williams, ASME J. Appl. Mech. 28, 78 (1961). Crossref, Google ScholarG. C. Sih, P. C. Paris and F. Erdogan, ASME J. Appl. Mech. 29, 306 (1962). Crossref, Google ScholarJ. K. Knowles and N. M. Wang, J. Math. Phys. 39, 223 (1960). Crossref, Google ScholarR. S. Alwar and K. N. Ramachandran, Eng. Fracture Mech. 17, 323 (1983), DOI: 10.1016/0013-7944(83)90083-8. Crossref, Google ScholarE. Reissner, Quart. Appl. Math. 5, 55 (1947). Crossref, Google ScholarM. J. Vizet al., Int. J. Fracture 72, 21 (1995). Crossref, Google ScholarA. Zucchini, C.-Y. Hui and A. T. Zehnder, Int. J. Fracture 104, 387 (2000), DOI: 10.1023/A:1007699314793. Crossref, Google Scholar S. P. Timoshenko , Theory of Plates and Shells ( McGraw Hill Book Company , Auckland , 1959 ) . Google Scholar I. N. Sneddon , Use of Integral Transforms ( McGraw Hill Book Company , New York , 1972 ) . Google ScholarE. F. Rybicki and M. F. Kanninen, Eng. Fracture Mech. 9, 931 (1977), DOI: 10.1016/0013-7944(77)90013-3. Crossref, Google Scholar Y. Murakami , Stress Intensity Factors Handbook 2 ( Pergamon Press , Oxford , 1987 ) . Google Scholar FiguresReferencesRelatedDetailsCited By 3Two-Dimensional Crack and Contact Problems – Transform MethodArabinda Roy and Rasajit Kumar Bera6 Dec 2019EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENTLALITHA CHATTOPADHYAY, S. SRIDHARA MURTHY and S. VISWANATH20 November 2011 | International Journal of Computational Methods, Vol. 04, No. 02Analytical Solution for an Orthotropic Elastic Plate Containing CracksLalitha Chattopadhyay1 Aug 2005 | International Journal of Fracture, Vol. 134, No. 3-4 Recommended Vol. 04, No. 01 Metrics History Received 28 August 2002 Accepted 24 January 2003 KeywordsStress intensity factorplatecrackbendingintegral transformPDF download

Determination of stress intensity factors in plates near convex curvilinear cracks

Determination of stress intensity factors in plates near convex curvilinear cracks

Photoelastic determination of mixed mode stress intensity factors for sharp reentrant corners

This paper uses photoelasticity and digital image analysis to develope an algorithm for determining stress intensity factors (SIFs) in 90° reentrant corners. To utilize the advantage of “whole-field” photoelasticity and to minimize the random experimental errors, the overdeterministic least squares method of Sanford combined with Newton-Raphson method is used to obtain SIFs. The algorithm is used to determine SIFs in plates with 90° reentrant corner(s) and the obtained SIFs agree well with the available numerical and theoretical values.

Stress intensity factors of plates under tensile load with welded-on flat side gussets

The effects of stress concentrations on stress intensity factors at plates under tensile load with welded-on flat side gussets have been studied. The correction function Yu of the crack configuration has been split into a function for the general configuration Y and a function for the local stress concentration Mk due to the weld and the gusset. The Mk values have been calculated by finite element analysis and by a simplified procedure based on the weight function approach. The results have been interpolated, giving a parametric formula for a wide range of variation in dimensions.

Two‐level finite element method for plane cracks

AbstractA new method to evaluate the stress intensity factors for plates of arbitary shape by conventional finite elements is introduced. The problems of the large number of unknowns and the round‐off errors associated with fine meshes are eliminated by means of global interpolation functions. These global interpolation functions are actually the analytical solutions of the displacement patterns near the crack tips. While the analytical solutions do not satisfy the boundary conditions in general, the present method considers the boundary conditions by master nodes. Very few unknowns can predict accurate results and no unconventional finite elements are required. The stress intensity factors can be calculated from the nodal displacements of the super‐element in one go. Plates with single and double notch edges and centre crack are taken as examples. The method can be generalized to other crack problems without difficulty.

Stress-intensity factors in plates with a partially patched central crack

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of patches is related to the reduction they cause in the stress-intensity factor of the crack. Hence, an accurate evaluation of SIF in terms of various parameters is required for reliable patch design. In this paper, the influence of patch parameters on the opening-mode stress-intensity factor for a plate with a central crack is studied by employing transmission photoelasticity. Cracked plates made of photoelastic material are patched on one side as well as both sides by epoxy, phenolic and E glass-epoxy composite materials. 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 50 magnification, converted into a polariscope. Irwin's method with extrapolation is employed to compute the stress-intensity factor from photoelastic data. The reduction in the stress-intensity factor is presented in graphic form as a function of pathch parameters, namely stiffness, width and length.

The effect of a stiffener on a cracked plate under skew-symmetric loading

In this paper, the title problem is studied by using Reissner's transverse shear theory. The main purpose of the paper is to investigate the effect of a stiffener on the stress intensity factors in plates under twisting moments and/or transverse shear loads. The asymptotic stress state near the crack tip terminating at the stiffener is examined, and normalized Mode II and Mode III stress intensity factors are tabulated for various crack geometries. The results also include the effect of Poisson's ratio, stiffness constants and material orthotropy for specially orthotropic materials on the stress intensity factors.

Determination of the dynamic stress intensity factors in plates with cracks in pulsed loading

Determination of the dynamic stress intensity factors in plates with cracks in pulsed loading

Study on cracked plates, shells and three dimensional bodies

This paper presents a summary of the authors' recent work in following areas: (1) The stress-strain fields at crack tip in Reissner's plate. (2) The calculations of the stress intensity factors in finite size plates. (3) The stress-strain fields at crack tip in Reissner's shell. (4) The calculations of the stress intensity factors and bulging coefficients in finite size spherical shells. (5) The stress-strain fields along crack tip in three dimensional body with surface crack. (6) The calculation of stress intensity factors in a plate with surface crack.

Stress intensity factors for plates in flexure

SummaryA method for determining stress intensity factors for cracked plates is proposed. The method uses a generalisation of Westergaard's stress functions to describe the stress intensity at the crack. Eigenfunctions of angular regions are used to satisfy the boundary conditions.

Internal and Edge Cracks in a Plate of Finite Width Under Bending

In this paper the title problem is studied by using Reissner’s transverse shear theory. The main purpose of the paper is to investigate the effect of stress-free boundaries on the stress intensity factors in plates under bending. Among the results found particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. Also studied is the effect of Poisson’s ratio on the stress intensity factors.

Influence of crack closure on the stress intensity factor for plates subjected to bending—A 3-D finite element analysis

Plates with central through cracks subjected to bending is analysed taking into account the closure of the crack faces on the compression side. A three-dimensional finite element method employing three-dimensional degenerate solid element is used for the analysis. The crack faces have been modelled such that they come in contact over an area on the compression side and interfere with each other. The influence of the crack closure on the variation of the stress intensity factor across the plate thickness is obtained for finite and infinite plate geometries.

An investigation of stress intensity factors for plates with equal and unequal parallel edge cracks

A semi-theoretical and experimental method is used to investigate thin plates with parallel edge cracks of equal and unequal length loaded in tension. Plates with equal and unequal periodic parallel edge cracks are treated under two separate cases:

Stress intensity factors from reflected caustics in birefringent plates with cracks

In the present paper the method of reflected caustics is used for the evaluation of stress intensity factors in plates made of birefringent materials with a crack submitted to the opening mode of loading. It has already been established that due to the optical anisotropy of the material the rays reflected from the rear face of the plate form a double caustic. In this paper the influence of the optical anisotropy factor ξ of the material on the relative position and sizes of the two constituent branches of the caustic is studied. Nomograms are given for the accurate evaluation of mode I stress intensity factors from the geometrical characteristics of the two branches of the caustic. A series of tests, undertaken on plates made of polycarbonate of bisphenol A with ξr = 0.153, showed that the accuracy of evaluation of κI is the same as with the same method applied to optically inert materials.