Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

Contact Analysis for Collinear Multiple Cracks in Residual Stress Field

1994 ◽  
Vol 116 (2) ◽  
pp. 169-174 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Plate ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Crack Face

A method is proposed for analyzing stress intensity factors and crack profiles for collinear multiple cracks perpendicular to welded joints in an infinite plate. Using the basic solution of a single crack and taking unknown density of fictitious tractions, Fredholm integral equations and algebraic equations are formulated based upon traction-free conditions and crack face displacements, respectively. These equations are solved simultaneously, considering the contact effect of crack surfaces. Using the derived density of fictitious tractions, the stress intensity factors and displacements of multiple cracks are determined. Some numerical examples are analyzed.

Stress Intensity Factors for Multiple Cracks in an Adhesively Bonded Sandwich Sheet

1993 ◽  
Vol 115 (1) ◽  
pp. 134-139 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mutual Interaction ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Shear Stresses ◽  
Basic Solution ◽  
Intensity Factors ◽  
Adhesively Bonded ◽  
Sandwich Sheet

A new method is proposed for analyzing stress intensity factors of multiple cracks in an adhesively bonded metallic sandwich sheet. Using a basic solution of a single crack and taking unknown density of surface tractions and adhesive shear stresses, Fredholm integral equations and compatibility equations are formulated based upon stress free condition along each crack and displacement continuity between the sheets and adhesive layers, respectively. These equations are solved simultaneously, and the stress intensity factors of multiple cracks are determined from the derived density of tractions. It is shown that the mutual interaction of multiple cracks in a sandwich sheet is smaller than that in a monolithic sheet. Also, mutual interaction of cracks in the same sheet is smaller than that of cracks in the different sheets.

A Crack in an Anisotropic Layered Material Under the Action of Impact Loading

1988 ◽  
Vol 55 (1) ◽  
pp. 120-125 ◽  
Author(s):  
W. T. Ang
Keyword(s):  
Stress Intensity ◽  
Laplace Transform ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Impact Loading ◽  
Layered Material ◽  
Fredholm Integral Equations ◽  
Transform Domain ◽  
Intensity Factors ◽  
The Laplace Transform

The problem of a plane crack in an anisotropic layered material under the action of impact loading is considered in this paper. The problem is reduced in the Laplace transform domain to a set of simultaneous Fredholm integral equations of the second kind. Once these integral equations are solved, the crack tip stress intensity factors in the Laplace transform domain may be readily calculated. The dynamic stress intensity factors can then be obtained through the use of a numerical technique for inverting Laplace transforms. Numerical results are given for specific examples involving particular transversely isotropic materials.

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

1999 ◽  
Vol 67 (3) ◽  
pp. 606-615 ◽  
Author(s):  
W.-H. Chen ◽  
C.-L. Chang ◽  
C.-H. Tsai
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Laplace Transform ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Alternating Method ◽  
The Laplace Transform

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

The Mixed-Mode Fracture Analysis of Multiple Embedded Cracks in a Semi-Infinite Plane by an Analytical Alternating Method

2002 ◽  
Vol 124 (4) ◽  
pp. 446-456 ◽  
Author(s):  
Chih-Yi Chang ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Fundamental Solutions ◽  
Multiple Cracks ◽  
Mixed Mode Fracture ◽  
Infinite Plane ◽  
Intensity Factors ◽  
Alternating Method ◽  
Mode Stress

An efficient analytical alternating method is developed in this paper to evaluate the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane. Analytical solutions of a semi-infinite plane subjected to a point force applied on the boundary, and a finite crack in an infinite plane subjected to a pair of point forces applied on the crack faces are referred to as fundamental solutions. The Gauss integrations based on these point load fundamental solutions can precisely simulate the conditions of arbitrarily distributed loads. By using these fundamental solutions in conjunction with the analytical alternating technique, the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane are evaluated. The numerical results of some reduced problems are compared with available results in the literature and excellent agreements are obtained.

Eccentric annular crack under general nonuniform internal pressure

2016 ◽  
Vol 25 (3-4) ◽  
pp. 69-76 ◽  
Author(s):  
S. Moeini-Ardakani ◽  
M.T. Kamali ◽  
H.M. Shodja
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Analytical Approach ◽  
Fredholm Integral Equations ◽  
Crack Model ◽  
Intensity Factors ◽  
Rigorous Solution ◽  
Annular Crack ◽  
Uniform Tension

AbstractFor a better approximation of ring-shaped and toroidal cracks, a new eccentric annular crack model is proposed and an analytical approach for determination of the corresponding stress intensity factors is given. The crack is subjected to arbitrary mode I loading. A rigorous solution is provided by mapping the eccentric annular crack to a concentric annular crack. The analysis leads to two decoupled Fredholm integral equations of the second kind. For the sake of verification, the problem of a conventional annular crack is examined. Furthermore, for various crack configurations of an eccentric annular crack under uniform tension, the stress intensity factors pertaining to the inner and outer crack edges are delineated in dimensionless plots.

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