The Elliptical Crack Subjected to Nonuniform Shear Loading

1974 ◽  
Vol 41 (2) ◽  
pp. 502-506 ◽  
Author(s):  
F. W. Smith ◽  
D. R. Sorensen
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Surface ◽  
Shear Loading ◽  
Elliptical Crack ◽  
Graphical Form ◽  
Shear Stresses ◽  
Intensity Factors ◽  
Degree Polynomial

The equations of elasticity are solved for the problem of a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. The shear stresses are prescribed independently in two directions on the crack surface and are expressed in the form of a third-degree polynomial. Mode two and mode three stress-intensity factors are presented in analytical and graphical form as functions of position along the crack border.

Dynamic Behavior of an Orthotropic Material Containing a Central Crack

1989 ◽  
Vol 111 (2) ◽  
pp. 172-176 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Orthotropic Material ◽  
Crack Surface ◽  
Frequency Factor ◽  
Wave Frequency ◽  
Intensity Factors ◽  
Central Crack ◽  
Material Constants ◽  
Principal Axes

The dynamic response of a central crack in an orthotropic material is investigated. The crack is situated along one of the principal axes of the material. The load is harmonic in time and normally applied to the crack surface. The Fourier transform is used to solve the dynamic fracture problem, and the results are simplified through a complete contour integration. The dynamic stress intensity factor is obtained in an exact expression in terms of the frequency factor and the material constants. The frequency factor is defined as the product of the wave frequency and the half-crack length, divided by the shear wave speed. Glass/epoxy and graphite/epoxy composite materials are used as example materials in calculating the numerical values of the stress intensity factors. The maximum values of the stress intensity factors are shown to be dependent on the value of the nondimensional frequency factor and the material anisotropy. The motion of the crack surface is also investigated. The crack surface distortion from the associated static crack shape also depends on the wave frequency and the orthotropic material constants.

Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method

1982 ◽  
Vol 104 (4) ◽  
pp. 299-307 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Pressure Vessels ◽  
Pressure Loading ◽  
Intensity Factors ◽  
Alternating Method ◽  
Magnification Factors

An alternating method, in conjunction with the finite element method and a newly developed analytical solution for an elliptical crack in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. The problems considered in the present paper are: (i) an outer semi-elliptical surface crack in a thick cylinder, and (ii) inner semi-elliptical surface cracks in a thin cylinder which were recommended for analysis by the ASME Boiler and Pressure Vessel Code (Section III, App. G, 1977). For each crack geometry of an inner surface crack, seven independent loadings, such as internal pressure loading on the cylinder surface and polynomial pressure loadings from constant to fifth order on the crack surface, are considered. From the analyses of these loadings, the magnification factors for the internal pressure loading and the polynomial influence functions for the polynomial crack surface loadings are determined. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived by using the polynomial influence functions to check the internal consistency of the present analysis. These values agree excellently with the magnification factors obtained directly. The present results are also compared with the results available in literature.

scholarly journals Compression and Shear Fracture Analysis of Boundary Cracks Containing Water in Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhensheng Yang ◽  
Fulin Li ◽  
Tianran Ma
Keyword(s):  
Stress Intensity ◽  
Friction Coefficient ◽  
Stress Intensity Factors ◽  
Underground Mining ◽  
Shear Fracture ◽  
Water Environment ◽  
Initial Crack ◽  
Open Boundary ◽  
Shear Stresses ◽  
Intensity Factors

In order to conserve the water resource during underground mining, the fracture and mechanical properties of rock are important for the stability of water-resisting layers, especially for the fracture behavior of boundary cracks containing water in rock. Considering the swelling of rock under water environment and the influence of water on rock, the stress intensity factors of modes I and II are derived for boundary cracks in rock under compressive and shear stresses. The cracks are divided into the closed and open states. The effects of the crack inclination angle, friction coefficient between crack surfaces, and initial crack length on stress intensity factors are also taken into account. The stress intensity factors for closed and open boundary cracks are verified by numerical and physical experiments, respectively, and the deviation of the results is within 5%. It is shown that pore pressure has different effects on the relationship between stress intensity factor and friction coefficient under different lateral pressures. The effect of water on crack propagation is mainly due to the deterioration of the fracture toughness of the rock. It is found that the critical coefficient λc is a key parameter to determine whether the boundary crack propagates in rock under compression-shear stress. Further studies should be performed to apply the present fracture theory to rock mass or water-resisting layers.

scholarly journals Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

2002 ◽  
Author(s):  
Patrick Le Delliou ◽  
Bruno Barthelet
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Atomic Energy Commission ◽  
Finite Thickness ◽  
Elliptical Crack ◽  
Intensity Factors ◽  
Normal Loading ◽  
Influence Coefficients ◽  
Wide Range

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

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