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.

Interface Crack Between Two Dissimilar Half Spaces Subjected to a Uniform Heat Flow at Infinity—Open Crack

1990 ◽  
Vol 57 (2) ◽  
pp. 359-364 ◽  
Author(s):  
An-Yu Kuo
Keyword(s):  
Thermal Stress ◽  
Stress Intensity ◽  
Temperature Distribution ◽  
Heat Flow ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Surface ◽  
Open Crack ◽  
Intensity Factors ◽  
Uniform Heat

The thermal stress problem of an “open” crack situated at the interface of two bonded, dissimilar, semi-infinite solids subjected to a uniform heat flow is studied. Heat transmission between adjacent crack surfaces is assumed to be proportional to the temperature difference between the crack surfaces with a proportional constant h, which is defined as the contact coefficient or interface conductance. Temperature distribution of the problem is obtained by superimposing the temperature field for a perfectly bonded composite solid and the temperature fields for a series of distributed thermal dipoles at the crack location. The distribution function of the dipoles is obtained by solving a singular Fredholm integral equation. Stresses are then expressed in terms of a thermoelastic potential, corresponding to the temperature distribution, and two Muskhelishvili stress functions. Stress intensity factors are calculated by solving a Hilbert arc problem, which results from the crack surface boundary conditions and the continuity conditions at the bonded interface. Thermal stress intensity factors are found to depend upon an additional independent parameter, the Biot number λ = (ah/k), on the crack surface, where a is half crack length and k is thermal conductivity. Dipole distribution and stress intensity factors for two example composite solids, Cu/Al and Ti/Al2O3, are calculated and plotted as functions of λ. Magnitude of the required mechanical loads to keep the interface crack open is also estimated.

A Surface Crack in a Graded Medium Under General Loading Conditions

2002 ◽  
Vol 69 (5) ◽  
pp. 580-588 ◽  
Author(s):  
S. Dag ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Local Perturbation ◽  
Local Problem ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Perturbation Problem

In this study the problem of a surface crack in a semi-infinite elastic graded medium under general loading conditions is considered. It is assumed that first by solving the problem in the absence of a crack it is reduced to a local perturbation problem with arbitrary self-equilibrating crack surface tractions. The local problem is then solved by approximating the normal and shear tractions on the crack surfaces by polynomials and the normalized modes I and II stress intensity factors are given. As an example the results for a graded half-plane loaded by a sliding rigid circular stamp are presented.

The General Fracture Problem of a Functionally Graded Thermal Barrier Coating (TBC) Bonded to a Substrate

2004 ◽  
Author(s):  
F. Delale ◽  
X. Long
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Surface ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Thermal Barrier ◽  
Intensity Factors ◽  
Barrier Coating ◽  
Fgm Layer

In this paper we consider the general fracture problem of a functionally graded thermal barrier coating (TBC) bonded to a substrate. Functionally Graded Materials (FGMs) used in TBCs are usually made from ceramics and metals. Ceramics provide thermal and corrosion resistance while metals provide the necessary fracture toughness and heat conductivity. The volume fractions of the constituents will usually vary from 100% ceramic at the surface to 0% at the interface continuously providing seamless bonding with the metal substrate. To study the general fracture problem in the TBC we consider an arbitrarily oriented crack in an FGM layer bonded to a half plane. The elastic properties of the FGM layer are assumed to vary exponentially, while those of the half plane are homogeneous. The elastic properties are continuous at the interface. As shown in [1], then the governing elasticity equations become partial differential equations with constant coefficients. Using the transform technique, and defining the crack surface displacement derivatives as the unknown auxiliary functions, the mixed-mode crack problem is reduced to a system of Cauchy type singular integral equations. It is shown that at the crack tips the stresses still possess the regular square-root singularity, making it possible to use the classical definition of stress intensity factors. The singular integral equations are solved numerically using a Gaussian type quadrature and the mode I and mode II stress intensity factors are calculated for various crack lengths and crack orientations. Also the crack surface displacements are computed for different crack inclinations. It is observed that the crack orientation, crack length and the nonhomogeneity parameter affect the stress intensity factors significantly.

Effects of Crack Surface Heat Conductance on Stress Intensity Factors

1990 ◽  
Vol 57 (2) ◽  
pp. 354-358 ◽  
Author(s):  
An-Yu Kuo
Keyword(s):  
Thermal Conductivity ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Crack Surface ◽  
Surface Heat ◽  
Mode Ii ◽  
Intensity Factors ◽  
Heat Conductance

Effects of crack surface heat conductance on stress intensity factors of modes I, II, and III are investigated. The crack problem is first solved by assuming perfect (infinite) heat conductance at crack surfaces. Finite heat conductance at crack surfaces is then accounted for by imposing a set of distributed dipoles at the crack surfaces. Distribution function of the dipoles is the solution of a Fredholm integral equation. It is shown that, for cracks in a homogeneous, isotropic, linear elastic solid, the degree of thermal conductivity at crack surfaces will affect the magnitude of mode I and mode II stress intensity factors but not mode III stress intensity factor. It is also shown that, for a geometrically symmetric cracked solid, only the mode II stress intensity factor will be influenced by different crack surface heat conductance even if the thermal loading is not symmetric. More importantly, for a given material thermal conductivity (K) and crack surface heat convection coefficient (h), effects of crack surface heat conductance on stress intensity factors is found to depend upon crack size. This “size effect” implies that, for a given set of K and h, an extremely small crack can be treated as if the crack surfaces are insulated and a very long crack can be treated as if the crack surfaces are perfectly heat conductive. As an example, the problem of a finite crack in an infinite plate subjected to a constant temperature gradient at infinity is studied.

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