On the Mechanical Modeling of the Interfacial Region in Bonded Half-Planes

1988 ◽  
Vol 55 (2) ◽  
pp. 317-324 ◽  
Author(s):  
F. Delale ◽  
F. Erdogan
Keyword(s):  
Crack Surface ◽  
Mixed Boundary ◽  
Crack Problem ◽  
External Loading ◽  
Interfacial Region ◽  
Mechanical Modeling ◽  
Intensity Factors ◽  
Single Crack ◽  
Collinear Cracks ◽  
Mixed Boundary Problem

In this paper the crack problem for two bonded dissimilar homogeneous elastic half-planes is considered. It is assumed that the interfacial region can be modeled by a very thin layer of nonhomogeneous material. Even though the formulation given is rather general, in the particular model used the elastic properties of the interfacial layer are assumed to vary continuously between that of the two semi-infinite planes. The layer is assumed to have a series of collinear cracks parallel to the nominal interface. The related mixed boundary problem is formulated for arbitrary crack surface tractions which can be used to accommodate any general external loading condition through a proper superposition. A single crack problem for two different material combinations is solved as examples, and Modes I and II stress-intensity factors, the energy release rate and the direction of a probable crack growth are calculated.

Thermal Shock of Semi-Infinite Cellular Ceramics

2012 ◽  
Vol 476-478 ◽  
pp. 1041-1045
Author(s):  
Y.X. Zhang ◽  
B.L. Wang
Keyword(s):  
Thermal Shock ◽  
Surface Stress ◽  
Edge Crack ◽  
Crack Surface ◽  
Opposite Sign ◽  
Mixed Boundary ◽  
Intensity Factors ◽  
Thermal Stress Field ◽  
Design And Manufacturing ◽  
Cellular Ceramic

Considered in this paper is a semi-infinite cellular ceramic solid containing an edge crack. The solid is subjected to a sudden cooling on its surface. The temperature field and associated thermal stress field for the uncracked solid are calculated. The stress for uncracked medium is used as the crack surface stress with opposite sign to formulate the mixed boundary value problem. The stress intensity factors as the function of crack length, time and relative density are calculated. It is found that the presence of porosity in the ceramic is generally beneficial to increasing the thermal shock strength of the ceramics if the failure is dominated by a pre-existing crack. The paper may be helpful for the design and manufacturing of advanced thermal shock resistive cellular ceramics.

Mixed Multi-Layered Model for Fracture Analysis of Functionally Graded Interfacial Zone under Anti-Plane Loading

2012 ◽  
Vol 452-453 ◽  
pp. 1154-1158
Author(s):  
Ke Di ◽  
Yue Cheng Yang
Keyword(s):  
Present Model ◽  
Mixed Boundary ◽  
Crack Problem ◽  
Functionally Graded ◽  
Interfacial Zone ◽  
Layered Model ◽  
Mixed Boundary Problem ◽  
Cauchy Singular Integral ◽  
Cauchy Singular Integral Equation ◽  
Graded Interfacial Zone

In this paper, a new mixed multi-layered model is put forward to study the crack problem of the functionally graded interfacial zone between tow homogeneous half-spaces. In the model, the interfacial zone is divided into some sub-layers with the properties of each layer varying in linear and exponential manners alternately. By applying Fourier transform and using the transfer matrix method, the mixed boundary problem of anti-plane fracture can be reduced to a Cauchy singular integral equation, which is solved numerically. Stress intensity factors of some examples are derived. The results show that the present model is effective and accurate and compared with the liner multi-layered model, the present one can save more CPU time in computation.

An Analysis of Cracking in a Layered Medium With a Functionally Graded Nonhomogeneous Interface

1996 ◽  
Vol 63 (2) ◽  
pp. 479-486 ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Layered Medium ◽  
Crack Problem ◽  
Crack Size ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Interfacial Region ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Transitional Layer ◽  
Homogeneous Surface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method of formulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.

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 Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

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.

Sign in / Sign up

Export Citation Format

Share Document