Three-Dimensional Analysis of Cracking Through the Boundary of a Two-Phase Material

1989 ◽  
Vol 56 (4) ◽  
pp. 850-857 ◽  
Author(s):  
M. T. Hanson ◽  
W. Lin ◽  
L. M. Keer
Keyword(s):  
Stress Intensity ◽  
Phase Boundary ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Three Dimensional ◽  
Singular Integral Equations ◽  
The Body ◽  
Intensity Factors ◽  
Two Phase ◽  
Penny Shaped Crack

The penetration through a two-phase boundary by a biplanar (kinked) crack of arbitrary shape is considered in this paper. The two-phase boundary is modeled as the interface between two perfectly-bonded elastic, isotropic, homogeneous half spaces with different elastic constants. The planar crack on either side of the interface may be arbitrarily orientated with respect to the interface boundary. The body-force method is used to derive a set of coupled two-dimensional singular integral equations which are solved numerically. The solution yields the three crack opening displacements as well as the three modes of stress intensity factors along the crack contour. Numerical results are given for a penny-shaped crack symmetrically oriented with respect to the interface. Mode I stress intensity factors are given for the biplanar crack that experiences a kink when passing through the interface.

Intensity of Singular Stress at the End of a Fiber under Pull-Out Force

2007 ◽  
Vol 353-358 ◽  
pp. 3100-3103
Author(s):  
Naoaki Noda ◽  
Yasushi Takase ◽  
Ryohji Shirao ◽  
Jun Li ◽  
Jun Suke Sugimoto
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
The Body ◽  
Intensity Factors ◽  
Infinite Body ◽  
Singular Stress ◽  
Pull Out ◽  
The Matrix ◽  
Cylindrical Inclusions

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pull-out force．The body force method is used to formulate those problems as a system of singular integral equations where the unknown functions are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions.Then generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed.

An Inverse Method for the Determination of Thermal Stress-Intensity Factors Under Arbitrary Thermal-Shocks

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
J. Meeker ◽  
A. E. Segall ◽  
E. Gondar
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
The Body ◽  
Temperature History ◽  
Transient Temperature ◽  
Intensity Factors ◽  
Thermal Boundary Conditions ◽  
Transient Temperature Distribution ◽  
Single Temperature

The analysis of stress-intensity factors is of immense importance when designing vessels, pipes, and end-caps as well as supporting structures and plates seen in high-temperature applications. Given this importance and the difficulty of measuring actual thermal boundary conditions, a generalized series based on a new and infinitely differentiable polynomial was employed to inversely determine the transient temperature distribution in a semi-infinite slab using only a single temperature history. These temperature distributions were in turn used to find the potential crack-opening stresses throughout the body. Using the found stresses and a weight-function approach, stress-intensity factors were then determined for both edge and semi-elliptical cracks under an arbitrary thermal-shock. When compared to other methods for various thermal scenarios, the method showed good agreement for both edge- and semi-elliptical surface cracks.

Analysis of Stress Intensity Factors of a Planar Rectangular Interfacial Crack in Three Dimensional Bimaterials

2007 ◽  
Vol 353-358 ◽  
pp. 2449-2452
Author(s):  
Naoaki Noda ◽  
Chun Hui Xu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Present Method ◽  
Body Force ◽  
Three Dimensional ◽  
Interfacial Crack ◽  
The Body ◽  
Density Functions ◽  
Intensity Factors ◽  
Aspect Ratios

In this study, a rectangular interfacial crack in three dimensional bimaterials is analyzed. First, the problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express a two-dimensional interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factor along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. It is found that the stress intensity factors K1 and K2 are determined by bimaterials constant e alone, independent of elastic modulus ratio and Poisson's ratio.

Weight functions for curved crack fronts using bem

1993 ◽  
Vol 28 (2) ◽  
pp. 67-78 ◽  
Author(s):  
R Bains ◽  
M H Aliabadi ◽  
D P Rooke
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Three Dimensional ◽  
Function Technique ◽  
Weight Functions ◽  
Intensity Factors ◽  
Penny Shaped Crack ◽  
Curved Crack ◽  
Shaped Crack

This paper presents an efficient numerical weight function technique, based on the boundary element method, for the determination of stress intensity factors of curved crack fronts in three-dimensional finite bodies. The weight functions are based on the notion of fundamental fields, which are defined from point loads acting at the crack front. A regularization procedure that incorporates the fundamental fields of the penny-shaped crack in an infinite elastic body is used to obtain weight functions for a penny-shaped edge crack in a cylindrical bar. Stress intensity factors for elliptical crack fronts can be generated by employing the properties of the fundamental fields at the load points on the crack front. Stress intensity factor variations along the crack-fronts are presented when these finite cracked geometries are subjected to various loads that produce mode I deformation of the crack faces. Wherever possible, solutions are compared with values published in the literature and are found to be in good agreement.

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