Stresses at the Surface of a Flat Three-Dimensional Ellipsoidal Cavity

1976 ◽  
Vol 98 (2) ◽  
pp. 164-172 ◽  
Author(s):  
L. Mirandy ◽  
B. Paul
Keyword(s):  
Stress Intensity ◽  
Applied Stress ◽  
Surface Stress ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Ellipsoidal Cavity ◽  
Isotropic Elastic Medium ◽  
Analytical Expressions

The stress field associated with a thin ellipsoidal cavity in an isotropic elastic medium with arbitrary tractions at distant boundaries is needed to generalize Griffith’s two-dimensional fracture criterion. Such a solution is given here. It is first formulated for a general ellipsoidal cavity having principal semiaxes a, b, and c, and then it is reduced to the specific case of a “flat” ellipsoid for which a and b are very much greater than c. An explicit solution of the general problem is possible but the results are somewhat unwieldy. The dominant terms of an asymptotic solution for small c/b, however, are shown to provide remarkably simple expressions for the stresses everywhere on the surface of the cavity. The applied normal stress parallel to the c axis and the shears lying in a plane perpendicular to it were found to produce surface stresses proportional to (b/c) × applied stress, with the amplification of other components of applied stress being negligible in comparison. Analytical expressions for the location and magnitude of the maximum surface stress are developed along with stress intensity factors for the elliptical crack (c = 0). Three dimensional effects due to ellipsoidal planform aspect ratio (b/a) and Poisson’s ratio are reported.

An Improved Fracture Criterion for Three-Dimensional Stress States

1976 ◽  
Vol 98 (2) ◽  
pp. 159-163 ◽  
Author(s):  
B. Paul ◽  
L. Mirandy
Keyword(s):  
Applied Stress ◽  
Stress Fracture ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Brittle Materials ◽  
Two Dimensional ◽  
Stress Concentrations ◽  
State Of Stress ◽  
Stress States ◽  
Free Material

A theory is developed to predict the onset of fracture in isotropic, brittle materials when subjected to three dimensional states of applied stress. It is assumed that fracture is precipitated by stress concentrations emanating from material flaws. The flaw model which has been adopted consists of randomly oriented, microscopic, flat triaxial ellipsoidal voids imbedded in an otherwise defect-free material. It is shown that the ensuing fracture criterion may be expressed as a parabolic Mohr’s envelope. These results are qualitatively similar to Paul’s earlier three-dimensional generalization of Griffith’s two-dimensional stress fracture criterion. To handle three-dimensional states of applied stress, Paul used an approximation based on two-dimensional elasticity to obtain the state of stress around a flat spheroid. Newly developed results for flat ellipsoidal cavaties are utilized herein to analyze the three-dimensional cavity. Pertinent effects due to Poisson’s ratio and ellipsoid geometry are reported.

The evolution of stress intensity factors in the propagation of two dimensional cracks

2000 ◽  
Vol 11 (5) ◽  
pp. 453-471 ◽  
Author(s):  
AVNER FRIEDMAN ◽  
BEI HU ◽  
JUAN J. L. VELAZQUEZ
Keyword(s):  
Stress Intensity ◽  
Elastic Medium ◽  
Plane Strain ◽  
Asymptotic Expansions ◽  
Stress Intensity Factors ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Plane Strain Deformation ◽  
Isotropic Elastic Medium

The aim of this paper is to describe a technique based on matched asymptotic expansions that allows us to derive the variation of the stress intensity factors in a homogeneous isotropic elastic medium under plane strain deformation. The case of antiplane shearing is also considered.

Multi-Order Stress Intensity Factors Along Three-Dimensional Interface Corners

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Tai-Liang Kuo ◽  
Chyanbin Hwu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Failure Behavior ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Order Stress ◽  
Definition Of ◽  
Domain Independent

Usually in the study of singularity problems, only the most critical singular order is considered. For three-dimensional interface corner problems, if only the most critical singular order of stresses is considered, it is possible to lose the opportunity to compute the full modes of stress intensity factors. To fully understand the failure behavior of three-dimensional interface corners, a definition of the stress intensity factors for the lower singular orders is proposed in this paper based on that of the most critical singular order. Moreover, to compute the proposed multi-order stress intensity factors accurately and efficiently, a path-independent H-integral, which has been proven useful for the two-dimensional interface corners, is now modified into a domain-independent H-integral for the three-dimensional interface corner problems. Because the stress intensity factors characterize the fracture behavior focused on an arbitrary tip along the corner front, based on anisotropic elasticity the near tip solutions and complementary solutions of two-dimensional generalized plane strain problems are introduced and then utilized for computation of three-dimensional H-integral. To illustrate the validity of the present work, several three-dimensional numerical examples are analyzed and compared with the existing published solutions. Finally, two examples about the interface corners, which occur frequently in electric packages, are solved to show the feasibility and practicability of the proposed approach.

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

Stress Intensity Factor for Repaired Circumferential Cracks in Pipe With Bonded Composite Wrap

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
F. Benyahia ◽  
A. Albedah ◽  
B. Bachir Bouiadjra
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Element Analysis ◽  
Composite Systems ◽  
Bonded Composite ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The use of composite systems as a repair methodology in the pipeline industry has grown in recent years. In this study, the analysis of the behavior of circumferential through cracks in repaired pipe with bonded composite wrap subjected to internal pressure is performed using three-dimensional finite element analysis. The fracture criterion used in the analysis is the stress intensity factor (SIF). The obtained results show that the bonded composite repair reduces significantly the stress intensity factor at the tip of repaired cracks in the steel pipe, which can improve the residual lifespan of the pipe.

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