Interaction of crack-tip and notch-tip stress singularities for circular cylinder in torsion

1993 ◽  
Vol 18 (3) ◽  
pp. 259-272 ◽  
Author(s):  
Y.L. Li ◽  
S.Y. Hu ◽  
R.J. Tang
Keyword(s):  
Circular Cylinder ◽  
Crack Tip ◽  
Stress Singularities ◽  
Notch Tip

The r−1/2 (ln r) Singularities at Interface Cracks in Monoclinic and Isotropic Bimaterials due to Heat Flow

1993 ◽  
Vol 60 (2) ◽  
pp. 432-437 ◽  
Author(s):  
G. Yan ◽  
T. C. T. Ting
Keyword(s):  
Heat Flow ◽  
Interface Crack ◽  
Simple Form ◽  
Crack Tip ◽  
Higher Order ◽  
Stress Singularities ◽  
Interface Cracks ◽  
Existence Conditions

It is known that the stress singularities at an interface crack tip of bimaterials with the effects of heat flow may have the form r−1/2 (ln r). The existence conditions of the higher order singularitiy r−1/2 (ln r) are studied for monoclinic bimaterials whose plane of symmetry is at x3 = 0. It is shown that the higher order singularity does not exist if the bimaterial is mismatched. If the bimaterial is non-mismatched, the higher order singularity does not exist when a certain condition is satisfied. This condition is given explicitly for monoclinic bimaterials with the plane of symmetry of x3 = 0 and in a simple form for isotropic bimaterials.

Mode II and mode III stress singularities and intensities at a crack tip terminating on a transversely isotropic-orthotropic bimaterial interface

1994 ◽  
Vol 444 (1922) ◽  
pp. 447-460 ◽  
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Transversely Isotropic ◽  
Bimaterial Interface ◽  
Mode Ii ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Mode Iii ◽  
Orthotropic Media

In a recent paper (referred to as I) we obtained inter alia , the stress and displacement fields at the tips of a transverse crack in an isotropic medium sandwiched between orthotropic media under in-plane loading (mode II). The crack was lying wholly within the isotropic medium so that the singularity at the crack tip was of the usual inverse square root type. In this paper, the analysis is extended to the case when the tip of the crack terminates on the transversely isotropic-orthotropic bimaterial interface and the nature of the singularity at the crack tip depends on the elastic properties of both media. The analysis is performed for both inplane (mode II) and out-of-plane (mode III) shear loading. General solutions are obtained for the crack tip stress singularities and corresponding stress intensity factors, together with the influence of the elastic properties and geometry of the media upon the stress field. These solutions are specialized to the limiting case when the crack terminates on the interface between dissimilar isotropic media in order to demonstrate consistency with published results. As in I, the solutions are used to investigate the influence of ply angle θ upon the stress singularities in [± θ /90°] s fibre-reinforced composite laminates. For this analysis, the outer angle-ply sublaminates are treated macroscopically as homogeneous orthotropic media whose elastic constants are obtained using the classical lamination approximation. Calculations are also carried out to study the variation of stress intensity factors with the ply angle and outer sublaminate thickness.

Elastic-Plastic Stress Singularities of Plane V-Notches in Power-Hardening Materials

2011 ◽  
Vol 465 ◽  
pp. 105-110 ◽  
Author(s):  
Zhong Rong Niu ◽  
Naman Recho ◽  
Zhi Yong Yang ◽  
Chang Zheng Cheng
Keyword(s):  
Linear Elasticity ◽  
Eigenvalue Problems ◽  
High Stress ◽  
Stress Singularity ◽  
Opening Angle ◽  
Radial Coordinate ◽  
Plastic Behavior ◽  
Stress Singularities ◽  
Notch Tip ◽  
Plastic Stress

Extensive studies have been carried out to deal with the stress singularity of V-notch problems in linear elasticity theory. In fact, the plastic deformation consequentially arises in the notch tip region because of the high stress concentration. The solution of linear elasticity is not adequate to explain the fracture failure of V-notch structures. Because of the difficulties of the nonlinear analysis and the singularity behavior, few results are given for the plastic stress singularities of general V-notch structures. In this paper, the plane V-notch structures in a power law hardening materials are considered. The Von Mises yield criterion and the plasticity total theory are adopted when the materials arise in plastic status. Similar to methods used in the elastic analysis, the plastic stress field near V-notch tips is assumed as an asymptotic expansion with respect to the radial coordinate originating from the notch tip. The governing equations of plastic behavior of plane V-notch are transformed to eigenvalue problems of nonlinear ordinary differential equations (ODEs) contained by the stress singularity order and the associated eigenfunctions. Consequently all of the stress singularities who are less than zero and the associated eigenvectors are accurately determined for the plane V-notches with arbitrary opening angle.

Stress Singularities near Interface Crack Tip for Mode II of Orthotropic Bi-Material

2014 ◽  
Vol 1004-1005 ◽  
pp. 473-478
Author(s):  
Mu Yang Li ◽  
Jun Lin Li ◽  
Xiu Feng Xie
Keyword(s):  
Composite Material ◽  
Interface Crack ◽  
Crack Tip ◽  
Mode Ii ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Complex Singularity ◽  
Singularity Exponents ◽  
Analytic Expressions ◽  
Stress Functions

Using the method of composite material complex and constructing new stress functions with complex singularity exponents, the problem of singularities near interface crack tip for mode II of orthotropic bi-material is studied. Boundary value problems of generalized bi-harmonic equations can be solved with the help of boundary conditions, then four kinds of stress singularities are deduced, respectively, such as the constant singularity at λ=-1/2, the non-constant singularity at λ=-1/2+ε , the constant oscillation singularity at λ=-1/2+iε, and non-constant oscillation singularity at λ=-1/2+c+iε. For each case, the analytic expressions for stress intensity factors near the central-penetrated interface crack tip for mode II of orthotropic bi-material are obtained.

Stress Singularity Analysis of a Crack Terminating at the Interface of an Anisotropic Layered Composite

1998 ◽  
Vol 65 (4) ◽  
pp. 829-836 ◽  
Author(s):  
P. Poonsawat ◽  
A. C. Wijeyewickrema ◽  
P. Karasudhi
Keyword(s):  
Stress Singularity ◽  
Crack Tip ◽  
Singularity Analysis ◽  
Layered Composite ◽  
High Modulus ◽  
Stress Singularities ◽  
Inclined Crack ◽  
Relative Slip ◽  
Frictional Interface ◽  
Crack Faces

The order of stress singularities at the tip of an inclined crack terminating at the interface of an anisotropic layered composite is investigated. Both fully bonded and frictional interfaces are considered. The expressions for stresses and displacements are obtained by using the Stroh formalism. The stresses at the crack tip are expressed in the form σij=r−kFij(θ), where k is the crack-tip singularity. The singularity k is obtained by solving a characteristic equation which incorporates the effects of the interface and the crack faces. The problem can be visualized as two wedges created by a crack, pressing on a half-plane. For the frictional interface, depending on the relative slip directions of the two wedges, both the case of the two wedges slipping in opposite directions and the case of the two wedges slipping in the same direction are treated. In the numerical calculation of the singularities, a high modulus graphite/ epoxy layered composite is used and the effect of the crack inclination on the stress singularity k is graphically presented. In general, there are three roots of k for the fully bonded interface, while there are only two roots of k for the slipping interface.

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