A closed crack tip model for interface cracks inthermopiezoelectric materials

1999 ◽  
Vol 36 (16) ◽  
pp. 2463-2479 ◽  
Author(s):  
Qing-Hua Qin ◽  
Yiu-Wing Mai
Author(s):  
Ali P. Gordon ◽  
David L. McDowell

Interface cracks are seldom subjected to pure Mode I or pure Mode II conditions. Stationary interface cracks between two distinct, bonded elastic-creep materials subjected to remotely applied mixed mode loading are simulated. The finite element method (FEM) is used to examine crack tip fields and candidate driving force parameters for crack growth. Plane strain conditions are assumed. In most cases a functionally graded transition layer is included between the two materials. Examples of such systems include weld metal (WM) and base metal (BM) interfaces in welded or repaired boiler components subjected to elevated temperatures. Numerical solutions based on the asymptotic fields of the homogeneous and heterogeneous Arcan-type specimens are presented. Creep ductility-based damage models are used to predict the initial crack propagation trajectory. The incorporation of functionally graded transition layer regions affects the evolution of time-dependent stress components in the vicinity of the crack tip. The magnitude and direction of crack tip propagation can then be optimized with respect to interface properties.


The asymptotic structure of near-tip fields around stationary and steadily growing interface cracks, with frictionless crack surface contact, and in anisotropic bimaterials, is analysed with the method of analytic continuation, and a complete representation of the asymptotic fields is obtained in terms of arbitrary entire functions. It is shown that when the symmetry, if any, and orientation of the anisotropic bimaterial is such that the in-plane and out-of-plane deformations can be separated from each other, the in-plane crack-tip fields will have a non-oscillatory, inverse-squared-root type stress singularity, with angular variations clearly resembling those for a classical mode II problem when the bimaterial is orthotropic. However, when the two types of deformations are not separable, it is found that an oscillatory singularity different than that of the counterpart open-crack problem may exist at the crack tip for the now coupled in-plane and out-of-plane deformation. In general, a substantial part of the non-singular higher-order terms of the crack-tip fields will have forms that are identical to those for the counterpart open-crack problem, which give rise to fully continuous displacement components and zero tractions along the crack surfaces as well as the material interface.


1993 ◽  
Vol 60 (2) ◽  
pp. 432-437 ◽  
Author(s):  
G. Yan ◽  
T. C. T. Ting

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.


1979 ◽  
Vol 46 (1) ◽  
pp. 97-100 ◽  
Author(s):  
Maria Comninou ◽  
J. Dundurs

Considering a crack that lies in one solid, but has a tip that touches an interface with a second solid, Bogy found that the assumption of a traction-free crack tip leads to oscillating singularities for certain combinations of materials. Such oscillating singularities lead to overlapping of the crack faces, and the purpose of this article is to eliminate the oscillating singularities by allowing the crack tip to be closed. Using an asymptotic analysis and incorporating the effect of friction, the nature of the singularity at the closed crack tip is established and the various consequences explored.


1986 ◽  
Vol 20 (6) ◽  
pp. 905-908 ◽  
Author(s):  
J. Kevin McCoy ◽  
Alan J. Markworth

1998 ◽  
Vol 14 (2) ◽  
pp. 83-89
Author(s):  
Ru-Min Chao

AbstractIn this paper, the problem of a debonding crack at the interface between a circular fiber and an infinite matrix opened by internal pressure is discussed. We concentrated on the effect of contact near the crack tips within the content of linear elastic fracture mechanics. The Muskhelishvili complex variable method is used in this analysis. The frictionless contact crack tip condition is adopted in this study in order to avoid the oscillatory stress singularity at the crack tip as shown in the classical solution. By using the crack opening displacement gradient as the primary variable, the problem is then reduced to two coupled singular integral equations, and the final discretization of the equations employs the method given by Erdogan and Gupta (1972). The comprehensive numerical results of stress fields and the mode II SIF at the closed crack tip will be given in the paper. It is also found from the numerical evidences that the contact length at the crack tip is independent of one of the Dundurs parameters, α.


Sign in / Sign up

Export Citation Format

Share Document