#### Date of Award

8-2010

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Legacy Department

Mechanical Engineering

#### Advisor

Joseph, Paul F

#### Committee Member

Thompson , Lonny L

#### Committee Member

Li , Gang

#### Abstract

A general method based on the singular integral equations is developed to

computationally determine the higher order coefficients in mixed mode fracture

mechanics. These 'k' and 'T' coefficients are defined with respect to a polar coordinate

system centered at a crack tip, and give asymptotic expressions for stresses and

displacements according to the William's eigenfunction expansions,

(r, ) (2r) k f (n, ) k f (n, ) IIk

ij

II

n

Ik

ij

I

n

n 0

2

1

n

ij

1

(0, ) (2 ) ( , ) ( , ) , , ; , , I IT n I IT II IIT

ij n ij n ij

n

T f r T f n T f n i r j r

In the above expression the n = 0 terms correspond to the modes I and II stress

intensity factors and the so called, T-stress. From a method point of view, the higher

order k-coefficients are easily obtained, while the T-coefficients require significant postprocessing

of the singular integral equation solution. A planar crack parallel to an

interface between two elastic materials and subjected to far-field tension is considered as

an example and extensive results are presented. This example is chosen due to the

anomalous behavior of a closing crack tip as the crack approaches the interface for

certain material combinations. Such 'Comninou contact zones' occur even in a tensile

field when the crack is within a critical distance from the interface. Numerous results are

provided that compare the asymptotic solutions with that of the full-field. It is shown that

up to four k-coefficients and many T-coefficients can be determined for h/a = 0.001,

where h is the distance of the crack from the interface and a is the half-crack length.

While the application of the method to the case of a crack parallel and very close to an

interface focuses on the anomaly of a closing crack tip, in general the ability to determine

iii

higher order coefficients can be used to quantify the size of the zone in which linear fracture mechanics is valid.

#### Recommended Citation

Kolluru, Venkata lakshman, "DETERMINATION OF HIGHER ORDER COEFFICIENTS FOR A CRACK PARALLEL TO AN INTERFACE" (2010). *All Theses*. 950.

https://tigerprints.clemson.edu/all_theses/950