Date of Award

Spring 1997

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

Department

Industrial and Manufacturing Engineering

First Advisor

Zhiming Ji

Second Advisor

Bernard Koplik

Third Advisor

Benedict C. Sun

Fourth Advisor

Rong-Yaw Chen

Fifth Advisor

A. C. Ugural

Abstract

Catastrophic failure of aircraft and other structures are often caused by undetected cracks. Fracture mechanics has been developed to augment traditional static and fatigue design. In the static theory of fracture mechanics, extensive treatment has been given to the stress distribution around sharp cracks and notches under various loading conditions. Previous works on the problems of dynamic loadings are not accurate in dealing with singularities at high frequencies. The numerical solutions become unrealistic at high frequencies in many practical applications.

To address the need to obtain the stress intensity factor in high frequency dynamic loading situations, we studied the use of dislocation to represent a crack by a continuous distribution of dislocation singularities. This study focused on the configuration of finite crack located in an infinite isotropic elastic solid which is subjected to harmonic shear waves. The most important contribution of this thesis is a new approach which is based on the development of dynamic dislocation model to investigate the dynamic problems of cracks, particularly the dynamic interaction between a surface crack and screw dislocations; dynamic interaction between a free surface and an internal crack; crack propagation under dynamic loadings. With this approach, we are able to derive the exact analytical expression for stress intensity factor at any given frequencies.

Results of the present investigation show the dynamic stress intensity factors will increase as the wave number (a measure of frequency of loadings) increases and the maximum value is about 25% more than the static stress intensity factor. At relatively high frequencies, the stress intensity factor drops rapidly beyond the first maximum value and exhibits oscillations of approximately constant period as wave number increases. This conclusion can be used to predict the useful life of a component at which consists of the crack propagation phase. The stress intensity factors at both sides of a finite crack have been performed for different inclined angle 0. The results show the right side stress intensity factor is bigger than the left side's when 0 < θ < π/2 or 3π/2< θ < 2π.

The dynamic interaction between screw dislocations and a surface crack has been investigated. It has been found, under the periodic dynamic stress, the surface crack can be repelled by the dislocation with proper direction of the applied stress and the negative Burgers vector of the dislocation.

Simulation results of the dislocation model for an internal crack show that free surface effect plays a very important role in crack propagation. The stress intensity factors at crack tip which is nearest to the free surface suffer a sharp increase. It indicates that an internal crack close to a free surface could easily be extended to a surface crack.

At the end, an analysis of the scattering of horizontally shear waves by a finite extending uniformly crack has been carried out by using the dislocation method. It is found that the peaks of dynamic stress intensity factor decrease at normal incidence and almost the same magnitude for incident angles equal to 0 and π as propagation velocity increases.

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