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Deformation Field Near a Crack Tip Under Thermal Stress

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Deformation Field Near a Crack Under Stress

ABSTRACT

In this research, we investigated the deformation field near a crack tip due to thermal stress. Crack tip singularities are examined using line integral that exhibits path independence of all contours near the tip of the crack in a two dimensional deformation field of an elastic material. The approach of using the J- Integral is used to extract the magnitude of crack tip stress intensity factor for thermal stress crack problem. The characteristics of the J-integral in the presence of thermal stress are determined and a process of accessing the crack tip stress intensity factors is developed.

OF CONTENTS

Cover page …………………………………………………………(i)
Title page ………………………………………………………….( ii)
Approval Page ………………………………………………….(iii)
Dedication …………………………………………………………(iv)
Acknowledgement ………………………………………………….(v)
Abstract …………………………………………………………(vi)
Table of Content ………………………………………………….(vii)
CHAPTER ONE
…………………………………………………………….(1)
CHAPTER TWO
REVIEW OF RELATED LITERATURE ………………………(4)
CHAPTER THREE
J – INTEGRAL …………………………………………………………..(19)
CHAPTER FOUR
ANALYSIS …………………………………………………(28)
CHAPTER FIVE
CUSSION, SUMMARY AND CONCLUSION………………..(45)
S ………………………………………………… (46)

CHAPTER ONE

In contemporary times, the society is challenged with the problem of fracture as long as there are structures made by man, and this limitation could be as a result of anomalies created in the course of structural design which culminate into failure in systems. This failure has been traced to high degree of stress concentration in a giving region of a body particularly solids thereby leading to deformation and crack.

Collapse in solids could be fatal and have greatly affected lives, properties and finances negatively in nations of the world. Cracks lower the structural integrity of structures. Beyond that, due to load bearing material property above and beyond conventional capacity is required to examine fracture resistance of a solid. When stress applied to solids is large enough, distortion, reformation of atomic bonds occur and move to a new position and the original material deform. Permanent deformation may take place under certain external load which is mainly due to activation of slip of system such as dislocation. However, when plastic deformation is very large, the contribution of elastic strain becomes negligible. Many engineering structures have cracks and we often see that some of them have failed around a small crack. When a material is under loading beyond its capacity crack is bound to occur and this failure is related to stress field in the neighborhood of crack tip as result of deformation. So, there are stress and strain that take place inside real bodies.

In this research, we investigate the deformation field near a crack tip due to thermal stress. This analysis is of great significance in field of Fracture Mechanics in which crack tip singularities are examined using line a integral that exhibits path that is independent of all contours near the tip of a crack in a two dimensional deformation field of an elastic material. The principle of continuous deformation path is related to path independence in which deformation the path consist of only points at which a function is analytic where the integral retain the same value.

According to Rice [1] and Amazigo [2], this integral provides not only an accurate characterization of the crack tip elastic-plastic field but also a good elastic fracture criterion. Therefore, there is an arbitrary contour that will yield the same value for different paths. Elastic deformation and irreversible dislocation flaw begin with the very first small increment of load and the dislocation flaw accelerates thereafter with increasing load up until the ultimate rupture.

Failure in materials caused by engineering structures that contain cracks is a menace to mankind. Normally, any structure that is containing crack should fail no matter how small the crack or how light the load. The act of predicting failure of these structures becomes paramount. In this work, we concentrate on the elastic analysis of deformation field in the neighborhood of a crack tip under thermal stress.

Advances in Fracture Mechanics have helped in understanding the mechanism of failure thus, helping to prevent structural failure and their frequencies.

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