Deformation Field Near a Crack Tip Under Thermal Stress

Deformation Field Near a Crack Tip Under Thermal 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.

TABLE OF CONTENTS

Cover page …………………………………………………………(i)
Title page ………………………………………………………….( ii)
Approval Page ………………………………………………….(iii)
Dedication …………………………………………………………(iv)
Acknowledgement ………………………………………………….(v)
Abstract …………………………………………………………(vi)
Table of Content ………………………………………………….(vii)

CHAPTER ONE

INTRODUCTION………..(1)

CHAPTER TWO

REVIEW OF RELATED LITERATURE ………………………(4)

CHAPTER THREE

J – INTEGRAL …………………………….(19)

CHAPTER FOUR

ANALYSIS ………………(28)

CHAPTER FIVE

DISCUSSION, SUMMARY AND CONCLUSION………………..(45)
REFERENCES ………………… (46)

INTRODUCTION

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.

REFERENCES

Rice, J. R. (1967): Stress Due to a Sharp Notch in a Work-Hardening Elastic Plastic Material Loaded by Longitudinal Shear, Journal of Applied Mechanics PP. 287-298.

Amazigo, J. C. (1974): Fully Plastic Crack in an Infinite Body Under Anti- Plane Shear; International Journal of Solid Structures. Vol. 10, PP. 1003- 1015, Pergamon Press, Britain.

Liangchi, Z. (2001) Solid Mechanics for Engineers, Palgrave Houndmill Basing Stock, New York, NY 10010

Anderson, T.L. (1995) Fracture Mechanics (Fundamentals and Applications)

CRC Press Boca Ratin London, New York, Washington D.C.

Griffith, A. A. (1920): The Phenomena of Rupture and Flow in Solid, Philosophical Transaction, Series A. Vol. 221, Pp. 163 – 198.