Progressive changes in material parameters during fatigue

PROGRESSIVE CHMGES IN MtTERIAL PARAMETERS DURING FATIGUE

by

VUPPULURI 1WIJft.T KUM1R

Thests submitted to the

Indian Institute of Technology, Delhi for 'the award of the degree of

DOCTOR OF PLOSOPHY

Department of Applied Mechanics Indian Institute of Technology, Delhi

December, 1974-

CERT IFICE

This is to certify that the thesis entitled.

,

PROGRESSIVE CROGES IN MIJERIAL PIRi.METERS DURING FATIGUE' submitted by Mr. Vuppuluri Maharaj Kumar has been prepared under my supervision in conformity to the rules and

regulations of the Indian Institute of Technology, Delhi.

I further certify that the thesis has att ained a standard required for a Ph.D. degree of the Institute. The research report and results presented in the thesis have not been

submitted for any degree in any University.

( B KJRUNES ) Head and Professor,

Department of Applied Mechanics, Indian Institute of Technology, Delhi.

ACKNOWLEDGEMENTS

The author is highly indebted to Prof. B. Karunes, Head of the Department of Applied Mechanics, Indian Institute of Technology, Delhi, for the kind guidance and help that the author roceived throughout the project. The project

is funded by the I,I.T., Delhi for which the author expresses his gratitude to the Director, Prof. N.M. Swani. Particular mention must be made of Prof. R.C. Malhotra, Prof. V. Raghavan, Dr. N.K. Gupta and Dr. P.C. Dumtr who had always been

encouraging and helping the author in many ways. The author is also grateful to all the laboratory and workshop staff of the department, and the staff of the Conuter Centre, who helped him at different stages during this project.

Thanks are also duo to Shri S,K. Mehra for typing the manuscript.

( V. M, Kumar

TLBLE OF CONTENTS

Acknowledgement s iii

List of Figures iv

List of Tables vi

Table of Contents vii

List of Symbols x

CHAPTERS

1. THE INTRODUCTION 1 - 1+

1.1 Review of Cumulative Damage Theories 2 1.2 Review of Hysteresis Loop Studies 8

1.3 Present Efforts 13

2. THE PROPOSITION 1 - 2

2.1 Stress-Strain Relations 16

2.2 Ludwik!s Relation 18

2.3 RanTherg-Osgood. Relation 20 2.+ Nature of Changes of the Parameters. 20 2.5 Ln Analytical Study of Hysteresis 23

viii

3. THE EXPERINENTS 26 -

3.1 Details of the Apparatus ₂₇

32 Specimen Materials 35

33 Test Procedure 36

3,)+ The Term 'Stress Level' 38 3.5 Analysis of the Observations 39 3.6 The Computations 1+1

+, THE RESULTS OF EXPERINENTS ON COPPER 53 ^- 69

.1 Modulus of Elasticity,E 54 +,2 Luthik's Strength Coefficient, K

~-.3 Ludwik' s Strain Hardening Exponent, n 58 Raithorg-Osgood Base Stress,

cr0

⁵⁸

45 Ramberg-Osgood. Strain Hardening 63 Coefficient, m

F.6 Hysteresis Loops 66

5, THE RESULTS OF EXPERIMENTS ON ALUMINUM 70 - 85 5.1 Copper versus Aluminum 71

5.2 Modulus of Elasticity, E 71 5,3 Ludwikts Strength Coefficient, K 72 5.+ Ludwik's Strain Hardening Exponent, n 72 5.5 Ramberg-Osgood Base Stress,

G- 0

₇₇

5.6 Ramberg-Osgood Strain Hardening 77 Coefficient, m

5,7 Hysteresis Loops 82

6.

ix

TEE CLOSURE 86

-

go

6.1 Summary of Results 87

62 Major 0ervations 89

6.3 Closing Remarks 89

T HE AP]DIXES 91

-

¹⁰³

A. Experimental Results

-

^{Copper 92}

B. Experimental Results

-

Aluminum

95

C. Computer Program 98

TI AUTHOR INDEX 10l1

-

¹⁰⁶