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A Study of the Effect of Drilled Holes on the Concentration of Elastic Stresses Around a Notch

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A Study of the Effect of Drilled Holes on the Concentration of Elastic Stresses Around a Notch Scholars' Mine Masters Theses Student Theses and Dissertations 1972 A study of the effect of drilled holes on the concentration of elastic stresses around a notch Glenn Michael Kmecz Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Engineering Mechanics Commons Department: Recommended Citation Kmecz, Glenn Michael, "A study of the effect of drilled holes on the concentration of elastic stresses around a notch" (1972). Masters Theses. 3541. https://scholarsmine.mst.edu/masters_theses/3541 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. A STUDY OF THE EFFECT OF DRILLED HOLES ON THE CONCENTRATION OF ELASTIC STRESSES AROu~D A NOTCH BY GLENN MICHAEL KMECZ, 1947- A THESIS Presented to the Faculty of the Graduate School of the u~IVERSITY OF MISSOURI-ROLLA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN ENGINEERING HECHANICS 1972 T2825 93 pages Approved by c.l ~~,!Adviso r) 220069 ii ABSTRACT Hole drilling as a method for improving the toughness of notch weakened tensile specimens is investigated by means of a photoelastic technique. Tests were performed on 20%, 40%, 60%, and 80% notch depth specimens machined from PSM-1 photoelastic material. The basic criteria for success was no increase in the elastic stress concentra­ tion factor. The photoelastic results '\-Jere verified by a finite element stress analysis of the 60% notch depth specimens. Comparison of the experimental and numerical results provide conclusive proof that no increase in the elastic stress concentration factor occurs when proper positioning of the drilled holes is accomplished. iii ACKN OvJLI:DGEl1ENT The author wishes to express his appreciation to his advisor, Professor Peter G. Hansen, for his guidance and motivation during the preparation of this manuscript and his entire graduate program. The writer wishes to thank Assistant Professor Edward E. Bornsey and Associate Professor Terry F. Lehnhoff for their participation on the examining committee and also Assistant Professor Edward J. Beckemeyer for his comments and suggestions. Special thanks are in order for Mr. wilson Sherrill, who machined and helped redesign many parts for the experiment and also for his encouragement and persistant help during the testing. Gratitude is also extended to Mr. Harvin Vogeler for an excellent job of machining the photoelastic templates. The typing of the Inanuscript was done by Mrs. Alice Crangle to whom I am deeply indebted for a job well done. Finally, I wish to express deepest thanks to my parents Andre\,v and Dolores Kmecz, for their understanding and financial assistance, without which this thesis would not have been possible. iv TABLE OF CONTENTS Page ABSTRACT ............................................................. ii ACKNOWLEDGEl-tJEl~T ••••••••••.•••.•.•.•.•••.•...•.•••.••...•.•.•..•••..•. iii LIST OF ILLUSTRATIONS .••••••••••••••••••••••••••••••••••••••••••••••• vi LIST OF TABLES •••••••••••••••••••••••••••••••.••••.•••••.•••••.••••• ''iii l~Ol.f£NCLATURE. • . • • • • • • • • • • • • . • • • • • • • • • • • • • • • . • • . • • • • • . • • • • • • . • . • • • • • • i..x I. INTRODUCTIOl'~ ••••••••••••••••••••••••.••••••••••••••.•••••••. 1 II. REVIE.w OF LITERATURE .•.•••••••••••.•.•.•••••.••••••.•.•..••. 5 III. TEST EQUIP}{El~T ••••••••.•••••••••••••••••••••••••••••••.••••. IV. TEST SPECilvffil~S • • • • • • . • • • • • • • . • • • . • • • . • • • . • . • • • . • . • • • • • • . • . • . 11 A. Material. ll 1. Strength Tests .•.................................... ll 2. Calibration ........................................ 12 B. Design of Notched Specimens •.....•........•............. 14 C. Machining of Notched Specimens .......................... 14 v. TEST PROCEDURE .............................................. 22 VI. ANALYSIS AND RESULTS •••••••••••••••••••••••••.•.•••••.•••••• 2} A. Finite Element Analysis ................................ 27 B. Pr1otoelastic Ar1alysis .................................. 31 c. Results ............•........•........................... 31 VII. CONCLUSION •••••••••••••••••••••••••••••••••••••••••••••••••• 57 BIBLIOGRAPHY •••••••••••••••••••••••••••••••••••••••••••••••••••• • • • • · 59 61 VITA ......•..•..... · · · · · · · · · · · · · · · · · · · · · · • · · · · · · · · · · · · · · · · · · · · · · ..... v Page APPENDICES .•......................................................... 62 A. PSM-·1 Calibration and Strength Test ...............•......... 63 B. Finite Element Program Input Structure ...................... 73 c. Photographic Measurements ................................... 80 vl LIST OF ILLUSTRATIONS Figure Page 1. Standard Circular Polariscope ................................... 9 2. Strength Test Number 12- Material Properties and Specimen ...... 13 3. Single-Edge-Notch Tension Specimen .............................. 15 4. Basic Notch Geometry ............................................ 16 5. Notched Tensile Specimens ....................................... 17 6. Machining Diagram ............................................... 20 7. Specimen Loading Fixture ....................................... 23 8. Circular Polariscope Lens Orientation .......................... 24 9. Finite Element Grid 60% A/W Undrilled Section A ................ 28 10. Finite Element Grid 60% A/W Drilled Section B ................... 29 11. Finite Element Grid 60% A/W Drilled and Undrilled Common Grid Sect ion.................................................... 30 34 12. 20% A/W SEN Specimen in Tension ... ~ ... ... .. 13. 40/~ A/"vJ SEN Specimen in Tension ...... ... .. .... 35 14. 60% A/W SEN Specimen in Tens ion ...... ..... ... ... .... 36 ., . 15. 80% A/W SEN Specimen in .LellSlOll .. ... .. .. J/' '"'(' 16. Close-up View of 60/~ A/H SEN Specimen ........................... -''~ 17. Stress Distribution for 60% A/tv (Drilled) ....................... 48 18. Stress Distribution for 60% A/W (Undrilled) ..................... 49 19. Stress Distribution for 60% A/W (Experimental) .................. so 20. Stress Distribution for 60% A/W (Numerical) ..................... 51 21. Stress Distribution for 20% A/W ••.•••.••...•...•••.•..•••.••...• 52 22. Stress Distribution for 40% A/W •••.•••••.•.••..•..•••.••..••..•• 53 23. Stress Distribution for 80% A/W •••••••••••••••••••••••••••..•••• 54 24. Experimental Results for Charpy V-Notch in Bending .............. 58 vii Figure Page A-1 Tensile Specimen for Strength Test Number 12 .................... 6 4 A-2 PSM-1 Strength Test Number 12 .................................. 66 A-3 Calibration Disc ..•...•..............•.......................... 68 A-4 PSH-1 Center Point Calibration Curve ........................... 70 A-5 PSM-1 Quarter Point Calibration Curve •.......•...•.............. 71 viii LIST OF TABLES Table I Notched Specimen Dimensions .................................... 18 II Specimen Test Loads and Film Exposures ......................... 26 III Computer Results - 60% A/W -- Undrilled ......................... 32 IV Computer Results - 60% A/W -· Drilled •.......................... 33 v Experimental Data - 20% A/W - Drilled .......................... 39 VI Experimental Data- 20% A/W- Undrilled ........................ ~O VII Experimental Data - 40% A/VJ ·- Drilled .......................... 41 VIII Experimental Data- 40% A/W- Undrilled ....................... 42 ''l 4J IX Experimental Data - 6o /a0 A/H - Drilled •......................... X Experimental Data- 60% A/W- Undrilled ........................ 44 XI Experimental Data- 80% A/W- Drilled .......................... 45 XII Experimental Data- 80% A/W- Undrilled ........................ 46 XIII K Values for 60% A/W ..............................•........... 4 7 0 XIV K Values for All Notched Specimens ............................ 55 0 A-I Strength Test Number 12 Data ................•.................. 65 A-II f'SM-1 Calibration Data. 69 ix NOMENCLATURE A notch depth in single-edge-notch specimen 8 angstrom, one hundred-millionth (10- ) of a centimeter A gross cross sectional area of SEN specimen nom ASA photographic term used in conjunction with film speed A/W ratio of notch depth, A, to specimen width, W, in percent b Burgers vector of a dislocation c one-half the length of an internal crack or the length of crack exposed to the surface d actual distance for close-up photographs a d photographic distance for close-up photographs p D one-half the crystallographic grain size D actual distance for full-view photographs a D photographic distance for full-view photographs p E modulus of elasticity F photoelastic material fringe constant h thickness of photoelastic specimen I moment of inertia K parameter that determines grain-size dependence of fracture strength K elastic stress concentration factor 0 L single-edge-notch specimen length N bending moment n isochromatic fringe order p specimen load R computer program notation for X-direction X SEN single-edge-notch S.F. scale factor for close-up photographs cu S.F.fv scale factor for full--view photographs w single-edge-notch specimen width X distance across plane of notch symmetry from specimen edge y distance from neutral axis for bending stress calculations y distance from plane of notch symmetry z computer program notation for Y-direction coefficient
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