CRACKS AND FRACTURE

1̂

Proceedings of the

Ninth National Symposium

on Fracture Mechanics

A symposium sponsored by

Committee E-24 on

Fracture Testing of Metals

AMERICAN SOCIETY FOR

TESTING AND AAATERIALS

University of Pittsburgh,

Pittsburgh, Pa., 25-27 Aug. 1975

ASTM SPECIAL TECHNICAL PUBLICATION 601

J. L. Swedlow and M. L. Williams, symposium co-chairmen

List price $51.75

04-601000-30

AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa. 19103

BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1976

Library of Congress Catalog Card Number: 76-1712

NOTE

The Society is not responsible, as a body, for the statements and opinions

advanced in this publication.

Printed in Baltimore, iVId. June 1976

Joseph A. Kies, 1906-1975

Dedication It was with great sorrow that those concerned with

the organization of the Ninth National Symposium on Fracture Mechanics learned that the community of fracture specialists would never again benefit from the wit and wisdom of Joe Kies, one of the pioneers of practical fracture mechanics, highly respected through the world, and held in great affection by those fortunate enough to know him well. The Officers of ASTM Committee E-24 on Fracture Testing of Metals, the members of the Executive Subcommittee, and the members of the National Symposia Task Group of the Executive Committee, all agreed that it would be most

appropriate to dedicate these Proceedings to Joe in recognition that much of our present work rests on foundations that he helped to lay.

In 1959 the progenitor of ASTM Committee E-24 was established to deal with Vanguard and Polaris motor case problems. Surely standardized tests for the case materials were needed; meantime, the analysis and remedial prescription of the disconcertingly fre-quent proof test failures had to proceed with deliber-ate haste. The original master of fracture failure analysis, Kies, got on with this task. With characteris-tic enthusiasm and sagacity, he would examine the "remains," interrogate witnesses, investigate the background, analyze, and report; dozens upon dozens of cases were handled. It was this wealth of experience that set practical objectives to be met by the ASTM test methods of Committee E-24. This was the Kies con-tribution; it was vital to Committee E-24.

Joe Kies became a member of ASTM in 1943 and was always an avid proponent of ASTM goals. After graduating from the University of Illinois in 1935, he became a physicist at the National Bureau of Stand-ards. In 1944, he joined the Western Regional Laboratory of the Department of Agriculture in Al-bany, California, and in 1947, the Oak Ridge Na-tional Laboratory. Taking a position at the Naval Research Laboratory in 1948, his collaboration with G. R. Irwin is now recognized to have been the pioneering effort in establishing the discipline of linear elastic fracture mechanics, the primary basis of Committee E-24 activities. He was responsible for basic papers on the interpretation of fracture surface markings, a skill which prepared him for his Commit-tee E-24 essential work on the Polaris submarine missile. He was first to recognize the superior fracture toughness of warm prestretched acrylics, leading to stronger and lighter aircraft glazing materials. Rec-ognizing his contributions, the Department of the Navy bestowed its highest civilian award in 1971, the Distinguished Civilian Service Award. After his re-tirement Joe contributed generously to the American Society for Metals Handbook, Volume 9, through membership on the Committee on Use of Fractog-raphy for Fracture Analysis. At the time of his death, he was working on Volume 10 as a member of the Committee on Analysis of Brittle and Ductile Failures.

Foreword This publication, Cracks and Fracture, contains papers presented at

the Ninth National Symposium on Fracture Mechanics which was held at the University of Pittsburgh, Pittsburgh, Pa., 25-27 Aug. 1975. The Symposium was sponsored by Committee E-24 on Fracture Testing of Metals of the American Society for Testing and Materials. J. L. Swed-low, Carnegie-Mellon University, and M. L. Williams, University of Pittsburgh, presided as symposium co-chairmen.

The record would not be complete without noting some of the people who lent their talents to the success of the symposium. E. F. Andrews, Corporate Vice President, Materials and Services, Allegheny-Ludlum Industries, spoke at the symposium banquet. His incisive and provocative comments on the criticahty of materials supply gave a clear view of many serious problems pertinent to all of us concerned with the concepts and applications of fracture mechanics. Dean M. C. Hav/k, University of Pittsburgh, handled many of the arrangements; his devoted efforts were central to the smooth running of the meeting. The Technical Steering Committee did the initial paper selection and much of the early planning; the members were P. C. Paris, Brown University, and E. T. Wessel, Research Center, Westinghouse Electric Corporation. Chairmen of the six sessions were J. E. Srawley, Lewis Research Center, National Aeronautics and Space Administration; H. T. Corten, University of Illinois; J. E. Scott, Bethlehem Steel; C. E. Feddersen, Battelle-Columbus; R. J. Goode, Naval Research Laboratory; and E. K. Walker, Lockheed-California. The symposium co-chairmen wish to express their sincere thanks to these many people.

Related ASTM Publications

Fracture Analysis, STP 560 (1974), $22.75, 04-560000-30

Fracture Toughness and Slow-Stable Cracking, STP 559 (1974), $25.25, 04-559000-30

Fatigue and Fracture Toughness—Cryogenic Behavior, STP 556 (1974), $20.25, 04-556000-30

A Note of Appreciation to Reviewers

This publication is made possible by the authors and, also, the un-heralded efforts of the reviewers. This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in review-ing the papers must be acknowledged. The quality level of ASTM publications is a direct function of their respected opinions. On behalf of ASTM we acknowledge their contribution with appreciation.

ASTM Committee on Publications

Editorial Staff

Jane B. Wheeler, Managing Editor Helen M. Hoersch, Associate Editor

Charlotte E. DeFranco, Senior Assistant Editor Ellen J. McGHnchey, Assistant Editor

Contents

Introduction 1

Method for Laboratory Determination of J^—j. D. G. SUMPTER AND C. E. TURNER 3

Determination of / Using Finite Element Based Correlations 4 J Estimation Procedures 5 General Relationship Between J and Absorbed Energy 6 Gage Point Location for Deflection Measurement 7 Ensuring Compatability Between J,, and G for Elastic Behavior 8 Evaluation of J^ from Mouth Opening Displacement 9 Effect on J of Work Hardening 10 Effect of7 of Slow Crack Growth 10 Effect on J of Laterial Constraint 12' Relationship Between J and COD 12 Summary and Discussion 14

Geometry Effects and tlie J-Integral Approacli to Elastic-Plastic Fatigue Crack Growth—N. E. DOWLING 19

Laboratory Investigation 21 Discussion 29 Conclusions and Recommendations 31

Derivation of a Low-Cycle Fatigue Relationship Employing the J-Integral Approach to Grack Growth—D. F. MOWBRAY 33

Nomenclature 33 Derivation 36 Discussion 42 Summary 45

Relevance of Nonlinear Fracture Mechanics to Creep Cracking—K. M. NIKBIN, G. A. WEBSTER, AND C. E. TURNER 47

Application of Nonlinear Fracture Mechanics to Creep Cracking 51 Comparison with Experimental Data 53 Discussion 58 Conclusions 59

Assessment of Strength-Probability-Time Relationships in Ceramics—E. M. LENOE AND D, M. NEAL 6 3

Experimental Procedures for Slow Crack Growth 65 Elementary Life Estimating Procedure 67 Alternate Life Estimating Procedures 70 Monte Carlo Method 74 Results and Discussion 76 Summary and Conclusions 80

Application of Fracture Mechanics to the Thermostructural Failure of Graphite—H. S. STARRETT, A. D. CULL, AND G. R. IRWIN 86

Temperature/Stress Test 91 Ki Solution for the Temperature/Stress Specimen 95 Reduction of the Data 101 Discussion 103 Conclusion 107

Fracture Toughness of ATJ-S Graphite and CVD Carbon-Carbon Composites at Elevated Temperatures—L. R. HETTCHE AND T. R. TUCKER 109

Material Description 110 Experimental Procedure 111 Results ' 113 Discussion 122

Mixed Mode Fracture in Anisotropic Media—j. G. WILLIAMS AND M. W. BIRCH 125 Experiments 127 Discussion and Conclusions 133

Applicability of theA"ĵ |̂, Concept to Very Small Defects—w. G. CLARK, JR. 138 Material 139 Experimental Procedure 140 Experimental Results 145 Discussion 147 Summary and Conclusions 152

Mean Stress and Environmental Effects on Near Threshold Fatigue Crack Growth—^JULIUS MAUTZ A N D V O L K E R WEISS 154

Experimental 155 Results and Discussion 159 Summary and Conclusions 166

Notch-Yield Ratio as a Quality Control Index for Plane-Strain Fracture Toughness—J. G. KAUFMAN, G. T. SHA, R, F. KOHM, AND R. J. BUCCI 169

Scope 170 Background 170 Specimen and Test Procedure 171 Correlation with Plane-Strain Fracture Toughness 175 Acceptance or Rejection 181 Summary 187

Ductile Fracture of Cylindrical Vessels Containing a Large Flaw—F. ERDO-G A N , G. R. IRWIN, AND M. RATWANI 191

Analytical Model 192 Load Carrying Capacity for Constant Crack Opening Stretch 197 Further Consideration of Fracture Failure by Net Ligament Plastic Instability 202 Conclusions 207

Pilot Study of the Fracture Arrest Capabilities of A553B Steel—G. T. HAHN, R. G. HOAGLAND, M. F. KANNINEN, AND A. R, ROSENFIELD 209

Nomenclature 209 Experimental Procedure 213 Dynamic Analysis 214 Experimental Results 224

Discussion 227 Conclusions 230

Note on the Dependence of Crack Velocity on Driving Force for an Epoxy Adliesive—s. MOSTOVOY, P. B. CROSLEY, AND E. J. RIFLING 234

Material and Test Procedure 237 Results and Discussion 241 Conclusions 243

Predicting Fatigue Crack Retardation Under Single and Intermittent Overloading—K. N. MORMAN, JR. AND R. G. DUBENSKY 245

Nomenclature •̂ -̂' Theoretical Development 248 Correlation Procedure and Results 251 Predictions and Discussion 254 Conclusions 260

Three-Dimensional Stress Distribution of a Double-Cantilever Beam with a Side Notch—w. F. KIRKWOOD AND M. E. PRADO 262

Nomenclature 262 Experimental Procedure 263 Model Slicing and Fringe Evaluation 264 Discussion of Experimental Analysis and Results 265 Conclusions 272

Fracture Dynamics of Wedge-Loaded Double Cantilever Beam Specimen— A. S. KOBAYASHI, S. MALL, AND M. H. LEE 2 7 4

Experimental Procedure 276 Results Discussion

279 286

Preliminary Results of a Program for Developing Fracture Toughness Data on Ferritic Nuclear Pressure Vessel Steels—K, E. STAHLKOPF, R. E. SMITH, W. L. SERVER, AND R. A. W U L L A E R T 291

Background 293 Materials and Test Matrix 294 Testing and Data Analysis Procedures 296 Interlaboratory Program 301 Preliminary Results on A533-B-1 Steel 302 Conclusion 306

7jj. Test Results from Two Steels—^i. H. UNDERWOOD 312 Nomenclature 312 Introduction and Objective 313 General/ic Test Method 316 Jic Test Procedure 316 Discussion of Test Results 317 Proposed /]

Discussion of Results 341 Concluding Remarks 344

Fatigue Crack Growth and J-Integral Fracture Parameters of Ti-6A1-4V at Ambient and Cryogenic Temperatures—s.. L. TOBLER 346

Experimental 347 Material and Specimen 349 Procedure 349 Results 354 Discussion 365 Summary 368

Effect of Cooling Rate on Fracture Behavior of Mill-Annealed Ti-6A1-4V— R. E. LEWIS, J. G. BJELETICH, T. M. MORTON, AND R. A. CROSSLEY 371

Material 372 Thermal Processing 373 Experimental Procedure 373 Computer Modeling 376 Results and Discussion 377 Conclusions 3g9 Recommendation 39O

Fracture Toughness Testing of Glassy Plastics—R. D. MARGOLIS, R. W. DUNLAP, AND H. MARKOVITZ 391

Nomenclature 391 Procedure 394 Results 395 Discussion of Instability 404 Conclusions 406

Brittle Fracture (ATĵ ) Behavior of Cracks Emanating from Notches—s. R. NOVAK AND J. M. BARSOM 4 0 9

Materials and Experimental Work 412 Results and Discussion 41g Summary and Conclusions 443

Weight Functions for Three-Dimensional Symmetrical Crack Problems—R. C. LABBENS, J. HELIOT, AND A. PELLISSIBR-TANON 448

Nomenclature 448 Weight and Influence Functions 450 Semi-Infinite Crack in an Infinite Solid 451 Penny-Shaped Crack in an Infinite Solid 453 Consistency with the Displacements of Bueckner's Fundamental Fields 454 Strength of the Singularity 457 Outline of the Numerical Calculation 457 Calculated Weight Function for a Penny-Shaped Crack in an Infinite Solid 459 Particular Problem of an Applied Stress Function of x Only 465 Mixed-Mode Problems 466 Conclusions 467

The Weight Function Method for Determining Stress Intensity Factors—^P. C. PARIS, R. M. MCMEEKING, AND H. TADA 4 7 1

A Special Method for Determining the Weight Function, Mode I 474 Mode II and III Weight Functions 476

Near Tip Beuckner Displacement Fields 477 Closed-Form Weight Functions 478 An Example of Finite Element Results 480 Closed Form Examples 483

A Laser Interferometry Method for Experimental Stress Intensity Factor Calibration—D. E. MACHA, W. N. SHARPE, JR., AND A. F. GRANDT, JR. 490

Experimental Procedures 494 Results and Discussion 502

Criteria for Growth of the Angled Crack— Ĵ. L. SWEDLOW 506 Tensile Loading 510 Compressive Loading 513 Concluding Remarks 518

Crack Tip Strain—^A Comparison of Finite Element Method Calculations and Moire Measurements—WAN-LIANG HU AND H. W. LIU 522

Qualitative Discussion on the Three Dimensional Characteristics of Crack Tip Deformation 523

Finite Element Calculation 525 Discussions 532 Summary and Conclusions 534

Theoretical and Experimental Analysis of Crack Extension at Nozzle Junctions—M. J. G. BROEKHOVEN 535

Finite Element Studies 539 Analytical Studies 54g Experimental Investigations 551 General Conclusions and Discussion 554

Side-Cracked Plates Subject to Combined Direct and Bending Forces—^J. E. SRAWLEY AND B. GROSS 559

Nomenclature 559 Boundary Collocation Analysis 562 Form and Use of Results 564 End-Point Values and Interpolation Expressions 569 Crack Mouth Displacement Slopes 571 Discussion 572 Summary 576