FLAW GROWTH AND FRACTURE Proceedings of the Tenth National Synnposium on Fracture Mechanics A symposiunn sponsored by ASTM Committee E-24 on Fracture Testing of Metals American Society for Testing and Materials Philadelphia, Pa., 23-25 Aug 1976 ASTM SPECIAL TECHNICAL PUBLICATION 631 J M Barsom, symposium chairman List price $49.75 04-631000-30 # AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa 19103 Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized © by AMERICAN SOCIETY FOR TESTING AND MATERIALS 1977 Library of Congress Catalog Card Number: 77-73543 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, Md, October 1977 Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword This publication, Flaw Growth and Fracture, contains papers presented at the Tenth National Symposium on Fracture Mechanics which was held 23-25 August 1976 at Philadelphia, Pa The American Society for Testing and Materials' Commitee E-24 on Fracture Testing of Metals sponsored the symposium J M Barsom, U S Steel Corporation, Monroeville, Pa., served as symposium chairman Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Related ASTM Publications Properties of Materials for Liquefied Natural Gas Tankage, STP 579 (1975), $39.75 (04-579000-30) Mechanics of Crack Growth, STP 590 (1976), $45.25 (04-590000-30) Fractography—Microscopic Cracking Process, STP 600, (1976), $27.50 (04-600000-30) Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized A Note Of Appreciation to Reviewers This publication is made possible by the authors and, also, the unheralded efforts of the reviewers This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing 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 with appreciation their contribution ASTM Committee on Publications Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Editorial Staff Jane B Wheeler, Managing Editor Helen M Hoersch, Associate Editor Ellen J McGlinchey, Senior Assistant Editor Kathleen P Zirbser, Assistant Editor Sheila G Pulver, Assistant Editor Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Introduction Fracture Mechanics in the Elastic-Plastic Regime—p c PARIS J-Integral—What Is It? Crack-Tip Stress and Strain Fields Linear-Elastic Crack-Tip Stress and Strain Fields Elastic-Plastic Crack-Tip Stress and Strain Fields The Intensely Deformed Nonlinear Zone J-Integral Analysis for Monotonic Loading with Abrupt Failure or Stable Tearing J-Integral Rate for Time-Dependent Plasticity Application of J-Integral Analysis to Fatigue-Crack Growth Computation Methods and Estimates for J Determination Summary of the Comprehensive Nature of J-Integral Analysis Comparative Applicability of J-Integral and Other Methods Conclusions 10 10 12 14 15 17 19 24 25 26 Path Dependence of the J-Integral and the Role of / as a Parameter Characterizing the Near-Tip Field—R M MCMEEKING 28 Definition of the J-Integral Path Dependence of the J-Integral Path Dependence of the J-Integral in a Rigid-Plastic Model Crack and Notch-Tip Blunting Deformation Near Notch Tips in Incremental and Deformation Theory Materials 30 31 35 38 39 Fracture Analysis Under Large-Scale Plastic Yielding: A Finite Deformation Embedded Singularity, Elastoplastic Incremental Finite-Element Solution—s N ATLURI, MICHIHIKO NAKAOAKI, AND WEN-HWA CHEN 42 Brief Description of Formulation Problem Definition Results for J-Integral Conclusions Copyright Downloaded/printed University 44 52 53 60 by by of Comparison of Compliance and Estimation Procedures for Calculating J-Integral Values—j p HICKERSON, JR Procedures Results and Discussion Conclusions 62 65 68 70 Evaluation of the Toughness of Tliick Medium-Strength Steels by Using Linear-Elastic Fracture Mechanics and Correlations Between Ki^ and Charpy V-Notch—B MARANDET AND G SANZ 72 Steels Studied—Heat Treatments Experimental Results Correlations Between ATje and Other Brittleness Parameters Conclusions 73 78 88 94 Correlation Between the Fatigue-Crack Initiation at the Root of a Notch and Low-Cycle Fatigue Data—A BAUS, H P LIEURADE, G SANZ, AND M TRUCHON 96 Materials Experiments Results of Initiation Tests Behavior of Metal at Notch Root Calculation of the Duration of the Initiation Phase Comparison of Different Analyses Conclusions 97 98 99 101 107 108 109 Ductile Rupture Blunt-Notch Fracture Criterion—j A BEGLEY, w A LOGSDON, AND J D LANDES 112 Experimental Procedures Results Discussion Summary and Conclusions 113 116 119 119 Stress-Corrosion Crack Initiation in High-Strength Type 4340 Steel—W G CLARK, JR 121 Material and Specimen Preparation Experimental Procedure Analysis of Blunt-Notch Specimens Experimental Results Discussion Summary and Conclusions Copyright Downloaded/printed University 123 124 126 128 133 136 by A by of W Fatigue-Crack Growth Rate Testing at Higli Stress Intensities— N E DOWLING 139 Laboratory Investigation Discussion Conclusions 140 148 155 Fatigue-Cracli Propagation in Electroslag Weldments—B M KAPADIA AND E J IMHOF, JR 159 Materials and Experimental Procedure Results and Discussion Summary 160 164 172 Fatigue Growtli of Surface Craclcs—T A CRUSE, G J MEYERS, AND R B WILSON 174 Surface Flaw Specimen Correlation Corner Crack Specimen Correlation Conclusions 175 182 188 Stress Intensities for Craclis Emanating from Pin-Loaded Holes— C W SMITH, M JOLLES, AND W H PETERS 190 Analytical Considerations Conclusions 191 200 Dependence of /i^ n tlie Meclianical Properties of Ductile Materials—j LANTEIGNE, M N BASSIM, AND D R HAY 202 J-Integral as a Function of Compliance Plastic Zone Correction Dependence of 7,^ on the Mechanical Properties Experimental Results Discussion Summary and Conclusions 203 205 207 208 213 215 Effect of Specimen Size on J-Integral and Stress-Intensity Factor at the Onset of Crack Extension—H P KELLER AND D MUNZ 217 General Remarks on the Effect of Specimen Size Materials and Experimental Procedure Experimental Results Conclusions Copyright Downloaded/printed University 218 221 223 229 by by of 506 FLAW GROWTH AND FRACTURE Plant, The Japan Steel Works, Ltd., for encouragement given to this study They also acknowledge the cooperation of M Horiuchi and K Nakao References [1] Emmer, L G., Clauser, C D., and Low, J R., Jr., "Critical Literature Review of Embrittlement in 2'/4Cr-lMo Steel," WRC Bulletin, No 183, Welding Research Council, May 1973 [2] Watanabe, J., Shindo, Y., Murakami, Y., Adachi, T., Ajiki, S and Miyano, K., "Temper Embrittlement of 2!4Cr-lMo Pressure Vessel Steel," presented at the ASME 29th Petroleum Mechanical Engineering Conference, Dallas, Tex., American Society of Mechanical Engineers, Sept 1974 [5] Landes, J D and Begley, J A in Fracture Analysis, ASTM STP 560, American Society for Testing and Materials, 1974, pp 170-186 [4\ Kobayashi, H., Hirano, K and Nakazawa, H., "Fractographic Study on Evaluation of Fracture Toughness," presented at the Fifty Third National Meeting of Japan Society for Mechanical Engineers, Sendai, Japan, Oct 1975 [5] Barsom, J M and Rolfe, S T in Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, 1970, pp 281-302 [6] Sailors, R H and Corten, H T in Fracture Toughness, ASTM STP 514, American Society for Testing and Materials, 1972, pp 164-191 [7] Begley, J A and Logsdon, W A., "Correlation of Fracture Toughness and Charpy Properties for Rotor Steels," Scientific Paper 71-1E7-MSLRF-P1, Westinghouse Research Laboratories, July 1971 {8] WuUaert, R A., Ireland, D R., and Tetelman A S., "The Use of the Precracked Charpy Specimen in Fracture Toughness Testing," presented at the Fracture Prevention and Control Symposium, WESTEC 72 Meeting, Los Angeles, Calif., American Society for Metals, March 1972 [P] Brothers, A J., Newhouse, D L., and Wundt, B M., "Results of Bursting Tests of Alloy Steel Disks and Their Applications to Design against Brittle Fracture," presented at the ASTM Annual Meeting, Philadelphia, Pa., 1965 [70] Begley, J A and Toolin, P R., International Journal of Fracture, Vol 9, 1973, pp 243-253 [II] Rice, J R., Paris, P C , and Merkle, J G., in Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536, American Society for Testing and Materials, 1973, pp 231-245 [12] Gentilicore, V J., Pense, A W and Stout, R D., Welding Journal Research Supplement, Vol 49, 1970, pp 341-353 [13] Shabbits, W O., Pryle, W H., and Wessel, E T., "Heavy Section Fracture Toughness Properties of A533 Grade B Class Steel," HSST-TR-6, Westinghouse Electric Corp., Dec 1969 [14] Greenberg, H D., Wessel, E T., Clark, W G., Jr., and Pryle, W H., "Critical Flaw Sizes for Brittle Fracture of Large Turbine Generator Rotor Forgings," Scientific Paper 69-1D9-MEMTL-P2, Westinghouse Research Laboratories, Dec 1969 [15] Kumeno, K., Nishimura, M., Mitsuda, D and Iwasaki, T., "Defects and Fracture Strength of Large Rotor Forgings for Steam Turbines," ASME Paper No 75-Pwr-lO, presented at the Joint Power Conference, Portland, Ore., American Society of Mechanical Engineers, Sept 1975 Copyright by ASTM Int'l (all rights reserved); Sat Dec 09:45:49 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized S R Varanasf Analysis of Stable and Catastrophic Crack Growth Under Rising Load REFERENCE: Varanasi, S R., "Analysis of Stable and Catastrophic Crack Growtli Under Rising Load," Flaw Growth and Fracture, ASTM STP 631, 1977, pp 507-519 ABSTRACT: Some metals exhibit slow crack growth prior to instability under rising load This paper is concerned with an elastic-plastic finite element plane-stress analysis of stable and catastrophic crack growth in a center-cracked panel of a ductile material, subjected to a monotonically increasing applied stress The stable crack growth phenomenon is modeled by incorporating a local failure criterion in the stress-analysis procedure An automatic reidealization procedure is developed to refine the finite element mesh at the new crack-tip position before external load is increased The method is applied to study the crack-growth behavior of geometrically similar panels of different material stress-strain curves, and results are compared with experiment The effects of some important parameters on crack growth and stability under rising load are discussed KEY WORDS: crack propagation, fractures (materials), rising load, elasto-plasticity, failure criterion, aluminum Experimental evidence shows that some metals exhibit slow crack growth prior to instabiUty under rising load, where the plastic region behind the advancing crack tip is unloaded while the region ahead of the crack tip is being loaded The analytical model required for the study of this phenomenon must be able to account for both the changing kinematic boundary conditions associated with crack extension and the hereditary properties of the elastic-plastic material Theoretically, it has been possible to study the phenomenon of stable crack growth only in the case of antiplane shear case (Mode III) [1,2].^ No theoretical solution exists for the opening mode (Mode I) stable crack growth of an elastic-plastic material with arbitrary strain hardening; therefore, a finite element method is used in this investigation Finite element methods were applied previously in the studies of a 'Specialist engineer Stress and Fatigue Research, Boeing Commerical Airplane Company, Seattle, Wash 98124 ^The italic numbers in brackets refer to the list of references appended to this paper 507 Copyright Copyriglil by 1977 Downloaded/printed University of by A S ASTM T M loternational Int'l by Washington (all www.astm.org (University rights of reserved); Washington) Sat pursuant Dec to 508 FLAW GROWTH AND FRACTURE steadily growing crack under monotonically increasing load [3-6] and fatigue crack growth under cyclic loading [7] Reference involved the numerical calculation of the J-integral but did not utilize any failure criterion for crack extension The criterion for crack extension in Ref is the opening angle between the two finite element sides that represent the crack tip Reference describes an initial attempt to explore crack sta^ bility concepts under rising load, utilizing a material dependent criterion; in this paper, a more accurate and efficient finite element method is used to investigate crack extension and crack stability This paper also shows the results of application of the method to panels of different materials and demonstrates the role of basic material strength parameters in ductile fracture Finite Element Analysis The problem of stable and catastrophic crack growth in a center-cracked panel of a ductile material, subjected to a monotonically increasing uniform applied stress, is considered here An incremental elastic-plastic, plane-stress analysis of this cracked panel is performed using a finite element program [8] Due to symmetry, only a quarter panel is discretized by an assemblage of 377 constant strain triangles with 225 nodes A fine mesh is used in the vicinity of the crack tip Away from the crack tip, the mesh size is gradually increased (Fig 1) The panel material is assumed to be isotropically strain hardening, characterized by Von Mises yield condition and Prandtl-Reuss incremental stress-strain relations Tangent Stiffness Method of Elastic-Plastic Analysis In this method, the external load is applied in small steps The matrix equation which governs the response of a discretized structure for n"" load step is given by [A:,]("){A(7}