Astm stp 995 v1 1989

STP 995 Nonlinear Fracture Mechanics: Volume I Time-Dependent Fracture A Saxena, J D Landes, and J L Bassani, editors ASTM 1916 Race Street Philadelphia, PA 19103 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Library of Congress Cataloging-in-Publication Data Nonlinear fracture mechanics/A Saxena, J D Landes, and J L Bassani, editors (STP ;995) Papers presented at the Third International Symposium on Nonlinear Fracture Mechanics, held 6-8 Oct 1986 in Knoxville, Tenn., and sponsored by ASTM Committee E-24 on Fracture Testing "ASTM publication code number (PCN) 04-995001-30." Includes bibliographies and indexes Contents: v Time-dependent fracture ISBN 0-8031-1174-6 Fracture mechanics Congresses I Saxena, A (Ashok) II Landes, J D (John D.) III Bassani, J L (John L.) IV International Symposium on Nonlinear Fracture Mechanics (3rd : 1986 : Knoxville, Tenn.) V ASTM Committee E-24 on Fracture Testing VI Series: ASTM special technical publication ; 995 TA409.N66 1988 620.1'126~dc19 88-38147 CIP Copyright by A M E R I C A N SOCIETY FOR TESTING AND MATERIALS 1988 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Peer Review Policy Each paper published in this volume was evaluated by three peer reviewers The authors addressed all of the reviewers' comments to the satisfaction of both the technical editor(s) and the ASTM Committee on Publications The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of these peer reviewers The ASTM Committee on Publications acknowledges with appreciation their dedication and contribution of time and effort on behalf of ASTM Printed in Ann Arbor, MI February 1989 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword This publication, Nonlinear Fracture Mechanics: Volume I Time-Dependent Fracture, contains papers presented at the Third International Symposium on Nonlinear Fracture Mechanics, which was held 6-8 Oct 1986 in Knoxville Tennessee ASTM Committee E-24 on Fracture Testing sponsored the event The cochairmen for the symposium section on Time-Dependent Fracture were A Saxena, Georgia Institute of Technology, and J L Bassani, University of Pennsylvania Both men, along with J D Landes, University of Tennessee, served as editors of this publication Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Overview CREEP CRACK GROWTH Evaluation of the C, Parameter for Characterizing Creep Crack Growth Rate in the Transient Regime JOHN L BASSANI, DONALD E HAWK, AND ASHOK SAXENA A Critical Assessment of Global Mechanical Approaches to Creep Crack Initiation and Creep Crack Growth in 316L Steel PHILIPPE BENSUSSAN, ROLAND PIQUES, AND ANDRE PINEAU 27 A Numerical Study of Non-Steady-State Creep at Stationary Crack Tips-CHUN-POK LEUNG, DAVID L MCDOWELL, AND ASHOK SAXENA 55 Crack Growth in Small-Scale C r e e p - - J O H N L BASSANI, DONALD E HAWK, AND FWU-HWEI WU 68 Growth of Macroscopic Cracks by Void Coalescence Under Extensive Creeping C o n d i t i o n s - - C H U N G - Y U E N HUI AND KUANG-CHONG WU 96 Creep Crack Growth of Alloy 800H in Controlled-Impurity Helium-JUDE R FOULDS Creep Embrittlement Susceptibility and Creep Crack Growth Behavior in Low-Alloy Steels: An Assessment of the Effects of Residual Impurity Elements and Postweld Heat Treatment Condition on Creep Ductility and Crack Growth sH[NJI KONOSU AND KEIKICH[ MAEDA 112 127 Influence of Aging on High-Temperature Creep Crack Growth in Type 304H Stainless Steel G M BUCHHEIM, C BECHT, K M NIKBIN, V DIMOPOLOS, G A WEBSTER~ AND D ft SMITH 153 An Anisotropic, Damage-Coupled Viscoplastic Model for Creep-Dominated Cyclic Loading DAVID L MCDOWELL,KWANG-ILHO, AND JAMES STALLEY 173 Experimental Determination of the High-Temperature Crack Growth Behavior of lncoloy 0 H - - T H O M A S HOLLSTEIN AND BERT VOSS 195 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized DYNAMIC FRACTURE Three-Dimensional Transient Analysis of a Dynamically Loaded Three-Point-Bend Ductile Fracture Specimen T NAKAMURA, C F SHIH, 217 A N D L B F R E U N D Influence of Loading Rate on the Deformation and Ductile Fracture of A533B Steel at ~ J SMITH A N D STEPHEN J G A R W O O D 242 Measurement of Dynamic Fracture Toughness of Ductile Materials-E D W I N M H A C K E T T , J A M E S A J O Y C E , A N D C H O O N F O N G S H I H 274 An Advanced Procedure for J-R Curve Testing Using a Drop Tower-J A M E S A J O Y C E A N D EDWIN M H A C K E T I " 298 Measurement of the J-Integral with Caustics: An Experimental and Numerical Investigation ALAN T Z E H N D E R , A R E S J R O S A K I S , A N D R A M A R A T N A M 318 NARASIMHAN Correlation of Optical Caustics with Fracture Behavior of High-Strength Steels-R A L P H W J U D Y , J R , A N D R O B E R T J S A N F O R D 340 CYCLIC LOADING An Experimental Study of the Validity of a Delta J Criterion for Fatigue Crack Growth DAVID A JABLONSKI 361 Combined-Mode Low-Cycle Fatigue Crack Growth Under Torsional Loading-R O Y A WILLIAMS A N D W E L D O N W W I L K E N I N G Fatigue Crack-Tip Mechanics in 7075-T6 Aluminum Alloy from High-Sensitivity Displacement Field Measurements GIANNI NICOLETFO 388 415 Dislocation-Free Zone Model of Fracture Under Reverse Loading-S H I H - J U N G C H A N G A N D S M I C H A E L O H R 433 F R A C T U R E OF N O N M E T A L S Fracture Toughness Testing of Polyethylene Pipe Materials ROBERT E J O N E S , J R , A N D W A L T E R L B R A D L E Y 447 Nonlinear Fracture of Concrete and CeramicS ALBERT S KOBAYASHI, JIA-JI DU, NIEL M H A W K I N S , A N D R I C H A R D C B R A D T 457 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions au INDEXES Author Index 475 Subject Index 477 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP995-EB/Jan 1988 OVERVIEW Elastic-Plastic Fracture Mechanics (EPFM) had its birth in the late 1960s and early 1970s In nearly two decades of growing effort, the field has seen a maturing trend as well as a change in emphasis EPFM developed in response to a real technology need: the parent technology, linear elastic fracture mechanics (LEFM), did not apply to many of the engineering materials used in modern structures New and better materials were developed to attain more ductility and higher fracture toughness Where LEFM could no longer be used for analyzing failures in these materials, EPFM provided the solution To organize and document the results of the growing research effort in the field, ASTM Committee E-24 on Fracture Testing sponsored the First International Elastic-Plastic Fracture Symposium in Atlanta, Georgia, in 1977 The bulk of this symposium, as peer-reviewed papers, is published in ASTM STP 668, Elastic-Plastic Fracture Subsequently, a second international symposium on this subject was held in Philadelphia in 1981, which resulted in the two-volume ASTM STP 803, Elastic-Plastic Fracture: Second Symposium The 1980s saw a rise in more general interest in nonlinear fracture mechanics topics, particularly time-dependent fracture mechanics Therefore, the title for the next symposium was modified to include this emerging field As a result, the Third International Symposium on Nonlinear Fracture Mechanics was held in Knoxville, Tennessee, in 1986 This symposium, sponsored by ASTM Committee E-24 and its Subcommittee E24.08 on Elastic-Plastic and Fully Plastic Fracture Mechanics Technology, featured both time-dependent and elasticplastic topics in fracture mechanics The time-dependent fracture mechanics papers are published in Volume I (this volume) of this Special Technical Publication (ASTM STP 995) Volume II features the elastic-plastic contributions to the symposium In the mid-1970s, when consensus in the approaches to elastic-plastic fracture was emerging, the attention of some researchers shifted to elevated-temperature crack growth behavior The motivation for this work came primarily from projects active at the time, and was directed toward building commercial advanced nuclear reactors, improving energy conversion efficiencies of conventional power plants and jet engines, exploring the feasibility of alternate energy sources such as coal gasification, and understanding failures in major equipment, such as Tennessee Valley Authority's Gallatin steam turbine rotor New concepts which could adequately account for the presence of time-dependent creep strains in cracked body analysis were needed for integrity assessment and prevention of failures in these components A creep analog to the J-integral called C* was proposed in 1974, which over time has proven to be the first major breakthrough in the development of time-dependent fracture mechanics (TDFM) In its range of applicability, C* is now a well-accepted cracktip parameter At the time of the second elastic-plastic fracture symposium in 1981, it was becoming clear that the application of C* is limited to cracked bodies undergoing dominantly secCopyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed Copyright9 bybyASTM lntcrnational www.astm.org University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized NONLINEAR FRACTURE MECHANICS: VOLUME I ondary-stage creep Researchers were engaged in understanding the limitations of C* and also in extending the concept into the small-scale creep (SSC) regime, where a good portion of the practical problems lie Only single session was devoted to papers on this subject at the second symposium In the third symposium, TDFM was one of the prominent themes and several sessions were organized on the subject The papers from these sessions are included in the first section of this volume Creep Crack Growth The papers on creep crack growth deal with the issues of crack growth under small-scale creep conditions, the usefulness of the recently proposed C, parameter, the applicability of damage mechanics concepts in understanding micromechanics and micromechanisms of creep crack growth, embrittlement due to aging in service and its influence on creep crack growth behavior, and experimental methods While significant progress has occurred since the last symposium on this topic, a lot more remains to be done Some issues not addressed in the papers at the symposium include the influence of cyclic loading and inclusion of creep deformation other than that represented by power-law creep These are areas of current research Also, further evaluation of the C, parameter is likely to continue until a consensus can be reached, and stable and unstable crack growth and fracture at elevated temperature should be addressed Therefore, a good number of problems still remain unresolved in this area Although some of the original reasons for developing TDFM are no longer the primary driving force, the field has found considerable use in remaining life assessment of fossil power-plant components and will be useful in the development of advanced aircraft Hence, this area is expected to be represented in future symposia on nonlinear fracture mechanics Dynamic Fracture The second section of this volume is devoted to dynamic fracture This is also one of the newer areas of research in fracture mechanics The papers in this section deal with the issue of calculating the crack driving force, with proper emphasis on inertial effects and the measurement of fracture toughness under conditions of high rate loading This area continues to be of significant interest to the nuclear power industry and the U.S Navy Cyclic Loading The papers in the section on cyclic loading are concerned with experimental evaluation of AJ for characterizing fatigue crack growth behavior under gross plasticity conditions and with cracking under mixed-mode loading Crack-tip mechanics under cyclic loading was studied by measuring displacements, using optical interferometry Damage accumulation in the form of dislocation motion at the crack-tip field was modeled in another paper Fracture of Nonmetals The final section of the book is devoted to papers based on exploratory work in the area of fracture in nonmetallic materials, such as polymers and ceramics This is an emerging field in which there is considerable need for new ideas On glancing over the Third International Symposium on Nonlinear Fracture Mechanics and Volume I of this Special Technical Publication, it is c/ear that very significant progress has occurred in the field of TDFM The field is not very far along in its readiness for Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions au OVERVIEW applications when we compare its recent progress to the status of its parent technologies, L E F M and EPFM The concepts are based on sound principles which should ensure their widespread acceptance and usage in the future The same is true for the status of dynamic fracture mechanics In the area of cyclic loading, the h J parameter has survived ten years of criticism, and it appears that the theory behind its success in correlating experimental data is becoming increasingly understood Fracture mechanics of new materials such as polymers, ceramics, and composites are fields in which considerable interest is expected in the near future A Saxena Georgia Institute of Technology, Atlanta, GA 30332; symposium cochairman and editor J D Landes University of Tennessee, Knoxville, TN 37996; symposium cochairman and editor J L Bassani University of Pennsylvania, Philadelphia, PA 19104; symposium cochairman and editor Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 466 NONLINEAR FRACTURE MECHANICS: VOLUME I 250 -FEH MODEL 200 - LEFH MODEL o 150- Z Q I00- o 50- ' ' '"'' I ' ' I ~ I ' ' ~ 80 10 I ~ ' 30 ' ' ' 40 LORD POINT DEFLECTION (micron) FIG 14 Load versus load-point deflection for RBSN prenotched bend specimen testing at 1200~ TENSILE STRENGTH 300 l'iPm HODULUS OF ELASTICITY 400 C.~~ POISSON'S RRTIO 0.15 ~ I I g mm FIG mm mum mm 15 SiC/mullite composite flexural specimen Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized KOBAYASHI ET AL ON CONCRETE AND CERAMICS 467 Finite-Element Model The three-segment model of the fracture process zone, as shown in Fig 4, was incorporated into a static and an implicit dynamic finite-element code The distribution of the three segments of the fracture process zone which satisfy the crack closure stress versus C O D relation for a particular material, such as that in Fig 5, are determined through a numerical iteration process This iteration process is similar to the incremental-iterative procedure of elastic-plastic analysis It consists of matching, through trial and error, an assumed variation in COD along the postulated fracture process zone with the computed C O D for the given load history and the appropriate material-dependent crack closure stress distribution for that fracture process zone Three-Point-Bend Specimens The state of stress in a CLWL-DCB specimen is similar to that in a segment on the tension side of a beam in bending Therefore, the foregoing crack closure stress versus crack-opening displacement relation can be used to analyze the nonlinear response of concrete beams or ceramic and ceramic/ceramic composite three-point-bend beams Impacted Concrete Beam A dynamic finite-element model was used to simulate the dynamic response of an impactloaded plain-concrete specimen [9,22,23], as shown in Fig The use of this static fracture process zone in the impact-loaded specimen was justified by demonstrating that the appropriate crack velocity for analyzing the bend specimens was less than 10% of the dilatational 400 - m 300 O_ In td 200 ttl U 1DO U 0 I0 12 CRRCK OPENING DISPLACEMENT ( M i c r o n ) FIG 16 Crack closure stress versus crack-opening displacement for a SiC/mullite composite flexural specimen Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 468 NONLINEAR FRACTURE MECHANICS: VOLUME I 800 c FEH MODEL 600- 3" ill U 0c 400 Z tU or 200 - " i/~l I I i I I I0 , , I I 80 , , , , I 30 I , I I I I 40 I I I I 50 I I I I I 60 RPPL I FD n 15PLACEMENT t I'I I c r o n FIG 17 Reaction force versus applied displacement velocity of concrete The minimum finite-element size for that analysis was taken as the average aggregate size, which was, in turn, assumed to be 10 mm The test beam, which was instrumented with two accelerometers, was impacted by a falling hammer at an impact velocity of about m/s The resultant load-time history is shown in Fig The dynamic finite-element model, which must be driven in its generation mode [20], requires as input data the experimental information on the crack position versus time history Because such experimental data were lacking, the two-step crack velocity history observed in Homalite100 dynamic-tear-test specimens [24] was used, with appropriate adjustments, to match the recorded total time to complete failure Figure shows the crack length versus time histories computed with and without the fracture process zone and the crack closure stress of Fig For finite-element models with and without the fracture process zones, the total times to failure were 0.7 and 1.6 ms, respectively The total time to failure for the test beam was estimated from sequential photographs to be between and ms Obviously, that value is closer to the lapse time predicted with a process zone than that predicted without such a zone This result demonstrates that linear elastic analysis is inadequate for characterizing the nonlinear fracture response of concrete and that the use of a fracture process zone is necessary to retard crack propagation rates to realistic values Figures and 10 show the load-point displacement and velocity variations, both measured and predicted, during the fracture process The continuously varying acceleration traces reported in Ref were integrated to provide velocity traces which were then compared with the numerical results The velocity-time traces are sensitive to the finite-element model used, while the load-displacement relations are not There is only fair agreement between the measured and computed velocities at 75 mm from the center of the beam Nevertheless, it is obvious that the predictions with a fracture process zone are more reasonable than those without that zone Mindess, S., personal communication, University of British Columbia, Vancouver, BC, Canada Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized KOBAYASHI ET AL ON CONCRETE AND CERAMICS 469 Reaction-Bonded Silicon Nitride Prenotched Bend Specimen at 1200~ A reaction-bonded silicon nitride (RBSN) prenotched bend specimen, as shown in Fig 11, was loaded to failure under a displacement-controlled condition in a rigid fixture The prenotched root radius was 0.15 mm, which was sufficiently blunt for this brittle Ceramics to fail catastrophically at room temperature At 1200~ however, the propagating crack arrested after traversing about 75% of the beam depth; it then grew in a stable manner to failure CMODs throughout the fracture process were monitored through fused silicate windows in the furnace with a laser interferometric strain gage The stable crack growth process was modeled using a static finite-element model with the crack closure stress versus COD relation of Fig 12 That relation is a slight variation of the relation of Fig 5, with appropriate changes to reflect the order of magnitude differences between the physical dimensions of concrete and ceramic specimens Since neither the location of the traction-free, physical crack tip nor the location of the true crack tip at the end of the fracture process zone were available, Fig 12 was established by the propagation mode of finite-element analysis where the experimentally determined, applied load versus CMOD relationship of Fig 13 were matched through a trial-and-error process The finite-element model with the resultant fracture process zone yielded the applied load versus load-point displacement relation indicated by the unbroken curve in Fig 14 Also shown in the figure by the broken curve is the corresponding relationship obtained by using linear elastic fracture mechanics The differences between the relations obtained using linear elastic fracture mechanics (LEFM) and the fracture process zone demonstrates that nonlinear analysis is needed to correctly model the fracture response of this seemingly brittle RBSN specimen Silicon Carbide Whisker/Mullite-Matrix Composite Flexural Specimen The ceramic composite specimen [25] modeled in this study was a mullite flexural bar with 30% by volume of randomly oriented and uniformly distributed silicon carbide (SIC) whiskers This unnotched beam, with the dimensions shown in Fig 15, was subjected to an increasing applied displacement loading at room temperature Again, lacking any experimental details on the fracture process zone, the linear crack closure stress versus COD relation, as shown in Fig 16, was assumed Larger crack closure stresses than those of the RBSN specimens, in the wake of the fracture process zone, are realistic because larger tensile forces appear to be transmitted across the fracture process zone by fibers bridging the crack [26] Figure 17 shows the reaction force versus the applied load-point displacement relationship predicted as the crack initiates and propagates through 93% of the beam depth While the results cannot be correlated with experimental results for this composite, the curve is qualitatively similar to those obtained in unnotched composite flexure specimens [27] Conclusions Dynamic and static finite-element models which can represent the fracture processes of an impacted unnotched concrete bend specimen, a RSBN prenotched bend specimen, and a SiC-whisker/mullite-matrix composite flexural specimen are reported The need for a different crack closure stress versus COD relationship for fracture process zones of those models is a clear indication of the complex nature of the nonlinear fracture processes involved in failures of these brittle materials Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions author 470 NONLINEAR FRACTURE MECHANICS: V O L U M E I Acknowledgements The results reported in this paper were obtained under National Science Foundation (NSF) Grant No MSM 851053, National Aeronautics and Space Administration (NASA) Grant No, N A G W 199, U.S Department of Energy (DOE) Contract No 86A-00209C References [1] Hillerborg, A., Modeer, M., and Petersson, R E., "Analysis of Crack Formation and Growth in Concrete by Means of Fracture Mechanics and Finite Elements," Cement and Concrete Research, Vol 6, No 6, November 1976, pp 773-782 [2] Modeer, M., "A Fracture Mechanics Approach to Failure Analysis of Concrete Materials." Report TVBM-1001, University of Lund, Lund, Sweden, 1979 [3] Petersson, P E., "Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials," doctoral dissertation, University of Lund, Lund, Sweden, 1981 [4] Wecharatana, M and Shah, S P., "Prediction of Nonlinear Fracture Process Zone in Concrete," Journal of Engineering Mechanics, Vol 109 (S), October 1983, pp 1231-1246 [5] Visalvanich, K and Naaman, A E., "Fracture Model for Fiber Reinforced Concrete," American Concrete Institute Journal, March/April 1983, pp 128-138 [6] Cho, K.-Z., Kobayashi, A S., Hawkins, N M., Barker, D B., and Jeang, E-L., "Fracture Process Zone of Concrete Cracks," Journal of Engineering Mechanics, Vol 110, No 8, August 1984, pp 1174-1184 [7] Jeang, E-L and Hawkins, N M., "Non-Linear Analysis of Concrete Fracture," Report SM 852, Department of Civil Engineering, University of Washington, Seattle, WA, July 1985 [8] Kobayashi, A S., Hawkins, N M., and Du, J J., An Impact Damage Model of Cement-Based Composites: Strain Rate Effects on Fracture, S Mindess and S P Shah, Eds., Material Research Society, Boston, MA, 1986, pp 203-216 [9] Bentur, A., Mindess, S., and Banthia, N., "The Behaviour of Concrete Under Impact Loading: Experimental Procedures and Methods of Analysis," Materials and Structures, Vol 19, No 113, September/October 1986, pp 371-378 [10] Bassani, J L and Vitek, V., "Propagation of Crack Under Creep Conditions," Proceedings, Ninth U.S Congress of Applied Mechanics, American Society of Mechanical Engineers, Los Angeles, CA, 1982, pp 127-133 [11] Rice, R L., "Pores as Fracture Origins in Ceramics," Journal of Material Sciences, Vol 19, 1984, pp 895-914 [12] Evans, A G and Faber, K T., "On the Crack Growth Resistance of Microcracking Brittle Materials," Journal of the American Ceramic Society, Vol 67, No 4, 1984, pp 255-260 [13] Evans, A G and Hener, A H., "Review-Transformation Toughening in Ceramics: Martensitic Transformations in Crack-Tip Stress Fields," Journal of the American Ceramic Society, Vol 63, 1980, pp 241-246 [14] McMeeking, R and Evans, A G., "Mechanics of Transformation-Toughening in Brittle Materials," Journal of the American Ceramic Society, Vol 65, 1982, pp 242-248 [15] Budiansky, B., Hutchinson, J., and Lambroupolos, J C., "Continuum Theory Of Dilatant Transformation Toughening in Ceramics," International Journal of Solids and Structures, Vot 19, 1983, pp 337-355 [16] Cedolin, L., Poli, S D., and Iori, I., "Experimental Determination of the Fracture Process Zone in Concrete," Cement and Concrete Research, Vol 13, 1983, pp 557-567 [17] Barker, D B., Hawkins, N M., Jeang, E-L., Cho, K Z., and Kobayashi, A S., "Concrete Fracture in CLWL Specimen," Journal of Engineering Mechanics, Vol 111, No 5, May 1985, pp 623-638 [18] Hughes, B P and Chapman, G P., "The Complete Stress-Strain Curve for Concrete in Direct Tension," RILEM Bulletin, No 30, 1966, pp 95-97 [19] Walraven, J., "Fundamental Analysis of Aggregate Interlock," Journal of Engineering Mechanics, Vol 107, November 1981, pp 2245-2270 [20] Kobayashi, A S., "Dynamic Fracture Analysis by Dynamic Finite-ElementMethod Generation and Propagation Analyses," Nonlinear and Dynamic Fracture Mechanics, N Perrone and S N Atluri, Eds., ASME AMD-35, American Society of Mechanical Engineers, New York, 1979, pp 19-36 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized KOBAYASHI ET AL ON CONCRETE AND CERAMICS 471 [21] Jenkins, M G., Kobayashi, A S., White, K W., and Bradt, R C., "Crack Initiation and Arrest in a SiC-Whisker/Al203-MatrixCeramic/Ceramic Composite," Journal of the American Ceramic Society, Vot 70, No 6, June 1987, pp 393-395 [22] Mindess, S., "Rate of Loading Effects on the Fracture of Cementitious Materials," Application of Fracture Mechanics to Cementitious Composites, S E Shah, Ed., Martinus Nijhoff Publishers, Amsterdam, The Netherlands, September 1985, pp 617-636 [23] Mindess, S and Bentur, A., "A Preliminary Study of the Fracture of Concrete Beams Under Impact Loading, Using High-Speed Photography," Cement and Concrete Research, Vol 15, No 3, 1985, pp 474-484 [24] Mall, S., Kobayashi, A S., and Urabe Y., "Dynamic Photoelastic and Dynamic Finite-Element Analyses of Dynamic-Tear-Test Specimens," Experimental Mechanics, Vol 18, No 12, December 1978, pp 449-456 [25] Lewis, D., III, "Cyclic Mechanical Fatigue in Ceramic-Ceramic Composites An Update," Ceramic Engineering and Science Proceedings, July-August, 1981, pp 661-701 [26] Marshall, D B and Evans, A G., "The Tensile Strength of Uniaxially Reinforced Ceramic Fiber Composites," Fracture Mechanics of Ceramics, Vol 7, R C Bradt, A G Evans, D P H Hasselman, and E E Lange, Eds., Plenum Press, New York, 1986, pp 1-15 [27] Sbaizero, O and Evans, A G., "Tensile and Shear Properties of Laminated Ceramic Matrix Composites," Journal of the American Ceramic Society, Vol 69, No 6, 1986, pp 481-486 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Indexes Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further rep STP995-EB/Jan 1988 Author Index B Bassani, J L., 1, 7, 68 Becht, C., 153 Bensussan, P., 27 Bradley, W L., 447 Bradt, R C., 457 Buchheim, G M., 153 C Chang, S.-J., 433 D Dimopolos, V., 153 Du, J-J., 457 F Foulds, J R., 112 Freund, L B., 217 K Kobayashi, A S., 457 Konosu, S., 127 L Landes, J D., Leung, C.-P., 55 M Maeda, K., 127 McDowell, D L., 55,173 N Nakamura, T., 217 Narasimhan, R., 318 Nicoletto, G., 415 Nikbin, K M., 153 O G Ohr, S M., 433 Garwood, S J., 242 It Hackett, E M., 274, 298 Hawk, D E., 7, 68 Hawkins, N M., 457 Ho, K.-I., 173 Hollstein, T., 195 Hui, C-Y., 96 J Jablonski, D A., 361 Jones, R E., Jr., 447 Joyce, J A., 274, 298 Judy, R W., Jr., 340 P Pineau, A., 27 Piques, R., 27 R Rosakis, A J., 318 Sanford, R J., 340 Saxena, A., 1, 7, 55 Shih, C E, 217, 274 Smith, D J., 153,242 Stalley, J., 173 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 475 2015 Downloaded/printed by Copyright9 by ASTMlntcrnational www.astm.org University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 476 NONLINEAR FRACTURE MECHANICS: VOLUME I V Voss, B., 195 Williams, R A., 388 Wu, F.-H., 68 Wu, K.-C., 96 W Webster, G A., 153 Wilkening, W W., 388 Z Zehnder, A T., 318 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP995-EB/Jan 1988 Subject Index A C ABAQUS, 58-66 ADINA, 390 Aging polyethylene pipes, 453 Type 304H stainless steel, 153-172, 181 Alloys 800/800H, 112-125, 195-213 316L steel, 27, 32-53 4340 steel, 340-357 7075-T6 aluminum, 416-431 A710 steel, 340-357 A533B steel, 243-272 chromium-molybdenum steel, 58-66, 129-152 chromium-molybdenum-vanadium steel, 15-19 HSLA steel, 340-357 HY100, 363-386 iron-nickel-chromium, 112-125,195-213 low-alloy steels, 129-152, 340-357 nickel-molybdenum-vanadium steel, 401413 nickel structural steels, 298,301-316,340357 Type 304H steel, 153-172, 363-386 Aluminum, 7075-T6 alloy, 416-431 Annealing, 453 ASTM Committee E-24, ASTM Standards A 469-82:401 E 292-83:154 E 399-83:154 E 647-83:362 E 813-81: 206, 302, 341, 345-347, 363, 448-449 E 1153-87:154 C* parameter Alloy 800H, 118-125,194-195,206-213 tow-alloy steels, 142-143 Type 304H stainless steel, 161-172 void growth mechanisms, 96-97, 105-108 Caustics, 318-339, 331(illustration), 341357, 343(illustration) Cavities (See Void growth mechanism) Center crack tensile specimens A533B steel, 250-264 chromium-molybdenum steel, 58-66 small scale creep, 58-66 Ceramics, 457-469 ceramic composite, 469 Chromium, in steel alloys, 15-19, 58-66, 129-152 Coherent optics, 415-431 Cold working, Alloy 800H, 113, 116118(tables) Compact tensile specimens 5% nickel steel, 340-357 4340 steel, 340-357 HSLA steel, 340-357 HY100 alloy, 154-157, 363 low-alloy steels, 131,340-357 nickel-molybdenum-vanadium steel, 401413 polyethylene, 448 Computer programs, 35-43, 58-66, 390 Computer simulation, 132(illustration), 148(illustration), 365-366 Concrete, 457-469 Crack bridging, 460fiber, 469 Crack closure Alloy HY100, 382-383, 386 ceramic/ceramic composite, 462,467-469 concrete, 462, 467-469 Type 304H stainless steel, 382-383 Crack-tip growth velocities, 77-83 B Bilby, Cottrell, and Swinden (BCS) model, 433-444 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 477 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 478 NONLINEAR FRACTURE MECHANICS: VOLUME I Crack-tip opening displacement 7075-T6 aluminum alloy, 421-423, 423(table) A533B steel, 249-250, 250, 251(tables), 264 Alloy 800H, 202 ceramic/ceramic composite, 462-469 concrete, 462-469 gage, 285-297, 299, 302, 316 polyethylene pipe, 454-455 Crack-tip stress fields caustics measurement of, 318-339 dislocation-free zone model, 433-444 Hutchinson-Rice-Rosengren, 28-29, 71, 274-281,319, 326-329, 336-339 Riedel and Hui, 71-74 Riedel and Rice, 29 Creep, small-scale (SSC) and C, parameter, 7-25, 55-66 Mode I propagating crack, 68-94 Creep crack growth at elevated temperatures (See Temperature, elevated) global approach, 47-48 in helium e n v i r o n m e n t , 112-125, 118(table) metals 316L stainless steel, 27, 32-53 Alloys 800/800H, 112-125, 116118(tables), 195-213 low-alloy steels, 127, 130-143,145-148 Type 304H stainless steel, 153,154-158, 158(table), 161-172, 164(table), 169172, 173-193 Mode I fracture, 68-94 nonproportional, 173-193 non-steady state, 55-66 one-dimensional model, 88-93 power law exponent, 77, 97 small scale, 7-25, 55-66, 68-94 transient regime, 8-25 by void coalescence, 96-110 continuous, 101-103 discrete, 103-105 Creep ductility Alloy 800H, 195-213 low-alloy steels, 136-142, 148-152 Type 304H stainless steel, 168-172 C, parameter, 7-25, 18(table), 55-66 D Damage mechanics, 125, 173-193 damage growth law, 177-181,184 Deformation behavior 7075-T6 aluminum alloy, 415-431 A533B steel, 252-264 Deformation plasticity, 389, 407 delta J fatigue crack growth, 361-386 usefulness of concept, Dislocation emission, 435,439-444 Dislocation-free zone (DFZ), 433-444 Drop-tower testing, 285-297, 298,301-316 Ductile fracture, 243 Dynamic fracture caustics measurement, 318-357 drop-tower fracture specimen, 247-297, 298-316 planar compact tension fracture specimen, 340-357 small-scale notched bend ductile fracture specimen, 242-272 three-point-bend drop-tower fracture specimen, 274-297 three-point-bend ductile fracture specimen, 217-240 uniaxial ductile fracture specimen, 242272 wide plate ductile fracture specimen, 242272 E Elastic-plastic fracture caustics measurement of, 318-339, 343, 347-357 metals 3% nickel structural steel, 298-316 Alloy 800H, 195-213 Alloy HY100, 363-386 high-strength steels, 318-339,343,347357 Type 304H stainless steel, 363,378-387 solid cylinder, 388-413 symposia on, 1-2 thin-walled tube, 388-413 Electron microscopy, 139, 141, 157, 165, 167-168(illustration) Embrittlement, due to creep, 127-152 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized SUBJECT INDEX 479 F J Fatigue constant-amplitude loading, 418-431 J-integral range, 361-386 precracking, 361-386, 448-449, 455-456 ASTM Standard E 813-81:363,448-449 torsional loading, 388-413 Finite element analysis caustics measurement, 327-329 center-crack specimens, 58-66 ceramic/ceramic composite materials, 467 concrete materials, 467 creep crack initiation/growth, 35-43 Mode I crack growth, 74-88, 323-339 nozzle neck, reactor, 143 small scale creep, 19-24, 37, 38(tables), 55, 74-88 three-point-bend fracture specimens, 227240, 274-297, 467 tubular specimens, 389-413 Fluid catalytic cracking units (FCCU), 153 Fractographs, 139, 158-159, 171,452 Fracture process zone, 458, 462-466 Fracture toughness, 264-272, 274-297 ASTM Standards E 399-83:154 E 813-81: 206, 302, 341,448-449 J-integral caustics measurement of, 318-339, 340357 fatigue crack growth, 361-386, 388-413 high temperature effects, 195-213 polyethylene pipe, 447-456 three-dimensional crack front, 218-240, 274-297,337-339 torsional loading, 388-413 usefulness of concept, viscoelastic material, 447-456 J-resistance curves ASTM Standards E 813-81:345-347 E 1151-87:154 A533B steel, 269-271 high temperature effects, 195-213 nickel structural steel, 298-316 G Gages, crack-tip opening displacement, 285297, 299, 302, 316 H Heat-affected zone (HAZ), 129 Helium, 117, ll8(table) High-temperature fracture mechanics (See Temperature, elevated) Impurity elements effect on ductility, 136-142 in reactor metals, 129, 133,137, 145-146 Incoloy 800/800H (See Alloys, 800/800H) Iron-nickel-chromium alloy, 112-125, 195213 L Load estimations, Nakamura, 282-283 Loading constant amplitude, 418-426 ASTM Standard E 647-83:362 cyclic, 181-193, 361-386, 388-413, 415431,433-444 direcf-current potential drop (DCPD), 196-202 drop-tower, 285-297, 298-316 Mode I, 69-94, 323-339, 388-413 Mode II, 388-413 Mode III, 388-413 partial unloading compliance (PUC), 196202 rate of, 242-272 small-scale, 323-339 variable amplitude, 415-431 M Metallographic studies, 123-124(illustration) Mode I fracture, 69-94, 323-339, 388-413 Mode II fracture, 388-413 Mode III fracture, 388-413 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 480 NONLINEAR FRACTURE MECHANICS: VOLUME I Moire interferometry, 416-431, 417(illustration), 421(table), 423(table) Molybdenum, in steel alloys, 15-19, 58-66, 129-152, 403-413 Multiaxial specimens, 173-174, 181-193 N Nickel, in steel alloys, 298, 301-316, 340357, 401-413 Nonmetals, 447-469 Notched bend specimens, 154, 242-272, 301-316 deformation of, 255-257 NOVNL, 35-43 O Optical measurements, 318-339, 331(illustration), 340-357,343(illustration), 415-431,417(illustration) Overload effects, 427 P Piping, 447-456 Plane strain, Type 304H stainless steel, 169170 Plane stress analysis, high-strength steels, 323-339, 340-357 Plasticity crack-tip, 420 cyclic, 173-174, 181-193 deformation, 389, 407 Polyethylene, 447-456 Post weld heat treatment (PWHT), 129 Potential drop, 407 Power-law creep exponent, 77, 97 R Ramberg-Osgood model, 321 Razor-notched specimens, 449, 455-456 Reactors, 127-152 life estimation of, 143-144 Recrystallization, Alloy 800H, 113, 116118(tables) Rupture tests, 154-158, 158(table), 169-171 ASTM Standard E 292-83:154 S Semielliptical surface notched tensile specimens, 250-264 Silicon nitride, 469 Single-edge notched specimen, 418 Slow constant extension rate technique (SERT), 129-131,135 Specimens (See specific types, i.e Center crack tensile, Tubular) Steels 4340, 340-357 A710, 340-357 A533B, 243-272 chromium-molybdenum, 58-66, 129-152 chromium-molybdenum-vanadium, 15-19 high-strength, 285-297, 340-357 HSLA, 340-357 low-alloy, 129-152, 340-357 nickel-molybdenum-vanadium, 401-413 nickel structural, 298, 301-316, 340-357 Steels, stainless 316L, 27, 32-53 Type 304H, 153-172, 363-386 Strain rate, A533B steel, 244, 246-272 Strain softening, ceramic specimens, 460 Stress-intensity factor, 37, 398-401, 406, 418 Stress-strain field, 35-43 T TDFM (See Time-dependent fracture mechanics) Temperature, elevated effect on creep crack growth, 15-19, 3143, 68-94, 115-118, 129-152, 130(table), 161, 169, 184-193, 195213 effect on deformation and ductile fracture, 242-272 effect on J-resistance curves, 195-196, 202-206, 207-213 Three-dimensional crack analysis, 217-240, 274-297, 337-339 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized SUBJECT INDEX Three-point-bend specimens, 218, 223-240, 274-297, 277(illustration), 301-316, 467 Time-dependent fracture mechanics (TDFM), 55 Torsion, 388-413 and tension, 174-193, 395-397 Transient regime, creep crack growth, 7-25, 55-66, 96-110 Transition time, 48-49, 277-281,290-291 Tubular specimens, 173-193,388-413 Turbine generator, 15,388-413 481 V Vanadium, in steel alloys, 15-19, 403-413 Viscoelastic materials, 447-456 Viscoplastic materials, 173-193 Void growth mechanism, 96-110, 143, 147(illustration) nucleation, 98-110, 99(illustration) W Wide-plate specimens, 250-252 deformation of, 252-264 fracture of, 264 U Uniaxial specimens, 245-249 deformation of, 252-253 Z ZEBULON, 35-43 Copyright by ASTM Int'l (all rights reserved); Sun Dec 13 19:24:38 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz