Astm stp 1220 1995

STP 1220 Fracture Mechanics: 25th Volume Fazil Erdogan, Editor ASTM Publication Code Number (PCN): 04-012200-30 ASTM 1916 Race Street Philadelphia, PA 19103 Printed in the U.S.A Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Library of Congress ISSN: 1040-3094 Copyright 1995 AMERICAN SOCIETY FOR TESTING AND MATERIALS, Philadelphia, PA A11 rights reserved This material may not be reproduced or copied, in whole or in part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of the publisher Photocopy Rights Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by the AMERICAN SOCIETY FOR TESTING AND MATERIALS for users registered with the Copyright CJearance Center (CCC) Transactional Reporting Service, provided that the base fee of $2.50 per copy, plus $0.50 per page is paid directly to CCC, 222 Rosewood Dr., I)anvers, MA 01923; Phone: (508) 750-8400; Fax: (508) 750-4744 For those organizations that have been granted a photocopy license by CCC, a separate system of payment has been arranged The fee code for users of the Transactional Reporting Service is 0-8031-1882-1/95 $2.50 + 50 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 To make technical information available as quickly as possible, the peer-reviewed papers in this publication were prepared "camera-ready" as submitted by the authors 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 to time and effort on behalf of ASTM Pdnted in Philadelphia, PA August 1995 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword This publication, Fracture Mechanics: 25th Volume, contains papers presented at the 25th National Symposium on Fracture Mechanics: New Trends in Fracture Mechanics, held in Bethlehem, Pennsylvania on 28 June through July 1993 The symposium was sponsored by ASTM Committee E-8 on Fatigue and Fracture Dr Fazil Erdogan of Lehigh University in Bethlehem, PA presided as symposium chairman and is the editor of the resulting publication Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents ix Overview F ERDOGAN FRACTURE MECHANICS OF CERAMICS Analysis of the Effect of Transformation-lnduced Shear Strains on Stability and Crack Growth in Zirconia Containing Ceramics ~ STAMAND E VAN DER GIESSEN Strength Properties of Surfaee-Machined Components of Structural Ceramics-W PFEIFFER, T HOLLSTEIN, AND E SOMMER 19 Fracture-Resistance Curve Characteristic of a Sintered Al203/ZrO2 C e r a m i c - K DUAN, Y.-W MAI, AND a COTFERELL 31 Three-Dimensional Cohesive Crack Analysis of Short-Rod Specimens-T N BII-I~NCOURT AND A R INGRAFFEA 46 Defect Problems in Piezoelectric Ceramics H A SOSA 61 Experimental and Analytical Studies of Crack Initiation and Arrest in Hot Pressed Silicon Nitride M GORELIK, A M CALOMINO, AND A CHUDNOVSKY 71 INTERFACE FRACTURE On the Directionality of Interracial Cracking in Bicrystais and the Loading Phase Angle Dependence J.-S WANGAND G E BELTZ 89 The Effect of Mode Mix on Interfaeial Toughness: A Ductile Mechanism K BOSE AND P P CASTAIq'EDA 106 Micromechanics of Fiber-Matrix Interface and Fracture of Advanced Composites with Engineered lnterfaces J.-K KIM AND V.-W MAI 125 Correlating lnterphase Glass Transition and lnterfacial Microcracking in Polymer Composites N R SOTFOS, D L HIEMSTRA,AND W R SCOTI" 140 Free Edge Problem for Bonded Orthotropic Elastic Layers s KADIOGLUAND F ERDOGAN 156 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Interface Cracks in Thermally Loaded Multilayer Ceramic Coatings K KOKINI 177 AND Y R TAKEUCHI Quasi-Three-Dimensional Stress Fields at an Interface Crack Tip z n JIU AND 191 N NODA Bimaterial Problem of Strip with Debondings Under Tension and Bending-206 N HASEBE, S KATO, AND T NAKAMURA Fatigue and Fracture of Adhesively Bonded and Weld-Bonded T-Peei J o i n t s - 222 M D GILCHRIST AND R A SMITH NEW TECHNIQUES Residual Stress Measurement in Sapphire-Fiber Composites: Through-Focus and Transmission Fluorescence Speetroscopy D M LIPKIN AND D R CLARKE 241 A New Technique to Produce Josephson Junctions Based on Controlled Crack Growth Techniques i PEREZ, D GRANATA, AND W R SCOTU Time Release of Chemicals into Hardened Cementitious Matrices for Crack Repair, Fiber Rebond and Increase in Flexural Toughening c M DRY 255 268 Dynamic Fracture of Concrete Under Mixed Mode Loading c.-T vu, 283 A S KOBAYASHI, AND N M HAWKINS Further Studies of a Modified-Charpy Specimen for Lower-Bound Toughness-294 R J BONENBERGER ,AND J W DALLY INELASTIC FRACTURE Two-Parameter Characterization of Crack Tip Fields in Edge-Cracked Geometries: Plasticity and Creep Solutions s M SHARMA, N ARAVAS, AND M G ZELMAN 309 Modeling of Ductile Damage and Complexity Across Scales P MATIC, G KIRBY, V DeGIORGL D HARVEY, A KEE, AND A GELTMACHER Application of Micromechauical Models to the Analysis of Ductile Fracture Under Dynamic Loading D.-Z SUN, A HONIG,W BOHME, AND w SCHMI'I'I" 328 343 Measurement and Analysis of Critical CTOA for an Aluminum Alloy S h eet - D S DAWICKE, M A SUTFON, J C NEWMAN, JR., AND C A BIGELOW 358 The J-Integral as a Fracture Criterion of Rubber-Like Materials: A Comparative Study Between a Compliance Method and an Energy Separation M e t h o d - M NAIT-ABDELAZIZ, H GHFIRI, G MESMACQUE, AND a G NEVIERE A Single Specimen Approach for J-Integral Evaluation for Semi-Elliptical Surface Cracks M H SHAROBEAM AND J D LANDES 380 397 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized J - I n t e g r a l C h a r a c t e r i z a t i o n of the Nozzle Steels f r o m I n t e r m e d i a t e Test Vessels IV-5 a n d I V - - - T A A[JTEN, B D MACDONALD, D W SCAVONE, AND D BOZIK 415 The F r a c t u r e of Sea I c e - - s J DeFRANCO AND J P DEMPSEY 433 Prediction of Cleavage F r a c t u r e P r o b a b i l i t y for Ferritic Steels in the T r a n s i t i o n R e g i o n - - v BICEGO, A ELLI, AND C RINALDI 448 FATIGUE AND FRACTURE S h e a r Fatigue C r a c k G r o w t h in L a r g e G r a i n Polycrystals -Q CHEN AND H W LIU 467 Analysis of Fatigue C r a c k Closure a n d T h r e s h o l d s - - K SADANANDA AND A K VASUDEVAN 484 T h e Effect of C r a c k Deflection a n d Surface Roughness on C o n s t a n t a n d V a r i a b l e A m p l i t u d e Loading Fatigue C r a c k G r o w t h in A l u m i n u m - L i t h i u m A l l o y s - A HULL AND D RAIZENNE P r o p a g a t i o n of Very Long Fatigue C r a c k s in a Cellular Box B e a m - A C NUSSBAUMER, R J DEXTER, J W FISH[-R, AND E J KAUFMANN 502 518 The Effect of Welding Discontinuities on the Variability of Fatigue L i f e - G R KOBER, R J DEXTER, E J KAUFMANN, B T YEN, AND J w FISHER 533 A d v a n c e d Technology Applications to Aging A i r c r a f t - - r e M RATWANI AND 546 H T TRAN A Proposal on D a m a g e T o l e r a n t Testing for S t r u c t u r a l Integrity of Aging A i r c r a f t - - L e a r n i n g f r o m J A L Accident in 1985 H TERAOA A Novel A p p r o a c h to Dynamic R i p - A r r e s t C h a r a c t e r i z a t i o n of H e a t - T r e a t e d LowAlloy S t e e l s - - w E ANDERSON 557 575 COMPUTATIONAL AND ANALYTICAL TECHNIQUES Singular Integral E q u a t i o n M e t h o d in the Analysis of I n t e r a c t i o n Between C r a c k s a n d O e f e c t s - - N - A NODA AND T MATSUO 591 Surface a n d Subsurface C r a c k s a n d Pores with Liquid U n d e r Action of a C o n t a c t Load in the Presence of a L u b r i c a n t - - i KADISH 606 Development of Fixed-Grid Finite Element A l g o r i t h m for T r a c k i n g Quasi-Static E q u i l i b r i u m C r a c k P r o p a g a t i o n - - T s LEE 622 Calculation of Stress Intensity Factors for C r a c k s U n d e r T h e r m a l Shock T r a n s i e n t s - - L HODULAK AND O SmGELE 637 T h e Use of F r a c t u r e M e c h a n i c s Analysis in the Design a n d Development of T h e r m o e l e c t r i c CelIs R J ROSKO 646 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz Analysis of Stress Intensity Factors for an Edge-Cracked T-Section in Tension-660 M L GENTILCORE AND R ROBERTS Pressure Vessel Fracture Simulation L MINNETYAN AND C C CHAMIS 671 Interpretation of Warm Prestress-Induced Fracture Toughness Based on Crack Tip Constraint D K M SHUM 685 Author Index 705 Subject Index 707 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Overview The origin of fracture mechanics as it is understood today goes back to Griffith's work on the fracture of glass in the 1920's After a rather long lapse, the field was revived in the 40's and 50' s During this period some key contributions to the physical understanding and analytical modeling of the phenomenon of fracture were made by Sneddon, Rivlin, and Thomas and, particularly, by Irwin and his coworkers Irwin's work was motivated by some well-known and costly failures of ships, aircraft, storage tanks, and other engineering structures due to brittle fracture Despite the apparent success of the techniques proposed by Irwin in explaining many of these spectacular failures, the acceptance of fracture mechanics as a design and maintenance tool by the engineering community was rather slow in coming Perhaps not surprisingly, the pioneers in the application of this new technology were the aircraft manufacturers, specifically, the Boeing Company These early applications demonstrated that the fracture mechanics parameters may be used quite effectively to model fatigue crack growth and fracture instability in some critical aircraft components As a consequence, fracture mechanics as a field of research started to attract widespread attention in applied mechanics and materials engineering communities and the field started to grow very rapidly in the early 60's It was then felt that a regular forum was needed to present and discuss new ideas and new applications, and to exchange views on the subject periodically; hence, the idea of a national symposium on fracture mechanics The first few of these symposia were organized by Professor P C Paris and were held at Lehigh University In 1971, ASTM, through its Committee E-24 on Fracture Testing, recognized the importance of the field and assumed the responsibility for sponsoring and organizing the symposia With few exceptions, the symposium has been an annual affair After the reorganization of the committee structure at ASTM, Committee E-8 on Fatigue and Fracture is now providing the necessary guidance for the organization of the symposium Even though the annual meeting has been called the National Symposium, from the beginning there has always been some participation from abroad In recent years such participation has been openly encouraged by ASTM Thus, of the 45 articles published in this volume, 14 are contributed by scientists and engineers from nine foreign countries Fracture mechanics is a very young field and is very much in the development stage The main purpose of the National Symposium on Fracture Mechanics is, therefore, to provide an open forum for the presentation of new ideas, new developments, and new applications Also, interest in the subject is very broad and is still growing Partly because of this, in recent years it has become customary to adopt a theme for each symposium The emphasis in selecting the papers for presentation at this symposium was on new trends in fracture mechanics research The topics covered included fracture mechanics of ceramics, interface fracture, and new testing methods, as well as new developments in inelastic fracture, fatigue, and computational and analytical techniques Thus, the contributions vary from basic research in micromechanics of interfaces and of transformation toughening in ceramics to the applications of some of the advanced techniques to aging aircraft Forty-five papers selected for publication in this volume are divided into six categories and are presented in six sections There are some papers that could be placed in more than one category and, hence, in some cases an arbitrary selection had to be made Following is a brief description of research presented in each section The material ix Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized x FRACTURE MECHANICS: 25TH VOLUME presented in this volume is intended to benefit those scientists and engineers involved in doing cutting edge research in various aspects of fracture mechanics as well as the engineers interested in the application of fracture mechanics to actual design problems Fracture Mechanics of Ceramics In such advanced technologies as high speed civil transport and advanced gas turbines, at the operating temperatures contemplated, the use of metal alloys will not be feasible For example, in large natural gas fired stationary turbines currently in service with 1260~ rotor inlet temperature, the lower heating value plant efficiency has been demonstrated to be around 54% It is estimated that with cycle innovations and certain changes in design and materials, it is possible to raise the efficiency to 60% This, however, requires raising the rotor inlet temperature to well over 1400~ which would, in turn, necessitate the development and use of new high-temperature materials and coatings In this and other high-temperature applications the use of structural ceramics and ceramic matrix composites is, therefore, becoming an absolute necessity Because of the nature of the material, cracking and spallation in ceramics and ceramic coatings have always been a problem One needs to understand the factors causing surface cracking and spallation, and develop mechanisms to improve the corresponding material toughness The papers in this section address various aspects of the fracture phenomenon in structural ceramics In studying the transformation toughening of ceramics in the neighborhood of a crack tip, the dilational component of the strain field is assumed to play the dominant role The first paper in this section considers the role of transformation-induced shear strains on the stability of crack growth Generally, the critical factors controlling the strength of ceramic components are known to be surface imperfections and residual compressive stresses that result from processing The second paper in this section investigates these factors by using a new technique to determine the microstrains and an X-ray diffraction technique to determine the residual stresses In the third paper, the crack extension resistance curve (R-curve) behavior of sintered Al203/ZrO2 ceramic is investigated by using various standard cracked specimens with long cracks and small indentation cracks The results show specimen dependence of the R-curve and the importance of crack-bridging on toughness In the fourth paper, a generalized three-dimensional DugdaleBarenblatt cohesive zone model is developed for short-rod specimens and the influence of the specimen size in toughness measurements is investigated The results demonstrate the applicability of small specimens with inelastic correction to toughness measurements in ceramics The fifth paper presents some analytical results for an elliptic cavity or a crack problem in piezoelectric ceramics The material is known to deform under electric voltage and, conversely, generate an electric charge when subjected to mechanical load These properties make piezoceramics quite attractive for applications in adaptive structures and in a broad variety of instrumentations The final paper in this section deals with the question regarding the difference between initiation and arrest values of the strain energy release rate in hot-pressed silicon nitride subjected to stable crack growth A new statistical model is used to study the variabilities in the critical crack length, initiation and arrest values of energy release rates, and the length of dynamic crack increments Interface Fracture Nine papers presented in this section deal with the general problem of fracture mechanics of interfaces and interfacial zones in bonded dissimilar materials and cover a broad range of topics from bicrystals to adhesively bonded T-peel joints In the first paper, the dependence of interfacial cracking on the nature of loading in Cu and Fe-Si alloy bicrystals and in metal/ sapphire studied Wed The Dec directionality interface Copyright by bimaterial ASTM Int'l systems (all rightsisreserved); 23 19:18:02ofEST 2015 cracking and the effect Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz 698 FRACTURE MECHANICS: 25TH VOLUME d e g r a d a t i o n effects, under a range of W P S - r e l a t e d l o a d - u n l o a d - r e l o a d c o n d i t i o n s is somewhat unexpected It might be s u g g e s t e d that the p r e d i c t i o n of c o n s t r a i n t increase is i n d i c a t i v e of errors a s s o c i a t e d with the SSY f o r m u l a t i o n p r e s e n t e d here The m o n o t o n i c - l o a d i n g results are c o n s i s t e n t with a v a i l a b l e results in the open literature C o n s e q u e n t l y , any p o t e n t i a l errors within the current f o r m u l a t i o n are likely to be l i m i t e d to the extent to which the a s s u m e d i s o t r o p i c h a r d e n i n g p l a s t i c i t y f o r m u l a t i o n can a c c u r a t e l y c a p t u r e the p h y s i c a l stress and strain response of R P V - g r a d e steels under l o a d - u n l o a d - r e l o a d conditions Recall that the i s o t r o p i c - h a r d e n i n g f o r m u l a t i o n is a d o p t e d b a s e d on rather l i m i t e d e x p e r i m e n t a l data F u r t h e r c o n f i r m a t i o n of the a p p r o p r i a t e n e s s of this choice awaits a d d i t i o n a l e x p e r i m e n t s to e l u c i d a t e the c y c l i c - y i e l d i n g b e h a v i o r of R P V - g r a d e steels The analysis a s s u m p t i o n of a s t a t i o n a r y crack has also b e e n i d e n t i f i e d as a p o t e n t i a l source of error w i t h i n the p r e s e n t f o r m u l a t i o n [I] Under c o n d i t i o n s r e p r e s e n t a t i v e of those e n c o u n t e r e d in an RPV under PTS conditions, a rough e s t i m a t e of the extent of crack b l u n t i n g / g r o w t h due to a load-full u n l o a d cycle is ~0.14 J/C o W i t h reference to Figs 9(a and b), it remains to be d e t e r m i n e d if a WPS c r a c k - t i p model that takes into account l i m i t e d crack b l u n t i n g / g r o w t h w o u l d e x h i b i t a n t i - s h i e l d i n g effects On the other hand, an i n t r i g u i n g p o s s i b i l i t y is that the antis h i e l d i n g results indeed c a p t u r e the e s s e n t i a l nature of the n e a r - t i p stress and strain d i s t r i b u t i o n s for an R P V - g r a d e steel after one loadu n l o a d - r e l o a d cycle M o t i v a t i o n for this v i e w p o i n t comes from the o b s e r v a t i o n that the results can be v i e w e d as q u a l i t a t i v e l y d e s c r i b i n g c e r t a i n aspects of the s o - c a l l e d "zero to tension" f u l l - u n l o a d i n g fatigue cycle [8] W i t h i n a fatigue interpretation, the results p r e s e n t e d here w o u l d suggest the p o s s i b i l i t y of a c o n s t r a i n t - b a s e d element to the fatigue c r a c k - g r o w t h process However, it is e m p h a s i z e d that this viewpoint c e r t a i n l y requires a d d i t i o n a l c o n f i r m a t i o n It is r e c o g n i z e d that d i f f e r e n c e s exist b e t w e e n the present m o d e l of a s t a t i o n a r y "sharp" crack and a s t e a d i l y p r o p a g a t i n g crack a s s o c i a t e d with fatigue For example, c r a c k - c l o s u r e is not o b s e r v e d in the present analysis results under full u n l o a d i n g (see Fig 5) , while it is o b s e r v e d for a s t e a d i l y p r o p a g a t i n g fatigue crack under full u n l o a d i n g [8] IMPLICATIONS TOWARD TRANSFERABILITY A n a l y s i s results p r e s e n t e d thus far have q u a n t i f i e d the n a t u r e of the c r a c k - t i p fields, within the a s s u m p t i o n s of K - d o m i n a n t SSY conditions, as a function of u n l o a d and reload ratios Insofar as these results not d e p e n d e x p l i c i t l y on g e o m e t r y and l o a d i n g conditions, these results p r o v i d e a first step t o w a r d u n i f y i n g the wide range of WPS l o a d i n g c o n d i t i o n s e n c o u n t e r e d in specimen and s t r u c t u r a l a p p l i c a t i o n s It is e m p h a s i z e d that these results represent s e l f - s i m i l a r fields in that they are v a l i d for the s p e c i f i e d ratios of u n l o a d i n g and reloading, and are not d e p e n d e n t on the m a g n i t u d e of i n d i v i d u a l K values themselves In this section, the i m p l i c a t i o n s of these n e a r - t i p cracktip fields t o w a r d the t r a n s f e r a b i l i t y of fracture t o u g h n e s s data under c o n d i t i o n s of WPS will be a d d r e s s e d in light of t r a n s f e r a b i l i t y m e t h o d o l o g i e s d e v e l o p e d for m o n o t o n i c - l o a d i n g conditions Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions author SHUM ON WARM PRESTRESS-tNDUCED TOUGHNESS Transferability 699 Based on Global Conditions Near-tip results presented thus far indicate that for a wide range of unload-reload conditions the near-tip fields are not uniquely related to the current value of the remote K However, transferability based on similarity of the global crack-tip fields remains possible within the present SSY framework if the loading conditions are specified in terms of both the unload and reload ratios ~hK/Kwps and K/Kwp s That is, a unique correlation does exist between the near-tip crack-tip fields and the remote K-dominant annular region when the unload and reload histories of that annular region, and not simply the current value of K, are specified The proposed history-dependent correlation is akin to the treatment of transferability of small-specimen fatigue data to structural applications based on various ermpirical fatigue Correlations [8] The strength of a transferability methodology based on "global" annular fields is that it does not involve explicit evaluation of the near-tip elastic-plastic crack-tip fields that more directly determine the fracture event However, the empirical nature of this transferability methodology requires close "matching" of the global conditions associated with small-scale specimens and structural application For example, a limitation of the SSY requirement is that small-specimen WPS toughness data generated under general-yielding conditions cannot be used to assess the fracture response of a structure under globally linear-elastic conditions Transferability Bas@d on Near-T~p Conditions In a manner analogous to K- and J-based approaches, the J-Q approach for monotonic loading permits a unique correlation between continuum crack-tip fields within a J-Q annulus and the stress and strain fields within the fracture process zone [2] Within a J-Q approach and based on theoretical considerations, the J-integral provides the characteristic near-tip length-scale (via J/~o ) that highlights the self-similar nature of the elastic-plastic crack-tip fields as a function of crack-tip constraint relative to conditions of SSY That is, when the spatial distributions of the crack-tip stress and strain fields are scaled with respect to the current value of J/~o, the resultant distributions permit the ordering and hence comparison of crack-tip constraint in a manner characteristic of the near-tip deformation states At present, there are no analogous theoretical considerations that establish the nature of the continuum elastic-plastic crack-tip fields under non-monotonic loading conditions For this reason, it was enkDhasized previously that the current value of J/~o merely represents a convenient length-scale by which to normalize the non-monotonic near-tip results, and that the relation between the current value of J/~o and the nature of the near-tip deformation is undetermined Indeed, the analysis results presented here represent a first attempt at a detailed numerical description of the non-monotonic crack-tip fields Consequently, work remains to develop an alternate approach to the establishment of transferability based on near-tip length-scales that can characterize the nature of the elastic-plastic crack-tip deformation under non-monotonic loading conditions A~ example of the type of approach that might be needed can be found in the development of the length-scale Zg associated with the characterization of near-tip cracktip fields under steady-state mode I crack growth conditions [10] The Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 700 FRACTURE MECHANICS: 25TH VOLUME m a i n a d v a n t a g e of a n e a r - t i p approach, s h o u l d its d e v e l o p m e n t prove successful, is to e l i m i n a t e the l i m i t a t i o n that s m a l l - s p e c i m e n WPS t o u g h n e s s data must be g e n e r a t e d under SSY c o n d i t i o n s for a p p l i c a t i o n s to s t r u c t u r a l s c e n a r i o s i n v o l v i n g g l o b a l l y l i n e a r - e l a s t i c conditions Kelation to M o n o t o n i c - L o a d i n a J-O C o n s t r a i n t Concepts w i t h i n a SSY formulation, Q - s t r e s s c o n s t r a i n t e f f e c t s under m o n o t o n i c - l o a d i n g c o n d i t i o n s are the c o n s e q u e n c e of n o n - z e r o values of the remote T-stress On the other hand, the c o n s t r a i n t e f f e c t s under n o n - m o n o t o n i c l o a d i n g c o n d i t i o n s d i s c u s s e d herein are e n t i r e l y a c o n s e q u e n c e of l o a d - p a t h effects and not a t t r i b u t a b l e to the T-stress since T = in this study The absence of a t h e o r e t i c a l f r a m e w o r k for o r g a n i z i n g the n o n - m o n o t o n i c n e a r - t i p results is the m a j o r reason why JQ c o n s t r a i n t c o n c e p t s d e v e l o p e d for m o n o t o n i c - l o a d i n g c o n d i t i o n s s t r i c t l y cannot be a p p l i e d in this case Nevertheless, a n u m b e r of s i m i l a r i t i e s in the c r a c k - t i p fields are e v i d e n t b e t w e e n these two sets of conditions Consequently, the q u e s t i o n remains c o n c e r n i n g the extent to which these two types of c o n s t r a i n t effects can be t r e a t e d w i t h i n a u n i f i e d framework C o m p r e h e n s i v e answers to these q u e s t i o n s are not a v a i l a b l e at this time Instead, a nun~ber of o b s e r v a t i o n s b a s e d on a formal (ie, without t h e o r e t i c a l rigor) i n t e r p r e t a t i o n of the nonm o n o t o n i c results within the J-Q a p p r o a c h are o f f e r e d for future considerations A c c o r d i n g to the J-Q approach, the loss of c r a c k - t i p c o n s t r a i n t is q u a n t i f i e d b a s e d on e v a l u a t i o n of the d i f f e r e n c e - f i e l d a s s o c i a t e d with a given application Specifically, the c o n s t r a i n t p a r a m e t e r s Q and Qm (based on ~ and ~m respectively) are d e f i n e d at c r a c k - t i p location r = J/C o The a p p r o p r i a t e n e s s of the J-Q c h a r a c t e r i z a t i o n is d e t e r m i n e d b a s e d on the gradient p a r a m e t e r s Q' and Qm' s a t i s f y i n g the i n e q u a l i t i e s Q' ~ 0.1 a n d Qm' ~ 0.i [2] One avenue to i l l u s t r a t e the effects of prior u n l o a d i n g on c r a c k - t i p c o n s t r a i n t under r e l o a d i n g c o n d i t i o n s is to follow the f o r m a l i s m of the J-Q m e t h o d o l o g y Specifically, Q - l i k e and Q m - l i k e p a r a m e t e r s are e v a l u a t e d b a s e d on the stress d i s t r i b u t i o n s i n d i c a t e d in Figs 7(b), 8(b) and 9(b) The results of this formal e v a l u a t i o n are p r e s e n t e d in Fig i0 as a function of the extent of prior u n l o a d i n g (AK/KwPs) and the m a g n i t u d e of the r e l o a d ratio K/Kwp s In Fig i0, the v e r t i c a l axis is l a b e l l e d as i n d i c a t e d to e m p h a s i z e the m a n n e r in which the c o n s t r a i n t p a r a m e t e r s are e v a l u a t e d w i t h o u t explicit i d e n t i f i c a t i o n with e i t h e r Q or Qm" However, it is of interest to note that for the case of 1/3 prior unload, the c o n s t r a i n t - l o s s i n d i c a t e d in Fig 10 can f o r m a l l y be p h r a s e d in terms of the Q and Q m p a r a m e t e r s for K/Kwp s ~ 0.93 b a s e d on s a t i s f y i n g the "validity" r e q u i r e m e n t s p e r t a i n i n g to the g r a d i e n t p a r a m e t e r s Q' a n d Qm'" For the case of 2/3 p r i o r unload, a formal d e s c r i p t i o n b a s e d on Q and Qm is p o s s i b l e for K/Kwp s 0.91 For the case of full unload, a formal d e s c r i p t i o n b a s e d on Q and Qm is p o s s i b l e for K/Kwp s ~ 0.73 N o t w i t h s t a n d i n g the a p p r o p r i a t e n e s s of a Q- or Q m - b a s e d d e s c r i p t i o n of the W P S - i n d u c e d c o n s t r a i n t loss, results in Fig i0 indicate that for a given m a g n i t u d e of the reload ratio K/KwPs, c o n s t r a i n t r e l a x a t i o n varies i n v e r s e l y with the extent of p r i o r unloading Therefore, to the e x t e n t that loss of c o n s t r a i n t (in terras of ~ or ~m) can be c o r r e l a t e d with a g r e a t e r " r e s i s t a n c e " to crack- Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions autho SHUM ON WARM PRESTRESS-INDUCED TOUGHNESS 701 i n i t i a t i o n relative to the SSY state, these results are in q u a l i t a t i v e a g r e e m e n t with the e x p e r i m e n t a l l y o b s e r v e d t r e n d of d e c r e a s e in WPSi n d u c e d t o u g h n e s s with increase in the amount of u n l o a d i n g d u r i n g the WPS cycle [6] However, the above c o n s t r a i n t - b a s e d i n t e r p r e t a t i o n of u n l o a d i n g effects is in some sense fortuitous It is o b s e r v e d f r o m Figs to that the nature of the d i f f e r e n c e - f i e l d s , in terms of their d e p e n d e n c e on d i s t a n c e s ahead of the crack tip, vary w i d e l y for the three cases considered Furthermore, the spatial d e p e n d e n c e is m o n o t o n i c for the case of 1/3 p r i o r u n l o a d but n o n - m o n o t o n i c for the cases of 2/3 and full prior unloading The nature of the c o n s t r a i n t d e v i a t i o n has also been q u a n t i f i e d b a s e d on two other c r a c k - t i p locations, r = J/G o and r = J/G o [1] In the latter two cases, when the results are p r e s e n t e d in the form of Fig 10, it is o b s e r v e d that the c o n s t r a i n t loss is now s l i g h t l y g r e a t e r for 2/3 p r i o r u n l o a d i n g than 1/3 prior unloading However, the c o n s t r a i n t loss for b o t h 2/3 and 1/3 p r i o r u n l o a d i n g remains s u b s t a n t i a l l y g r e a t e r than that for the case of full unloading ! ~- Q', Q~ < 0.t (2 ~J~ f AK K = / / $ ~t.4 0.5 p o - / ~ I 0.6 0.7 o =2/3 :~K/Kw~ =l -. 4$ a m i i i 0.8 0.9 1.0 l.l Magnitude of Reload Ratio, K / KwPs FIG 10 Crack-tip ADDITIONAL Effects constraint as a function of ~K/Kwp s and K/Kw? $ CONSIDERATIONS of M u l t i P l e Cycles A comment on the p r a c t i c a l u t i l i t y of a c o n s t r a i n t - b a s e d d e s c r i p t i o n of the e f f e c t s of type-If and type-III WPS on c r a c k - t i p Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions aut 702 FRACTURE MECHANICS: 25TH VOLUME fields and fracture toughness is appropriate at this point For the p u r p o s e of ease in illustration, it will prove convenient to phrase the comment within the context of a J-Q constraint approach That is, it is a s s u m e d that the J-Q m e t h o d o l o g y provides a viable m e a n s to c h a r a c t e r i z e the n e a r - c r a c k - t i p fields (crack-driving force and c r a c k - t i p constraint) over certain ranges of the WPS load-path in terms of the l o a d - t r a j e c t o r y J(Q) and hence a toughness locus e x p r e s s i b l e in terms of Jc(Q) P o t e n t i a l limitations on the p r a c t i c a l utility of the J-Q approach to WPS loading conditions exist if J(Q) and/or Jc(Q), in addition to b e i n g dependent on the load-path, are also dependent on the n u m b e r of loadpath cycles N such that J(Q,N) and Jc(Q,N) Example RPV a p p l i c a t i o n s that p o t e n t i a l l y involve m u l t i p l e - c y c l e W P S - t y p e load-paths include the start-up/cool-down refueling cycles and PTS transients with thermal and pressure oscillations Note that limited results for an A508 steel indicate that the W P S - i n d u c e d toughness is independent of the number of WPS cycles [Ii] Clearly, much e x p e r i m e n t a l and analytical work remain t o w a r d resolving the impact of cyclic loading on a c o n s t r a i n t - b a s e d d e s c r i p t i o n of WPS effects Effects of General Yieldina Within the present SSY formulation, the load-path has no effects on the c r a c k - d r i v i n g force since the c r a c k - d r i v i n g force is part of the s p e c i f i e d b o u n d a r y conditions Instead, the effects of u n l o a d i n g and reloading are to shield the crack-tip via decrease in the c r a c k - t i p constraint relative to SSY conditions However, it is conceivable that under general large-scale y i e l d i n g conditions, u n l o a d i n g and reloading can s h i e l d the c r a c k - t i p by d e c r e a s i n g both the c r a c k - t i p constraint and the c r a c k - d r i v i n g force (or e q u i v a l e n t l y the d e f o r m a t i o n level) Consequently, as the nature of the near-tip fields under n o n - m o n o t o n i c conditions are not known, the p o s s i b i l i t y of different s h i e l d i n g effects under small scale and general y i e l d i n g provide another m o t i v a t i o n for e s t a b l i s h i n g t r a n s f e r a b i l i t y b a s e d on m a t c h i n g of global conditions ImDlications T o w a r d Vessel Analysis The W P S - i n d u c e d crack-tip fields in an RPV s u b j e c t e d to a series of related PTS transients that include r e p r e s s u r i z a t i o n have recently become available [i] An approximate but direct c o m p a r i s o n b e t w e e n the K-dominant SSY and the RPV results indicate that the vessel WPS loading does indeed take place under near K-dominant SSY conditions Consequently, the present SSY formulation can be used to model a variety of P T S - r e l a t e d WPS loading conditions A significant finding from the RPV analyses is that d e v i a t i o n of the RPV c r a c k - t i p fields f r o m the reference K-dominant SSY conditions is significant only for transient times b e y o n d the initial u n l o a d i n g of the crack tip Consequently, inclusion of load-path effects on crack-tip constraint is indeed a n e c e s s a r y p r e c u r s o r to the application of constraint concepts (eg J-Q) t o w a r d the fracture-margin assessment of RPVs under PTS conditions Implications Toward Interpretation of Small-Specimen Data The c r a c k - t i p fields in small-scale specimens s u b j e c t e d to a complete WPS load cycle are not yet available P r e l i m i n a r y analysis results for a T - p l a n f o r m c o m p a c t - t e n s i o n specimen g e o m e t r y for which WPS e x p e r i m e n t a l data are available indicate the presence of significant t h r e e - d i m e n s i o n a l crack-tip constraint effects d u r i n g the m o n o t o n i c loading phase of the WPS load cycle [i] Consequently, inclusion of T- Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized SHUM ON WARM PRESTRESS-INDUCED TOUGHNESS 703 stress effects in the present SSY formulation is necessary toward a more realistic simulation of the small-specimen WPS-induced crack-tip fields CONCLUS IONS Evaluation of load-path effects associated with monotonic unloading type-I WPS indicates progressive loss of crack-tip constraint with increase in the amount of unloading The progressive loss of constraint is consistent with the absence of crack-initiation under type-I WPS Evaluation of reloading effects associated with type-II and type-III WPS indicates that for a given state of reloading as characterized by the reload ratio K/KwPs, the degree of crack-tipconstraint relaxation at r / (J/Co) varies inversely with the extent of prior unloading The inverse relationship is qualitatively consistent with the experimental observation of decrease in WPS-induced toughness with increase in the amount of unloading during the WPS cycle The nature of the constraint effects under unloading and reloading corresponds to a spatially varying hydrostatic stress field relative to K-dominant SSY conditions in a manner somewhat similar to that associated with the Q-stress parameter The range of WPS conditions under which a global measure of the crack-driving force in terms of K can be used to uniquely describe the crack-tip conditions are identified REFERENCES [i] D K M Shum, Martin Marietta Energy Systems, Inc., Oak Ridge Natl Lab., Preliminary Investigation on the Inclusion of Warm Prestress Effects in Fracture-Margin Assessment of Reactor Pressure Vessels, USNRC Report NUREG/CR-5946 (ORNL/TM-12236), to be published [2] N P O'Dowd, C F Shih, Two-Parameter Fracture Mechanics: Theory and Applications, USNRC Report NUREG/CR-5958 (CDNSWC/SMECR-16-92), February 1993 [3] D K M Shum, Martin Marietta Energy Systems, Inc., Oak Ridge Natl Lab., Implications of Warm Prestress on Safety-Margin Assessment of Reactor Pressure Vessels, USNRC Letter Report ORNL/NRC/LTR-91/9, May 1992 [4] United States Nuclear Regulatory Commission R e g u l a t o r y Guide 1.154, "Format and Content of Plant-Specific Pressurized Thermal Shock Safety Analysis Reports for P r e s s u r i z e d Water Reactors," January 1987 [5] D J Naus et al., Martin Marietta Energy Systems, Inc., Oak Ridge Natl Lab., Crack-Arrest Behavior in SEN Wide Plates of Quenched and Tempered A533 Grade B Steel Tested Under Nonisothermal Conditions, USNRC Report NUREG/CR-4930 (ORNL-6388), August 1987 [6] R.B Stonesifer, E.F Rybicki and D.E McCabe, Warm Prestress Modeling: Comparison of Models and Experimental Results, USNRC Report NUREG/CR-5208 (MEA-2305), April 1989 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 704 FRACTURE MECHANICS: 25TH VOLUME [7] Abaqus User Manual, V e r s i o n 4-9-1, Hibbit, Inc., Providence, Rhode Island, 1991 [8] M F Kanninen and C H Popelar, Chapter of A d v a n c e d F r a c t u r e Mechanics, O x f o r d U n i v e r s i t y Press, New York, pp 498-532, 1985 [9] T J Theiss, D K M Shum, S T Rolfe, M a r t i n M a r i e t t a Energy Systems, Inc., Oak Ridge Natl Lab., E x p e r i m e n t a l and A n a l y t i c a l I n v e s t i g a t i o n of the S h a l l o w - F l a w Effect in R e a c t o r P r e s s u r e Vessels, USNRC Report N U R E G / C R - 8 (ORNL/TM-12115), July 1992 [10] A G Varias and C F Shih, "Quasi-Static Crack Advance U n d e r a Range of C o n s t r a i n t s - Steady-State Fields B a s e d on a C h a r a c t e r i s t i c Length", Division of Engineering, Brown University, June 1992 [11] D E McCabe and R K Nanstad, "Effects of Cyclic S t r a i n i n g on I r r a d i a t i o n - H a r d e n e d Steel," Chapter of H S S T S e m i a n n u a l P r o g r e s s R e p o r t for O c t o b e r 1990 - March 1991, USNRC Report N U R E G / C R - (ORNL/TM-9593/Vg&NI), pp 25-26, N o v e m b e r 1992 Karlsson & Sorensen, Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP 1220-EB/Aug 1995 Author Index A G Anderson, W E., 575 Aravas, N., 309 Auten, T A., 415 Geltmacher, A., 328 Gentilcore, M L., 660 Ghfiri, H., 380 Gilchrist, M D., 222 Gorelik, M., 71 Granata, D., 255 B Beltz, G E., 89 Bicego, V., 448 Bigelow, C A., 358 Bittencourt, T N., 46 B6hme, W., 343 Bonenberger, R J., 294 Bose, K., 106 Bozik, D., 415 H Harvey, D., 328 Hasebe, N., 206 Hawkins, N M., 283 Hiemstra, D L., 140 Hodulak, L., 637 Hollstein, T., 19 HOnig, A., 343 Hull, A., 502 C Calomino, A M., 71 Castafieda P P., 106 Chamis, C C., 671 Chen, Q., 467 Chudnovsky, A., 71 Clark, D R., 241 Cotterell, B., 31 I Ingraffea, A.R., 46 J Jin, Z.-H., 191 II K Dally, J W., 294 Dawicke, D S., 358 DeFranco, S J., 433 DeGiorgi, V., 328 Dempsey, J P., 433 Dexter, R J., 518, 533 Dry, C M., 268 Duan, K., 31 Kadioglu, S., 156 Kato, S., 206 Kaufmann, E J., 518, 533 Kee, A., 328 Kim, J.-K., 125 Kirby, G., 328 Kobayashi, A S., 283 Kober, G R., 533 Kokini, K., 177 Kudish, I I., 606 E Elli, A., 448 Erdogan, F., 156 L Landes, J D., 397 Lee, T S., 622 Lipkin, D M., 241 Liu, H W., 467 F Fisher, J W., 518, 533 705 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Copyright9 by ASTM Downloaded/printed by lntcrnational www.astm.org University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 706 FRACTURE MECHANICS: 25TH VOLUME M Macdonald, B D., 415 Mai, Y.-W., 31, 125 Matic, P., 328 Matsuo, T., 591 Mesmacque, G., 380 Minnetyan, L., 671 N Nait-Abdelaziz, M., 380 Nakamura, T., 206 N~viere, R G., 380 Newman, J C., Jr., 358 Noda, N., 191 Noda, N.-A., 591 Nussbaumer, A C., 518 Sadananda, K., 484 Scavone, D W., 415 Schmitt, W., 343 Scott, W R., 140, 255 Sharma, S M., 309 Sharobeam, M H., 397 Shum, D K M., 685 Siegele, D., 637 Smith, R A., 222 Sommer, E., 19 Sosa, H A., 61 Sottos, N R., 140 Stam, G T M., Sun, D.-Z., 343 Sutton, M A., 358 T Takeuchi, Y R., 177 Terada, H., 557 Tran, H T., 546 V P van der Giessen, E., Vasudevan, A K., 484 Perez, I., 255 Pfeiffer, W., 19 W Wang, J.-S., 89 Y R Raizenne, D., 502 Ratwani, M M., 546 Rinaldi, C., 448 Roberts, R., 660 Rosko, R J., 646 Yen, B T., 533 Yu, C.-T., 283 Z Zelman, M G., 309 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP 1220-EB/Aug 1995 Subject Index A Adhesive bonding, 222, 268 Aircraft, aging, 546, 557 Alumina, 19 Aluminum, 222 alloys, 358, 467, 546 copper alloy, 502 lithium alloy, 502 Antiplane shear effect, 191 Asperity, 484 ASTM standards A 710, 533 E-813, 415 Asymptotic analysis, 156 Asymptotic stresses, 309 B Bending, effects on partially bonded strips, 206 Bending moment crack growth method, 255 Body force method, 591 Bonded orthotropic infinite strips, 156 Boundary simulation, moving, 622 Box beam, cellular, 518 Brittle fracture, 71 C Calibration factor, 380 CCT specimens, 380 Cellular automata, 328 Cellular box beam, 518 Ceramic coatings, 177 Ceramics, 46 piezoelectric, 61 structural, 19 zirconia-containing, 3, 31 Charpy specimen testing, 294, 343 Chemicals, time release for crack repair, 268 Cladding, 637 Cleavage, 448 Collinear cracks, 156 Compact tension, 31, 358 Composites cementitious, 268 patch repair, 546 polymer, 140 polymer matrix, 125 sapphire fiber, 241 Concrete, 46, 268, 283 Conduction coupled thermoelectric cell, 646 Copper and aluminum alloy, 502 Corrosion resistance, 546 Crack analysis, 591 Crack closing stress, 283 Crack closure, 484 Crack, collinear, 156 Crack distribution, 557 Crack effects, 61 Crack, equilibrium, 622 Crack growth bending moment method, 255 crack tip to tip bridging method, 255 fatigue, 467, 484 stable, 106 subcritical, 71 thermal stressing method, 255 zirconia-containing ceramics, Crack, indentation, 255 Cracking, interfacial, 89, 140, 177 Crack initiation, 380 Crack, mixed mode, 467 Crack model, cohesive, 46, 433 Crack mouth opening displacement, 397 Crack opening displacement, 283 Crack path deflection, 502 Crack, planar, 622 Crack, repair, 268 Crack resistance, 31 Crack, semi-elliptical, 397 Crack, shallow edge, 309 Crack shearing stress, 283 Crack sliding displacement, 283 Cracks, long, 518 707 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 708 FRACTURE MECHANICS: 25TH VOLUME Cracks, multiple-ended, 518 Cracks, subsurface, 606 Cracks, surface, 606 Crack tip, 191 constraint, 685 deformations, 177 fields, 685 growth method, 255 opening angle, 358 Crack tunneling, 358 Crack-wake bridging, 31 Creep, 309 Crystallographic cracking, 502 Crystals, large grain, 467 Cylinder correction factor, 575 D Damage growth, 671 Damage tolerant evaluation, 557 Debonding bimaterial problem of strip, 206 interfacial, 125 Decohesion, 89 Defect, 591 Deformation, 343 quasi-three-dimensional, 191 Degradation, 671 Delta process, rip-driving-force variation, 575 Diffusion problems, nonlinear, 622 Dimensional similarity, 660 Direction dependence, interracial cracking, 89 Discontinuities, 533 Dislocation emission, 89 Displacement behavior, 433 Double cantilever beam specimens, 31 Double hull, 518 Ductile brittle transition, 89 Ductile damage, 328 Ductile failure, 397 Ductile fracture, 106 Ductile tearing, 415 Dundurs' constants, 206 E Edge-cracked geometries, 309 Edge-cracked T-section, 660 Elasticity, 591 Electromechanical response, piezoceramics, 61 Ellipsoidal cavity, 591 Elliptical cavity, problems of, 61 Elliptical hole, 591 Energy separation method, 380 EPDM, 380 F FALSTAFF, 502 Fastener joint, 557 Fatigue cracks, 518 Fatigue resistance, 546 Fatigue thresholds, 484 Fiber fragmentation tests, 140 Fiber-matrix interface, 125, 140 Fiber pullout, 125 Finite element code, 358 Finite element analyses, 125, 309, 637 boundary layer formulation, 685 crack prediction, 646 dynamic, 283 models, 328, 397, 622, 660, 671 three dimensional, 222 two dimensional, 222, 358 Finite size effects, 380 Flaw tolerance, reactor pressure vessels, 415 Flexural toughening, 268 Fluorescence, 241 Frictional contact, 606 G Gas cylinder, 575 Glass transition, interphase, 140 Grinding, 19 Groove welds, 533 H Heat-treated low-alloy steels, 575 Heavy Steel Section Technology Program, 415 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized INDEX 709 Hoop stress, 575 HSLA steel, 518 HSLA-80, 533 Hydrotest, 575 I-beams, 533 Ice, 433 Impact testing, 294 instrumented, 343 Indentation microcracks, 255 Initiation toughness, 294 Integro-differential equations, 606 Interaction, 591 Interface, 156 Interfacial cracking, 89, 177, 191, 206 Interfacial debonding, 125 Interfacial fracture, 191 Interfacial microcracking, 140 Interfacial shear strength, 140 Interfacial toughness, 89 J-integral, 309, 380, 397 nozzle steel characterization, 415 Joints fastener, 557 T-peel, 222 Josephson junctions, 255 J-Q theory, 685 J-R curve, 448 J-resistance curve, 415 K KR curve, 31 L Lanthanum aluminate, 255 Lapping, 19 Lithium and aluminum alloy, 502 Load, applied, 106, 358 Load displacement curves, 46, 484 Loading, dynamic, models, 343 Loading phase angle dependence, 89 Loading, shear, 191 Loading, structural degradation under, 671 Loading, tensile, 191 Load motion, contact, 606 Load, nonlinear, 433 Load ratio, 484 Load separation, 397 Load transfer, 140 Load transmission, 557 M Magnesia, 255 Mapping, 671 Martensitic phase, Mesoscale, 328 Microindentation techniques, 255 Microstructure, 328 Mismatch stress, 646 Mixed mode conditions, 106 Mixed mode crack, 467 Mixed mode loading, 283 Models and modeling cohesive crack, 46, 433 dislocation, 484 ductile damage, 328 fatigue crack growth, 533 finite element, 397, 622, 660, 671 focal point, 46 Gurson, 343 hierarchical, 328 hydraulic fracturing processes, 622 loading, dynamic, 343 micromechanical, 343 single fiber cylindrical composite, 125 stochastic variability of toughness, 448 Modulus of elasticity, 177 Moire interferometry, 283 Monte Carlo method, 71 N Nonlinear load behavior, 433 Nozzle corner flaw tests, 415 Numerical analysis, 3, 591 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 710 FRACTURE MECHANICS: 25TH VOLUME O Orthotropic layers, 156 P Photoelasticity, dynamic, 294 Piezoelectric ceramics, 61 Piezo-spectroscopy, 241 Plasticity, 309, 484, 502 Plate thickness, effect on stress intensity factors, 191 Polymer, 380 Pores with liquid, 606 Powder metallurgy, 546 Pressurized cylindrical shells, 671 R Random hole array experiments, 328 Rebond fibers, 268 R curve, 433 Residual stresses, 19, 241, 518 Resistance curve, 31 Rip resistance, 575 Roughness induced closure, 502 Roughness, surface, 502 Rubber, 380 Ruby, 241 S Sapphire-fiber composites, 241 Scatter, 71 Sea ice, 433 SENB specimens, 343 SENT specimens, 309, 380 Shear decohesion mechanism, 467 Shear strains, Shear stress, resolved, 467 Ship design, 518, 533 Short rod beam specimens, 46 Silicon nitride, 19, 71 Single edge notched beam specimens, 31 Single separation technique, 397 Singular integral equations, 156, 591 Slip system, 467 Small scale yielding, 106, 685 Splitting cavities, 606 Stability, Stable ductile tearing, 415 Statistical Fracture Mechanics approach, 71 Steel A710, 533 ferritic, 448 heat-treated low-alloy, 575 HSLA, 518 HSLA-80, 533 low alloy, 415 reactor grade, 294 Stochastic, 71 Stochastic variability of toughness, 448 Strain energy release rate, 177, 646 Strain gages, 294 Strain rate effect, 343 Strain rate Gurson model, 343 Stress concentrations, 61, 591 Stress, crack closing, 283 Stress, crack shearing, 283 Stress field, hydrostatic, 685 Stress intensity factors, 156, 191, 206, 518, 591 calculation, 637 solutions, 660 Stress, pre-, warm, 685 Stress, residual, 125,241, 606 Strips, 156 partially bonded, 206 Superconductors, 255 Superplastic forming, 546 Surface flaws, 397 T Tearing, 448 Tensile force, 206 Tensile stress distribution, 222 Tensile test, dynamic, 343 Thermal expansion, 646 Thermal expansion coefficient, 177 Thermal shock, 637 Thermal stressing method, 255 Thermal stress, residual, 646 Thermoelectric cell, 646 Thermomechanics, 125 Thermoplastic coating, 125 Thin web sections, 660 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:18:02 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized INDEX 711 Three dimensional analysis, 191, 343 Titanium aluminum matrix, 241 Toughening, transformation, Toughness, lower bound, 294 T-peel joint, 222 Transformation toughening, Transition region, cleavage fracture, 448 Transmission fluorescence spectroscopy, 241 Tunneling, 358 Two dimensional analysis, 222, 358 Weibull statistics, 448 Weld, 533 Weld bonding, 222 X X-ray diffraction, 19 Y Yielding, small scale, 106 W Water tests, 575 Weakest link approach, 448 Weibull distribution, 557 Z Zirconia, 3, 31 ISBN 0-8031-1&&2-1