FRACTURE MECHANICS Proceedings of the Eleventh National Symposium on Fracture Mechanics: Part I A symposium sponsored by ASTM Committee E-24 on Fracture Testing of Metals AMERICAN SOCIETY FOR TESTING AND MATERIALS Virginia Polytechnic Institute and State University Blacksburg, Va., 12-14 June 1978 ASTM SPECIAL TECHNICAL PUBLICATION 677 C W Smith, Virginia Polytechnic Institute and State University, editor List price $60.00 04-677000-30 # (AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa 19103 Copyright© AMERICAN SOCIETY FOR TESTING AND MATERIALS 1979 Library of Congress Catalog Card Number: 78-74567 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, Md August 1979 Foreword This publication, Fracture Mechanics, contains papers presented at the Eleventh National Symposium on Fracture Mechanics which was held 12-14 June 1978 at Virginia Polytechnic Institute and State University, Blacksburg, Va The American Society for Testing and Materials' Committee E-24 on Fracture Testing of Metals sponsored the symposium C W Smith, Virginia Polytechnic Institute and State University, served as editor of this publication The proceedings have been divided into two volumes: Part \—fracture Mechanics and Part II—Fracture Mechanics Applied to Brittle Materials Related ASTM Publications Developments in Fracture Mechanics Test Methods Standardization, STP 632 (1977), $24.75, 04-632000-30 Fractography—Microscopic Cracking Process, STP 600 (1976), $27.50, 04-600000-30 Mechanics of Crack Growth, STP 590 (1976), $45.25, 04-590000-30 A Note of Appreciation to Reviewers This publication is made possible by the authors and, also, the unheralded efforts of the reviewers This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing the papers must be acknowledged The quality level of ASTM publications is a direct function of their respected opinions On behalf of ASTM we acknowledge with appreciation their contribution ASTM Committee on Publications Editorial Staff Jane B Wheeler, Managing Editor Helen M Hoersch, Associate Editor Ellen J McGlinchey, Senior Assistant Editor Helen Mahy, Assistant Editor Contents Introduction I FATIGUE CRACK GROWTH STUDIES Effect of Biaxial Stresses on Crack Growth—A F LIU, J E ALLISON, D F DITTMER, AND J R YAMANE Fatigue Crack Growtli Threshold in Mild Steel Under Combined Loading— L P POOK AND A F GREENAN 23 Sequence Effects on Fatigue Crack Propagation; Mechanical and Microstructural Contributions—H NOWACK, SCHULTE, AND G LUTJERING K H TRAUTMANN, K Variations in Crack Growth Rate Behavior—M E ARTLEY, J P GALLAGHER, AND H D STALNAKER 36 54 Application of Fracture Mechanics to Damage Accumulation in High Temperature Fatigue—M J DOUGLAS AND A PLUMTREE 68 Cryogenic Effects on the Fracture Mechanics Parameters of Ferritic Nickel Alloy Steels—R L TOBLER, R P MIKESELL, AND R P REED 85 Evaluation of Temperature Effects on Crack Growth in Aluminum Sheet Material—D E PETTIT AND J M VAN ORDEN 106 Effects of Temperature and Frequency on the Fatigue Crack Growth Rate Properties of a 1950 Vintage CrMoV Rotor Material—T T SHIH AND G A CLARKE 125 Structural Memory of Cracked Components Under Irregular Loading— H FURRING AND T SEEGER 144 Effect of the Active Plastic Zone on Fatigue Crack Growth Rates— GUNTER MARCI 168 A Comparative Experimental Study on the Fatigue Crack Closure Behavior Under Cyclic Loading for Steels and Aluminum Alloys—j A VAZQUEZ, AUGUSTO MORRONE, AND J C GASCO 187 Effect of Residual Stresses on Fatigue Crack Growth in Steel Weldments Under Constant and Variable Amplitude Loads—GRZECORZ GLINKA 198 Role of Crack-Tip Stress Relaxation in Fatigue Crack Growth—A SAXENA AND S J HUDAK, JR 215 Crack Closure During Fatigue Crack Propagation—w j D SHAW AND I LE MAY 233 Fatigue at Notches and the Local Strain and Fracture Mechanics Approaches— N E DOWLING 247 A Strain Based Intensity Factor Solution for Short Fatigue Cracks Initiating from Notches—M H EL HADDAD, K N SMITH, AND T H TOPPER 274 Cracli Initiation in a High-Strength Low-Alloy Steel—B L BRAGLIA, R W HERTZBERG, AND RICHARD ROBERTS Effect of Spherical Discontinuities on Fatigue Crack Growth Rate Performance—W G CLARK, JR 290 303 Prediction of Fatigue Crack Growth Under Spectrum Loads—A E GEMMA AND D, W SNOW 320 SURFACE FLAWS Semi-Elliptical Cracks in a Cylinder Subjected to Stress Gradients—j HELIOT, R C L A B B E N S , AND A PELLISSIER-TANON 341 Stress Intensity Factor Solutions for Internal Longitudinal Semi-Elliptical Surface Flaws in a Cylinder Under Arbitrary Loadings—J j MCGOWAN AND M RAYMUND 365 Theoretical and Experimental Analysis of Semi-Elliptical Surface Cracks Subject to Thermal Shock—G YAGAWA, M ICHIMIYA, AND Y ANDO 381 Growth of Part-Through Cracks—L HODULAK, H KORDISCH, S KUNZELMANN, AND E SOMMER 399 Stress Intensity Factors for Two Symmetric Corner Cracks—i s RAJU AND J C NEWMAN, JR 411 Influence of Flaw Geometries on Hole-Crack Stress Intensities—c w SMITH, W H PETERS, AND S F GOU 431 EXPERIMENTAL FRACTURE MECHANICS—X^ic, J,c,SPECIMEN GEOMETRY EFFECTS, AND E X P E R I M E N T A L TECHNIQUES Variation of Fracture Toughness with Specimen Geometry and Loading Conditions in Welded Low Alloy Steels—A PENELON, M N BASSIM, AND J M DORLOT 7,t Results and Methods with Bend Specimens—J H UNDERWOOD 449 463 Investigation of Specimen Geometry Modifications to Determine the Conservative, JfR Curve Tearing Modulus Using the HY-130 Steel System—J P GUDAS, J A JOYCE, AND D A DA VIS 474 An Experimental Study of the Crack Length/Specimen Width (a/W) Ratio Dependence of the Crack Opening Displacement (COD) Test Using Small-Scale Specimens—P M S T DE CASTRO, J SPURRIER, A N D p HANCOCK 486 Dynamic Photoelastic and Dynamic Finite Element Analyses of Polycarbonate Dynamic Tear Test Specimens—s MALL, A S KOBAYASHI, AND Y URABE 498 Effect of Specimen Geometry on Crack Growth Resistance—s j GARWOOD 511 Single-Edge-Cracked Crack Growth Gage—j A ORI AND A F GRANDT, JR 533 Measurement of Crack-Tip Stress Distributions by X-Ray Diffraction—J E ALLISON 550 Correlations Between Ultrasonic and Fracture Toughness Factors in Metallic Materials—ALEX VARY 563 SPECIAL TOPICS Analysis of Load-Displacement Relationships to Determine J-R Curve and Tearing Instability Material Properties—HUGO ERNST, p C PARIS, MARK ROSSOW, AND J W HUTCHINSON Path Dependence of J in Three Numerical 58] Examples—M E KARABIN, JR., AND J L SWEDLOW 600 Description of Stable and Unstable Crack Growth in the Elastic Plastic Regime in Terms of/r Resistance Curves—c E TURNER 614 Strain Energy Release Rate Method for Predicting Failure Modes in Composite Materials—R s WILLIAMS AND K L REIFSNIDER 629 An Analysis of Tapered Double-Cantilever-Beam Fracture Toughness Test for Adhesive Joints—s s WANG 651 Analytical Modeling and ND Monitoring of Interlaminar Defects in FiberReinforced Composites—R L RAMKUMAR, S V KULKARNI, R B PIPES, A N D S N CHATTERJEE 668 Stress Intensity Factors for a Circular Ring with Uniform Array of Radial Cracks Using Cubic Isoparametric Singular Elements—s L PU AND M A HUSSAIN 685 Interpretations of Crack Surface Topologies for Poly(Vinyl Chloride)— E M SMOLEY 700 ENGINEERING APPLICATIONS Experimental Determination of ^ | for Hollow Rectangular Tubes Containing Corner Cracks—M E MCDERMOTT AND R I STEPHENS 719 Fracture Analysis of a Pneumatically Burst Seamless-Steel Compressed Gas Container—B w CHRIST, J H SMITH, AND G E HICHO 734 Crack Growth in Externally Flawed, Autofrett^ed Thick-Walled Cylinders and Rings—J A KAPP AND R EISENSTADT Estimating Fatigue Crack Propagation Lives at the Test Site—D R GALLIART 746 757 On the Cup and Cone Fracture of Tensile Bars—B KONG AND P C PARIS 770 776 FRACTURE MECHANICS FIG 2—Typical cup and cone fractures of ASTM A471 m-d^m^ iUs wm FIG 3—Interrupted tests of necked tensile bars {two center bars) compared to unstretched and fractured bars KONG AND PARIS ON CUP AND CONE FRACTURE 777 flaws prior to fatiguing, but the X-ray method did not lead to any observations of cracks Figure shows typical cup and cone fractures of the bars tested to failure Figure shows two interrupted necked bars between an untested bar and a fractured bar Results and Calculations for Tests-To-Fracture Failure Compliances of the test machines were estimated by considering only the bending of the crosshead, the most compliant part The results are CM V L^ = — = 7^ P ~ 24 E\ CMTS ~ 2.3 X 10-8 in ib-i CBUW ~ 2.9 X 10-« in lb"' For incorporation into computations using Eq 8, L, is replaced-by an effective length, Lgfi, which is adjusted for testing machine compliance and the bar ends of enlarged diameter L _ J ^ specimen ' ^ M elf ~ ^specimen X ^' specimen where ^specimen -L'-'gage +L ^^^"^ ' •'-'grip X ' />grip where dimensions are illustrated in Fig In addition the slant fracture surface area, A up, of the cup and cone fracture was estimated from the diameters of the flat area, d, and the neck, Z)neck • From this result and the fracture load, Piracture, the adjusted flow stress, trup, was computed Results of these measurements and computations are given in Table Results for Interrupted Tests At the necked section of interrupted tests surface flaws up to 1/20 in long and 1/40 in wide were observed with the unaided eye The X-ray photographs (have low resolving power) showed no clear indication of the visible surface flaws nor interior flaws for these same tests Therefore the X-ray technique led to doubtful results 778 FRACTURE MECHANICS D grip / bit marks ^ grip 'N D u -D gage o gage neck FIG 4—Test bar dimensions On the other hand the fracture surface of one of the two specimens subject to fatigue subsequent to necking revealed that substantial cracks developed prior to fatiguing Thus stable growth of flaws preceded instability Discussion The previous analysis for fracture instability of a microflaw, Eq 9, gives ^'applied approximately equal to 2.6 which is lower than all rmatenai values given in Table This agrees with the hypothesis that the ductile fracture of tensile bar initiates with stable development of interior microflaws Interrupted tests also support this contention Comparison of rmatenai and ^applied values based on Eq shown in Table also supports the hypothesis as well, since instability is predicted only for substantial cracks Fatiguing to fracture after interrupting a test only revealed one plane, and the location of this plane was determined by a small surface flaw which dominated fatigue cracking Thus, that plane may be some longitudinal distance away from the center flaw which would have dominated static fracture Therefore, the fatigued plane does not necessarily expose the interior flaw of interest A better X-ray technique or longitudinal sectioning are suggested for future studies Nevertheless one of the fatigued surfaces showed both interior and exterior flaws, verifying the possibility of interior flaw development prior to unstable fracture This project was a preliminary study of applying the tearing instability theory [1 ] to ductile tensile bar fracture Therefore for simplification some assumptions and approximations were included; such as assuming dJIda does not change with large plastic deformation; o-/is uniform throughout KONG AND PARIS ON CUP AND CONE FRACTURE 779 the cross section, the interior crack is unique, circular, and symmetric with respect to the longitudinal axis, etc Consequently, it is quite surprising to find that the Tmateriai and Jappued values for each test agree within a factor of in Table Since the values are quite independently obtained, this is regarded as excellent agreement In future studies it will be appropriate to further investigate the theory by varying parameters such as temperature, gage length, gage diameter, and materials, as well as exploring the assumptions of the theory discussed here However, while this preliminary study has left many questions unanswered, it did indeed show the distinct possibility that the theory of tearing instability may explain ductile cup and cone fractures Following completion of the current work some additional results were obtained which add further to the credibility of this work A resume of these results is given in the Appendix Conclusions Tearing instabiliy theory [7] has been appUed to cup and cone fractures of A471 steel tensile bars with quantitatively consistent results Interrupting tests upon necking but prior to fracture and then fatiguing to failure leads to concluding that microflaws grew in a stable manner prior to instability The application of tearing instability to these tests of A471 predicted, as observed, that microflaw growth would be stable Presuming that stable microflaw growth generated the flat center of the cup and cone fracture, then instability occurred with the being of formation of the shear wall The application of tearing instability theory with the flat center, as the final stable flaw size leads to quantitative prediction of instability (within a factor of for Jmatenai versus ^applied) and implies a switch to the shear wall as observed Additional studies should be performed to explore further the variables involved in cup and cone fractures Acknowledgment The partial support of this and previous [/] work under contract with the Division of Operating Reactors, The U.S Nuclear Regulatory Commission at Washington University, is acknowledged The encouragement of W Hazelton and R Gamble of the National Resetirch Council has been instrumental to these studies The continued support of this study under National Science Foundation Grant ENG 77-20937 is also gratefully acknowledged Moreover, material and data suppUed by Westinghouse Research, through the cooperation of E T Wessel is noted with thanks 780 FRACTURE MECHANICS APPENDIX Additional Rssults on A453 Steel Tension test results of ASTM A453 stainless steel were made available by Westinghouse Research Laboratories for tests at different temperatures according to the ASTM Standard Methods of Tension Testing of Metallic Materials (E 8-69) They also provided J-R curve results The chemical composition of the material is listed in Table The tension test results and the J-R curves, together with the assumption that the load at fracture is 80 percent of the maximum load, and the compliance of the test machine is zero, 7"materiai and ^applied are calculated as in Eq and shown in Table TABLE 3—Chemical composition of ASTM A453 Material ASTMA453 (A286) Si 0.036 0.017 0.0025 0.57 Mn Ni Cr Mo 1.72 25.8 14.9 1.31 0.31 TABLE A—Test results for ASTM A453 Specimen Number Temperature, op dJIda, Ibin.-^ ^ material -' applied Ta 75 75 400 400 800 800 18800 18800 10500 10500 7140 7140 9.7 14.4 7.3 3.7 8.7 8.1 8 5 7"31 7-24 7^32 T^, T34 References [i] Paris, P C , Tada, H., Zahoor, A., and Ernst, H in Elastic-Plastic Fracture, ASTM STP 668, American Society for Testing and Materials, 1979, pp 5-36 [2] Rice, J R., The Mechanics of Fracture, F Erdogan, Ed., American Society of Mechanical Engineers, 1976 [3] Paris, P C in Flow Growth and Fracture, ASTM STP 631, Proceedings of the 10th National Symposium on Fracture Mechanics, American Society for Testing and Materials, 1977, pp 3-27 \4] Rice, J R., "Elastic-Plastic Models for Stable Crack Growth," Mechanics and Mechanisms of Crack Growth, British Steel Corp., 1973 [5] Polakowski, N H., and Ripling, E J., Strength and Structure of Engineering Materials, Prentice-Hall, Englewood Cliffs, N J., 1964 Summary STP667-EB/Aug 1979 Summary Approximately half of this volume has been devoted to the general subject of fatigue crack growth, including effects of combined stress, nonperiodic load spectra, temperature, crack closure and residual stress, notches and material discontinuities Other topics treated include the analytical and experimental analysis of surfaceflaws,A^jc-Jic determination, elasto-plastic analysis, specimen geometry effects, experimental techniques for measuring fracture toughness and crack growth parameters, crack initiation, and a group of papers describing the application of fracture mechanics to engineering problems of current technological importance involving cracked bodies of complex geometry The influence of combined fields in fatigue crack growth studies was investigated From experiments on aluminum alloys, Liu, Allison, Dittmer, and Yamane concluded that the transverse stress exerted no influence upon crack growth when constant stress ratios were applied cyclicly In another study, Pook and Greenan found that the fatigue crack growth threshold depended upon the A^i of the branch crack in some cases and upon the AK^ of the original crack in others where Mode II loads were combined With Mode I loads on the original crack Several papers focused on load spectrum effects Based upon a comparison of experimental results with a continuum model, Nowack, Trautmann, Schulte, and Liitjering found that mechanical processes exert a strong influence upon load sequence effects on the fatigue crack growth in aluminum alloys, but that microstructural changes could produce significant deviations from the continuum mechanical analysis In another study, Artley, Gallagher, and Stalnaker concluded, from an analysis of experimental data on aluminum alloy, that both overload magnitude and frequency exert significant effects upon crack growth rate Gemma and Snow developed a mechanical model which used constant amplitude fatigue crack growth data at various stress ratios to predict reduced crack growth rates caused by high-low load sequences and showed that correct trends were predicted when compared with test results on several alloys The influence of temperature on fatigue crack growth was investigated Douglas and Plumtree utilized a unified life prediction theory based upon damage accumulation in order to predict crack growth rates at elevated temperature Tobler, Mikesell, and Reed recorded variations in Ki^ with temperature over a wide range of temperatures including the transitional 783 Copyright® 1979 b y AS FM International www.astm.org 784 FRACTURE MECHANICS range for low-carbon steels On the basis of experiments on aluminum alloys at low temperatures, Pettit and VanOrden concluded that service temperature R-curves should be used in ranking materials for use in the cryogenic temperature region Shih and Clark found that the influence of temperature on fatigue crack growth rates in rotor steel was frequency dependent, primarily at low frequencies However, at all frequencies studied, the fatigue crack growth rate decreased initially with increasing temperature and then increased with continued temperature increase Several investigations were conducted which focused upon the influence of crack tip plasticity upon fatigue crack growth Fiihring and Seeger developed a continuum mathematical model for describing load history induced residual stress effects upon crack-tip plasticity and fatigue crack growth In another analytical study, Marci quantified the concentration of crack closure effects near specimen surfaces Vazquez, Morrone, and Gasco conducted an experimental study of fatigue crack closure in steel from which they identified ^max ^s the most suitable parameter for correlating fatigue crack closure behavior Glinka showed how the influence of residual stresses in cracked steel weldments on fatigue crack growth could be predicted qualitatively from existing models On the basis of observations of experiments on aluminum alloys and steel, Saxena and Hudak explained the dependence of load ratio effects on crack growth rates through mean stress relaxation Based upon experimental observations, Shaw and LeMay concluded that crack growth curves could be predicted accurately provided the proper crack closure load was used Several studies were reported upon which dealt with the initiation and growth of fatigue cracks from notches, where the use of Linear ElasticFracture Mechanics may be questionable Dowling described a general approach to notch size effects based upon the growth of small cracks El Haddad, Smith, and Topper presented an approach to the short fatigue crack emanating from a notch based upon a strain intensity factor Braglia, Hertzberg, and Roberts identified the micromechanisms responsible for crack initiation in notched high-strength low-alloy steel Finally, an investigation by Clark is included which studies the influence of macroscopic spherical discontinuities upon the fatigue crack growth rate in powder metal steel specimens Several papers, both analytical and experimental, addressed three dimensional cracked body problems involving surface flaws Using a boundary integral-influence function approach, Heliot, Labbens, and Pellissier-Tanon computed stress intensities for semi-elliptic cracks in meridional planes of thin-walled cylinders under internal pressure McGowan and Raymund addressed the same problem utilizing a finiteelement approach and their results correlated well with those of the previously mentioned study Yagawa, Ichimiya, and Ando used the finite element method to compute the time dependent thermal stresses induced by the sudden cooling of a thick plate containing a surface crack The SUMMARY 785 results predicted by the model were compared with test results on plexiglas plates and estimated times to fracture agreed fairly well Hodulak, Kordisch, Kunzelmann, and Sommer, in an experimental study of the fatigue crack growth of surface flaws in plates found evidence of nonuniform material behavior along the flaw border which they suggest may be due to a stress state dependent mechanical response Raju and Newman, using a finite element model, computed stress intensities for the technologically important problem of a crack emanating from the intersection edge of a hole with a plate In a frozen stress photoelastic study of the same problem, Smith, Peters, and Gou found that nonselfsimilar flaw growth appeared to produce changes in the stress intensity distribution duringflawgrowth and suggested that the cause may be due to an effect such as suggested by Hodulak et al Several papers were devoted to A^ic-^ic evaluations for different materials, some of which included tear modulus measurements Penelon, Bassim, and Dorlot, in evaluating J-integrals for material in the heat affected zone of steel alloys, observed a strong dependence of 7,0 upon geometry Underwood measured Jjc in steel using a bend test and presented a correction procedure for computing Jje values from C-shaped specimens Several papers presented studies which were directed towards the analysis and measurement of specimen geometry effects upon test results Gudas, Joyce, and Davis studied such an influence upon the Jif curve Tear Modulus in HY130 steel and found that face-grooving effects were significant deCastro, Spurrier, and Hancock quantified the influence of the crack length to specimen width ratio upon the crack opening displacement for structural steels in the cryogenic to room-temperature region Mall, Kobayashi and Urabe conducted dynamic photoelastic studies on dynamic tear test specimens in order to measure the variation of the dynamic stress intensity factor with time A finite element model was constructed which correlated with the experimental results Garwood showed that the values of and the crack opening displacements were essentially the same for both three-point bend and center-cracked tension specimens of pipeline steel The corresponding resistance curves, however, were different, and analytical explanations were offered Several papers utilized particular experimental techniques for obtaining information on fracture parameters Ori and Grandt evaluated the use of cracked coupons bonded to structures with expected preexistent cracks so that the coupons experienced load histories similar to the structure for predicting crack growth Allison used X-ray stress analysis to measure both residual and applied stresses near a crack tip Results confirmed the presence of crack closure type stress fields Vary described a mechanical model which is based upon the assumption that microcracking is promoted by elastic wave interactions, and relations between ultrasonic and fracture parameters were obtained 786 FRACTURE MECHANICS Reflecting the continued effort to adapt fracture concepts to plastic cracking, several papers focused upon the analysis of such cases Ernst, Paris, Rossow, and Hutchinson developed analytical methods for computing J from load displacement test records which take into account the influence of the extension of the crack Karabin and Swedlow, in a finite element analysis, found a path dependence in J when the plastic zone size is not small They suggest that this effect is related to a resharpening of the crack flank near the tip in center-cracked specimens Turner provided a description of stable and unstable crack growth for elasticplastic behavior in terms of/^ resistance curves Three papers addressed the general topic of composite fracture Williams and Reifsnider presented a strain energy release based finite element model for predicting failure modes in composite laminates which was correlated with experimental observations Wang described a hybrid stress finite element analysis of the tapered double cantilever beam fracture toughness specimen which revealed a number of important features Ramkumar, Kulkarni, Pipes, and Chatterjee presented an analysis of delaminations in a laminated cantilever beam of various locations in the beam The model suggests mechanisms for progressive cracking in laminates A number of interesting papers were contributed which addressed special topics in fracture mechanics Kong and Paris used a model of ductile fracture in tensile bars to suggest that tearing instabiUty theory might apply to some cases of fracture in the presence of extensive plastic deformation Pu and Hussain estimated stress intensity factors for a uniform array of radial cracks around a circular ring using a finite element approach Smoley studied crack surface topologies in poly(vinyl chloride) for nucleation, subcritical and critical flaw growth for both plasticized and unplasticized material Both craze and crack growth regimes were observed The preceding contributions to the developmental aspects of fracture mechanics were augmented by several papers which focused upon the utilization of fracture mechanics in specific engineering applications McDermott and Stephens conducted tests on hollow rectangular tubes containing comer cracks and described a procedure for predicting K^ values and crack growth based upon existing solutions Christ, Smith, and Hicho described the post failure analysis of a pneumatically burst seamless steel compressed gas cylinder which led to recommendations for minimizing the occurrence of such failures Kapp and Eisenstadt described a procedure for modeling flaw growth in autofrettaged cylinders for use in design Finally, Galliart described a design technique which utilized test data from a field test of a prototype as input data to a computerized program for designing against failure from fatigue crack growth in the ground vehicle industry The papers included in this volume show that fatigue crack growth SUMMARY 787 continues to occupy an important position in fracture mechanics Moreover, while crack initiation appears to be controlled mechanically, crack growth is shown to be sensitive to many other side effects as well, a number of which are quantified herein Another area of substantial activity involves the extension of the basic concepts of fracture mechanics to the prediction of fracture in the presence of substantial amounts of plasticity New results, both analytical and experimental, suggest that more complex models will be necessary in order to provide an acceptably accurate description of crack growth and fracture in problems involving complex three-dimensional geometries It is encouraging to note that, as the problems under study become more complex, new analyses and experimental techniques are being developed for use in dealing with such problems Taken collectively, this volume records advances in the development and application of fracture mechanics along a broad front It would seem to portend a trend which will extend the use of fracture mechanics to a wider range of environments and to more complex problems in the future C W Smith Department of Engineering and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Va 24061; symposium chairman and editor STP667-EB/Aug 1979 Index Opening displacement, 106, 486 Resistance, 511 Retardation, 198 Shape, 399 Surface topology, 700 Tip stress field, 651 Craze, 700 Cumulative damage, 290 Cyclic loads, 144, 247, 303 Delay cycles, 320 Cylinders, 341,685 Adherend, 651 Adhesive, 651 Aluminum alloys, 5, 36, 54, 106, 168, 187, 215, 320 Autofrettage, 746 B Bending loads, 463 Biaxial loading, Block loading, 290 Boundary integral method, 341 D equation Combined loading, 23 Complex stress functions, 651 Composite materials, 629, 668 Crack closure, 144, 168 Crack growth Gage, 533 Prediction, 399 Retardation, 550 Cracks, 700, 719 Arrest, 498 Closure, 36, 215, 233 Initiation, 23, 247, 511 Nucleation, 700 Damage accumulation, 68 Defects, 303 Deformation, 247, 600 Delaminations, 668 Design, 719 Displacements (deformations), 36 Ductile-brittle transition, 700 Ductile fracture, 734 Dynamic Fracture toughness, 498 Photoelasticity, 498 E Elastic analysis, 411, 651 Elastic-plastic Analysis, 614 Fracture, 474, 486 789 Copyright' 1979 b y A S I M International www.astm.org 790 FRACTURE MECHANICS Failure, 303 Failure modes, 629 Fatigue crack initiation, 290 Crack closure, 187 Fatigue crack growth, 5, 23, 36, 54, 68, 85, 106, 125, 144, 168, 187, 198, 215, 233, 247, 274, 290,303,320,533,550,614, 629, 700, 719, 746, 757 Fiber-reinforced epoxy, 668 Field test, 757 Finite elements, 381,411,498, 600, 629,651,746 Fractographic results, 106, 290,700 Fracture parameters, 341 Properties, 463, 685 Strength, 511 Tests, 486 Toughness, 85, 106, 381, 449, 463,474,511,563,734 Frequency, 125 Geometry effects, 486, 511 H Heat affected zone, 449 High temperature fatigue, 68 Hole-cracks, 411, 431 Hollow rectangular tube, 719 I Influence functions, 341 Instability, 511, 614 Iron-nickel-chromium alloys, 68 Jic tests, 463, 474 Jr, 614 J-R curves, 580 J-integral, 68, 449, 486, 580, 600, 614 Joints, 651 Loss-of-coolant accident, 381 M Materials Aluminum alloys, 5, 36, 54, 106, 168, 187, 215, 320 Composites, 629, 668 Nickel alloys, 67, 85 Plastics, 381,498, 700 Powdered metal, 303 Steel alloys, 23, 68, 85, 125, 187, 198,215,233,290,303,449, 463, 474, 486, 550, 719, 734 Titanium alloys, 320 Material memory, 144 Mathematical methods (see Elastic analysis Elastic-plastic analysis, Boundary integrals, Finite element Weight functions Stiffness derivative Mechanical properties, 85,486, 580 Microstructural crack propagation mechanism, 36 Microstructure, 563 Microvoid coalescence, 700 Mode II, 23 Multiple cracks, 685 INDEX 791 Strain Concentration, 144 Energy, 629 Nickel alloys, 68, 85 Intensity factor, 274, 365, 411, Nondestructive evaluation, 550, 431 563,668 Stress, 247, 274, 550 Notch size effects, 247 Analysis, 381 Cycling, 23, 533 Intensity distributions, 341, 365, O 381,411,431 Intensity factor, 54, 233, 341, Overload, 144, 320 651,685 Relaxation, 215 Waves, 563 Stress and strain concentration factors, 274 Photoelastic analysis, 431, 498 Structural memory, 144 Plastic instability, 700 Subcritical velocity, 700 Plasticity effects, 144, 247, 600 Surface flaws, 341, 365, 381, 399, PMMA, 381 411,431 Pneumatic burst test, 734 Polycarbonate, 498 Poly(vinyl chloride), 700 Pressure vessels, 365, 734, 746 N R-curve, 106, 614 Residual stress, 144, 198, 550 Retardation, 320 Tapered DCB specimen, 651 Tearing modulus, 474,511, 580,770 Temperature, 85, 106, 125 Thermal shock, 381 Three-dimensional problems, 341, 431 Titanium alloys, 320 Tubes, 719 U Scanning electron microscope studies, 629 Ultrasonics, 563 Spot-welded joints, 23 Underload, 144 Stage II fatigue (materials), 168 Statistical methods, 54 Steel alloys, 23, 85, 125, 187, 198, 215,233,290,303,449,463, 474, 486, 550, 719, 734 Variable ampUtude loading, 36, 54 Stiffness derivative method, 365 792 FRACTURE MECHANICS w Wearout concept, 668 Weight functions, 365 Welding residual stresses, 198 X-ray diffraction, 550