Astm stp 1296 1997

STP 1296 Fatigue and Fracture Mechanics: 27th Volume Robert S Piascik, James C Newman, Jr., and Norman E Dowling, Editors ASTM Publication Code Number (PCN): 04-012960-30 ASTM 100 Barr Harbor Drive West Conshohocken, PA 19428-2959 Printed in the U.S.A Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a ISBN: 0-8031-2412-0 PCN: 04-012960-30 ISSN: 1040-3094 Copyright 1997 AMERICAN SOCIETY FOR TESTING AND MATERIALS, West Conshohocken, PA All 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, personal, or educational classroom use, or the internal, personal, or educational classroom use of specific clients, is granted by the American Society for Testing and Materials (ASTM) provided that the appropriate fee is paid to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923; Tel: 508-750-8400; online: http://www.copyright.com/ Peer Review Policy Each paper published in this volume was evaluated by two peer reviewers and at least one editor 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 the 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 April 1997 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword The Twenty-Seventh International Symposium on Fatigue and Fracture Mechanics was held in Williamsburg, Virginia on 26-29 June 1995 The sponsor of the event was ASTM Committee E-08 on Fatigue and Fracture The symposium chairman was Robert S Piascik, NASA Langley Research Center, Hampton, VA Symposium co-chairmen were J C Newman, Jr., NASA Langley Research Center, Hampton, VA; R P Gangloff, University of Virginia, Charlottesville, Virginia; and Norman E Dowling, Virginia Polytechnic Institute and State University, Blacksburg, Virginia Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Overview ix PROFESSOR J L SWEDLOW MEMORIAL LECTURE Life Prediction: A Case for Muitidisciplinary Research ROBERT P WEI ELASTIC-PLASTIC FRACTURE Application of a J-Q Model for F r a c t u r e in the Ductile-Brittle T r a n s i t i o n - JOHN D LANDES 27 Constraint Effect in Brittle Fracture Jun-JiN CHAO AND XIANG H ZHANG 41 T* Integral Under Plane Stress C r a c k Growth YOSHIKA OMORI, HIROSHIOKADA, LEONG MA, SATYAN ATLURI,AND ALBERTS KOBAYASHI 61 Application of Constraint Modeling to Evaluation of C r a c k Growth Experiments~JONAS FALESKOG,FRED NILSSON, SKENDERSHEHU,AND HANS OBERG 72 Prediction of Stable Tearing and F r a c t u r e of a 2000-Series A l u m i n u m Alloy Plate Using a C T O A C r i t e r i o n - - o s DAWICKE,R S PIASCIK, AND J C NEWMAN,JR 90 Effects of Mixed Mode I/II Loading and G r a i n Orientation on Cr ack Initiation an d Stable Tearing in 2024-T3 Aluminum BYRON E AMSTtrrz, MICHAEL A SUTTON,DAVIDS DAWICKE,AND MICHAELL BOONE 105 The E n e r g y Dissipation Rate -A New Tool to Interpret G e o m e t r y and Size Effects -OTMAR KOLEDNIK,GUOXINSHAN, AND DIETER F FISCHER 126 Effects of C r ack Surface Morphology on F r a c t u r e Behavior u n d e r Mixed Mode I/ II I Loading K JIMMY HSIA,TONG-LIANGZHANG, AND DARRELLF SOCIE 152 An Analytical Investigation of the Effect of C r a c k Depth (a) and Cr ack Depth to Width (a/W) Ratio on the F r a c t u r e Toughness of A533-B S t e e l - JEFFREY A SMITH AND STANLEYT ROLFE 175 Ductile Tearing of Welded Structural Details MICHAEL L GENTILCOREAND ROBERT J DEXTER 201 An Experimentally Verified Finite Element Study of the Stress-Strain Response of C r a c k Geometries Experiencing Large-Scale Yielding TINA L PANONTINAND SHERI D SHEPPARD 216 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a Analysis of Warm P r e s t r e s s D a t a - - B R U C E D MACDONALD, GEORGE T EMBLEY, HUGO IRIZARRY-QUINONES, WALLY J McAFEE, DONALD E McCABE, PAUL D SMITH, AND J W WUTHRICH 243 FATIGUE The Three Thresholds for Fatigue Crack Propagation KEiTH J MILLER 267 How Fatigue Cracks Grow, Interact with Microstructure, and Lose Similitude-DAVIDL DAVIDSON 287 Short Crack Growth Behavior K SADANANDAAND A K VASUDEVAN 301 A Practical Methodology for Elastic-Plastic Fatigue Crack Growth-R CRAIG McCLUNG, G GRAHAM CHELL, DALE A RUSSELL, AND GEORGE E ORIENT 317 Effect of Absorbed Hydrogen on the Microstructure in the Vicinity of NearThreshold Fatigue Cracks in Low-Alloy SteeI JENS HELOTAND HELMUT KAESCHE 338 S-N Curve for Crack Initiation and an Estimate of Fatigue Crack Nucleus S i z e - - - c Y YANG, P K LIAW, S S PALUSAMY, AND W REN 352 ADVANCED MATERIALS AND APPLICATIONS Fracture Analysis of Full-Thickness Clad Beam Specimens JANXS A ~ENEY, B RICHARD BASS, AND WALLACE J McAFEE 367 The Analysis of Underclad Cracks in Large-Scale Tests Using the Local Approach to Cleavage Fracture DOMINIQUE MOINEREAUANDGILLESROUSSELIER 387 The Effect of Cyclic Loading During Ductile Tearing on the Fracture Resistance of Nuclear Pipe Steels -DAVIDL RUDLANDAND FREDERICKBRUST 406 Experimental Investigation of Mismatched Weld Joint Performance ROBERT L TREGONING 427 Fracture Testing of Large-Scale Thin-Sheet Aluminum Alloy ROLAND DEWIT, RICHARD J FIELDS, SAMUEL R LOW III, DONALD E HARNE, A N D TIM FOECKE 451 Resistance Spot Weld Failure Loads and Modes in Overload Conditions-STEVE ZUNIGA AND SHERI D SHEPPARD 469 Fatigue Response of Perforate Titanium for Application in Laminar Flow C o n t r o l - - J E N N I F E R L MILLER, JAMES C NEWMAN, JR., AND W STEVEN JOHNSON 490 Fatigue Crack Growth Damage in Elastomeric Materials CLAUDE BATHIAS, KARIME LEGORJU, CHUMING LU, AND LUC MENABEUF 505 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further repro ANALYTICAL METHODS Boundary Element/Dislocation Density Methodology for Analysis of Cracks in Anisotropic Solids n HELM, L XIAO, AND M E MEAR 517 Stress Intensity Factor Calibration of Edge-Notched Beam WALTER H GERSTLE, LARY R LENKE, AND GWANGHEE HEO 530 Elastic Analysis of the Interaction Between Two Surface Cracks LIAN KUI SUN, LI ZHANG, AND HONG QIN 550 A Three-Dimensional Weight Function MethodmEvaluation and Applications-WEI ZHAO, JAMES C NEWMAN, JR., AND MICHAEL A SUTTON 563 Simple Two- and Three-Dimension Adhesive Finite Elements for Stress Analysis and Energy Release Rate Calculations in Adhesively Bonded Joints DAVID A DILLARD, MARK W TAYLOR, RAUL ANDRUET, AND SIEGFRIED M HOLZER 580 Analysis of Fatigue Crack Growth in Pin-Loaded Lug Joints Under Inelastic Deformations RAGHU v PRAKASH, K N RAJU, K SATISH KUMAR, B DATTAGURU, AND T S RAMAMURTHY 598 An Efficient Method for Calculating Multiaxial Elasto-Plastic Notch Tip Strains and Stresses under Proportional Loading w REINHARDT, A MOFTAKHAR, AND G GLINKA Indexes 613 631 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Overview With the formation of ASTM Committee E-8 on fatigue and fracture, the Twenty-Seventh National Symposium was expanded and hence forth will represent both the Fatigue and Fracture Mechanics communities at the annual "National Symposium on Fatigue and Fracture Mechanics." With this new charter, the symposium chairmen (R S Piascik and J C Newman, Jr of the NASA Langley Research Center, R P Gangloff of the University of Virginia, and N E Dowling of the Virginia Polytechnic Institute and State University) formed a symposium organizing committee that represented both technical communities The organizing committee consisted of the symposium chairmen, A Saxena of the Georgia Institute of Technology, R C McClung of the Southwest Research Institute, M R Mitchell of the Rockwell International Company, and R H Dodds, Jr of the University of Illinois During the two and one-half day symposium held in Williamsburg, VA in June of 1995, an international group of experts from the United States, Canada, the United Kingdom, The Netherlands, Sweden, Germany, Austria, Japan, France, the Peoples Republic of China, India, and Korea presented their research findings concerning issues relating to fatigue and fracture mechanics Published herein are papers grouped in four technical categories relating to elasticplastic fracture, fatigue, advanced materials and applications, and analytical methods Papers relating to a fifth category on elevated temperature effects have been published as Elevated Temperature Effects on Fatigue and Fracture, ASTM STP 1297, edited by R S Piascik of the NASA Langley Research Center, R P Gangloff of the University of Virginia, and A Saxena of the Georgia Institute of Technology Professor Robert P Wei of Lehigh University, the Twenty-Seventh National Symposium J L Swedlow Memorial Lecturer, set the stage for the symposium by addressing important fatigue and fracture issues relating to life prediction Professor Wei's lecture, entitled "Life Prediction: A Case for Multidisciplinary Research," illustrated the need for multi-disciplinary research by presenting examples based on his research directed at the development of environmentally assisted crack growth models The collection of papers published in this volume describes the current research in the following technical areas Elastic-Plastic Fracture R H Dodds, Jr and W G Reuter chaired several sessions on elastic-plastic fracture Several papers presented recent work on the study of constraint, in particular the J integral and the constraint parameter Q A J-Q model for predicting failure in the ductile-brittle fracture transition region for steels was presented with experimental verification' The J-Q theory was also applied to large surface-cracked tension plates and other standard laboratory fracture specimens (compact, three-point bend, and single-edge-notched tension) to study crack initiation and growth under monotonic loading Ductile crack growth initiation is well characterized by J alone and appears to be insensitive to constraint effects in both the transition region and the upper shelf region But ductile crack growth is clearly sensitive to constraint effects, and Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized ix X FRACTUREMECHANICS: TWENTY-SEVENTH SYMPOSIUM the JR-curve is lower for higher Q values The constraint effects on brittle fracture (specimen size and geometry effects) were studied with a constraint parameter based on the second term in the normal stress field expansion at a crack tip The theory was then applied to the prediction of fracture toughness values for a brittle material Several papers presented results on other crack-tip parameters, such as crack-tip-opening displacement (CTOD), crack-tip-opening angle (CTOA), the T*-integral, and the energy dissipation rate (D) Large-strain, three-dimensional finite element analyses were performed for a variety of crack geometries to study local crack-front stress-strain fields The results showed that the deformations at the crack front are highly constrained with nearly plane-strain behavior in the mid-region and plane stress on the free surface, even in relatively thin specimens of finite size An evaluation of J- and T*-integrals on stabile tearing cracks in a thin aluminum alloy showed large differences between far-field and near-field J values for small amounts of stable crack growth But the CTOA computed by the near-field J was in reasonable agreement with the measured CTOA values during crack extension In another study, a two-dimensional, elastic-plastic finite element analysis was used with a critical CTOA to predict stable tearing in aluminum alloy plates The analyses showed good correlation with the measured load-againstcrack-opening displacement data Stable tearing experiments under mixed-mode (Modes I and II) loading indicated that the critical CTOD measured at mm behind the crack tip was nearly constant after a small amount of stable tearing In a study of mixed mode (Modes I and Ill) loading on a surface-crack specimen, a micromechanical model was developed to account for the effects of crack-face friction on fracture toughness The model predictions on fracture toughness agreed well with test results from the literature The application of elastic and elastic-plastic fracture mechanics concepts to structural components was demonstrated in papers on reactor pressure vessels to determine warm-prestress effects on fracture toughness and on stable tearing in welded structural I-beams The more advanced methods of analysis, such as the finite-element method, gave predicted results in better agreement with the measured load-deformation curves of the cracked members Fatigue The technical session on fatigue chaired by R C McClung and T H Topper covered a variety of topics Research was presented on improved understanding of fatigue endurance limits Here, three proposed mechanisms are correlated with fatigue crack growth thresholds and fatigue limits, i.e., (1) dislocation morphology, (2) material texture, and (3) stress-state Further understanding of fatigue crack growth in terms of interaction with microstructure and loss of similitude was presented Microstructure was found to influence the kinetics of the growth process, but not the growth processes It was also concluded that similitude concepts should extend to microstructure and response of the material to Cyclic loading An engineering methodology for elastic-plastic fatigue crack growth (EPFCG) for life and instability assessment was presented Experimental verification of the &/-based predictions of EPFCG was shown The effect of hydrogen on near-threshold fatigue crack growth was also discussed The damaging effect of hydrogen was correlated to microstructural effects, including dislocation transport of hydrogen and trapping at interfaces A method for performing stress-strain analysis of notched components subjected to multi-axial loading was compared to strain-gaged 2-D and 3-D notched bodies subjected to fatigue loading and also compared to finite element analysis of notches The new method was shown to be useful for analysis of notches where numerical solutions become time consuming and impractical Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz OVERVIEW xi Advanced Materials and Applications M R Mitchell chaired the session on advanced materials and applications A number of papers presented were related to the fracture of nuclear reactor components A finite element analysis to quantify the fracture toughness for shallow cracks contained in pressure vessels was presented The model appears to be effective in adjusting test data to account for in-plane loss of constraint for uniaxially tested beams The "local approach to cleavage fracture" method for evaluating the probability of cleavage failure of reactor pressure vessel components subjected to mechanical and thermal loading was also discussed Details of the Weibull-based model are discussed and related to the probability of failure The result of a study to confirm decreased ductile tearing resistance of nuclear pipe steels due to fully reversed loading was presented Experiments showed that as the stress ratio was decreased, i.e., the amount of compressive plasticity increased and the ductile tearing resistance of the material decreased Crack tip sharpening and void flattening were observed, which could be the mechanism contributing to cyclic degradation A finite element code for predicting overload pull-out failures in resistance spot-welded joints was presented The elements of this code will lead to a spot weld impact fail~ure criterion for an advanced crashworthiness code The results of an experimental investigation of mismatched weld performance show that the effect of mismatch in welds is minimized in more highly constrained configurations Therefore, fracture toughness measurement and constraint indexing procedures are applicable with little modification to the homogeneous methodology for many typical weld joints The results of tests conducted to investigate the effect of multiple site damage (MSD) in large-scale thin sheet panels were presented The data are analyzed by a plastic zone model and R-curve analysis to predict the affect of MSD on residual strength The fatigue and tensile properties of an advanced perforated titanium component for laminar flow control applications were studied A detailed description of the fatigue failure response of the perforated sheet material is presented A model for fatigue damage in elastomeric materials was presented The model of fatigue life and damage is given versus parameters and temperature ( - to 80~ Analytical Methods The technical session on analytical methods chaired by J C Newman, Jr and M A Sutton covered a variety of different methods to determine stress-intensity factors (SIF) and strainenergy release rates for linear-elastic cracked bodies For two-dimensional cracked bodies, a boundary-element/dislocation density method, called FADD, was presented as an easy and convenient method to perform stress analyses of bodies with or without cracks, and the finiteelement method was used to determine the SIFs for a single-edge-notched "shear" beam and for through cracks growing from pin-loaded, interference fit, lug joints The strain-energy release rates (G) were calculated for delamination cracks in adhesively bonded joints using both two- and three-dimensional finite-element analyses with special adhesive element models For three-dimensional cracks, the finite-element method with a new quasi-compatible element and equation solver was used to analyze the interaction between two semi-elliptical surface cracks An evaluation of a three-dimensional weight-function method (3D-WFM) for surface and comer cracks in plates or at holes was made, and the results compared well with the accepted solutions for these crack configurations The 3D-WFM provides an inexpensive method to obtain SIFs Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 622 FATIGUEAND FRACTURE MECHANICS: 27TH VOLUME Comparison with Numerical Data The application of the proposed method is illustrated by two examples The first example is a curved cantilever beam with a very sharp notch (Figs and 5) The stress concentration factor was 6.63 This case has been solved previously in Ref 4, and the solution is reproduced here The numerical data for the second example were taken from Hoffman and Seeger [5], who studied a cylindrical specimen with a circumferential notch subjected to simultaneous tensile and torsional loadings (Fig 6) Notched Cantilever Beam A curved cantilever beam specimen was cut out transversely from a pressure tube with a notch as shown in Fig The dimensions of the beam were as follows: Notch depth = 1,0 mm Notch root radius = 0,18 mm Notch opening angle = 45 ~ Tube internal radius = 52 mm FIG ,Notched cantilever beam i/ h p=O.I8 mm O ~t h=l.O~ FIG, Detailed representation of the notch in the cantilever beam Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized REINHARDT ET AL ON NOTCH TIP STRAINS AND STRESSES 9, - - - - - - - - R X2 = t T' o~02 x t ~ 623 = X3 ~/.,.~ = X3 I I I o / t =0.3 R/t= FIG, Geometry and dimensions of the cylindrical specimen tested by Hoffman and Seeger [51 Wall thickness = m m Width = 3.124 m m The material was Zr-2.5%Nb alloy for which the uniaxial stress-strain relationship is given in the form of a Ramberg-Osgood relation e = - + - & E E (33) The material properties were: E = 94 400 MPa, v = 0.4, n = 22.7, c~ = 1.128 10 -6~ ~Y0 = 550 MPa Figure shows a three-dimensional representation of the specimen including the coordinate system, the boundary conditions, and the applied bending moment The nominal bending stress for this model was 250 MPa The theoretical linear-elastic notch tip stress and strain components corresponding to that load level were determined by finite element analysis using A B A Q U S [6] software Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions 624 FATIGUEAND FRACTURE MECHANICS: 27TH VOLUME The FE model used 20-noded 3-D elements, resulting in (r~ = 1657.0 MPa, o~3 = 532.0 MPa Solution Substituting o~2 and ~ stress components into Hooke's law results in the elastic strain components at the notch tip e P I~ E~ =- ~ 0"2 ~ 0-~; 1) ~ = ~, 0-'J - ~, ~2; (34) = 0.0153 ~S = -0.00140 (35) When the values of the theoretical linear elastic notch tip stress and strain components are known, the total strain energy density (o~/eT) can be calculated as: o~/e[ = t~z~ + o'~3e~; o~/C = 24.61 MNm m3 (36) By substituting the plastic strain from the Ramberg-Osgood relation (Eq 33) into Eq 16, the total plastic energy density for the generalized Neuber rule can be obtained W~p = t ~"+' got x~ (37) Similarly, the plastic strain energy density for the ESED method is 2n ot W~e - n + 1E (0-,q).+l (38) TO solve the energy equivalence in the form of Eq 15, the hydrostatic-to-equivalent stress ratio was approximated by the ratio of the fictitious elastic stresses 0-eq O~eq - 2x/(O~2) "J- (O~3)2 ~20~3 = 0.7470 (39) After substitutions and rearrangements Eq 15 takes the form of Eq 40 24.61 = 0-~ 2.8 + 0.2 (0.747) 1.129 10 - ~ 94400 + 94400 (0-eq)23"7 (40) Solving Eq 40 for Creqyields the Neuber solution Oeq = 623.43MPa Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproduct REINHARDT ET AL ON NOTCH TIP STRAINS AND STRESSES 625 Now, the parameters Cl, (?2, and C3 can be calculated using Eqs 20 through 22 C= = 6.363" 10 -5, (72 = 3.0758" 10 -5, (73 = -0.02938 Then substitute CI, C2, and Ca into Eq 29 to determine two values of ao a~ = 0.429 and ao = 0.0685 The theoretical elastic stress ratio, a~ = 0.321, can be used in Eqs 31 and 32 to select the correct sign and the solution for the stress ratio a , , 0.40 • (0.321) - 2.0 • 0.321 + 0.40 = - < 0.0 - 0.40 X 0.321 (41) Hence, due to Eq 32, the correct solution for the stress ratio is ao = 0.429 Subsequently, the stress components can be calculated from Eq 42 and Eq 18 (Yeq or2 = x/a2 _ a,~ + (42) and they ate o~2 = 7 M P ~ o~3 = 307.9MPa If the hydrostatic-to-equivalent stress ratio is recalculated with the stresses above, it would be found to equal 0.822 The error in the energy equation, Eq 15, resulting from this inaccuracy is 0.13%, and hence the present approximation for the stresses is deemed satisfactory By substituting o~2 and o~3 into the stress-strain relationship, Eqs 11 through 13, the Neuber (upper bound) strain components are determined: E~ = 0.0354, E~ = -0.0024, e~ = -0.0308 For the ESED method, the procedure is analogous except that Eq 17 is substituted into Eq 15 This gives an approximation for the notch tip stresses, o'~22 = 698.3 MPa and o'~33= 299.3 MPa, and the corresponding strains The results are summarized and compared with the notch tip elasto-plastic stress and strain components calculated by FEM [4] (see Table 1) TABLE Comparison of results for the notched beam example Solution Method o'22, MPa 0"33, MPa E22 E33 ~11 Simplified solution Neuber Finite element method Simplified solution ESED 717.5 700.0 698.3 307.9 300.0 299.3 0.0354 0.0242 0.023 -0.0024 -0.0016 -0.0015 -0.031 -0.020 -0.018 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions a 626 FATIGUE AND FRACTURE MECHANICS: 27TH VOLUME Shaft with Circumferential Notch under Tensile and Torsional Loads A shaft with circumferential notch as in Ref was studied as the second example to assess the accuracy of the multiaxial Neuber and ESED methods The calculated strains e~ and eft and stresses ~ and ~ are compared with elasto-plastic finite element results The finite element strains and stresses in the notch tip were calculated using an incremental elasto-plastic finite element model The ratio of the notch tip nominal shear to tensile stress is x~/or,r = 0.411 The nominal stresses are determined using the net cross-section dimensions F ornF = t) ~T(R and T % = "tr(R " - - - - ~ -t) (43) The stress concentration factors for tension and torsion are Kr = 3.89 and Kr = 2.19, respectively The stress concentration factors were defined as (Fig 4) KF- or~2 and ornF or52 Kr = - - Tn (44) The ratio of the notch tip hoop stress to axial stress in tension is or53/o~22 = 0.2 A bi-linear stress-strain relation was used for the calculations Its mathematical form is given by or e =-~ for or choose sign - , otherwise choose sign + Calculate or2 = sign(c~2)o'eq/((a,)2 - a~, + 1) 1/2, tr3 = a,,tr2; determine ~r~,~)d= (or2 + cr3)/2 Calculate the residual R = ll3(tr,q)2[llG + (1 - 2v)IE" (~r~)dhr~))2] + W({~eq ) - (o~2~_ dr" O~3f.~) Compare R with desired accuracy ~R: R < eR? (if no, set n: = n + and go to 2) (if yes, leave loop and go to 9) Determine el, e2, and E3 from Hencky's equations References [1] [2] [3] [4] [5] Neuber, H., "Theory of Stress Concentration Shear Strained Prismatic Bodies with Arbitrary NonLinear Stress-Strain Law," ASME Journal of Applied Mechanics, Voi 28, 1961, pp 544-550 Molski, K and Glinka, G., "A Method of Elastic-Plastic Stress and Strain Calculation at a Notch Root," Material Science and Engineering, Voi 50, 1981, pp 93-100 Moftakhar, A., Buczynski, A., and Glinka, G., "Calculation of Elasto-Plastic Strains and Stresses in Notches under Multiaxial Loading," International Journal of Fracture, Vol 70, 1995, pp 357-373 Moftakhar, A and Glinka, G., "Localized Time-dependent and Ttme-independent Plasticity," Report No 2, Fracture Technology Section, Ontario Hydro Research Division, Toronto, 1991 Seeger, T and Hoffman, M., "The Use of Hencky's Equations for the Estimation of Muitiaxial ElasticPlastic Notch Stresses and Strains," Report No FB-3/1986, Technische Hochschule Darmstadt, 1986 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized REINHARDT ET AL, ON NOTCH TIP STRAINS AND STRESSES 629 [6] Hibbit, H., Karlsson, B., and Sorenson, E, "ABAQUS Theory Manual," Version 4.8, 1989 [7] Moftakhar, A., "Calculation of Time-independent and Time-dependent Stresses and Strains in Notches," Ph.D dissertation, University of Waterloo, Ontario, Canada, 1995 [8] Barkey,M E., Socie, D E, and Hsia, K J., "A Yield Surface Approach to the Estimation of Notch Strains for Proportional and Non-proportional Cyclic Loading," ASME Journal of Engineering Materials and Technology, Vol 116, 1994, pp 173-180 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP1296-EB/Apr 1997 Author Index A Amstutz, Byron E., 105 Andruet, Raul, 580 Atluri, Satya N., 61 B Bass, B Richard, 367 Bathias, Claude, 505 Boone, Michael L., 105 Brust, Frederick, 406 C Chao, Yuh-Jin, 31 Chell, G Graham, 317 D Dattaguru, B., 598 Davidson, David L., 287 Dawicke, David S., 90, 105 deWit, Roland, 451 Dexter, Robert J., 201 Dillard, David A., 580 Dowling, Norman E., ix E Embley, George T., 243 F Faleskog, Jonas, 72 Fields, Richard J., 451 Fischer, Dieter E, 126 Foecke, Tim, 451 G Gentilcore, Michael L., 201 Gerstle, Walter, H., 530 Glinka, G., 613 It Harne, Donald E., 451 Heim, D., 517 Heldt, Jens, 338 Heo, Gwanghee, 530 Holzer, Siegfried M., 580 Hsia, K Jimmy, 152 I Irizarry-Quinones, Hugo, 243 J Johnson, W Steven, 490 K Kaesche, Helmut, 338 Keeney, Janis A., 367 Kobayashi, Albert S., 61 Kolednik, Otmar, 126 Kumar, K Satish, 598 L Landes, John D., 27 LeGorju, Karime, 505 Lenke, Lary R., 530 Liaw, P K., 352 Low, llI, Samuel R., 451 Lu, Churning, 505 M Macdonald, Bruce D., 243 Ma, Leong, 61 McAfee, Wallace J., 243, 367 McCabe, Donald E., 243 McClung, R Craig, 317 Mear, M E., 517 Menabeuf, Luc, 505 Miller, Jennifer L., 490 Miller, Keith J., 267 Moftakhar, A., 613 Moinereau, Dominique, 387 N Newman, Jr., James C., ix, 90, 490, 563 Nilsson, Fred, 72 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23631 19:36:15 EST 2015 Downloaded/printed by Copyright9of Washington by ASTM International www.astm.org University (University of Washington) pursuant to License Agreement No further reproductions authorized 632 FATIGUE AND FRACTURE MECHANICS: 27TH VOLUME O Oberg, Hans, 72 Okada, Hiroshi, 61 Omori, Yoshika, 61 Orient, George E., 317 Shehu, Skender, 72 Sheppard, Sheri D., 216, 469 Smith, Jeffrey A., 175 Smith, Paul D., 243 Socie, Durreil E, 152 Sun, Lian Kui, 550 Sutton, Michael A., 105, 563 P Palusamy, S S., 352 Panontin, Tina L., 216 Piascik, Robert S., ix Piascik, R S., 90 Prakash, Raghu V., 598 Q Qin, Hong, 550 R Raju, K N., 598 Ramamurthy, T S., 598 Reinhardt, W., 613 Ren, W., 352 Rolfr Stanley T., 175 Rousselier, Gilles, 387 Rudland, David L., 406 Ruju, K N., 598 Russell, Dale A., 317 S Sadanada, K., 301 Shan, Guoxin, 126 T Taylor, Mark W., 580 Tregoning, Robert L., 427 V Vasudevan, A K., 301 W Wei, Robert P., Wuthrich, J W., 243 X Xiao, L., 517 Y Yang, C Y., 352 Z Zhang, Li, 550 Zhang, Teng-Liang, 152 Zhang, Xiung H., 31 Zhao, Wei, 563 Zuniga, Steve, 469 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP1296-EB/Apr 1997 Subject Index A Adhesive joints, stress analysis and energy release rate, 580 Aluminum alloy crack-tip opening angle, 90 large-scale thin-sheet, 451 mixed mode l/II loading, 105 Anisotropic solids, cracks, boundary element method, 517 ASTM A 533, 352 ASTM E 399, 31 ASTM E 1152, 406 B Beam-truss elements, 580 Biaxial stress effect, 31 Boundary element method, cracks in anisotropic solids, 517 Boundary force method, stress intensity factor, 530 Brittle fracture, 550 constraint effect, 31 C Calibration, stress intensity factor, 530 Cbell WPS model, 243 Cladding, 387 Cleavage fracture, local approach, 387 Coach-peel specimen, 469 Constraint, 175, 367 brittle fracture, 31 modelling, crack growth, 72 Contact stresses, pin-loaded lug joints, 598 Comer crack, 563 Crack aspect ratio, 550 Crack closure, 301,317, 352 Crack depth, effect on fracture toughness, 175 Crack depth to width ratio, 175 Crack geometries, 216 Crack growth constraint modelling, 72 initiation, 72 stable, 61, 105 suberitical, Crack growth resistance geometry and size effects, 126 mismatched weld joints, 427 Crack initiation mixed mode I/II loading, 105 S-N curve, 352 Crack interacting factor, 550 Cracks anisotropic solids, 517 perforate titanium, 490 Crack shape, 352 Crack surface, morphology, fracture behavior and, 152 Crack surface friction, 152 Crack tip ductile-brittle transition, 27 stress fields, 31 Crack tip opening angle mixed mode I/II loading and grain orientation, 105 plane stress, 61 stable tearing and fracture prediction, 90 Crack tip opening displacement, 105 crack depth and, 175 Crack tip plastic zone, 287 Crack-tip stress strains, 216 Crack-tip stress triaxiality, 367 Cyclic loading, ductile tearing, 406 D Deformation, inelastic, 598 Delta J, 317 Dislocations anisotropic solids, 517 mobility, hydrogen effects, 338 Dodds-Anderson scaling model, 367 Ductile-brittle transition, fr~ture, 27 Ductile tearing cyclic loading, 406 welded structural details, 201 E Edge-notched beam, stress intensity factor calibration, 530 C o p y r i g h t b y A S T M I n t ' l ( a l l r i g h t s r e s e r v e d ) ; W6 3e 3d D e c : : E S T Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproduction 634 FATIGUEAND FRACTURE MECHANICS: 27TH VOLUME Elastic analysis, interaction between surface cracks, 550 Elastic-plastic analysis, pin-loaded lug joints, 598 Elastic-plastic fatigue crack growth, 317 Elastic-plastic fracture, 61 mechanics, 267 mismatched weld joints, 427 Elastic-plastic notch tip stresses and strains, 613 Elastomeric materials, fatigue crack growth damage, 505 Embedded crack, 563 Energy dissipation rate, 126 Environment absorbed hydrogen effect, 338 natural rubber, 505 "q-factor method, 367 Fracture toughness A533-B steel, 175 brittle fracture, 31 cyclic loading effect, 406 finite element analysis, 367 J-Q model, 27 large-scale thin-sheet aluminum alloy, 451 underclad cracks, 387 Front solver, 550 Full-thickness clad beams, fracture analysis, 367 G Geometry effects, 126 Grain orientation, 105 Griffith's criterion, 505 H Hydrogen, absorbed, effect on microstructure, 338 Fatigue crack, nucleus size, 352 Fatigue crack growth, 287 damage, elastomeric materials, 505 near-threshold, absorbed hydrogen effect, 338 perforate titanium, 490 pin-loaded lug joints, 598 short crack, 301 Fatigue crack propatagion, thresholds, 267 Finite element analysis crack depth role, 175 crack-tip opening angle, 90 ductile tearing, 406 energy dissipation rate, 126 full-thickness clad beams, 367 pin-loaded lug joints, 598 stable tearing analysis, 201 stress intensity factor, 530 stress-strain response, 216 two and three dimension adhesive elements, 580 warm prestress data, 243 weight function method, 563 Fractography natural rubber, 505 pin-loaded lug joints, 598 Fracture, crack-tip opening angle, 90 Fracture analysis, full-thickness clad beam specimens, 367 Fracture mechanics, 287 constraint modelling, 72 large-scale thin-sheet aluminum alloy, 451 natural rubber, 505 two and three dimension adhesive elements, 580 underclad cracks, 387 Fracture resistance, cyclic loading effect, 406 Fracture stress, 31 Impact failure, resistance spot welds, 469 Instability, energy dissipation rate, 126 Integral equation, 152 Interference fit, 598 Internal stresses, 301 Iosipescu beam, 530 J-integral, 61, 175, 406 energy dissipation rate, 126 stable tearing analysis, 201 J-Q methodology, 367 crack growth experiments, 72 fracture in ductile-brittle transition, 27 J-R curve, 406 mismatched weld joints, 427 L Laminar flow control, 490 Large deformation, finite element analysis, 216 Life prediction, 287, 317 multidisciplinary research, nuclear pressure vessel steel, 352 perforate titanium, 490 Limit load, 201 Linear elastic fracture mechanics, 31,267 Loading, combined, 317 Load ratio, natural rubber, 505 Local approach cleavage fracture, 387 Low-alloy steel, absorbed hydrogen effect, 338 Lug joints, pin-loaded, 598 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized SUBJECT INDEX M Materials, life prediction, Mechanisms, life prediction, MFM threshold condition, 267 Microstructural fracture mechanics, 267 Microstructure absorbed hydrogen effect, 338 fatigue crack growth, 287 Mismatching, 427 Mixed mode fracture, crack surface morphology, 152 Mixed mode I/lI loading, 2024-T3 aluminum, 105 Mixed mode I/III loading, fracture behavior, 152 Modelling constraint, crack growth, 72 fracture in ductile-brittle transition, 27 Multiaxial loading, proportional, 613 Multidisciplinaty approach, life prediction, Multiple cracks, 550 Multiple site damage, large-scale thin-sheet aluminum alloy, 451 N Neuber rule, generalized, 613 Notch fatigue, 301 Notch stress fields, 301 Notch tip stresses and strains, 613 Nuclear pipe steels, cyclic loading effect, 406 Numerical solution algorithm, 613 O Overload conditions, resistance spot welds, 469 Oxygen, effect on natural rubber, 505 P PD 6493, 201 Peel stresses, 580 Pin-loaded lug joints, fatigue crack growth, 598 Plane stress crack growth, 61 Plastic zone, large-scale thin-sheet aluminum alloy, 451 Q Quasi-compatible dements, 550 R R-curve, 451 Reactor pressure vessel, 367 Replication method, 352 Residual stresses, 301 Resistance spot weld failure, overload conditions, 469 635 RKR model, 72 Rubber, natural, fatigue crack growth, 505 Self-consistency, 152 Shallow crack, 367 Shallow flaw, 175, 387 Shear beam, edge-notched beam, 530 Short crack growth, 301 Similitude, 287, 301 Single crystal threshold, 267 Single-edge notch bend specimens, 367 Singular elements, 550 Size effects, 126 brittle fracture, 31 Small cracks, 352 S-N curve, 352 Stable tearing analysis, 201 Strain energy density method, generalized, 613 Stress ductile-brittle transition, 27 reference, 317 Stress analysis, 517 Stress intensity factor edge-notched beam, 530 normalized, 550 pin-loaded lug joints, 598 weight function method, 563 Stress-strain response, finite element analysis, 216 Structural integrity, 387 Subclad flaw, 243, 387 Surface cracks, 317, 550 interaction between, 550 weight function method, 563 Surface flaw, 243 Tear-fatigue, 317 Tearing, stable crack-tip opening angle, 90 mixed mode I/II loading, 105 Temperature, natural rubber, 505 Tensile response, perforate titanium, 490 Tensile-shear specimen, 469 T* integral, 61 Testing, life prediction, Threshold stress intensity factor, 287 Titanium, commercially pure, fatigue response, 490 Toughening, 152 Transition, crack growth, 72 Transition toughness, 27 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 636 FATIGUE AND FRACTURE MECHANICS: 27TH VOLUME U Underclad cracks, fracture mechanics, 387 Undermatched welds, 427 W Warm prestressing, 243 Weak link, stress-controlled fracture, 27 Weibull model, 387 Weight function method, 563 Welded structural details, ductile tearing, 201 Weld joint geometry, mismatched, 427 Weldments resistance spot weld failure, 469 strength, 427 Weld nugget/heat affected zone, 469 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:36:15 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorize ISBN - - -