THREE-DIMENSIONAL STRESS FIELDS AND SLIP SYSTEMS FOR SINGLE CRYSTAL SUPERALLOY NOTCHED SPECIMENS By SHANNON M. MAGNAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002 I would like to dedicate this work to my family here inGainesville, Creekside Community Church, whose members have taught me many things Icould not have learned in school. ACKNOWLEDGMENTS IwouldliketothankmyadvisorD, r.NagaraAjrakerea,ndDr.Fereshteh Ebrahimfiorprovidingmuch-needebdackgrounidnformationg,uidancaend encouragemenTth.eworkpresentehdereisnotonlymyown,butacollaboratiownith thesetwoprofessorasndanothesrtudentL,uisForero.Luis'experimentawlorkwasof greathelp,andalsomademeappreciatteheadvantageosfcomputemr odeling.Thanks arealsoduetomyroommateJ,en,forputtingupwithmeandforculturingmethrough bizarremoviesandplaysoverthelasttwoyears.Finally,I thankGodforleadingme hereandsustaininmgeeachday;I hopethisworkisworthy. TABLEOFCONTENTS ACKNOWLEDGEMENT...S.................................................................... iii TABLEOFCONTENT.S.......................................................................... iv LISTOFTABLES.................................................................................. vi LISTOFFIGURES................................................................................ vii ABSTRACT.......................................................................................... x CHAPTERS INTRODUCTION ................................................................................ 1 Project Background and Goals ............................................................ 1 Test Methods ............................................................................... 13 2 LITERATURE REVIEW ....................................................................... 16 Slip Activation and Deformation .............................................. 16 Anisotropy of Elasticity ......................................................... 19 Notch Tip Deformation ......................................................... 23 ANALYTICAL PROCEDURE ................................................................ 43 Coordinate System Transformation ..................................................... 43 Slip System Shear Stresses and Strains ................................................ 54 4 NUMERICAL SOLUTION" FINITE ELEMENT METHOD ............................ 57 Finite Element Model ..................................................................... 57 Model Characteristics ..................................................................... 61 Solution Location ......................................................................... 65 Assumptions ............................................................................... 66 5 RESULTS AND DISCUSSION .............................................................. 68 Specimen A................................................................................ 68 Specimen B................................................................................. 79 Specimen C................................................................................. 89 Specimen/Orientation Comparison ..................................................... 99 Experimental Results .................................................................. 100 Application ............................................................................... 103 6 CONCLUSIONS ...........................................................1.0.7.................. 7 RECOMMENDATIONS FOR FUTURE WORK ........................................ 108 APPENDIX A Coordinate Transformation Test ............................................. 109 REFERENCES .................................................................................... 111 BIOGRAPHICAL SKETCH .................................................................... 114 LIST OF TABLES Table 1-1 Slip systems in an FCC crystal ................................................................ 5 2-1 Atomic density on FCC crystal planes ...................................................... 20 2-2 Symmetry invarious crystal structures ...................................................... 21 2-3 Stress subscripts ................................................................................ 21 2-4 Experimental sector boundary angles ........................................................ 30 2-5 Orientation II sector boundary angle comparisons .......................................... 32 2-6 Sector boundary angles for Crone and Shield ........................................................... 36 2-7 Slip sectors for plane stress and plane strain assumptions ................................ 40 2-8 Slip sectors for plane stress and experimental results ....................................... 41 3-1 Direction cosines ................................................................................. 49 4-1 Analytical and numerical component stresses for Specimen A.......................... 58 4-2 Analytical and numerical component strains for Specimen A........................... 59 4-3 Actual (Specimen A) and finite element specimen geometry ............................ 61 5-1 Specimen A dominant slip system sectors ......................................................... 78 5-2 Specimen B dominant slip system sectors ......................................................... 88 5-3 Specimen C dominant slip system sectors ......................................................... 98 5-4 Specimen A experimental results ........................................................... 102 LISTOFFIGURES Figure Pa_g_ 1-1 Helical mold cast turbine blade ................................................................................... 2 1-2 Primary and secondary turbine blade crystallographic orientations; ............................ 3 1-3 Slip lines on the surface of a [100] loaded tensile specimen ....................................... 6 1-4 Turbine blade failure on a {111}octahedral plane ...................................................... 6 1-5 Radial arcs for numerical stress field calculations ....................................................... 9 1-6 Slip sectors occurring under plastic deformation ...................................................... 10 1-7 Microstructure of PWA 1480..................................................................................... 11 2-1 Primary resolved shear stress planes and directions .................................................. 17 2-2 Load and slip directions and angles ........................................................................... 18 2-30ctahedral slip bands ................................................................................................. 18 2-4 FCC crystal structure ................................................................................................. 19 2-5 Notch direction terminology .................................................................. 24 2-6 Yield surface based on plane strain component stresses ........................................... 25 2-7 Specimen orientation for Shield's test specimen .......................................... 27 2-8 Slip systems predicted by Rice .............................................................. 28 2-9 Four-point bending setup used by Crone and Shield ................................................. 29 2-10 Moir_ interferometry strain field ............................................................ 29 2-11 Orientations experimentally tested by Crone and Shield ......................................... 32 2-12 Experimental slip sectors from Crone and Shield .................................................... 33 2-13 Full field slip sectors and slip line traces from Crone and Shield ............................ 34 2-14SchulsoanndXu'sspecimeonrientation......................................................3..7.......... 2-15Slipsectorsunder[-10-1]load...................................................................3..9............. 2-16MaximumRSSslipsystemplots............................................................. 40 3-1 Materia(lXoY,o,Zo)andspecime(nx",y",z")coordinatseystem.s.....................4..5... 3-2 Firstrotationaboutthezo-axi.s...................................................................4..6............. 3-3 Originalandrotatedaxesprojectio.n...........................................................4..6............ 3-4 Secondrotationaboutthey-axis.................................................................4..7............. 3-5 Thirdrotationaboutthex'-axis..................................................................4..8............. 3-6 Loadinthe[213]direction........................................................................5..0.............. 3-7 Twostepcoordinatteransformatio..n...........................................................5..0........... 4-1 Finiteelemenatnalysisspecimenasndorientation.s........................................5..7....... 4-2 Specimednimension..s.............................................................................6..0................ 4-3 Globaal ndmateriacloordinatseystem.s.......................................................6..2.......... 4-4 Finiteelemenmt eshaboutthenotchtip........................................................6..3.......... 4-5 Elemenstizingonthefrontfaceandthroughthethicknes.s..............................6..4..... 4-6ANSYSSOLID95elemen..t.......................................................................6..4.............. 4-7Radiaal rcsusedforelemenltocationandsizing............................................ 65 5-1SpecimeAnprimaryresolvedsheasrtressesr;=0.25"p....................................7..0..... 5-2 SpecimeAnprimaryresolvedsheasrtressesr;=0.5*p....................................7..1...... 5-3 SpecimeAnprimaryresolvedsheasrtressesr;=1.0*p....................................7..2...... 5-4 SpecimeAnprimaryresolvedsheasrtressesr;=2.0*p....................................7..3...... 5-5 SpecimeAnprimaryresolvedsheasrtressesr;=3.0*p....................................7..4...... 5-6 SpecimeAnprimaryresolvedsheasrtressesr;=5.0*p....................................7..5...... 5-7 SpecimeAncompleteresolvedsheasrtresfsield............................................7..7........ 5-8 SpecimeBnprimaryresolvedsheasrtressesr;=0.25*9..................................8..0...... 5-9 SpecimeBnprimaryresolvedsheasrtressesr;=0.5*9....................................8..1...... 5-10SpecimeBnprimaryresolvedsheasrtressesr;= 1.0"9...................................8..2...... 5-11SpecimeBnprimaryresolvedsheasrtressesr;=2.0*p...................................8..3...... 5-12SpecimeBnprimaryresolvedsheasrtressesr;=3.0*9...................................8..4...... 5-13SpecimeBnprimaryresolvedsheasrtressesr;=5.0*9...................................8..5...... 5-14SpecimeBncompletreesolvedsheasrtressfield............................................8..7....... 5-15SpecimeCnprimaryresolvedsheasrtressesr;=0.25*9..................................9..0..... 5-16SpecimeCnprimaryresolvedsheasrtressesr;=0.5*9...................................9..1...... 5-17SpecimeCnprimaryresolvedsheasrtressesr;=1.0*p...................................9..2...... 5-18SpecimeCnprimaryresolvedsheasrtressesr;=2.0*9....................................9..3..... 5-19SpecimeCnprimaryresolvedsheasrtressesr;=3.0*p....................................9..4..... 5-20SpecimeCnprimaryresolvedsheasrtressesr;=5.0*9....................................9..5..... 5-21SpecimeCncompletreesolvedsheasrtressfield............................................9..7....... 5-22ExperimentaloladforSpecimeAn....................................................... 101 5-23ExperimentatelnsiletestspecimeMnateriaAl ......................................... 102 5-24Tensiletestspecimeanndsurfacesliplines............................................. 103 5-25Numericapllotadjustedforexampleload;yieldstressindicate.d................... 104 5-26Numericapllotadjustedforexampleload;maximumRSSchangewsiththeta....105 AbstracotfThesisPresentetdotheGraduatSechool oftheUniversityofFloridainPartialFulfillmenotfthe RequiremenfotsrtheDegreeofMasterofScience THREE-DIMENSIONASLTRESSFIELDSANDSLIPSYSTEMSFORSINGLE CRYSTALSUPERALLONYOTCHEDSPECIMENS By ShannoMn.Magnan May2002 ChairmanN: agaraAj rakereP,h.D. MajorDepartmentM: echanicaElngineering Singlecrystasl uperalloyhsavebecomeincreasinglpyopulafrorturbinebladeand vaneapplicationdsuetotheirhighstrengtha,ndcreepandfatigueresistancaetelevated temperatureTs.hecrystallographoicrientatioonfasinglecrystaml ateriaglreatlyaffects itsmateriapl ropertiesin,cludingelasticmoduluss,heamr odulusa,ndductility.These directionaplropertiesa,longwiththetypeofloadingandtemperaturdei,ctatean anisotropircesponsientheyieldstrengthc,reepresistancec,reepruptureductility, fatigueresistanceet,c..Asignificanatmounotfresearchhasbeenconductetdo determintehemateriapl ropertieisnthe<001>orientationy,etthemateriaplroperties deviatingfromthe<001>orientationhavenotbeenassessefodrallcasesB. asedonthe desiredapplicationanddesigncriteria,acrystaol rientationisselectetdoyieldthe maximumpropertiesC.urrentlys,inglecrystaml anufacturinisgabletocontrotlhe