Anisotropic Mechanical Properties Of Zircaloy
ABSTRACTYan, Jinyuan. Crystallographic Texture and Creep Anisotropy in Cold Worked andRecrystallized Zirlo (under the direction of Dr. K. Linga Murty)ZirloTM, a special zircaloy material alloyed with niobium, tin and iron is a successorof Zircaloy-4. Zirlo is materials used in fuel rod cladding, structural and flow mixinggrids, instrumentation tubes, and guide thimbles. It increases margin to fuel rod corrosionlimits and enhance fuel assembly structural stability in Pressurized Water Reactor.Zirconium and its alloys, being hexagonally close packed, have limited number of slipsystems, and exhibit preferred orientations following thermo-mechanical treatments,which result in anisotropic mechanical properties. The objective of this project is toinvestigate the anisotropic mechanical properties, crystallographic texture, andmicrostructure of crept zirlo materials.The anisotropic mechanical properties were investigated using uniaxial and biaxialcreep tests. The specimen was loaded axially by a dead weight pan, and the hoop stresseswas achieved by internally pressurizing the specimen with inert argon. Different axialand hoop stress, which produced different stress ratios (0, 0.67,0.75, 1, and 2) areselected for creep tests at 450 C. The axial displacement was measured by a linearvariable differential transducer and the diameter change by a laser extensometer. Creepdata are used to determine strain rate ratios vs stress ratios, the anisotropic parameters ( Rand P), and creep loci for cold-worked and recrystallized zirlo.ZirloTM developed by Westinghouse Electronic Company
The crystallographic textures were characterized in terms of inverse and direct polefigures using X-ray diffraction techniques. Inverse pole figures were constructed forspecimens in the rolling direction, transverse direction, and normal direction for both coldworked and recrystallized tubes. Direct pole figures were constructed for specificreflection planes, such as basal (0002), prismatic (10 1 0) and pyramidal (10 1 2).Crystallite orientation distribution function (CODF) was derived from the pole figuredata. Euler plots were obtained from crystallite orientation distribution coefficients (wlmn )and subsequently therefore, ideal orientations were calculated. These CODFs werecombined with the Lower-Bound model to predict creep anisotropy assuming thedominance of prismatic, basal and pyramidal slip systems. Creep strain rate ratios vsstress ratios, creep loci and anisotropy parameters (R and P) were predicted. Thepredictions based on the prismatic dominance matche with the experimental data verywell.Microstructure of the crept specimens was characterized by Transmission ElectronMicroscopy for different stress ratios ( 0, 0.75 and 1). The results show mainlydislocations in the matrix with no subgrain formation. The samples tested underequibiaxial loading revealed deformation twins. More detailed work is called for incharacterizing the influence of stress-states and stress levels as well as cold work ondeformation microstructures.
CRYSTALLOGRAPHIC TEXTURE AND CREEPANISOTROPY IN COLD WORKED ANDRECRYSTALLIZED ZIRLObyJINYUAN YANA dissertation submitted to theGraduate Faculty of North Carolina State Universityin partial fulfillment of the requirements forthe Degree of Doctor of PhilosophyDepartment of Nuclear EngineeringNorth Carolina State UniversityRaleigh, NC 27695-7909March, 2005Approved byChairman of Advisory Committee
BIOGRAPHYJinyuan Yan was born on August 10, 1966 in a small town in Henan Province, People’sRepublic of China, where he spent his wonderful childhood. He studied in NanLe middleschool from 1981 to 1984. From 1984 to 1988, he studied for heat treatment in materialdepartment, Xian’s Institute of Technology, and graduated with a Bachelor of Science inMaterials Science and Engineering. In 1988, he proceeded to enter the Master of Scienceprogram in China Institute of Atomic Energy for Nuclear Materials and graduated in1991. He worked there until 2000 when he went to study in Cornell University. After oneand half year study in Cornell University, he earned an M.S.E. in Nuclear Science andEngineering.In January of 2002, Jinyuan entered a Ph.D program in the Nuclear Engineering at NorthCarolina State University under the direction of Dr. K. L. Murty. He worked as a researchassistant in the nuclear materials group in the following years and will graduate in May2005.ii
ACKNOWLEDGMENTI would especially like to thank to my supervisor Dr. K. Linga Murty for his technicaland personal guidance, and his constant encouragement and friendship during the courseof the work. I would like to thank my committee member, Dr. Man-Sung Yim, Dr.Mohamed Bourham, and Dr. Ron Scattergood for support and advice.Thanks are also given to the members of the nuclear materials group for their advise,support and practical help. Thanks are also due to Khaled Youssef, Ramesh K.Guduru ,and Honghui Zhou for their advice and help to my tests.Thanks are given to Daniel J.Lichtenwalner and Jon-Pauland Maria for the help in textureanalysis.I would like to express special thanks to my wife, Suxia Liang, my sons, Jimmy zhiyaoYan and Kelvin zhiyu Yan for their encouragement and patience during the course of mystudy.Thanks are given to those people whose names are not shown in this list but give me helpfor this study.iii
TABLE OF CONTENTSList of Figures . ⅶList of Tables. ⅹ1 Introduction . 12 Literature Review. 32.1 Zirconium and Its Alloys . 32.2 Irradiation on Fuel Rod and Fuel Assembly. 42.2.1 Fuel-Rod Elongation . 72.2.2 Cladding Creep-Down and Collapse . 82.2.3 BWR Channel and PWR Fuel Assembly Bow. 82.2.4 Grid—Spacing Relaxation. 92.3 Storage of Fuel Rods and Fuel Assembly. 92.4 Creep Behavior . 102.4.1 General Creep Description . 102.4.2 Creep Mechanisms . 122.4.2.1 Diffusional Creep . 122.4.2.2 Harp-Dorn Creep . 132.4.2.3 Power-Law Creep Controlled by Dislocation . 142.4.2.4 Grain-Boundary Sliding . 162.5 Deformation Slip Systems . 172.5.1 Slip Modes. 192.5.2 Twinning Modes. 20iv
2.6 Texture Development. 212.6.1 The Effect of Crystal Structure. 222.6.2 The Effect of Thermo-Mechanical Process . 222.6.3 The Effect of Re-Crystallization Process . 242.6.4 Texture Expression . 252.6.4.1 Inverse Pole Figure. 282.6.4.2 Direct Pole Figure. 292.6.4.3 Crystallite Orientation Distribution Function. 292.7 Plastic Anisotropy in HCP . 303 Experimental Procedure . 323.1 Test Materials. 323.2 Creep Test . 363.3 Crystallographic Texture Measurement. 393.3.1 Preparation of Samples for Inverse Pole Figure. 403.3.2 Preparation of Samples for Direct Pole Figure. 413.3.3 Data Acquisition and Construction of Pole Figure. 423.3.3.1 Data Acquisition for Inverse Pole Figure . 423.3.3.2 Data Acquisition for Direct Pole Figure. 483.4 CODF and Model Predictions. 533.4.1 CODF . 533.4.1.1 The Calculation of CODF . 553.4.1.2 Eta, Kai and Intensities. 573.4.1.3 Euler Space . 59v
3.4.1.4 Ideal Orientation . 613.4.2 Model Prediction . 623.5 Characterization of Mechanical Anisotropy . 644 Results and Discussion. 674.1 Uniaxial Creep and Biaxial Creep for Zirlo. 674.2 Texture Analysis . 874.2.1 Texture Coefficients and f-factors. 874.2.2 Inverse Pole Figure. 934.2.3 Direct Pole Figure. 974.2.4 Euler Space and Euler Plot . 1024.2.5 The Ideal Orientation. 1064.3 Model prediction. 1084.4 Microstructure. 1225 Summary and Conclusion . 1276 References . 1297 Appendix . 137Appendix A: Published paper . 138Appendix B: Texture Analysis Procedures. 146Appendix C: FORTRAN Codes . 179vi
LIST OF FIGURESFigure 1: A schematic diagram of a typical PWR . 5Figure 2: A perspective on PWR nuclear fuel assembly by Mitsubishi Materials Corporation . 5Figure 3: A schematic diagram of typical BWR. 6Figure 4: A perspective on BWR nuclear fuel assembly. 6Figure5:A schematic diagram of typical dry storage of spent fuel . 10Figure 6: Typical creep curve of strain vs. time . 11Figure 7: Important planes in hexagonal crystals . 18Figure 8: Ideal orientations (a) in cold-worked, and (b) recrystallized zirconium alloys. 24Figure 9: Knoop hardness vs annealing temperature for Zirlo . 33Figure 10 Microstructures for different anneal temperature of Zirlo. 34Figure 11 Tube sample assembly used for biaxial creep . 35Figure 12 A schematic diagram of the biaxial creep test. 38Figure 13 A schematic diagram of the pressure automatic control unit . 38Figure 14: The texture samples used for inverse pole figure. 40Figure 15: The texture samples used for direct pole figure . 41Figure 16: An overview of the Rigaku Geigerflex X-ray diffractometer used for IPF. 43Figure 17: Schematic illustration for the inverse pole figure measurement . 43Figure 18: Standard projection of diffracting planes of zircaloy . 47Figure 19: An overview of the Brucker X-ray machine used for DPF . 49Figure 20: A close look of the area detector used for DPF measurement . 49Figure 21: The specimen rotation axes for DPF measurements . 50Figure 22: Initial Orientation Setups of the specimens in the Goniometer. 52Figure 23 Sample coordinate system and crystal coordinate system. 54vii
Figure 24: Definition of the polar and co-latitude angle χ and η . 58Figure 25: The relation between crystallite coordinates (Xc,Yc,Zc) and specimencoordinates(Xs,Ys,,Zs) of Euler space . 60Figure 26: Creep curves of cold-worked Zirlo at α 2, σ(z) 45MPa and 450 C . 68Figure 27: Creep curve of cold-worked Zirlo for α 2, σ(z) 100MPa and 450 C . 68Figure 28: Creep curves of cold-worked Zirlo at α 1 and 450 C for different stresses . 69Figure 29: Creep curves of cold-worked Zirlo at α 1, σ(z) 150MPa,and 450 C . 69Figure 30: Creep curves of cold work Zirlo at α 0 and 450 C. 70Figure 31: Creep curves of cold work Zirlo at α 0 and 450 C. 70Figure 32: Creep curvees of recrystallized Zirlo at different α and stresses at 450 C . 71Figure 33: Creep curves of recrystallized Zirlo at α 0, σ(z) 125MPa and 450 C. 71Figure 34: Creep curves of recrystallized Zirlo at α 0.75 and450 C for different stresses . 72Figure 35: Creep curves of recrystallized Zirlo at α 0.75 and 450 C at different stresses. 72Figure 36 Stain rate vs 1/T of recrystallized Zirlo. 76Figure 37: Strain rate ratios (hoop vs radial) vs stress ratios (hoop to axial) of CW Zirlo. 77Figure 38: Double-log plot of dissipation energy rate Vs axial stress for CW Zirlo . 78 Figure 39: Creep loci for CW Zirlo at constant dissipation energy rate ( w 5 Jm-3s-1) . 79Figure 40: Strain rate ratios (hoop vs radial) vs stress ratios (hoop to axial) for RX . 81Figure 41: Double-log plot of dissipation energy rate vs axial stress of RX Zirlo . 81 Figure 42: Creep locus of RX Zirlo at constant dissipation energy rate ( w 5 Jm-3s-1) . 82 Figure 43 Creep loci for CW and RX Zirlo at constant dissipation energy rate ( w 5 Jm-3s-1) . 82Figure 44 Normalized strain vs normalized stress for Zirlo and zircaloy-4 at α 0. 84Figure 45: Comparison of creep loci of CWSR of Zirlo and Zry-4. 85Figure 46: Comparison of creep loci of Rx of Zirlo and Zry-4 . 86viii
Figure 47: Diffraction intensities vs 2θ in RD of cold-worked Zirlo . 88Figure 48: Diffraction intensities vs 2θ in TD of cold-worked Zirlo . 88Figure 49: Diffraction intensities vs 2θ in ND of cold-worked Zirlo . 89Figure50: Diffraction intensities vs 2θ in RD of recrystallized Zirlo. 89Figure51: Diffraction intensities vs 2θ in TD of recrystallized Zirlo . 90Figure 52: Diffraction intensities vs 2θ in ND of recrystallized Zirlo. 90Figure 53: Inverse pole figures for cold-worked Zirlo . 95Figure 54: Inverse pole figures for recrystllized Zirlo. 96Figure 55 : Direct Pole Figure for Cold work Zirlo. 98Figure 56: The intensities of basal pole vs tilt angle in the ND-RD and ND-TD plane of the CWZirlo . 99Figure 57: Direct pole figures of recrystallized Zirlo . 100Figure 58: Basal pole distribution in the ND-RD and ND-TD plane of RX Zirlo. 101Figure 59: Euler Plots representing CODF for Cold work Zirlo . 104Figure60: Euler Plots representing OCDF for Re-recrystallized Zirlo . 105Figure61:Strain rate ratio vs stress ratio from model prediction and experiment of CWSR Zirlo. 113Figure 62: Strain rate ratios vs stress ratios from model prediction and experiment of Rx Zirlo 114Figure 63: Creep loci from model prediction and experiment for CWSR Zirlo . 117Figure 64: Creep loci from model prediction and experiment for Rx Zirlo . 118Figure 65 Schematic of a columnar grain under the present biaxial loading condition. 120Figure 66 Schematic depicting two-dimensional stress redistribution resulting from grainboundary sliding in the columnar grain structure. 121Figure 67 The effect of f factor on the creep loci of Zirlo CWSR. 122Figure 68: Deformation microstructure at α 0 and σ(z) 120MPa of Rx Zirlo . 124ix
Figure 69: Deformation microstructure at α 0 and σ(z) 120MPa of Rx Zirlo . 124Figure70: Deformation microstructure at α 0 .75 and σ(z) 95MPa of Rx Zirlo . 125Figure71: Deformation microstructure at α 0.75 and σ(z) 95MPa of Rx Zirlo . 125Figure72: Deformation microstructure at α 1 and σ(z) 120MPa of Rx Zirlo . 126Figure73: Deformation microstructure at α 1 and σ(z) 120MPa of Rx Zirlo . 126x
LIST OF TABLESTable 1: Chemical composition of Zircaloy ( in wt%) . 3Table 2: Allowed reflections, Bragg angles and random intensity of zircaloy. 26Table 3. Chemical composition of Zirlo, wt%. 32Table 4 Angles between the pole of (0002) and other specific planes . 47Table 5 The hidden value of (χ,η) for the Intensity Matrix used for CODF calculation. 58Table 6 Normalized strain rate vs axial stresses for activation energy of Rx Zirlo . 75Table 7: Cold worked Zirlo creep data at 450 C . 77Table 8 Recrystallized Zirlo creep data at 450 C . 80Table 9: Creep data for recrystallized Zirlo and recrystallized zr-4 at α 0 . 83Table10: Normalized axial stress vs normalized hoop stress for CWSR Zry-4 and zrilo . 85Table11: Normalized axial stress vs normalized hoop stress for Rx Zry-4 and zrilo . 86Table12: Calculated TC values of cold-worked Zirlo . 92Table 13: Calculated TC values for re-crystallized Zirlo . 93Table 14: The maxima intensity peaks in Euler space and ideal orientation for CW Zirlo. 107Table 15: The maxima intensity peaks in Eule space and ideal orientation for Rx Zirlo . 107Table 16: Ideal Orientaion corresponding to the peak position in Euler Space. 108Table 17: the input axial stress and hoop stress for code calculation . 112Table 18: Calculated R P for cold-worked Zirlo . 115Table 19: Calculated R P for cold Recrystallized Zirlo. 116xi
1 INTRODUCTIONZirlo, a special zircaloy material with niobium, tin and iron, developed by WestinghouseElectric Company, is a substitute for Zircaloy-4. Extensive tests in high-temperature,high-pressure autoclaves, microscopic evaluation, and irradiation testing demonstrategood corrosion resistance, while corrosion resistance is a main limit to extended fuelburnup. Zirlo, used for fuel rod cladding, structural and flow mixing grids,instrumentation tubes, and guide thimbles, increase margin to fuel rod corrosion limits,and enhances fuel assembly structural stability in pressurized water reactor (PWR).Because of service environment of high temperature, high pressure, and high irradiationenvironment, knowledge of texture and anisotropic mechanical properties is required inpredicting the in-service behavior of the fabricated components. The objective of thisstudy is to characterize texture and mechanical anisotropy of both cold-worked andrecrystallized tubes. This work was divided into the following several parts.(1) Uniaxial and biaxial creep testsThe first part of this study was creep test. Creep tests were carried out for different axialstresses and hoop stresses, which produced different stress ratios ( 0, 0.67,0.75, 1, and 2 )at 450 C. The purpose of the creep tests was to determine the strain-rate, strain ratios vsstress ratios, the anisotropy parameters ( R and P), and creep loci of cold-worked andrecrystallized Zirlo.(2) Texture analysisTexture measurements were carried out on cold-worked and recrystallized Zirlo tubes.The textures were represented in the forms of inverse pole figures and direct pole figuresusing x-ray diffraction techniques. Inverse pole figures were constructed for normal1
direction sample (ND), and rolling direction sample (RD), and transverse directionsample (TD) of both cold-worked and recrystallized Zirlo tubes. Texture coefficients andf-factor were calculated based on raw x-ray data for the inverse pole figure. Direct polefigures were constructed on spatial distribution on specific reflection planes, such asbasal (0002), prismatic (10 1 0) and pyramidal (10 1 2), of both cold-worked andrecrystallized Zirlo tubes.(3) CODF calculation and plasticity modelingCrystallite Orientation Distribution Function (CODF) is a quantitative measure ofcrystallographic texture. Based on spatial distribution of three reflection planes,crystallite orientation distribution coefficients (wlmn) and were calculated. Euler plotswere obtained from wlmn. Anisotropic parameters (R and P), creep strain-rate ratios vsstress ratios, and creep loci were predicted from CODF combined with lower-bounddeformation model.(4) TEM studyThe microstructures of recrystallized Zirlo crept under three different stress ratios werestudied by Transmission Electron Microscopy. The study showed that the dislocationdensity was the highest for uniaxial crept specimen, and the lowest for equiaxial creptspecimen.2
2 LITERATURE REVIEW2.1 ZIRCONIUM AND ITS ALLOYSPure α zirconium (Zr) has a hexagonal close-packed (HCP) crystal structure up to 1135Kwhere it transforms to a body-centered cubic β phase. The addition of alloying elementsproduces α-β structures over a wide range of temperatures, and greatly improvesmechanical properties and the corrosion resistance of pure zirconium at hightemperatures.Most of zircaloys are used in the power plants because of its mechanical strength,ductility, neutron cross-section and corrosion resistance. Table 1 gives the composition ofsome of the zirconium alloys developed for cladding and structural materials in waterreactors [1].Table 1: Chemical composition of Zircaloy ( in .01rest 0.007Pure zirconium was first used in the STR Mark Ⅰprototype reactor. Addition of 2.5% tinto pure zirconium generated Zircaloy-1 and improved its corrosion resistance, strengthand formability. Zircaloy-1 was intended to substitute for the pure zirconium in the3
prototype reactor but it was never used in the reactor since it did not improve the posttransition corrosion resistance compared to pure zirconium [2]. Accidental addition of Feand Cr to Zircaloy-1 produced Zircaloy-2 and improved corrosion resistance with similarstrength compared with Zircaloy-1. Zircaloy-2 is used as fuel cladding in boilingwater(BWR) reactors and pressure tubes for heavy water reactors. Addition of more Snand a slight reduction in Fe content led to the generation of Zircaloy-3. However,Zircaloy-3 actually reduced the mechanical strength compared with Zircaloy 2 andZircaloy-3 was abandoned. Due to hydrogen absorption and hydride from Ni, Zircaloy 4was developed with higher content of Fe and no Ni on the basis of Zircaloy-2. Zircaloy 4has as good steam corrosion resistance with less hydrogen absorption compared withZircaloy-2. Zircaloy-4 is employed as fuel element cladding in PWR, spacer gridstructural material in LWR and channel box structural material in BWR. For the extendedburnup, new alloys, such as Zirlo, M5 were developed2.2 IRRADIATION EFFECT ON FUEL ROD AND FUELASSEMBLYZircaloy-4 is employed as fuel cladding in PWR’s, spacer grid structural material inLWR, and channel box structural material in BWR. Figure 1 shows a typical PWRsystem and Figure 2 shows a typical fuel assembly in a PWR fuel assembly. Whereas,Figure 3 shows a typical BWR system and 4 shows a channel box and spacer grids in aBWR.4
Figure 1: A schematic diagram of a typical ene/reactor.html#c3 )Figure 2: A perspective on PWR nuclear fuel assembly by Mitsubishi MaterialsCorporation (http://www.mnf.co.jp/pages2/pwr2.htm)5
Figure 3: A schematic diagram of typical ene/reactor.html#c1 )Figure 4: A perspective on BWR nuclear fuel uel1.jpg)6
Zirconium alloy claddings, used in nuclear reactors, are subjected to hightemperatures, high stresses, a corrosive environment, and radiation effects. Therefore, theperformance of the zirconium alloy has been a big concern. Since the reactor componentsare designed to operate at stress levels well below yield strength and high temperature,two major significant deformations are the time dependant creep deformation andirradiation growth which is stre
which result in anisotropic mechanical properties. The objective of this project is to investigate the anisotropic mechanical properties, crystallographic texture, and microstructure of crept zirlo materials. The anisotropic mechanical properties were investigated using uniaxial and biaxial creep tests.
material is isotropic if its mechanical and elastic properties are the same in all directions. When this is not true, the material is anisotropic. Many materials are anisotropic and inhomogeneous due to the varying composition of their constituents. Every day passed, the number of anisotropic materials is increasing by
48 for Al, 2:57 for Ni, 3:21 for Cu, and 2:85 for Au [5]. Dilute alloys based 49 on Ni, Cu, and Au should thus be treated within anisotropic elasticity, and many 50 fcc HEA families (e.g. Co-Cr-Fe-Mn-Ni-Al, Rh-Ir-Pt-Pd-Au-Ag-Ni-Cu) are at least 51 moderately anisotropic. The aim of this paper is therefore to provide general results 52 for solute-strengthening in the anisotropic elastic .
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The mechanical behaviour of metals during real forming processes must be related to their anisotropic properties. Concerning the analysis of the anisotropic behaviour of aluminium alloys this one has been the subject of various studies, generally in the field of sheet forming processes ((Malo et al., 1998), (Lademo et al., 1999)).
Microstructure and Oxidation Behavior of CrAl Laser-Coated Zircaloy-4 Alloy Jeong-Min Kim 1,*, Tae-Hyung Ha 1, Il-Hyun Kim 2 and Hyun-Gil Kim 2 . the oxidation resistance of metals at high temperatures [6]. Since Al2O3 and Cr2O3 can form on the surface of Cr-Al coated alloys, the high temperature oxidation resistance is expected to increase .
P. A. Raynaud,1 D. A. Koss,1 A. T. Motta,2 and K. S. Chan3 Fracture Toughness of Hydrided Zircaloy-4 Sheet Under Through-Thickness Crack Growth Conditions ABSTRACT: The susceptibility of fuel cladding to failure in the case of a postulated reactivity-initiated accident may be determined by crack initiation within a hydride blister or rim and subsequent crack growth
Recent experiments at 700 to 900 C with steam pressures from 0.1 MPa to 15 MPa suggest that the oxidation rate of zircaloy-4 increases with the steam pressure; however, this pressure dependence does 100not appear at 1 C [60,57]. Zircaloy oxidation tests have also been conducted in various steam-hydrogen mixtures at temperatures between
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