496T fm i-xxvi 01/10/06 22: 13 Page xiv xiv· Preface provided invaluable assistance in updating and upgrading important material in a number of chapters. In addition, I sincerely appreciate Grant E. Head's expert pro- gramming skills, which he used in developing the Virtual Materials Science and En gineering software. Important input was also furnished by Carl Wood of Utah State University and w. Roger Cannon of Rutgers University, to whom I also give thank In addition, helpful ideas and suggestions have been provided by the following Tarek Abdelsalam, East Carolina University Maureen Julian. Virginia Tech Keyvan Ahdut, University of the District of James Kawamoto, Mission College Columbia Edward Kolesar, Texas Christian University Mark Aindow, University of Connecticut(Storrs) Stephen Krause, Arizona State University(Tempe) Pranesh Aswath, University of Texas at Arlington Robert McCoy, Youngstown State Universit Mir Atiqullah, St Louis University Scott Miller, University of Missouri(Rolla) Sayavur Bakhtiyarov, Auburn University Devesh Misra, University of Louisiana at Kristen Constant. lowa State Universit Lafayette Raymond Cutler, University of Utah Angela L. Moran, U.S. Naval Academy Janet Degrazia, University of Colorado James Newell, Rowan University Mark De Guire, Case Western Reserve University Toby Padilla, Colorado School of Mines Timothy Dewhurst, Cedarville University Timothy Raymond, Bucknell University Amelito Enriquez, Canada College Alessandro Rengan, Central State University Jeffrey Fergus, Auburn University Bengt Selling, Royal Institute of Technology Victor Forsnes, Brigham Young University(Idaho) Stockholm, Sweden) Paul Funkenbusch, University of Rochester Ismat Shah, University of Delaware Scott Giese, University of Northern lowa ersity Patricia Shamamy, Lawrence Technological University Brian P. Grady, University of oklahoma Adel Sharif, California State University at Theodore greene. Wentworth Institute of Los Angeles Susan Sinnott, University of Florida Todd Gross, University of New Hampshire Andrey Soukhojak, Lehigh Universit Jamie Grunlan, Texas a M University Erik Spjut, Harvey Mudd College Masanori Hara, Rutgers University David Stienstra Rose-Hulman Institute of Russell Herlache, Saginaw Valley State University Te Susan holl. california State Universit Alexey Sverdlin, Bradley University (Sacramento) D Um. Texas sta Zhong Hu, South Dakota State University Raj Vaidyanatha, University of Central Florida Duane Jardine, University of New Orleans Kant Vajpayee, University of Southern Mississippi un Jin, Texas a M University at Galveston Kumar Virwani, University of Arkansas Paul Johnson, Grand Valley State University Fayetteville) Robert Johnson, University of Texas at Arlington Mark Weaver, University of Alabama(Tuscaloosa) Robert Jones, University of Texas(Pan American) Jason Weiss, Purdue University(West Lafayette) I am also indebted to Joseph P. Hayton, Sponsoring Editor, and to Kenneth Santor, Senior Production Editor at Wiley for their assistance and guidance on this revision. Since I undertook the task of writing my first text on this subject in the early 60,s, instructors and students too numerous to mention have shared their input and contributions on how to make this work more effective as a teaching and learning tool. To all those who have helped, I express my sincere"Thanks! Last, but certainly not least, the continual encouragement and support of my family and friends is deeply and sincerely appreciated. WILLIAM D. CALLISTER, JR
provided invaluable assistance in updating and upgrading important material in a number of chapters. In addition, I sincerely appreciate Grant E. Head’s expert programming skills, which he used in developing the Virtual Materials Science and Engineering software. Important input was also furnished by Carl Wood of Utah State University and W. Roger Cannon of Rutgers University, to whom I also give thanks. In addition, helpful ideas and suggestions have been provided by the following: xiv • Preface Tarek Abdelsalam, East Carolina University Keyvan Ahdut, University of the District of Columbia Mark Aindow, University of Connecticut (Storrs) Pranesh Aswath, University of Texas at Arlington Mir Atiqullah, St. Louis University Sayavur Bakhtiyarov, Auburn University Kristen Constant, Iowa State University Raymond Cutler, University of Utah Janet Degrazia, University of Colorado Mark DeGuire, Case Western Reserve University Timothy Dewhurst, Cedarville University Amelito Enriquez, Canada College Jeffrey Fergus, Auburn University Victor Forsnes, Brigham Young University (Idaho) Paul Funkenbusch, University of Rochester Randall German, Pennsylvania State University Scott Giese, University of Northern Iowa Brian P. Grady, University of Oklahoma Theodore Greene, Wentworth Institute of Technology Todd Gross, University of New Hampshire Jamie Grunlan, Texas A & M University Masanori Hara, Rutgers University Russell Herlache, Saginaw Valley State University Susan Holl, California State University (Sacramento) Zhong Hu, South Dakota State University Duane Jardine, University of New Orleans Jun Jin, Texas A & M University at Galveston Paul Johnson, Grand Valley State University Robert Johnson, University of Texas at Arlington Robert Jones, University of Texas (Pan American) Maureen Julian, Virginia Tech James Kawamoto, Mission College Edward Kolesar, Texas Christian University Stephen Krause, Arizona State University (Tempe) Robert McCoy, Youngstown State University Scott Miller, University of Missouri (Rolla) Devesh Misra, University of Louisiana at Lafayette Angela L. Moran, U.S. Naval Academy James Newell, Rowan University Toby Padilla, Colorado School of Mines Timothy Raymond, Bucknell University Alessandro Rengan, Central State University Bengt Selling, Royal Institute of Technology (Stockholm, Sweden) Ismat Shah, University of Delaware Patricia Shamamy, Lawrence Technological University Adel Sharif, California State University at Los Angeles Susan Sinnott, University of Florida Andrey Soukhojak, Lehigh University Erik Spjut, Harvey Mudd College David Stienstra, Rose-Hulman Institute of Technology Alexey Sverdlin, Bradley University Dugan Um, Texas State University Raj Vaidyanatha, University of Central Florida Kant Vajpayee, University of Southern Mississippi Kumar Virwani, University of Arkansas (Fayetteville) Mark Weaver, University of Alabama (Tuscaloosa) Jason Weiss, Purdue University (West Lafayette) I am also indebted to Joseph P. Hayton, Sponsoring Editor, and to Kenneth Santor, Senior Production Editor at Wiley for their assistance and guidance on this revision. Since I undertook the task of writing my first text on this subject in the early- 80’s, instructors and students too numerous to mention have shared their input and contributions on how to make this work more effective as a teaching and learning tool. To all those who have helped, I express my sincere “Thanks!” Last, but certainly not least, the continual encouragement and support of my family and friends is deeply and sincerely appreciated. WILLIAM D. CALLISTER, JR. Salt Lake City, Utah January 2006 1496T_fm_i-xxvi 01/10/06 22:13 Page xiv
496T fm i-xxvi 01/10/06 22: 13 Page xxii List of Symbols he number of the section in which a symbol is introduced or explained is giver parentheses. A= area DP= degree of polymerization(14.5) A=angstrom unit d= diameter Ai= atomic weight of element i (2.2) d average grain diameter(7. 8) PF=atomic packing factor(3. 4) dnk= interplanar spacing for planes of a=lattice parameter: unit cell Miller indices h, k, and /(3.16 x-axial length(3. 4) E= energy(2.5) a= crack length of a surface crack(8.5) E= modulus of elasticity or Youngs t%=atom percent(4.4) modulus(6.3) B= magnetic flux density 8= electric field intensity(18.3) (induction)(20.2) Ef= Fermi energy (18.5) B,= magnetic remanence(20.7) Eg= band gap energy(18.6) BCC= body-centered cubic crystal (=relaxation modulus(15.4) structure(3. 4) oEL= ductility, in percent b= lattice parameter: unit cell ongation(6.6) y-axial length(3.7) ge per electron(18.7) b= Burgers vector (4.5) e= electron(17. 2) C= capacitance(1818) erf Gaussian error function (5.4) Ci= concentration(composition )of exp =e, the base for natural logarithms component i in wt%(4. 4) F= force interatomic or mechanical Ci=concentration(composition )of (2,6.3) component i in at%(4. 4) 9= Faraday constant(17.2) Cu, Cp= heat capacity at constant volume, FCC= face-centered cubic crystal CPR= corrosion penetration rate(17.3) G= shear modulus(6.3) CVN= Charpy V-notch(8.6) H= magnetic field strength(20.2) Hc magne c=lattice parameter: unit cell HB= Brinell hardness(6.10) z-axial length(3.7) HCP= hexagonal close-packed crystal c= velocity of electromagnetic radia structure(3. 4) tion in a vacuum(21.2) HK= Knoop hardness(6.10) D= diffusion coefficient (5.3) HRB HRF= Rockwell hardness: B andF D= dielectric displacement(18.19) ales
The number of the section in which a symbol is introduced or explained is given in parentheses. List of Symbols A area Å angstrom unit Ai atomic weight of element i (2.2) APF atomic packing factor (3.4) a lattice parameter: unit cell x-axial length (3.4) a crack length of a surface crack (8.5) at% atom percent (4.4) B magnetic flux density (induction) (20.2) Br magnetic remanence (20.7) BCC body-centered cubic crystal structure (3.4) b lattice parameter: unit cell y-axial length (3.7) b Burgers vector (4.5) C capacitance (18.18) Ci concentration (composition) of component i in wt% (4.4) Ci concentration (composition) of component i in at% (4.4) Cv, Cp heat capacity at constant volume, pressure (19.2) CPR corrosion penetration rate (17.3) CVN Charpy V-notch (8.6) %CW percent cold work (7.10) c lattice parameter: unit cell z-axial length (3.7) c velocity of electromagnetic radiation in a vacuum (21.2) D diffusion coefficient (5.3) D dielectric displacement (18.19) DP degree of polymerization (14.5) d diameter d average grain diameter (7.8) dhkl interplanar spacing for planes of Miller indices h, k, and l (3.16) E energy (2.5) E modulus of elasticity or Young’s modulus (6.3) electric field intensity (18.3) Ef Fermi energy (18.5) Eg band gap energy (18.6) Er(t) relaxation modulus (15.4) %EL ductility, in percent elongation (6.6) e electric charge per electron (18.7) e electron (17.2) erf Gaussian error function (5.4) exp e, the base for natural logarithms F force, interatomic or mechanical (2.5, 6.3) Faraday constant (17.2) FCC face-centered cubic crystal structure (3.4) G shear modulus (6.3) H magnetic field strength (20.2) Hc magnetic coercivity (20.7) HB Brinell hardness (6.10) HCP hexagonal close-packed crystal structure (3.4) HK Knoop hardness (6.10) HRB, HRF Rockwell hardness: B and F scales (6.10) f e • xxiii 1496T_fm_i-xxvi 01/10/06 22:13 Page xxiii
496T fm i-xxvi 01/11/060: 06 Page xxiv xx· List of Symbols HRISN, HR45W= superficial Rockwell n= number of conducting hardness: 15N and 45W electrons pe I cubIc meter(18.7) iV= Vickers hardness(6.10) n= index of refraction(21.5 h= Planck's constant(21.2) for ceramics the number (hkl)= Miller indices for a of formula units per unit crystallographic plane(3.10) cell(12.2) I= electric current (18.2) n;=intrinsic carrier(electron and ntensity of electromagnetic hole) concentration(1810) radiation(21.3) P= dielectric polarization(18.19) i= current density(17.3) P-B ratio= Pilling-Bedworth ratio(17.10) ic=corrosion current density p= number of holes per cubic (174) meter(18.10) J= diffusion flux (5.3) Q= activation energy J= electric current density(18.3) Q= magnitude of charge stored fracture toughness(8.5) plane strain fractur R=atomic radius(3. 4) toughness for mode I R= gas constant crack surface displacement PoRa= ductility, in percent reduction (8.5) in area(6.6) k= Boltzmanns constant(4.2) r= interatomic distance(2.5) k= thermal conductivity (19.4) r= reaction rate(17.3) I= length TA, rc= anion and cation ionic radii lc= critical fiber length(16.4) In natural logarithm S=fatigue stress amplitude(8. 8) log= logarithm taken to base 10 SEM scanning electron M= magnetization(20.2) microscopy or microscope M,= polymer number-average temperature molecular weight(14.5) T= Curie temperature(20.6) Mu= polymer weight-average Tc= superconducting critical tem- molecular weight (14.5) perature(20.12) mol%= mole percent Tg= glass transition temperature N= number of fatigue cycles(8.8) (139,15.12) A= Avogadro's number( 3.5) Im= melting temperature s= fatigue life( 8.8) TEM transmission electron microscopy or microscope n= principal quantum number TS =tensile strength(6.6) n= number of atoms per unit cell (3.5) tr= rupture lifetime(8.12) strain-hardening exponent U,= modulus of resilience(6.6) (6.7) uww= indices for a crystallographic n= number of electrons in direction(3.9) an electrochemical V= electrical potential difference reaction(17. 2) ( voltage)(172,18.2)
xxiv • List of Symbols HR15N, HR45W superficial Rockwell hardness: 15N and 45W scales (6.10) HV Vickers hardness (6.10) h Planck’s constant (21.2) (hkl) Miller indices for a crystallographic plane (3.10) I electric current (18.2) I intensity of electromagnetic radiation (21.3) i current density (17.3) iC corrosion current density (17.4) J diffusion flux (5.3) J electric current density (18.3) Kc fracture toughness (8.5) KIc plane strain fracture toughness for mode I crack surface displacement (8.5) k Boltzmann’s constant (4.2) k thermal conductivity (19.4) l length lc critical fiber length (16.4) ln natural logarithm log logarithm taken to base 10 M magnetization (20.2) polymer number-average molecular weight (14.5) polymer weight-average molecular weight (14.5) mol% mole percent N number of fatigue cycles (8.8) NA Avogadro’s number (3.5) Nf fatigue life (8.8) n principal quantum number (2.3) n number of atoms per unit cell (3.5) n strain-hardening exponent (6.7) n number of electrons in an electrochemical reaction (17.2) Mw Mn n number of conducting electrons per cubic meter (18.7) n index of refraction (21.5) n for ceramics, the number of formula units per unit cell (12.2) ni intrinsic carrier (electron and hole) concentration (18.10) P dielectric polarization (18.19) P–B ratio Pilling–Bedworth ratio (17.10) p number of holes per cubic meter (18.10) Q activation energy Q magnitude of charge stored (18.18) R atomic radius (3.4) R gas constant %RA ductility, in percent reduction in area (6.6) r interatomic distance (2.5) r reaction rate (17.3) rA, rC anion and cation ionic radii (12.2) S fatigue stress amplitude (8.8) SEM scanning electron microscopy or microscope T temperature Tc Curie temperature (20.6) TC superconducting critical temperature (20.12) Tg glass transition temperature (13.9, 15.12) Tm melting temperature TEM transmission electron microscopy or microscope TS tensile strength (6.6) t time tr rupture lifetime (8.12) Ur modulus of resilience (6.6) [uvw] indices for a crystallographic direction (3.9) V electrical potential difference (voltage) (17.2, 18.2) 1496T_fm_i-xxvi 01/11/06 0:06 Page xxiv
496T fm i-xxvi 01/10/06 22: 13 Page xxv st of Symbols Vc=unit cell volume(3. 4) v= frequency of electromagnetic potential (17.4 VH= Hall voltage(18.14) p= density (3.5) Vi= volume fraction of phase i(9.8) p= electrical resistivity(18.2) vol%= volume percent crack(8.5) Wi= mass fraction of phase i(9. 8) o=engineering stress, tensile or (6.2) electrical conductivity(18.3) o= longitudinal strength space coordinate (composite)(16.5) Y= dimensionless parameter or function in Tc= critical stress for crack propagation racture toughness expression(8.5) y=space coordinate ofs=flexural strength(12.9) z= space coordinate Um= maximum stress(8.5) a= lattice parameter: unit cell y-z Um= mean stress(8.7) interaxial angle(3.7) a,B,y= phase designations om= stress in matrix at composite failure(16.5) ar= linear coefficient of thermal expansion r= true stress(6.7) B= lattice parameter: unit cellx-z Ou= safe or working stress(6. 12) interaxial angle(3.7) strength(6.6) y=lattice parameter: unit cell x-y T= shear stress(6.2 nteraxial angle(3.7) Te= fiber-matrix bond strength/matrix shear y=shear strain(6.2) yield strength(16.4) 4= precedes the symbol of a parameter to Tcrss critical resolved shear stress(7.5) denote finite change Xm= magnetic susceptibility(20.2) engineering strain(6.2) E= dielectric permittivity (18.18) SUBSCRIPTS Er dielectric constant or relative C= composite permittivity(18.18) cd= discontinuous fibrous composite steady-state creep rate( 8.12) cl= longitudinal direction(aligned fibrous ∈r= true strain(6.7) m= viscosity(12. 10) ct= transverse direction(aligned fibrous m= overvoltage(17. 4) composite) 8= Bragg diffraction angle(3.16) BD= Debye temperature(19.2) f= at fracture A= wavelength of ele diation (3. 16) u= magnetic permeability(20.2) matrix B= Bohr magneton(20.2) u,- relative magnetic permeability(20.2) minimun We electron mobility (18.7) 0= original uh= hole mobility(18.10) 0= at equilibrium Poisson's ratio(6.5)
List of Symbols • xxv VC unit cell volume (3.4) VC corrosion potential (17.4) VH Hall voltage (18.14) Vi volume fraction of phase i (9.8) v velocity vol% volume percent Wi mass fraction of phase i (9.8) wt% weight percent (4.4) x length x space coordinate Y dimensionless parameter or function in fracture toughness expression (8.5) y space coordinate z space coordinate lattice parameter: unit cell y–z interaxial angle (3.7) , , phase designations l linear coefficient of thermal expansion (19.3) lattice parameter: unit cell x–z interaxial angle (3.7) lattice parameter: unit cell x–y interaxial angle (3.7) shear strain (6.2) precedes the symbol of a parameter to denote finite change engineering strain (6.2) dielectric permittivity (18.18) r dielectric constant or relative permittivity (18.18) s steady-state creep rate (8.12) T true strain (6.7) viscosity (12.10) overvoltage (17.4) Bragg diffraction angle (3.16) D Debye temperature (19.2) wavelength of electromagnetic radiation (3.16) magnetic permeability (20.2) B Bohr magneton (20.2) r relative magnetic permeability (20.2) e electron mobility (18.7) h hole mobility (18.10) n Poisson’s ratio (6.5) n frequency of electromagnetic radiation (21.2) density (3.5) electrical resistivity (18.2) t radius of curvature at the tip of a crack (8.5) engineering stress, tensile or compressive (6.2) electrical conductivity (18.3) * longitudinal strength (composite) (16.5) c critical stress for crack propagation (8.5) fs flexural strength (12.9) m maximum stress (8.5) m mean stress (8.7) m stress in matrix at composite failure (16.5) T true stress (6.7) w safe or working stress (6.12) y yield strength (6.6) shear stress (6.2) c fiber–matrix bond strength/matrix shear yield strength (16.4) crss critical resolved shear stress (7.5) m magnetic susceptibility (20.2) SUBSCRIPTS c composite cd discontinuous fibrous composite cl longitudinal direction (aligned fibrous composite) ct transverse direction (aligned fibrous composite) f final f at fracture f fiber i instantaneous m matrix m, max maximum min minimum 0 original 0 at equilibrium 0 in a vacuum 1496T_fm_i-xxvi 01/10/06 22:13 Page xxv
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