E45F10_Midterm01_Review

E45F10_Midterm01_Review - REVIEW MIDTERM 01 LOCATION TIME...

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Unformatted text preview: REVIEW: MIDTERM 01 LOCATION / TIME Two rooms, assigned alphabetically Last name A-N: 105 Stanley Last name O-Z: 277 Cory Monday, October 4, 2010 12:10 PM — 1:00 PM GRADING 5 equally-weighted problems 100 points total 10% of course grade BRING Pencils in different colors Erasers Straightedge (“ruler”) STOW AWAY Books Notes Digital Communicators CROWD CONTROL Questions CANNOT be entertained during exam. If uncertain, explain your work. COVERAGE constant crosshead speed Load Cell Gage Length STRESS, STRAIN • Load is normalized to the cross sectional area over which it acts, called STRESS (force per unit area) is normalized to the length of the sample, called STRAIN (dimensionless) σengr P = A0 σtrue ￿engr P = Ai l − l0 ∆l = = l0 l0 ￿l dl l = = ln l0 l0 l • Elongation ￿true true Stress ( ) engineering Strain ( ) STRESS-STRAIN PLOTS • Engineering • Area • To stress more commonly used than true stress reduction causes stress concentration retain constant crosshead speed, load is reduced as necking occurs, accounting for the drop in stress NECKING • Occurs at the peak in the engineering stress strain curve establishing the ultimate tensile strength occur within the gage length; otherwise test is invalid Gage Length • Must DEFORMATION • Elastic deformation stretching; temporary, recoverable portion of stress-strain curve where σ = E ε • Bond • Linear • Plastic deformation breaking; permanent shape change from linearity in stress-strain curve at “yield” point • Bond • Deviation Stress ( ) Low carbon steel may show “serrated” yielding UTS A UYS LYS Fracture Plastic strain at “A” Elastic strain at “A” Strain ( ) Stress ( ) UTS YS Al alloys may require 0.2% offset method to determine yield strength Fracture 0.002 Strain ( ) DUCTILITY • Ductility: • Defined “ability to be plastically deformed” as “percent elongation to failure” or “percent reduction in area” • Ductile materials have good formability, can locally relieve stresses at crack tips during structural loading TOUGHNESS • Toughness: ability of a material to absorb energy by area under stressstrain curve σ • Indicated ε SHEAR LOADING Cross-sectional area AS α PS τ= AS γ = tan α τ = Gγ ( Area is parallel, not perpendicular, to shear load) MODULI • Young’s • Shear • For modulus (E) is also the Modulus of Elasticity modulus (G) is also the Modulus of Rigidity metals, ratio G / E lies in range 0.35 to 0.45 DBTT • Temperature effect • Ductile-to-brittle transition can occur at low temperatures R L Klueh and D R Harris, “High-Cr Ferritic and Martensitic Steels for Nuclear Applications,” ASTM,(2001). FRACTURE TOUGHNESS • Effect of pre-existing flaws, crack length a value of stress intensity factor KIC at crack tip necessary to produce catastrophic failure under simple uniaxial loading • Critical KI C = Y σ f π a √ PRIMARY BONDS • Primary • They • They bonds are CHEMICAL bonds occur between individual atoms or ions involve electron transfer or sharing bond energies are high (200 to 700 kJ/mol) • Primary • They may be covalent, metallic, or ionic SECONDARY BONDS • Secondary • They • They bonds are PHYSICAL bonds occur between groups of atoms (ions) involve no electron transfer or sharing bond energies are low (under 50 kJ/mol) • Secondary • They may be dipole bonds or Van der Waals bonds BONDING IN MATERIALS • Metals: Metallic bonding, some mixed character Ionic / covalent Covalent and secondary Covalent or covalent / ionic • Ceramics: • Polymers: • Semiconductors: DIRECTIONALITY • Non-Directional • Metallic • Ionic • Fluctuating • Directional • Covalent • Permanent Bonds M dipole O Bonds S dipole LATTICE • Array of points in space with identical environment in extent of “origin” is • Infinite • Location arbitrary BRAVAIS LATTICES sc bcc fcc st bct so bco base-co fco sr sh sm base-cm triclinic LATTICE GEOMETRY • Positions: i,j,k [uvw], <uvw> • Directions: • Planes: • Crystal • Unit (hkl), {hkl} structure = lattice + motif Cell is basic building block LATTICE GEOMETRY z • Lattice Directions [uvw]? 0,0,0 ¼, ½, 0 x • Specified by coordinates on a parallel line through the origin fractions by [uvw] y • Clear [120] • Denote SYMMETRY-RELATED z • Structurally equivalent directions are known as a "family" of directions indicated by angular brackets <uvw> six equivalent <110> cubic directions comprise all of the face diagonals y • Example: x MILLER INDICES z • Lattice Planes are specified by "Miller Index" Notation reciprocal of the fractional intercepts that the plane of interest makes with the coordinate axes gives the Miller Indices y • The (200) x MILLER INDICES z • intercepts • axial = 2,3,4 lengths = 4,4,4 intercepts = 2/4, 3/4, 4/4 y • fractional • reciprocals • clear = 2, 4/3, 1 x (hkl)? fractions = 6 4 3 Indices = (643) • Miller MILLER-BRAVAIS INDICES c (0001) • Hexagonal systems use the four-index (hkil) Miller Bravais notation axes are not independent; h+k = –i always holds a3 (01¯ 11) • Crystalline a2 a1 [1¯ 213] c c [0001] ⅓,-⅔, ⅓, 1 1 [¯ ¯ 1210] a3 a3 [¯¯ 1120] a2 a1 [2¯¯ 110] ⅓ -⅓ -⅓ a1 0,0,0,0 ⅓ a2 REAL CRYSTALS Motif must preserve stoichiometry Contents of unit cell must preserve stoichiometry “B2” STRUCTURE • Cesium • Bravais • Motif: Chloride (CsCl) Structure lattice: sc (not bcc!) z 2 ions (one Cl– at 000 one Cs+ at ½, ½, ½) x y •# Ions/unit cell = 1 Cs+ at center + 1 Cl– at corners (8 x 1/8) HALITE z • Sodium • Bravais • MOTIF: Chloride (NaCl) Structure lattice: fcc Cl– at 000 x y 2 ions (one one Na+ at 1/2, 0, 0) • Ions/unit cell = 1 Na+ at body center + 3 Na+ at edges (12 x ¼) + 1 Cl– at corners (8 x 1/8) + 3 Cl– at face centers (6 x ½) MgO, CaO, FeO, NiO • Examples: DIFFRACTION • The periodic structure of crystals causes patterns of constructive and destructive interference for small wavelength radiation (x-rays) distinguishes crystal structures • Diffraction Bragg’s Law: nλ = 2d sin θ Structure Factor: h,k,l unmixed largest d-spacing [anion vacancy + cation vacancy] = charge neutral φ=√ φ= IN EQUILIBRIUM ¯¯ [1120] [¯¯ 1120] • Number 52 1 + 2 (n) of point defects or point defect pairs per total number (N) of lattice sites in equilibrium = formation energy for isolated point defect = formation energy for point defect pairs n = Ae−Ef /kT n N = Ae−Ef /kT N n −Ep /2kT = Be N • Ef • Ep 5+1 φ =¯ [¯120] 1 [111] 2 [¯¯ ¯ ¯ 1120] [101]b √ [¯¯ 1120] [111] ¯ ξ [10¯ 1] [111] n [10¯ −Ef /kT 1] = Ae a N [111] ¯ b= [111] Initial n = ¯B e−Ep /2kT ξ N n = Ae−Ef /kT ¯N b 2 [10¯ 1] ¯ b Final n −E = Ae N a¯ ¯ = [101] b 2 n [10¯ 1] RH screw [111] [¯¯ 1120] [10¯ 1] [111] ¯ ξ Negative edge Positive edge ¯ b mixed n = Ae−Ef /kT N LH screw n a¯ −Ep /2kT ¯ = Be b = [101] N 2 Extra half-plane Slip Plane Dislocation Line (1 11 ) Sli p Pla n e [10¯ 1] [111] ¯S1 b F 32 Burgers Vector? 2 31 4 N 23 4 1 2 13 n −Ef /kT 4 = Ae FSRH Convention n = B e−Ep /2kT N DISLOCATION SLIP • Slip • Slip plane contains both b and ξ or glide occurs “on” (between) closest-packed planes, and “in” closest-packed directions 4 x 3 = 12 slip systems {111} / < 10¯ > 1 6 x 2 = 12 slip systems {1¯ } / < 111 > 10 1 x 3 = 3 slip systems {0001} / < 11¯ > 20 • FCC: • BCC: • HCP: Nucleation Crystallites Growth Crystalline grains Atomic stacking within each crystallite follows lattice. Orientation of lattice changes from grain to grain. STUDY THESE TOPICS • Mechanical • Bonding • Lattice • Crystal Behavior Geometry Structure = Lattice + Motif • Diffraction • Defects ...
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This note was uploaded on 01/28/2011 for the course E 45 taught by Professor Gronsky during the Fall '08 term at Berkeley.

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