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Unformatted text preview: REVIEW: MIDTERM 01 LOCATION / TIME
Two rooms, assigned alphabetically Last name AN: 105 Stanley Last name OZ: 277 Cory Monday, October 4, 2010 12:10 PM — 1:00 PM GRADING
5 equallyweighted 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 ( ) STRESSSTRAIN 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 stressstrain curve where σ = E ε • Bond • Linear • Plastic deformation breaking; permanent shape change from linearity in stressstrain 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
Crosssectional 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 • Ductiletobrittle transition can occur at low temperatures
R L Klueh and D R Harris, “HighCr Ferritic and Martensitic Steels for Nuclear Applications,” ASTM,(2001). FRACTURE TOUGHNESS
• Effect of preexisting 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
• NonDirectional • 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 baseco fco sr sh sm basecm 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 SYMMETRYRELATED
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 MILLERBRAVAIS INDICES
c (0001)
• Hexagonal systems use the fourindex (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 (xrays) distinguishes crystal structures • Diffraction Bragg’s Law: nλ = 2d sin θ Structure Factor: h,k,l unmixed largest dspacing [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 halfplane 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) closestpacked planes, and “in” closestpacked 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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 Fall '08
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