Crib Sheet- Ch 6, 18, 19

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Materials Science and Engineering
Joey Kish

Chapter 6 – Mechanical Properties of Metals Types of stresses: Tensile, Compressive, Shear, Biaxial Tension Compression, Hydrostatic. F Δl Stress: σ = , Strain: ε =Δl Shear stress: τ = , Shear strain: γ = = tan θ A0 0 A0 l0 σ ∂F ∂ U Stress and strain are proportional to each other using σ =ε (E – Young’s Modulus) or τ = Gγ (G – Shear Modulus). Physics of elasticity: E = :: , ε ∂r ∂r2 Energy stored: 1 σ V , Poisson’s ratio: ε (bottom of ratio – strain in direction of applied force) . W = σεV = 0 υ = εx E = 2 G1 + υ 2 0 2E z Deformation: Metallic materials deform elastically (reversible) until strains of about .005. After that, plastic (irreversible) deformation occurs. *Note: Elastic doesn’t conserve volume, plastic does.* Work hardening: After they yield, metals get harder to deform. Tensile Strength = F max/ A 0 Ductility: % elongation = ](l – l )f/ l 0 * 100, % area reduction = [(A – A ) / A ] * 000 f 0 P Hardness tests: indent (pressure vs. area) H : A Chapter 18 – Electrical Properties of Solids Brinell: HB = 2 P (P-load, D-diameter of steel ball: 10 mm, d-indent diameter), Resilience: σy π ( D −D −d 2) UR= 2E Ohm’s Law: V = IR J = σε (σ - electrical conductivity, σ=1/ , ε - electric field intensity, ε = V / l ), Resistivity: ρ =RA/ or , where l is the distance where voltage is measured, A is the area perpendicular to the direction of the current. − Eg kT p : e (p–probability, #of electrons excited (holes created)), if E >2 eV, theg p→0 ⇒insulator. For semiconductors, as T↑, N ↑. e - - Metals: Electron Drift Velocity σ = nμe T↑⇒n↑, but μ↓ ⇒μ dominant ⇒σ↓ (more vd = μ e Conductivity: e (n - #free e ‘s, e – charge of e μ- electron mobility) collisions impede movement). Resistivity (Matthiessen’s Rule): T↑⇒R↑⇒μ↓ ρ = ρ + ρ + ρ thermal impurity dislocatio.s −E 2kT - Semiconductors: Intrinsic (pure): σ = n e ( μ + μ ) (n=p), Temp. dependence: n = n e
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