University:
Massachusetts Institute of Technology
Course:
3.225 | Electronic and Mechanical Properties of Materials
Academic year:

2019
Views:

124

Pages:

5
Author:

Zaria Bauer

E1 = 12.9 GPa S1 = √(E1) = 7.61 × 10^9 GPa E2 = 20.1 GPa S2 = √(E2) = 4.48 × 10^9 GPa E3 = 11.47 GPa S3 = √(E3) = 3.39 × 10^9 GPa E4 = 5.7 GPa S4 = √(E4) = 2.39 × 10^9 GPa E5 = 9.23 GPa S5 = √(E5) = 3.04 × 10^9 GPa E6 = 5.7 GPa S6 = √(E6) = 2.39 × 10^9 GPa E7 = 18 GPa S7 = √(E7) = 4.24 × 10^9 GPa E8 = 22 GPa S8 = √(E8) = 4.69 × 10^9 GPa E9 = 11.14 GPa S9 = √(E9) = 3.34 × 10^9 GPa E10 = 11.28 GPa S10 = √(E10) = 3.36 × 10^9 GPa E11 = 12.28 GPa S11 = √(E11) = 3.50 × 10^9 GPa E12 = 12.28 GPa S12 = √(E12) = 3.50 × 10^9 GPa E13 = 12.28 GPa S13 = √(E13) = 3.50 × 10^9 GPa S1a = -0.28 ------------------ E1 S1a = -0.28 / 12.9 = -2.19 × 10⁻² S1b = -0.28 ------------------ E2 S1b = -0.28 / 20.1 = -1.39 × 10⁻² [Matrix 1] 7.61 -2.19 -2.19 -2.19 4.48 -1.39 -2.19 -1.39 4.98 [Matrix 2] 10 5 20 4 3 0 [Matrix 1] * [Matrix 2] = [Matrix 3] 14.9 17.5 21.3 10 E1 = 7.24 x 10^5 E2 = 25.3 x 10^5 E3 = 6.88 x 10^5 E4 = 2.26 = 5.96 x 10^4 E5 = 2.613 = 5.11 x 10^4 E6 = 2.61 = 0 16) E = (1/2) (du/dx - T/2 (d^2ψ/dx^2)) crystalline materials - uniaxial dett - atoms pulled apart or pushed together - relative positions don't change much - σ stretch bonds - small; ε small; change in entropy small rubbers - random c-c chains, occasionally cross-linked by covalent cross-links. Uniaxial dett - aligns chains, making them more ordered - c-c bonds can slide over one another without shedding C-C bonds along the length of the chain. d^2ε/du^2 >> d^2ψ/du^2 crystalline materials: E = f(ε, T) dimensionless group: E/kT_m = constant U_a = kT_m E = ckT_m/n (2) boundo an isotropic material G* = E/2(1+ν) = 0 -> ν = -1 rubbers w/ large k, small E large k, small E high pressure, small ω ω = 0 ?

3.225 Exam#4 (Solutions)

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