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cee60-Fall04-mt1-Monteiro-soln

# cee60-Fall04-mt1-Monteiro-soln - UNIVERSITY OF CALIFORNIA...

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UNIVERSITY OF CALIFORNIA AT BERKELEY DEPARTMENT OF CEE FALL SEMESTER, 2004 Instructor: P.J. M. Monteiro Name: Solution CE 60 - EXAMINATION Question 1 (30 points) I) Calculate the volume of an FCC unit cell in terms of the atomic radius R. (5 points) 4R = sqrt(2).a a = 4R/sqrt(2) = 2Rsqrt(2) Vol = a^3 = (4R/sqrt(2))^3 = 16sqrt(2).R^3 II) Draw a stress-strain diagram for a material that: a) has high-strength but low toughness, b) high strength and high toughness, and c) low strength and low toughness (9 points) III) A metallic rod is tested in tension and the following data are reported. A) Determine the elastic modulus (5 points), b) after reaching a load of 32680, the sample is unloaded to 15,000 N. Compute the plastic strain at this point (load of 15,000N) 11points Load (N) Gage length (mm) 0 50.8 4,890 50.8102 9,779 50.8203 24,450 50.8508 29,390 50.8711 32,680 50.9016 Original, specimen diameter: 12.7 mm Specimen area, A = π d 2 /4 = 126.68 mm 2 Linear behavior up to 24,450N σ = P/A = 24,450N/126.68mm 2 = 193 MPa σ ε a b c

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ε = L/L o = (50.8508 - 50.8)/50.8 = 0.001 (or 0.1%) E = σ / ε = 193/0.001 = 193 GPa After reaching 32,680N ( σ = P/A = 258MPa), the sample is unloaded to 15,000N (118.4Mpa):
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