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Homework 2 solutions

# Homework 2 solutions - 01Ch01.qxd 7:50 PM Page 19 SECTION...

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SECTION 1.3 Mechanical Properties of Materials 19 Problem 1.3-6 A specimen of a methacrylate plastic is tested in ten- sion at room temperature (see figure), producing the stress-strain data listed in the accompanying table. Plot the stress-strain curve and determine the proportional limit, modulus of elasticity (i.e., the slope of the initial part of the stress-strain curve), and yield stress at 0.2% offset. Is the material ductile or brittle? P P STRESS-STRAIN DATA FOR PROBLEM 1.3-6 Stress (MPa) Strain 8.0 0.0032 17.5 0.0073 25.6 0.0111 31.1 0.0129 39.8 0.0163 44.0 0.0184 48.2 0.0209 53.9 0.0260 58.1 0.0331 62.0 0.0429 62.1 Fracture Solution 1.3-6 Tensile test of a plastic Using the stress-strain data given in the problem statement, plot the stress-strain curve: H9268 PL H11005 proportional limit H9268 PL H11015 47 MPa Modulus of elasticity (slope) H11015 2.4 GPa H9268 Y H11005 yield stress at 0.2% offset H9268 Y H11015 53 MPa Material is brittle , because the strain after the proportional limit is exceeded is relatively small. ; ; ; ; Problem 1.3-7 The data shown in the accompanying table were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 0.505 in. and a gage length of 2.00 in. (see figure for Prob. 1.3-3). At fracture, the elongation between the gage marks was 0.12 in. and the minimum diameter was 0.42 in. Plot the conventional stress-strain curve for the steel and determine the proportional limit, modulus of elasticity (i.e., the slope of the initial part of the stress-strain curve), yield stress at 0.1% offset, ultimate stress, percent elongation in 2.00 in., and percent reduction in area. TENSILE-TEST DATA FOR PROBLEM 1.3-7 Load (lb) Elongation (in.) 1,000 0.0002 2,000 0.0006 6,000 0.0019 10,000 0.0033 12,000 0.0039 12,900 0.0043 13,400 0.0047 13,600 0.0054 13,800 0.0063 14,000 0.0090 14,400 0.0102 15,200 0.0130 16,800 0.0230 18,400 0.0336 20,000 0.0507 22,400 0.1108 22,600 Fracture 01Ch01.qxd 9/25/08 7:50 PM Page 19

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SECTION 1.4 Elasticity, Plasticity, and Creep 23 Problem 1.4-4 A circular bar of magnesium alloy is 750 mm long. The stress- strain diagram for the material is shown in the figure. The bar is loaded in tension to an elongation of 6.0 mm, and then the load is removed. (a) What is the permanent set of the bar? (b) If the bar is reloaded, what is the proportional limit? ( Hint : Use the concepts illustrated in Figs. 1-18b and 1-19.) (MPa) 0 0 200 100 0.005 0.010 s e Solution 1.4-4 N UMERICAL DATA L H11005 750 mm H9254 H11005 6 mm S TRESS AND STRAIN AT PT B H9255 B H11005 8 H11003 10 H11002 3 H9268 B H11005 180 MPa E LASTIC RECOVERY slope H11005 4.45 H11003 10 4 H9255 E H11005 4.045 H11003 10 H11002 3 R ESIDUAL STRAIN H9255 R H11005 H9255 B H11002 H9255 E H9255 R H11005 3.955 H11003 10 H11002 3 (a) P ERMANENT SET ; â R L H11005 2.97 mm â E H11005 s B slope slope H11005 178 0.004 â B H11005 d L (b) P ROPORTIONAL LIMIT WHEN RELOADED ; s B H11005 180 MPa Problem 1.4-5 A wire of length L H11005 4 ft and diameter d H11005 0.125 in. is stretched by tensile forces P H11005 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by the following equation: in which is nondimensional and H9268 has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material.
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Homework 2 solutions - 01Ch01.qxd 7:50 PM Page 19 SECTION...

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