Week 3 HW - mechanical properties

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Apr 3, 2024

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MSE 23000 Homework Assignment – Week 3 (10 pts) Mechanical Behavior Over the next week, think about the following problems and provide your responses as prompted below using this document as a template . Responses can be typed and/or inserted as scans or images ( e.g. , of hand-written calculations or sketches). These questions are reflective of typical exam questions – hence, the students who complete their homework assignments are the best prepared for their upcoming exams. Additionally, you are encouraged to attempt all homework problems before attending your weekly recitation so that you are prepared to ask questions and seek guidance & hints from your recitation instructor. This assignment is worth 10 points and will be graded for completion only. Submit your assignment as a single PDF document by using the appropriate link on Brightspace. You may choose to complete this assignment independently or work in groups but all submitted responses must be unique/your own work. Correct responses will be discussed in your next recitation lecture. (1 pt) 1. Callister 6.4: A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa and an original diameter of 3.8 mm will experience only elastic deformation when a tensile load of 2,000 N is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is 0.42 mm. (2 pts) 2. Callister 6.7: For a bronze alloy, the stress at which plastic deformation begins is 275 MPa and the modulus of elasticity is 115 GPa. (1 pt each) (a) What is the maximum load that may be applied to a specimen with a cross-sectional area of 325 mm 2 without plastic deformation occurring? (b) If the original specimen length is 115 mm, what is the maximum length to which it may be stretched without causing plastic deformation?

(2 pts) 3. Callister 6.23: A cylindrical rod 100 mm long and having a diameter of 10.0 mm is to be deformed using a tensile load of 27,500 N. It must not experience either plastic deformation or a diameter reduction of more than 7.5 x 10 -3 mm. Of the materials listed in the following table, which are possible candidates and why? Material E (GPa) Yield Strength (MPa) Poisson’s Ratio Aluminum alloy 70 200 0.33 Brass alloy 101 300 0.34 Steel alloy 207 400 0.30 Titanium alloy 107 650 0.34 (5 pts) 4. Callister 6.29: A cylindrical specimen of aluminum having a diameter of 12.8 mm and a gauge length of 50.800 mm is pulled in tension. Use the load-elongation data in the following table to compute parts (a) through (e). (1 pt each) Load (N) Length (mm) 0 50.800 7330 50.851 15100 50.902 23100 50.952 30400 51.003 34400 51.054 38400 51.308 41300 51.816 44800 52.832 46200 53.848 47300 54.864 47500 55.880 46100 56.896 44800 57.658 42600 58.420 36400 59.182 Fracture! (boom) (a) Use a computer to create a scatter plot of all the data in the above table as engineering stress vs. engineering strain.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 50 100 150 200 250 300 350 400 Engineering Stress v Engineering Strain Strain Stress (MPa) (b) Compute the modulus of elasticity. 0 0.01 0 50 100 150 200 250 f(x) = 59618.92 x − 1.22 Zoomed-in plot in Elastic Zone Strain Stress (MPa) The formula for the modulus of elasticity is stress / strain, or the slope of the graph in the elastic zone. Since each point did not have the exact same slope, I created a line of best fit for only the points in the elastic zone. This way, I was able to take the average of the slopes and use that value for the modulus of elasticity, which is 59,619 MPa. (c) Determine the yield strength using the “0.2% strain offset” method. Hint: it might be easiest to do this using a “zoomed-in” plot of only the small-strain data, e.g. from 0 to 0.010.

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0 0.01 0.02 0.03 0 50 100 150 200 250 300 350 Zoomed-in plot of Yield Strength Strain Stress (MPa) (d) Determine the tensile strength of this alloy. (e) What is approximate ductility, in percent elongation?