Homework 01_2021 PDF

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MECH 3351 Homework 01 – Stress-strain curve (Graded over 100 pts.) Due date: 02/02 – Keep your report under 4 pages A dataset has been posted in e-learning containing the results of a tensile test carried out in a silicon rod. Your job is to calculate the stress-strain curve and the metrics we have discussed in class. We will do these calculations based on the professional standards that you are likely to encounter in your engineering practice. In particular, before starting this assignment, please read these two ASTM International (formerly the American Society for Testing of Materials) standards, which have been posted in e-learning as well: • •

ASTM E111−17: Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus E8/E8M−16a: Standard Test Methods for Tension Testing of Metallic Materials

We will only scratch the surface of what these and other standards cover. Suffice to say, if you encounter that you need to conduct a test in your professional practice, chances are there is an ASTM standard for it, which will give you very detailed parameters of how your test must be conducted. If you are curious, head to the website of ASTM international (use the database gateway of the library website). You will find there are standards for many kinds of materials and types of testing. Carry out the calculations in this homework in whatever software you prefer (Excel, Matlab, Mathematica, etc.). There is an excel example posted in e-learning. However, please keep a copy of your calculations for your records (code, excel file); you do not need to turn-in those files. Upload a pdf with your results and plots. Please note that the reports will be parsed using the turn-it in software that detects plagiarism and copying by comparing the text of all the reports. Ensure you cite and quote correctly whatever sources you use and that you do not plagiarize each other (in certain cases, paraphrasing other people can be considered plagiarism). 1. (10 pts.) The dimensions of the specimen are the standard dimensions (Specimen 1) specified in Figure 8, first table, E8 standard. Using these dimensions, calculate and plot the engineering stress and strain diagram. 2. (10 pts.) Compute the true-stress, true strain diagram and plot on top of the plot in point 1. Use the formulas discussed in class that use the engineering strain to calculate the true stress and strain. Up to what value of the engineering strain is the true stress-strain plot valid? Why? From here on, use the engineering diagram for your calculations. 3. (20 pts.) Calculate the Young’s modulus using the a linear fit. a. Explain your rationale for choosing the points that were included in the fit. b. In deciding your fitting parameters, keep in mind the recommendations of E111, section 9.3, and report your coefficient of variation (V1) and how you computed it. There are other methods for computing Young’s modulus, which you can see in other parts of Section 9 if you are curious.

4. (20 pts.) Calculate the 0.2% offset yield strain and strength, using the guidelines in E8M, section 7.7. Report how you calculated the intercept with the curve. 5. (5 pts.) Calculate and report the EUL 0.5% yield strength. Report the percentage difference with the 0.2% offset yield strength. 6. (20 pts.) Compute numerically the resilience of the specimen. Report your result and the method of calculation. Also, compute the resilience using the approximate method discussed in class; compute the percentage difference between these two methods. 7. (15 pts.) Compute numerically the toughness of the specimen. Report your result and the method of calculation. Also, compute the toughness using the approximate method discussed in class; compute the percentage difference between these two methods....