Test 2 Solution

# Test 2 Solution - EMSE 201 Introduction to Materials...

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EMSE 201 — Introduction to Materials Science & Engineering 3 November 2010 Name: SOLUTION Department of Materials Science and Engineering 1 of 5 Case Western Reserve University Test #2 — 75 minutes; 100 points; 5 questions; 5 pages; 10% of course grade Partial credit will be given for correct set-ups and reasoning. Give units on numerical answers where appropriate and use the correct number of significant figures. Please write all answers on these pages; use the backs if needed. 1) The figure below shows a log-log plot of ultimate tensile strength σ ut versus strain to failure ε f for a wide variety of engineering materials at room temperature. a) (10 points) A material’s modulus of toughness, defined as the total area under the engineering stress-strain curve to failure, can be approximated by the expression U t = ut f On the graph above, draw the line that corresponds to a value of U t = 10 MPa. In the space below, determine the value of the slope that this line must have, and justify the location that you chose. Taking logs of both sides of the above relationship, and rearranging ( 4 pts ): log( U t ) = log( ut ) + log( f ) log( ut ) = log( t ) – log( f ) So on a plot of log( ut ) versus log( f ), lines representing materials with equal values of t will have slope of –1 ( 2 pts ). The line representing t = 10 MPa will include (for example) the point ut = 10 7 Pa and f = 1 (100% strain), and the point ut = 10 6 Pa and f = 10, as indicated above ( 4 pts ). continued on next page Metals Polymers Ceramics

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EMSE 201 — Introduction to Materials Science & Engineering 3 November 2010 Department of Materials Science and Engineering 2 of 5 Case Western Reserve University 1) b) (12 points) Though not labeled, polymers and metals are included in the plot. Indicate and label the region that shows the mechanical properties of polymers, and the region that shows the mechanical properties of metals. Ceramics are not shown on the plot; if they were included, indicate where ceramics would appear. In the space below, quantitatively justify the locations you chose. Among engineering materials, polymers exhibit the widest range of strain to failure, ranging from a few percent to several hundred percent ( ε f = 1) ( 1 pt ). Their strengths tend to be low ( 1 pt ). This general area is indicated in the graph on p. 1 ( 2 pts ). With ceramics out of the picture, metals will have the highest strengths ( 1 pt ) and ductilities from a few percent to several tens of percent ( 1 pt ). This general area is indicated in the graph on p. 1 ( 2 pts ). Ceramics have comparable or higher strengths than metals (
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Test 2 Solution - EMSE 201 Introduction to Materials...

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