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MatSci 201 HW7 2008

MatSci 201 HW7 2008 - 3 Callister Question 6.49 4 For the...

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MatSci 201: Introduction to Materials Homework #7: Due Monday, December 1, 2008 by 5 PM Submit in class or in the hanging folder outside 3035 Cook Hall No late homework accepted. Mechanical Behavior and Ceramics 1. (a) For an iron bar of length 10 cm and cross-section area of 1 cm 2 , calculate the force required in newtons (N) to produce an elongation of 0.1 mm, assuming elastic deformation and a Young’s modulus of 200 GPa. Be careful about units. (b) For the same iron bar, we first apply stress of 400 MPa. This produces a total strain of 0.3%. The stress is then reduced to zero. The material sustains a permanent strain because the elastic limit is exceeded. Calculate the value of this permanent strain. (c) The same iron bar discussed above has surface cracks 2 mm long. The relevant fracture toughness is 20 MPa-m 1/2 (2 × 10 7 Pa-m 1/2 ). Assume the geometric factor Y to be 1.0. What is the maximum stress this iron bar can withstand before fracture? 2. Callister, Question 6.19
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Unformatted text preview: 3. Callister, Question 6.49 4. For the data given below, draw a graph of yield strength versus d-1/2 . If Hall-Petch behavior holds, what is the average grain diameter if the yield strength is 310 MPa? Comment on why there is a grain size dependence of the yield strength. d [ μ m] Yield strength [MPa] 100 230 60 275 5. Callister, Question 8.20 (a) (b) and (d). Why should there be a fatigue limit? 6. Explain why a second hardness measurement made adjacent to a previous measurement indicates a higher hardness. 6. A TiO 2 crystal is grown with some Cr 2 O 3 impurities. The valence of Ti is +4, and the valence of Cr is +3. Chromium ions occupy titanium sites substitutionally. Explain what type of vacancy will be introduced. 7. (a) How does the internal stress state of Corelle dishware (as demonstrated in class) affect its mechanical properties? (b) What sort of behavior would you expect if the internal stress state were reversed?...
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MatSci 201 HW7 2008 - 3 Callister Question 6.49 4 For the...

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