Homework 8-solutions

Homework 8-solutions - MAT 33 Fall 2007 Due: 11/05/07...

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MAT 33 – Fall 2007 Homework #8 – Solutions Due: 11/05/07 1.) The yield stress for an iron that has an average grain diameter of 5 x 10 -2 mm is 135MPa. At a grain diameter of 8 x 10 -3 mm, the yield stress increases to 260MPa. At what grain diameter will the yield stress be 200MPa? The best way to solve this problem is to first establish two simultaneous expressions of the Hall- Petch equation, solve for σ o and k y , and finally determine the value of d when σ y = 200 MPa. The data pertaining to this problem may be tabulated as follows: σ y d (mm) d -1/2 (mm) -1/2 135 MPa 5 x 10 -2 4.47 260 MPa 8 x 10 -3 11.18 The two equations thus become 135 MPa = σ o + (4.47)k y 260 MPa = σ o + (11.18)k y Which yield the values, σ o = 51.7 MPa and k y = 18.63 MPa(mm) 1/2 . At a yield strength of 200 MPa 200 MPa = 51.7MPa + [18.63 MPa(mm) 1/2 ] d –1/2 or d -1/2 = 7.96(mm) -1/2 , which gives d = 1.57 x 10 -2 mm . 2).
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Homework 8-solutions - MAT 33 Fall 2007 Due: 11/05/07...

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