HW 7-Sol - HW7 solution Restricting or hindering...

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HW7 solution Restricting or hindering dislocation motion renders a material harder and stronger. According to the equation related to yield strength and grain size, we can get two equations as y o k MPa 0 . 10 230 + = σ and y o k MPa 91 . 12 275 + = σ which yield the values MPa 4 . 75 0 = σ and 2 / 1 ) ( 49 . 15 mm MPa k y = . At a yield strength of 310 MPa, we have 2 / 1 ) 46 . 15 ( 4 . 75 310 + = d Therefore, ) ( 10 34 . 4 3 mm d × = In order for these two cylindrical specimens to have the same deformed hardness, they must be deformed to the same percent cold work. For the first specimen CW r r r A A A CW d d % 36 100 ) 15 ( ) 12 ( ) 15 ( 100 100 % 2 2 2 2 0 2 2 0 0 0 = × = × = × = For the second specimen, the deformed radius is computed using the above equation and solving for d r as ) ( 80 . 8 100 36 1 11 100 % 1 0 mm CW r r d = = =
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Computing the value of the constant A (in the equation provided in the problem statement) from the one set of data as mm MPa mm MPa MPa A D crss × = = = 3 2 0 10 21 . 6 ) ( 10000 ) ( 069 . 0 ) ( 69 . 0
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