The flow stress of a coarse-grained dilute copper alloy increased from 2 to 55 MPa when the dislocation density was increased from a low value of 10² cm² via cold working to a modest value of 100 cm². Calculate the flow stress for this alloy when heavy cold working introduces a dislocation density of 10¹2 cm². An equation similar to the Hall-Petch equation has been proposed for dislocations, and is: To ka √Paist + Tflow where Tflow is the flow stress (i.e., the force per unit area necessary to get plastic deformation), Pdisi is the dislocation density (the dislocation line length per unit volume). and to and ka are constants for a given material. The easiest way to solve this problem is to put values into this equation twice, subtract one expression from the other, and solve for ka. Then enter your value of k into either original equation to determine To. Keep track of units, and then solve the problem stated above.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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The flow stress of a coarse-grained dilute copper alloy increased from 2 to 55
MPa when the dislocation density was increased from a low value of 10 cm via
cold working to a modest value of 100 cm2. Calculate the flow stress for this
alloy when heavy cold working introduces a dislocation density of 10¹2 cm². An
equation similar to the Hall-Petch equation has been proposed for dislocations,
and is:
Tflow To ka Paisl
where Tflow is the flow stress (i.e., the force per unit area necessary to get plastic
deformation), pdisi is the dislocation density (the dislocation line length per unit volume),
and To and ka are constants for a given material.
The easiest way to solve this problem is to put values into this equation twice,
subtract one expression from the other, and solve for ka. Then enter your value
of ka into either original equation to determine To. Keep track of units, and then
solve the problem stated above.
Transcribed Image Text:The flow stress of a coarse-grained dilute copper alloy increased from 2 to 55 MPa when the dislocation density was increased from a low value of 10 cm via cold working to a modest value of 100 cm2. Calculate the flow stress for this alloy when heavy cold working introduces a dislocation density of 10¹2 cm². An equation similar to the Hall-Petch equation has been proposed for dislocations, and is: Tflow To ka Paisl where Tflow is the flow stress (i.e., the force per unit area necessary to get plastic deformation), pdisi is the dislocation density (the dislocation line length per unit volume), and To and ka are constants for a given material. The easiest way to solve this problem is to put values into this equation twice, subtract one expression from the other, and solve for ka. Then enter your value of ka into either original equation to determine To. Keep track of units, and then solve the problem stated above.
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