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Please derive the maximum drag force of particle on the grain boundary: f=pi rsigma and the driving force for boundary movement to the retarding force

Please derive the maximum drag force of particle on the grain boundary:

f=\\\\pi r\\\\sigma

and the driving force for boundary movement to the retarding force of the inclusions (Zener's relationship): R =

4(r)/(3)\\\\zeta

. ( 10 points)\ What is the driving force for recovery of deformed metals? What are the differences between recovery processes at high and low temperatures? ( 8 points)

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3. Please derive the maximum drag force of particle on the grain boundary: f=r; and the driving force for boundary movement to the retarding force of the inclusions (Zener's relationship): R= 4r/3. (10 points) 4. What is the driving force for recovery of deformed metals? What are the differences between recovery processes at high and low temperatures? ( 8 points)

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