Question

Suppose that all the dislocations in 4700 mm3 of crystal were somehow removed and linked end to end. Given 1 m = 0.0006214 mile, how far (in miles) would this chain extend for dislocation densities of (a) 105 mm-2 (undeformed metal)? Enter your answer for part (a) in accordance to the question statement miles (b) 1010 mm-2 (cold-worked metal)?

Answer 1

Answer:

a. The required chain length = 292.1 miles

b. Length of the required chain = $29.2*10^6miles$

Explanation:

Cold work is the work performed on a material at a temperature below the re-crystallization temperature of the material.

Dislocation density is the measure of the total number of dislocation of a crystalline material of unit volume.

Deformation is the process of change in an objects shape due to the application of force

a. In order to find the length of required chain for the given dislocation density

length of required chain = total length of dislocation line =  dislocation density * volume

where dislocation density = $10^5mm^{-2}$

and volume is given as = $4700mm^3$

$=10^5*4700mm(\frac{1mi}{1.609*10^6mm} )=292.1miles$

b. To find the length of required chain

length of required chain = dislocation density * volume

where dislocation density = $10^{10}mm^{-2}$

we substitute in the equation above to get

$=10^{10}mm^{-2}*4700mm^3\\=47*10^{12}mm*(\frac{1mile}{1.609*10^6mm} )=29.2*10^{6}miles$