How Do You Calculate Shear Strain in a Crystal?

[ralden]

I don't know how to solve this kind of problem:

Given a crystal and its volume V. This Crystal is subjected to a shear stress making a slip plane (h k l ) in a slip direction [h k l]. Given also the lattice parameter a and slip plane spacing L, and the edge dislocation a/2 that passed halfway through the crystal on every fourth plane.

The question is what is the shear strain?

So to solved this problem i used this equation

y(shear strain) = pbX

p= dislocation density, b =burger vector, and X= average dislocation

where p = L/V and b =a/2

my problem is how to compute X?

 

[Achy47]

Hello there,

Thank you for bringing this problem to my attention. I can understand how it can be confusing, but I am here to help you solve it.

To compute X, we need to first understand what it represents in this equation. X is the average dislocation, which is the average distance between dislocations in the crystal. This distance can be calculated by dividing the total slip plane spacing (L) by the total number of dislocations in the crystal.

Since we know that the crystal has a dislocation on every fourth plane, we can calculate the total number of dislocations by dividing the total number of planes (V/L) by 4. This gives us the value of X, which we can then plug into the equation to find the shear strain.

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!