Question

Calculate the resolved shear stress on the (111) 01%1 slip system of a unit cell in an FCC nickel single crystal if a stress of 13.7 MPa is applied in the [001] direction of the unit cell.

Answer 1

I have attached an image showing the shear stresses and direction.

Answer:

Resolved shear stress = 5.6MPa

Explanation:

From the diagram attached,

Cos λ = [(0,-1,1)•(0,0,1)]/[(√(0^2 + (-1)^2 + 1^2)) + (√(0^2 + 0^2 + 1^2))]

= 1/(√2 x√1) = 1/√2

Also, Cos Φ = [(1,1,1)•(0,0,1)]/[(√(1^2 + 1^2 + 1^2)) + (√(0^2 + 0^2 + 1^2))]

= 1/(√3 x√1) = 1/√3

So resolved shear stress (τ resolved) = 13.7 x (1/√2) x (1/√3) = 13.7 x (1/√6) = 5.593 or approximately 5.6MPa