A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [100] direction. If the critical resolved shear stress for this material is 1.98 MPa, calculate the magnitude of applied stress necessary to cause slip to occur on the (111) plane in the direction.

the magnitude of the stress necessary to cause slip to occur on the (111) plane in the direction is 4.85 MPa

Explanation:

From the given information;

To determine the angle between the direction [100] and [111]; we have:

where;

[u₁,v₁,w₁] and [u₂, v₂, w₂] are directional indices.

replacing 1 for u₁ , 0 for v₁ and 0 for w₁  ;

also replacing 1 for u₂, 1 for v₂ and  1 for w₂ ; we have :

To determine the angle for the slip direction

replacing 1 for u₁ , 0 for v₁ and 0 for w₁  ;

also replacing 1 for u₂, 1 for v₂ and  -1 for w₂ ; we have :

The yield strength  for the slip process can now be calculated as:

where

= 1.98 MPa

Hence, the magnitude of the stress necessary to cause slip to occur on the (111) plane in the direction is 4.85 MPa