Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] direction. If slip occurs on a (101) plane and in a direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.9 MPa.

Complete Question

Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] direction. If slip occurs on a (101) plane and in a [111]  direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.9 MPa.  

The  stress is

Explanation:

From the question we are told that

  The critical yield resolved shear stress is  

First we obtain the angle   between the slip direction [121] and  [111]

Where are the directional indices

Next is to obtain the angle between the direction [121] and [101]

 Substituting 1 for , 2 for   , 1 for , 1 for  , 0 for  , and 1 for  

   The stress is mathematically represented as

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