A single crystal of BCC iron Fe is oriented such that a tens

A single crystal of BCC iron (-Fe) is oriented such that a tensile stress of 63 MPa is applied along the 0 1 0 direction. Calculate the magnitude (absolute value) of the resolved stress on the 1 1 1 plane in the -1 1 0 direction. (answer format X.X)

Solution

the magnitude of the resolved stress is calculated as follows:

stress = (tensile stress) {[(1*0) + (1*1) + (1*0) / (12 + 12 + 12)^1/2 * (02 + 12)^1/2]

         * [(-1*0) + (1*1) + (0*0) / (-12 + 12)^1/2 * (02 + 12)^1/2]}

   =[63 MPa] {1/3^1/2 * 1/21/2}

        = 25.7 MPa