Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1 degrees and 47.9 degrees, respectively, with the tensile axis. If the critical resolved shear stress is 20.7 MPa (3000 psi), will an applied stress of 45 MPa (6500 psi) cause the single crystal to yield? If not, what stress will be necessary?

resolved shear stress = 22.0 MPa

so we can say that here single crystal will yield because critical resolved shear stress i. e 20.7 MPa is less than resolved shear stress i. e 22.0 MPa

Explanation:

given data

angles φ = 43.1 degrees

angles λ = 47.9 degrees

shear stress = 20.7 MPa (3000 psi)

stress σ = 45 MPa (6500 psi)

solution

we have given shear stress so first we calculate here resolved shear stress that is express as

resolved shear stress = σ cosφ cosλ ... 1

here σ is stress and φ and λ are angles given

so put here value we get

resolved shear stress = σ cosφ cosλ

resolved shear stress = 45 cos (43.1) cos (47.9)

resolved shear stress = 22.0 MPa

so we can say that here single crystal will yield because critical resolved shear stress i. e 20.7 MPa is less than resolved shear stress i. e 22.0 MPa