Question

Consider a metal single crystal oriented such that the normal to the slip plane and slip direction are at angles of 60° and 35°, respectively, with the tensile axis. If the critical resolved shear stress is 8 MPa, will the applied stress of 12 MPa cause the single crystal to yield? If not, what stress will be necessary?

Answer 1

Answer:

19.5324 MPa

Explanation:

Information provided

Angle between the normal to the slip plane with tensile axis, $\alpha=60^{o}$

Angle by slip direction with tensile axis, $\beta=35^{o}$

Critical resolved shear stress, $\tau_{c}=8 MPa$

Applied stress $\sigma=12 MPa$

Shear stress at slip plane

$\tau=\sigma cos\alpha cos\beta$

$\tau=12cos60^{o}cos35^{o}=4.915 MPa$

$\tau$ hence crystal won’t yield

Applied stress, $\sigma$ for crystal to yield is given by

$\sigma=\frac {\tau_{c}}{cos\alpha cos\beta}$

$\sigma=\frac {8}{cos60cos35}=19.53239342 MPa$

$\sigma=19.5324 MPa$