Consider a single crystal oriented such that the slip direction and normal to the slip plane are at angles 42.7° and 48.3°, respectively, with the tensile axis. If the critical resolved shear stress is 29.4 MPa, what applied stress (in MPa) will be necessary to cause the single crystal to yield?

Respuesta :

Given:

slip direction angle, [tex]\phi = 42.7^{\circ} [/tex]

angle normal to slip plne, [tex]\lambda = 48.3^{\circ} [/tex]

critical resolved shear stress, [tex]\tau_{r} = 29.4 MPa[/tex]

Solution:

To calculate the applied stress, [tex]\sigma_{a}[/tex] the formula for critical resolved shear stress is given by:

[tex]\tau_{r} = \sigma_{a} cos\lambda cos\phi [/tex]          (1)

Putting the given values in eqn (1):

[tex]29.4\times 10^{6} = \sigma_{a} \times cos48.3^{\circ}\times cos 42.7^{\circ} [/tex]

[tex]\sigma _{a} = 60.14 MPa[/tex]

Therefore, necessary applied stress is 60.14 MPa

Q&A Education