Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 60 and 35, respectively, with the tensile axis. If the critical resolved shear stress is 6.2 MPa (900 psi), will an applied stress of 12 MPa (1750 psi) cause the single crystal to yield? If not, what stress will be necessary?

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CarliReifsteck CarliReifsteck · Answer 1 · 2019-11-05T11:31:25+01:00

Explanation:

Given that,

Angle by the normal to the slip α= 60°

Angle by the slip direction with the tensile axis β= 35°

Shear stress = 6.2 MPa

Applied stress = 12 MPa

We need to calculate the shear stress applied at the slip plane

Using formula of shear stress

[tex]\tau=\sigma\cos\alpha\cos\beta[/tex]

Put the value into the formula

[tex]\tau=12\cos60\times\cos35[/tex]

[tex]\tau=4.91\ MPa[/tex]

Since, the shear stress applied at the slip plane is less than the critical resolved shear stress

So, The crystal will not yield.

Now, We need to calculate the applied stress necessary for the crystal to yield

Using formula of stress

[tex]\sigma=\dfrac{\tau_{c}}{\cos\alpha\cos\beta}[/tex]

Put the value into the formula

[tex]\sigma=\dfrac{6.2}{\cos60\cos35}[/tex]

[tex]\sigma=15.13\ MPa[/tex]

Hence, This is the required solution.