Mumbai University > Mechanical Engineering > Sem 4 > Material Technology

Marks: 5M

Year: Dec 2015

Critical Resolved Shear Stress (CRSS):

• minimum stress to initiate slip, or stress required to initiate slip on a given slip plane and in a given direction [most favorably oriented slip system].

i.e. FCC crystal with 12 slip systems

$\tau = \frac{\text{Load}}{\text{Aeea}} \\ \tau = \frac{P cos \theta}{\frac{A}{cos \phi}}, \text{Since} \sigma = \frac{\pi}{A} \rightarrow \text{tensile stress} \\ \tau = \sigma cos (\phi) cos (\theta), and \ \ \theta = \frac{\pi}{2} - \phi \\ \tau \text{is max when} \ \ cos (\phi) \ \ cos(\theta) \text{is max}(45^0) \\ \tau_{max = \sigma (.707)(.707) \simeq} \frac{\sigma_y}{2}\ \ \sigma_y = \text{yeild strength} \\ \tau_{max} = \frac{\sigma_y}{2} \ \ \tau_{critical observed} \lt\lt \tau_{critical calculated}$

Reason : Slip is aided by dislocation movement.