Mumbai University > Mechanical Engineering > Sem 4 > Material Technology

Marks: 6M

Critical Resolved Shear Stress

Slip begins when the shearing stress on the slip plane is the slip direction reaches a threshold value called Critical Resolved Shear Stress.

Consider

$A_0$= Cross section of cylindrical single crystal

Φ= Angle between tensile axis and normal to slip plane

$F_s$=Resolved force in slip direction =Fcosλ

$A_s$=Transverse C/S area of Cylinder = A0/cosΦ

A = Angle between slip direction with Tensile axis

$CosΦ=A_0/A_s$

$A_s= A_0/CosΦ$

CRSS acting on slip plane in slip direction is

$Τ_s$=Force in slip direction/Transverse C/S area

$Τ_s=Fcosλ/A_s Substitute value of A_sin …..(i)$

$Τrss= Fcosλ/(A_0/CosΦ)$

Τrss=F. CosΦ. Cosλ/A_0OR σ/m

Where $σ=F/A_0$

m=1/CosΦ.Cosλ orientation of slip system w.r.to tensile axis

Above equation gives sheer stress resolved on slip plane in slip section. This sheer stress is maximum when Φ=λ=45°

So that, $Τr=F/2 A_0$