# Plotting the plastic zone — Tresca criterion

I've tried to plot the Tresca criterion from maximum shear stress theory.

|S1 - S2| = (KI/Sqrt[2*Pi*r])*Sin[phi/2]

|S2 - S3| = (KI/Sqrt[2*Pi*r])*Cos[phi/2]*(1 - Sin[phi/2])

|S3 - S1| = (KI/Sqrt[2*Oi*r])*Sin[phi/2]*(1 + Sin[phi/2])


where:

KI = 100 MPasqrt(m) && Sy = 70  MPasqrt(m)


Now, how do I plot the function r[phi] that tracks the maximum function of the three along interval {phi, -Pi, Pi}

The r[phi] functions and the plot of all three are given as:

PolarPlot[
{(50 Sin[θ/2]^2)/(49 π),
(50 Cos[θ/2]^2 (-1 + Sin[θ/2])^2)/(49 π),
(50 Cos[θ/2]^2 (1 + Sin[θ/2])^2)/(49 π)},
{θ, -π, π}]


However, it should look alike the righthand figure (b) below:

• Assuming the Oi should be Pi in the definitions? – MelaGo Apr 18 at 23:21