A solid disk of radius b is subjected to an angular velocity ω [rad/s]. The disk has mass density ρ, modulus of elasticity E, Poisson’s ratio v, and yield strength Y. Temperature effects are negligible.
a. Determine the angular velocity ωγ at which the disk yields initially. Assume that σzz = 0 and that the maximum shear-stress criterion applies.
b. Determine the angular velocity ωP at which the disk becomes fully plastic. Compare ωp to ωY.
c. After the disk becomes fully plastic, it is returned to rest. Determine the resulting residual stresses in the disk.
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