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¿7

r

Integrating:

Or

— 0 y loge r + constant

Now

Or

= -P3 at r = Rp

constant = — Pi — crv log^ Rp ar - ay loge r-Pi- ay loge Rp r

These equations thus yield the hoop and radial stresses throughout the plastic zone in terms of the radial pressure at the elastic-plastic interface P^. The numerical value of P3 may be determined as follows (the sign has been allowed for in the derivation of eqn. (3.29)).

At the stage where plasticity has penetrated partly through the cylinder walls the cylinder may be considered as a compound cylinder with the inner tube plastic and the outer tube elastic, the latter being subjected to an internal pressure P3. From eqns. (10.5) and (10.6)^ the hoop and radial stresses in the elastic portion are therefore given by

PiRl and oh

P3*l

i.e. the maximum shear stress is oH - or

0 0

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