The term stress intensity comes from the Nuclear code Sec III and B & PV code SEC VIII DIV 2 APPENDIX 4.

It means twice the max. shear stress. As you know that max. shear stress is the algebraic difference between the maximum and minimum principal stresses and the Tresca ( see John's reply above)criteria calls for failure when max. shear stress equals max. shear stress in simple tension test at yield point, which effectively makes it half y.p. value in tension , so we have an equation where the left hand side and the right hand side has a factor 0.5 . So to keep things simple it is better to divide both sides by a factor 0.5 is what we get as "stress intensity".

CAESAR II also allows the user the Von Mises criteria which is also essentially the max. Octahedral shear stress criteria ( max. shear stress on a plane which is equally oriented to the three principal directions).

Regards