Biaxial correction factor

Uniaxial tensile criteria can lead to gross inaccuracies when applied to situations where combined stresses lead to failure in multiaxial stress fields. Often one assumes that combined stresses have no influence and that the maximum principal stress governs the failure behavior. An improved approach applied to biaxial tension conditions relies upon a pragmatic biaxial correction factor which is applied to uniaxial data,... 

Both Eqs. (11.1) and (11.2) account for the effect of transverse strain on plastic strain intensity factor characterized by the modified Poisson s ratio, V. In Eq. (11.1), this is accounted for by the ratio Sy/Sa, whereas in Eq. (11.2) the ratio Eg/E serves the same purpose as will be shown later. The modified Poisson s ratio in each case is intended to account for the different transverse contraction in the elastic-plastic condition as compared to the assumed elastic condition. Therefore this effect is primarily associated with the differences in variation in volume without any consideration given to the nonlinear stress-strain relationship in plasticity. Instead the approaches are based on an equation analogous to Hooke s law as obtained by Nadai. Gonyea uses expression (rule) due to Neuber to estimate the strain concentration effects through a correction factor, K, for various notches (characterized by the elastic stress concentration factor, Kj). Moulin and Roche obtain the same factor for a biaxial situation involving thermal shock problem and present a design curve for K, for alloy steels as a function of equivalent strain range. Similar results were obtained by Houtman for thermal shock in plates and cylinders and for cylinders fixed to a wall, which were discussed by Nickell. The problem of Poisson s effect in plasticity has been discussed in detail by Severud. Hubei... 

In summary, the simplified inelastic analysis rules as indicated in subsections NB 3327.6 and NB 3228.3 of the ASME Boiler and Pressure Vessel Code Section III have been critically appraised. The first rule is shown to be equivalent to a correction factor, K, to be applied to local thermal stresses, and is based on an analysis involving a modified Poisson s ratio. For a simplified situation of thermal stress in a plate with a through the thickness temperature gradient (perfect biaxiality) the solution using NB 3227.6 are comparable to the existing solutions in the literature. However, the solutions obtained using finite-element methods and a different form of Poisson s ratio than that specified in NB 3227.6 (Eq. (11.1)) typically yield higher values of K. ... 

---