Nadai correction

Tubular specimens (thin walls) can also be used and do not require a Nadai correction (Nadai 1931). The specimen geometry used by Gali et al. (1981) is presented in O Fig. 19.12b. Again, relevant properties are determined from the shear stress-strain curve. 

In a modification of the napkin ring shear test, the adherends are solid bars and the adhesive forms a penny-shaped slab similar to the butt joint tensile test. Such a test will give the relationship between torque and twist, but whereas in the napkin ring test it may be assumed that all the adhesive is at the same stress and strain, with a solid butt joint there is a radial variation of strain, but a non-linear variation of stress after yield. It is then necessary to use the Nadai correction (see Adams and Wake") to determine the true stress-strain curve of the adhesive. 

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... 

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