Cm. Lombard et al., NUMERICAL-ANALYSIS OF THE HOT TENSION TEST, Metallurgical transactions. A, Physical metallurgy and materials science, 24(9), 1993, pp. 2039-2047
Plastic flow during the round bar, uniaxial tension test has been anal
yzed for conditions representative of the hot-working of metals. Two m
ethods of analysis were employed: the finite element method and a simp
ler finite-difference technique using a so-called ''direct equilibrium
'' approach. Variables which were investigated included material prope
rties (strain-hardening exponents of 0 or 0.1; strain-rate sensitivity
exponents between 0.02 and 0.30) and sample geometry (gage length-to-
diameter ratios between 4 and 15; samples with and without tapers from
the fillet to the center of the gage section). Results were summarize
d in terms of nominal (engineering) stress-strain curves, axial strain
distributions after the onset of rapid flow localization, and total e
longations. A comparison of the results from the two types of numerica
l analyses were very similar. This similarity was interpreted to resul
t from the similar degrees of stress triaxiality during neck formation
which were predicted via the finite element method and assumed (based
on the Bridgman analysis) for the direct equilibrium approach. Total
elongation predictions from the numerical models were compared to meas
urements and to a simple closed form analytical solution contained in
the literature. The numerical results showed good agreement with the m
easurements but differed greatly from the analytical solution, thereby
quantifying the effect of the neglect of stress triaxiality in simple
analytical models on predicted elongations.