202
A. V. Basalin et al.
Fig. 13.12 Geometric characteristics of the neck
σ real (t) =
σ mean (t)
1 +
2R(t)
a(t)
· ln
1 +
a(t)
2R(t)
(13.8)
here, R is the minimum cross-section curvature radius of a neck, a is the minimum
cross-section radius of the deformed specimen (Fig. 13.12).
Davidenkov and Spiridonova have got the following estimation of effective true
stress (Davidenkov and Spiridonova 1946):
σ real (t) =
σ mean (t)
1 +
a(t)
4R(t)
(13.9)
There are also other less known models.
Szczepinski (Dietrich et al. 1970) deduced the following equation:
σ real (t) =
σ mean (t)
2R(t)
a(t)
exp
a(t)
4R(t)
− 1
(13.10)
Corrective formula of Malinin and Petrosian for stress calculation (Malinin and
Rzysko 1981) is the following: