418
32 On Boundary Value Problems of Inelastic Body Mechanics
Fig. 32.8 Distribution of
radial normal stresses
Fig. 32.9 Distribution of
tangential normal stresses
As already mentioned, when the tensile force reaches the value P t = σ t F , an
increase in the displacement of the end of the rod leads to a drop in the load to
P . Due to the infinitely small displacement of the ends of the beam, its absolute
elongations before and after the load drop should coincide
σ t
E
l 0 = l
e
+ l
p ,
(32.26)
where l e , ,l p are the absolute elongation of the elastic and plastic parts of the
bar. Using the stretch chart (Fig. 32.2), it can be written as
l
e
=
σ 0
E
(l 0 − l p ); l
p
=
σ s
E
+
σ 0 − σ s
E t
l p .
(32.27)
From formulas (32.26)–(32.27), the desired dependence follows:
32 On Boundary Value Problems of Inelastic Body Mechanics
Fig. 32.8 Distribution of
radial normal stresses
Fig. 32.9 Distribution of
tangential normal stresses
As already mentioned, when the tensile force reaches the value P t = σ t F , an
increase in the displacement of the end of the rod leads to a drop in the load to
P . Due to the infinitely small displacement of the ends of the beam, its absolute
elongations before and after the load drop should coincide
σ t
E
l 0 = l
e
+ l
p ,
(32.26)
where l e , ,l p are the absolute elongation of the elastic and plastic parts of the
bar. Using the stretch chart (Fig. 32.2), it can be written as
l
e
=
σ 0
E
(l 0 − l p ); l
p
=
σ s
E
+
σ 0 − σ s
E t
l p .
(32.27)
From formulas (32.26)–(32.27), the desired dependence follows: