338
24 Specimen Elongation with Yield Drop
24.6 Steady-State Yield
After plastic strain in the element x, low-frequency oscillations caused by the
formation of the yield drop converge. Before the formation of another boundary
layer, the stress reaches the upper yield stress and is then reduced in a zigzag manner
causing waves of elastic unloading. These waves partially propagate into the testing
device and are partially reflected from specimen fillets. Rapid calculations can be
used to show that these wave processes significantly fade after the fourfold reflection
of the wave from fillets. If V is the speed of relative displacement of tester grips, the
mutual distancing of grips during the fourfold reflection of the wave will be
l = V Vt,
(24.11)
whereas
t =
4l
c 0
.
Let us use x 1 to designate the length of another element where plastic strain
occurred. Since the relative strain of this element after going to the plastic state is
ε 0 , we have
ε 0 =
l
x 1
.
(24.12)
Formulas (24.11)–(24.12) allow getting a condition when wave process will fade
before a new rise of stress:
x 1 =
4V l
ε 0 c 0
.
(24.13)
24.7 Building an Elongation Diagram
The mechanism of the yield drop and plateau formation described above is based on
the fact that the initial shear resistance is below the upper yield stress. In accordance
with the considered model, the true stress diagram in those elementary volumes of
the material with stress drop looks as shown in Fig. 24.3a. After the stress drop,
hardening occurs. However, it will be hidden in the “stress–strain” diagram for the
entire specimen until the observed yield plateau reaches the limit value. This is
when the entire specimen will go to the plastic state and the hardening visible in the
diagram is continued hardening shown in Fig. 24.3a with a dashed line.
For the specimen in general, the stress diagram on the yield plateau represents a
number of rises shown in Fig. 24.3b by a dashed line; a continuous line reflects the
24 Specimen Elongation with Yield Drop
24.6 Steady-State Yield
After plastic strain in the element x, low-frequency oscillations caused by the
formation of the yield drop converge. Before the formation of another boundary
layer, the stress reaches the upper yield stress and is then reduced in a zigzag manner
causing waves of elastic unloading. These waves partially propagate into the testing
device and are partially reflected from specimen fillets. Rapid calculations can be
used to show that these wave processes significantly fade after the fourfold reflection
of the wave from fillets. If V is the speed of relative displacement of tester grips, the
mutual distancing of grips during the fourfold reflection of the wave will be
l = V Vt,
(24.11)
whereas
t =
4l
c 0
.
Let us use x 1 to designate the length of another element where plastic strain
occurred. Since the relative strain of this element after going to the plastic state is
ε 0 , we have
ε 0 =
l
x 1
.
(24.12)
Formulas (24.11)–(24.12) allow getting a condition when wave process will fade
before a new rise of stress:
x 1 =
4V l
ε 0 c 0
.
(24.13)
24.7 Building an Elongation Diagram
The mechanism of the yield drop and plateau formation described above is based on
the fact that the initial shear resistance is below the upper yield stress. In accordance
with the considered model, the true stress diagram in those elementary volumes of
the material with stress drop looks as shown in Fig. 24.3a. After the stress drop,
hardening occurs. However, it will be hidden in the “stress–strain” diagram for the
entire specimen until the observed yield plateau reaches the limit value. This is
when the entire specimen will go to the plastic state and the hardening visible in the
diagram is continued hardening shown in Fig. 24.3a with a dashed line.
For the specimen in general, the stress diagram on the yield plateau represents a
number of rises shown in Fig. 24.3b by a dashed line; a continuous line reflects the