316
21 Strain Specifics of Plastic Bodies
Fig. 21.1). This phenomenon is called deformational aging in the literature on the
strength of physical materials.
21.2 Delay of Yield
Assume that elongating stress σ (t) is created in the specimen at the moment of time
t. If it appears that σ (t) exceeds some value σ ∗ , which is constant for this material,
the specimen yield does not occur at the moment t, but only after some time (σ ).
This phenomenon is called delay of yield, and the time period (σ ) is the yield
time of delay. It depends on the type of the loading function σ (t). When studying the
delay of yield, σ (t) = const is usually adopted [2] (rectangular loading impulse).
In this case, the stress σ is applied to the specimen instantaneously.
An exemplary type of dependency between the time of yield delay t and the
instantaneously applied maximum tangential stress τ m in an elongated specimen is
shown in Fig. 21.4. Here τ ∞
p designates the maximum tangential stress in specimen
elongation causing the instantaneous occurrence of yield, and τ y means the highest
maximum tangential stress when the specimen yield is not observed yet, however
long we may be waiting for it.
The yield delay has been a subject matter of multiple studies since the middle
of the previous century. Most theoretical studies are done in terms of dislocation
theory. These studies were started in the pioneering works by Cottrell [6, 8]. The
condition of yield occurrence is represented [7] as
1
τ 0
t
0
(σ, T
0 )dτ = 1,
(21.1)
Fig. 21.4 Delay of yield
21 Strain Specifics of Plastic Bodies
Fig. 21.1). This phenomenon is called deformational aging in the literature on the
strength of physical materials.
21.2 Delay of Yield
Assume that elongating stress σ (t) is created in the specimen at the moment of time
t. If it appears that σ (t) exceeds some value σ ∗ , which is constant for this material,
the specimen yield does not occur at the moment t, but only after some time (σ ).
This phenomenon is called delay of yield, and the time period (σ ) is the yield
time of delay. It depends on the type of the loading function σ (t). When studying the
delay of yield, σ (t) = const is usually adopted [2] (rectangular loading impulse).
In this case, the stress σ is applied to the specimen instantaneously.
An exemplary type of dependency between the time of yield delay t and the
instantaneously applied maximum tangential stress τ m in an elongated specimen is
shown in Fig. 21.4. Here τ ∞
p designates the maximum tangential stress in specimen
elongation causing the instantaneous occurrence of yield, and τ y means the highest
maximum tangential stress when the specimen yield is not observed yet, however
long we may be waiting for it.
The yield delay has been a subject matter of multiple studies since the middle
of the previous century. Most theoretical studies are done in terms of dislocation
theory. These studies were started in the pioneering works by Cottrell [6, 8]. The
condition of yield occurrence is represented [7] as
1
τ 0
t
0
(σ, T
0 )dτ = 1,
(21.1)
Fig. 21.4 Delay of yield