Chapter 23
The Fluidity at the Finite Speed
of Loading
23.1 Yield Strength at the Final Loading Speed
Let us consider the loading of a body element beyond the elastic limit at any final
rate. In this case, the body will have diffusion processes even before yield, which
will cause low non-elastic strains of pre-yield (see, for example, [1, 6, 7]). These
diffusion processes may significantly decrease the shear resistance of the considered
materials due to changes in the arrangement of dislocations in the cloud of Cottrell
[2, 3, 5].
Let us designate the time to reach the yield stress (t y ) until the moment (T 0 ) of
reaching the yield stress as T 1 . During the time T 1 , the material will have diffusion
processes that will cause structural softening. As a result, the yield stress of the
material will go down to some value S m < S ∞
m .
If the stress τ m (t) exceeding the yield stress τ y was applied at the moment t,
which acted for the time dt, this stress will give some change in the yield stress
as a result of structural softening. Let us assume that for the studied materials, the
following conclusion is true.
Hypothesis Structural softening is defined only by maximum tangential stress.
This hypothesis expands formula (22.2) to the case of loadings differing from
the uniaxial elongation. Based on the suggestion formulated in the hypothesis, the
contribution of the stress τ m (t) over the time dt to the change in the yield stress can
be represented as
dS m = −F [τ m (t)]dt,
where F is a yet unknown function that we will call the aging function. We will find
as follows for the entire time interval T 1 :
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_23
327
The Fluidity at the Finite Speed
of Loading
23.1 Yield Strength at the Final Loading Speed
Let us consider the loading of a body element beyond the elastic limit at any final
rate. In this case, the body will have diffusion processes even before yield, which
will cause low non-elastic strains of pre-yield (see, for example, [1, 6, 7]). These
diffusion processes may significantly decrease the shear resistance of the considered
materials due to changes in the arrangement of dislocations in the cloud of Cottrell
[2, 3, 5].
Let us designate the time to reach the yield stress (t y ) until the moment (T 0 ) of
reaching the yield stress as T 1 . During the time T 1 , the material will have diffusion
processes that will cause structural softening. As a result, the yield stress of the
material will go down to some value S m < S ∞
m .
If the stress τ m (t) exceeding the yield stress τ y was applied at the moment t,
which acted for the time dt, this stress will give some change in the yield stress
as a result of structural softening. Let us assume that for the studied materials, the
following conclusion is true.
Hypothesis Structural softening is defined only by maximum tangential stress.
This hypothesis expands formula (22.2) to the case of loadings differing from
the uniaxial elongation. Based on the suggestion formulated in the hypothesis, the
contribution of the stress τ m (t) over the time dt to the change in the yield stress can
be represented as
dS m = −F [τ m (t)]dt,
where F is a yet unknown function that we will call the aging function. We will find
as follows for the entire time interval T 1 :
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_23
327