21.3 Yield Stress and Loading Rate
317
where τ 0 is the constant value, T 0 is the absolute temperature, t is the moment of
yield occurrence, and is some function. 1
The following empirical representations were proposed for the function :
= (|σ |/σ ∗ )
n
;
(21.2)
=
a(|σ |/σ ∗ − 1) n
at σ > σ ∗ ,
0
a t σ < σ ∗ ;
(21.3)
= A exp(|σ |/b).
(21.4)
The parameters n, a, A, and b in these expressions are temperature functions.
Formula (21.2) proposed by Yekobori [1] gives the final time of yield delay at
σ = σ ∗ and therefore is contradictory. The equation of Campbell 21.4 also gives
[16] incorrect results for stress close to σ ∗ . The function ( 21.3) whose use in the
yield conditions (21.1) satisfactorily coordinates [16] with the experiment remains
non-contradictory.
Let us shortly consider experimental studies of yield delay. A rather comprehensive overview of these studies is contained in materials with a pronounced yield
plateau. Let us call the highest value of the maximum tangential stress preceding
the formation of yield drop or plateau as the yield stress of such materials.
A sufficiently complete overview of these researches is contained in the article by
Yu.V. Suvorova [19]. It should be noted that the number of experiments intended to
study this phenomenon is rather limited. Apparently, this is related to the complexity
of setting experiments and with a wide scatter of experimental data. Among the
existing experimental results, the most reliable are experiments by Clark, Wood, and
Gendrikson [2, 22], as well as Lomakin E. V. [11]. Let us also note that as of now,
we do not know any experimental works in the field of studying the yield delay in
the conditions of complex stressed state. All known experiments belong to uniaxial
elongation or compression. Characteristics of yield delay given in the literature are
defined by various authors for various rates of loading, and therefore their analysis
and comparison are rather problematic.
21.3 Yield Stress and Loading Rate
We already noted (p. 333) that this book discusses materials with a pronounced yield
plateau. Let us agree that the yield point of such materials is the highest value of the
maximum tangential stress preceding formation of a yield drop or a yield plateau.
During elongation tests, the effect of yield delay is expressed by the fact that the
yield stress of a plastic material is very sensitive to the loading rate (to be more
1 This book considers athermal plasticity at normal temperatures.
317
where τ 0 is the constant value, T 0 is the absolute temperature, t is the moment of
yield occurrence, and is some function. 1
The following empirical representations were proposed for the function :
= (|σ |/σ ∗ )
n
;
(21.2)
=
a(|σ |/σ ∗ − 1) n
at σ > σ ∗ ,
0
a t σ < σ ∗ ;
(21.3)
= A exp(|σ |/b).
(21.4)
The parameters n, a, A, and b in these expressions are temperature functions.
Formula (21.2) proposed by Yekobori [1] gives the final time of yield delay at
σ = σ ∗ and therefore is contradictory. The equation of Campbell 21.4 also gives
[16] incorrect results for stress close to σ ∗ . The function ( 21.3) whose use in the
yield conditions (21.1) satisfactorily coordinates [16] with the experiment remains
non-contradictory.
Let us shortly consider experimental studies of yield delay. A rather comprehensive overview of these studies is contained in materials with a pronounced yield
plateau. Let us call the highest value of the maximum tangential stress preceding
the formation of yield drop or plateau as the yield stress of such materials.
A sufficiently complete overview of these researches is contained in the article by
Yu.V. Suvorova [19]. It should be noted that the number of experiments intended to
study this phenomenon is rather limited. Apparently, this is related to the complexity
of setting experiments and with a wide scatter of experimental data. Among the
existing experimental results, the most reliable are experiments by Clark, Wood, and
Gendrikson [2, 22], as well as Lomakin E. V. [11]. Let us also note that as of now,
we do not know any experimental works in the field of studying the yield delay in
the conditions of complex stressed state. All known experiments belong to uniaxial
elongation or compression. Characteristics of yield delay given in the literature are
defined by various authors for various rates of loading, and therefore their analysis
and comparison are rather problematic.
21.3 Yield Stress and Loading Rate
We already noted (p. 333) that this book discusses materials with a pronounced yield
plateau. Let us agree that the yield point of such materials is the highest value of the
maximum tangential stress preceding formation of a yield drop or a yield plateau.
During elongation tests, the effect of yield delay is expressed by the fact that the
yield stress of a plastic material is very sensitive to the loading rate (to be more
1 This book considers athermal plasticity at normal temperatures.