Chapter 24
Specimen Elongation with Yield Drop
24.1 Original Assumption
Let us remind (p. 333) that during elongation tests of specimens (Fig. 24.1) of
structural materials such as low-carbon steels and some other bodies, the following
situation is observed (Fig. 21.1). After elastic strain, there is a short non-linear
section of the diagram followed by an abrupt drop of the force acting on the
sample revealing the so-called yield drop [3]. In some time, the force preserves
almost the constant value; the respective section of the diagram is called the yield
plateau followed by a hardening section in the diagram. Given below the physical
phenomena are drawn to describe the graphic images [2] described above, and a
simplified mathematical model is constructed.
24.2 Occurrence of Non-elastic Strain
When the yield plateau starts to form, plastic strain develops extremely unevenly. At
first, a small zone (as compared to the specimen length) goes to a plastic condition.
As the strain grows, this zone expands, and the stress–strain state of the plastic zone
material becomes almost homogeneous everywhere except for the vicinity of the
boundary between the plastic and elastic zones. After the yield plateau ends, the
entire working part of the specimen experiences homogeneous plastic strain. After
that moment, the diagram shows the final hardening that was hidden on the yield
plateau creating an illusive image of ideal plasticity.
The fact that plastic strain is not localized in some volume after the drop occurs
(similarly to what takes place in the formation of a “neck”) but rather distributed
across the specimen proves the material hardening from plastic strain immediately
after the yield drop occurs.
© 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_24
333
Specimen Elongation with Yield Drop
24.1 Original Assumption
Let us remind (p. 333) that during elongation tests of specimens (Fig. 24.1) of
structural materials such as low-carbon steels and some other bodies, the following
situation is observed (Fig. 21.1). After elastic strain, there is a short non-linear
section of the diagram followed by an abrupt drop of the force acting on the
sample revealing the so-called yield drop [3]. In some time, the force preserves
almost the constant value; the respective section of the diagram is called the yield
plateau followed by a hardening section in the diagram. Given below the physical
phenomena are drawn to describe the graphic images [2] described above, and a
simplified mathematical model is constructed.
24.2 Occurrence of Non-elastic Strain
When the yield plateau starts to form, plastic strain develops extremely unevenly. At
first, a small zone (as compared to the specimen length) goes to a plastic condition.
As the strain grows, this zone expands, and the stress–strain state of the plastic zone
material becomes almost homogeneous everywhere except for the vicinity of the
boundary between the plastic and elastic zones. After the yield plateau ends, the
entire working part of the specimen experiences homogeneous plastic strain. After
that moment, the diagram shows the final hardening that was hidden on the yield
plateau creating an illusive image of ideal plasticity.
The fact that plastic strain is not localized in some volume after the drop occurs
(similarly to what takes place in the formation of a “neck”) but rather distributed
across the specimen proves the material hardening from plastic strain immediately
after the yield drop occurs.
© 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_24
333