Chapter 21
Strain Specifics of Plastic Bodies
21.1 Elongation Diagram of a Plastic Material Specimen
Figure 21.1 gives a typical elongation diagram for a specimen made of plastic
material. Here we can find the following characteristic features.
The area OA of elastic strain in some section AB is followed by a low nonelastic strain that is most frequently called pre-yield (or micro-yield) strain; its value
is within 10 −5 . . . 10 −4 .
Then a loading drop can be observed (to the point C); the peak forming thereat
is referred to as the yield drop [14]. It is followed by the area CD (or BE)
corresponding to the occurrence and growth of micro-yield strain. Hereafter we will
refer to the strain process on the yield plateau as yield. During yield, the specimen
strain is characterized by high heterogeneity. A detailed study of yield development
in a specimen of low-carbon steel at various testing rates is made, for instance, in
papers by Yu. N. Rabotnov and his colleagues [10, 12].
It has been found [12] that plastic strain occurs at first in a small area as compared
with the specimen length, which is in the place of stress concentrations in the
cylindrical specimen, most frequently in the vicinity of one of the fillets. When
plastic strain occurs, stress starts dropping from σ v (point B, Fig. 21.1) to some
value σ s (point C, Fig. 21.1). Simultaneously with the stress drop, strain in the area
of the initial plastic strain quickly rises to some value ε 0 (Fig. 21.2, [12], curve
1), which is constant for the defined elongation rate. At that time, the material is
partially unloaded in the entire remaining volume of the specimen, which can be
noticed on curve 2 (Fig. 21.2) built upon indications of the strain sensor attached in
the middle of the specimen.
Then the plastic strain area grows; the interface of elastic and plastic zones moves
along the specimen as a front. t ∗ is used in Fig. 21.2 to designate the moment when
plastic strain occurs in the initial plasticity area and t ∗∗ is the moment corresponding
to the plastic strain front approaching the middle of the specimen, and T 0 is the time
while the plastic strain front covers the entire working length of the specimen. After
© 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_21
313
Strain Specifics of Plastic Bodies
21.1 Elongation Diagram of a Plastic Material Specimen
Figure 21.1 gives a typical elongation diagram for a specimen made of plastic
material. Here we can find the following characteristic features.
The area OA of elastic strain in some section AB is followed by a low nonelastic strain that is most frequently called pre-yield (or micro-yield) strain; its value
is within 10 −5 . . . 10 −4 .
Then a loading drop can be observed (to the point C); the peak forming thereat
is referred to as the yield drop [14]. It is followed by the area CD (or BE)
corresponding to the occurrence and growth of micro-yield strain. Hereafter we will
refer to the strain process on the yield plateau as yield. During yield, the specimen
strain is characterized by high heterogeneity. A detailed study of yield development
in a specimen of low-carbon steel at various testing rates is made, for instance, in
papers by Yu. N. Rabotnov and his colleagues [10, 12].
It has been found [12] that plastic strain occurs at first in a small area as compared
with the specimen length, which is in the place of stress concentrations in the
cylindrical specimen, most frequently in the vicinity of one of the fillets. When
plastic strain occurs, stress starts dropping from σ v (point B, Fig. 21.1) to some
value σ s (point C, Fig. 21.1). Simultaneously with the stress drop, strain in the area
of the initial plastic strain quickly rises to some value ε 0 (Fig. 21.2, [12], curve
1), which is constant for the defined elongation rate. At that time, the material is
partially unloaded in the entire remaining volume of the specimen, which can be
noticed on curve 2 (Fig. 21.2) built upon indications of the strain sensor attached in
the middle of the specimen.
Then the plastic strain area grows; the interface of elastic and plastic zones moves
along the specimen as a front. t ∗ is used in Fig. 21.2 to designate the moment when
plastic strain occurs in the initial plasticity area and t ∗∗ is the moment corresponding
to the plastic strain front approaching the middle of the specimen, and T 0 is the time
while the plastic strain front covers the entire working length of the specimen. After
© 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_21
313