14.5 Experimental Study of Elastic–Plastic Materials
187
Multiple experiments to check plasticity conditions have shown that the Huber–
Mises condition is fulfilled for poly-crystalline materials (in particular, for steels)
somewhat better than the condition of the constancy of the maximum tangential
stress. Together with that, for some alloys, the Tresca condition better conforms
with experimental data. Due to the closeness of results defined by these criteria and
the unavoidable error of the experiment, the Huber–Mises and Tresca conditions
can be viewed as equal formulations of the yield condition. Kachanov suggests [5]
decreasing the difference between the Tresca and Mises conditions by assuming a
cylinder as the yield surface, whose trace on the deviator plane lies in the middle
between the Huber circumference and a circumference described within the Tresca
hexagon.
However, there are other proposals. One of them suggests that plastic strain
occurs when the reduced stress (S max ) reaches a specific value constant for the
material:
S max = max {|σ 1 − σ 0 |, |σ 2 − σ 0 |, |σ 3 − σ 0 |} = const.
(14.19)
Condition (14.19) also slightly differs from the Tresca and Huber–Mises conditions.
On the deviator plane, it circumscribes an equilateral hexagon, for which the Huber
circumference is described.
14.5 Experimental Study of the Elastic–Plastic Properties of
Materials
For an experimental study of strain laws in general and for the establishment and
check of plasticity conditions in particular, power units, measurement equipment,
and specially prepared material specimens are used. The latter are the object of
the research since the two first belong to test equipment. To understand modern
test equipment, Fig. 14.6 gives a general view of test systems supplied by Schenck,
[4]. Position a depicts a unit with a horizontal arrangement of the test specimen,
and position b shows a four-column machine with a vertical arrangement of the
specimen.
These devices belong to servohydraulic machines. Depending on the model, they
can develop axial forces of up to 2000 kN in the specimen. There are principally
different unique testing machines of special purposes. Among them is a Russian
hydraulic machine of proportional loading designed by VNIMI (Saint Petersburg)
scientists and engineers. The device is intended to test specimens of hard rocks in
axial compression imposed over confining pressure (up to 3000 MPa!).
In the experiment intended to study the mechanical properties of materials,
first of all, we must select a geometric shape of the specimen and then set its
loading method. Frequently, one tries to achieve a homogeneous stress–strain state
in the working area of the specimen. Currently, researchers avail of a program
187
Multiple experiments to check plasticity conditions have shown that the Huber–
Mises condition is fulfilled for poly-crystalline materials (in particular, for steels)
somewhat better than the condition of the constancy of the maximum tangential
stress. Together with that, for some alloys, the Tresca condition better conforms
with experimental data. Due to the closeness of results defined by these criteria and
the unavoidable error of the experiment, the Huber–Mises and Tresca conditions
can be viewed as equal formulations of the yield condition. Kachanov suggests [5]
decreasing the difference between the Tresca and Mises conditions by assuming a
cylinder as the yield surface, whose trace on the deviator plane lies in the middle
between the Huber circumference and a circumference described within the Tresca
hexagon.
However, there are other proposals. One of them suggests that plastic strain
occurs when the reduced stress (S max ) reaches a specific value constant for the
material:
S max = max {|σ 1 − σ 0 |, |σ 2 − σ 0 |, |σ 3 − σ 0 |} = const.
(14.19)
Condition (14.19) also slightly differs from the Tresca and Huber–Mises conditions.
On the deviator plane, it circumscribes an equilateral hexagon, for which the Huber
circumference is described.
14.5 Experimental Study of the Elastic–Plastic Properties of
Materials
For an experimental study of strain laws in general and for the establishment and
check of plasticity conditions in particular, power units, measurement equipment,
and specially prepared material specimens are used. The latter are the object of
the research since the two first belong to test equipment. To understand modern
test equipment, Fig. 14.6 gives a general view of test systems supplied by Schenck,
[4]. Position a depicts a unit with a horizontal arrangement of the test specimen,
and position b shows a four-column machine with a vertical arrangement of the
specimen.
These devices belong to servohydraulic machines. Depending on the model, they
can develop axial forces of up to 2000 kN in the specimen. There are principally
different unique testing machines of special purposes. Among them is a Russian
hydraulic machine of proportional loading designed by VNIMI (Saint Petersburg)
scientists and engineers. The device is intended to test specimens of hard rocks in
axial compression imposed over confining pressure (up to 3000 MPa!).
In the experiment intended to study the mechanical properties of materials,
first of all, we must select a geometric shape of the specimen and then set its
loading method. Frequently, one tries to achieve a homogeneous stress–strain state
in the working area of the specimen. Currently, researchers avail of a program