188
14 On the Plasticity Conditions of an Isotropic Body
Fig. 14.6 Servohydraulic testing machines
Fig. 14.7 Tubular specimen for tests
of an arbitrary plane stressed state with an independent change of stress tensor
components. The implementation of an arbitrary plane stressed state is still an
unsolved problem. Therefore, strain laws are checked when testing thin-wall tubular
specimens (Fig. 14.7).
During tests, the axial force P , twisting moment M, and inner pressure q can be
set as arbitrary functions of time from the range of values permitted by the loading
device characteristics. For the directions of the axes x, y, and z shown in Fig. 14.7,
the stress components will be as follows:
σ x =
P
F
=
P
2πRδ
, σ y =
qR
δ
, τ xy =
M
2πR 2 δ
,
(14.20)
where R is the average tube radius and δ is the thickness of its wall (see the
superimposed cross-section in Fig. 14.7). Apart from the three stress components
given in the formulas (14.20), for q = 0 there is also stress σ z that equals −q on
14 On the Plasticity Conditions of an Isotropic Body
Fig. 14.6 Servohydraulic testing machines
Fig. 14.7 Tubular specimen for tests
of an arbitrary plane stressed state with an independent change of stress tensor
components. The implementation of an arbitrary plane stressed state is still an
unsolved problem. Therefore, strain laws are checked when testing thin-wall tubular
specimens (Fig. 14.7).
During tests, the axial force P , twisting moment M, and inner pressure q can be
set as arbitrary functions of time from the range of values permitted by the loading
device characteristics. For the directions of the axes x, y, and z shown in Fig. 14.7,
the stress components will be as follows:
σ x =
P
F
=
P
2πRδ
, σ y =
qR
δ
, τ xy =
M
2πR 2 δ
,
(14.20)
where R is the average tube radius and δ is the thickness of its wall (see the
superimposed cross-section in Fig. 14.7). Apart from the three stress components
given in the formulas (14.20), for q = 0 there is also stress σ z that equals −q on