STRENGTH, PLASTICITY, AND CREEP CONDITIONS
FOR CERAMIC AND OTHER DILATANT MATERIALS
A. A. Treshchev
and P. V. Bozhanov
Translated from Ogneupory i Tekhnicheskaya Keramika, No. 11, pp. 16 – 20, November, 2001.
Huber-Mises conditions of strength and plasticity for materials with different resistances are discussed. The
yield strength or shear strength can be taken as a material constant under these conditions. A region of consis
tent functions based on general postulates is explored and creep equations are derived.
The strength of certain structural materials is determined
by the type of stress to which they are subjected [1 – 8]. The
relation between stress and strain in such materials has been
considered in a number of studies where quasi-linear
[4, 11 – 15, 18] or nonlinear equations [1 – 4, 7, 8, 14, 16, 17]
were proposed. Shortcomings of those models were analyzed
in [15 – 18].
The experimental studies [1 – 8] provide evidence that
the strain of nonequiresistant materials (materials with differ-
ent resistances) as a function of stress is most pronounced in
the nonlinear region where plastic processes come into play.
Therefore, plasticity and strength are characteristics that are
most sensitive to stress.
In this work, we give an analysis of the results of experi
mental studies concerned with the plasticity and strength of
isotropic materials. We propose a formulation of the condi
tions of plasticity and strength for stress-sensitive materials
and give governing equations for describing the plastic strain
in materials of this class.
The strength of many polymers and polymer-based com
posite materials is quite sensitive to hydrostatic pressure .
Thus, under an additional confining pressure, the stress in
tensity corresponding to the conventional yield strength or
ultimate strength increases markedly. Typical stress-strain di
agrams for K-17-2-type phenoplast (based on phenol-formal
dehyde resin and sawdust filler) subjected to uniaxial com
pression simultaneously under the conditions of confining
pressure P of the working medium are shown in Fig. 1. Simi
lar strain diagrams were reported for polymethyl metha
crylate specimens , which clearly showed a yield point,
and for low-density polyethylene .
The diagrams in Fig. 1 disprove the hypothesis of a uni
que stress-strain diagram for these materials by virtue of the
fact that both plasticity and strength show dependence on the
type of stress. A similar behavior was observed in many
polymer materials, graphite, cast iron, ceramics, and com-
posites. In order to take account of the effect due to stress on
the hardness of materials under stress-strain conditions, con-
ventionally appropriate stress intensity parameters are intro-
duced [4, 7, 8, 11 – 18]. Generally, stress parameters are also
introduced into the plasticity and strength conditions for
For defining stress, characteristics of one of the two nor-
malized stress spaces were proposed in [15 – 18]. The nor-
malized stresses in this case are qualitative characteristics of
Refractories and Industrial Ceramics Vol. 42, Nos. 11 – 12, 2001
1083-4877/01/1112-0393$25.00 © 2001 Plenum Publishing Corporation
Tula State University, Tula, Russia.
0 0.1 0.2 0.3
Fig. 1. Stress-strain diagram for K-17-2 phenoplast based on phe
nol-formaldehyde resin and sawdust subjected to uniaxial compres
sion under the conditions of confining pressure P of the working me
dium. Curves 1 – 6 correspond to P = 0.1, 30, 50, 100, 150, and
200 MPa; s is the axial stress and e is the axial strain.