CERTAIN MODELS OF THE INELASTIC DEFORMATION OF MATERIALS. REPORT 2. SOME ASSUMPTIONS AI~D GENERALIZATIONS V. I. Levitas UDC 539.374 Certain experimental data on the behavior of materials under high pressure and during brittle failure are interpreted in the present study using the theory developed by Levitas [1]. The classical model of a plastic medium is further developed by accounting for the strain history in the elastic region and complication of the understanding of kinematic couples. The results are generalized for rheonomic media witha memory and with interaction between thermo- mechanical phenomena. 1. Let us employ the theory developed by Levitas [1] to describe the plastic flow of materials under a high hydrostatic pressure. The ~-= p(a) relationship derived by Vereshchagin and Shapochkin [2] for certain materials, where ~- is the ultimate shear strength and a >0 is the hydrostatic pressure, can be approximated by the following equations: for steel 45 - ~ - - 0~35 -{- 0.154(~ for 25 ~ a ~ 100; hv = 7,1.10-4 (o -100) 2 for 100~(~350; A~ ---- 39,9 -6 0,26 (~-- 350) for 350 ~. o ~ 500; for steel 2KhlSN9 = --0,78 -{- 0,169~ A~ = 0,069 ( o - - 191,3) for 2 5 ~ ( ~ 191,3; for 191.3~ a~ 500; for tungsten = 4.2 -6 0,072(~ for 25 ~ g ~ 50; A~ = 0.006 (~ - - 50)1'77 for 50 <~ g <~ 350, where (~ and ~- are expressed in 10 2 MPa, AT denotes the addition to the quantity T, derived from equations for the first interval of the variation in a. It is apparent from the equations that the limiting curve ~-= #(~) is concave, beginning with the second in- terval of variation in a. To determine the shear rate 7 and the shear rate caused by three-dimensional deformation (breakup) (here, we can disregard the compressibility caused by hydrostatic pressure [3]), it is necessary to isolate those a for which differentiation will be performed and those a 0 on which ~ depends parametrically under the condi- tion q~(,, a) = "r-~(a)= O. Consequently, itisnecessarytoderivethe condition fly, (~, X(~0)] = 0, where • is a pa- rameter characterizing the structural changes that take place in the material [1], and f= 0 is nonconcave for any • in this case, substituting a 0 = a in f, one obtains q~(,% a) = 0. This is associated with the introduction of additional assumptions. Since it is primarily the structural changes that are analyzed as a function of the quan- tity a (phase and polymorphic transformations, variation in porosity and the dislocation structure, etc.), we can assume that the parameter • is independent of 1- 0. Let us further assume that f( v, a, X) is linear for all X = eonst. This can be based on the fact that in the first interval of variation in a, when the dependence of f on • can be neglected, f is linear. Consequently, the coefficient before a in f(v, a, X) should be equal to the coef- ficient before a in ~', (r) in the first interval of variation in (r, and X = A~-: Institute of Superhard Materials, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prob- lemy Prochnosti, No. 12, pp. 77-83, December, 1980. Original article submitted June 14, 1979. 0039-2316/80/1212-1545507.50 Plenum Publishing Corporation 1545