Physica 139 & 140B (1986) 782-784 North-Holland, Amsterdam FUNDAMENTALS OF STRENGTH AND DURABILITY CALCULATIONS FOR HIGH- PRESSURE APPARATUS ELEMENTS N.V. NOVIKOV, V.I. LEVITAS and S.I. SHESTAKOV Institute for Superhard Materials of the Ukrainian Academy of Sciences, Kiev, USSR The high-pressure apparatus for the synthesis of materials are devices of repeated application. They comprise many elements made of materials with different elasticity, plasticity and thermal conductivity characteristics. The dependence of the mechanical characteristics of these materials on the stressed state mode and temperature causes problems in analyzing their stressed-strained state. Theoretical aspects of the mechanics of deformable bodies have been considered and an example of numerical calculation has been presented for the fields of temperature and mechanical stresses in load-bearing elements for different models of high pressure apparatus. In this case the pressure and temperature dependence of metals and non-metals properties, substantial thermoplastic deformations and contact interaction of separate elements in high-pressure apparatus have been taken into account. The thermoplastic critical state of the reaction cell container made of natural stone has been investigated. The selection of critical mechanical characteristics (strength and durability) taking into account the scale effect has been theoretically proved. The distribution of equivalent stresses and the durability of the elements of different modes of the high-pressure apparatus has been considered. The effect of the scale factor has been investigated, Estimated values have been compared with experimental ones obtained for the models of elements of the high-pressure apparatus. The problem has been considered concerning the numerical determination of temperature and stress fields in an axisymmetric high-pressure apparatus (HPA) of the recessed anvil type used to synthesize superhard materials. The possibility has been examined of estimating the strength and durability of HPA elements under repeated heat- ing and loading. The temperature distribution is determined by the finite element method (FEM) applied to the solution of a coupled nonlinear and nonstationary problem of the electrical and thermal conduct- ivities of HPA elements under heating the reac- tion cell by the direct passage of the low voltage current [1]. The high-pressure apparatus of con- ventional type, one quarter of the axial section of which is shown in fig. 1, comprises inhomogene- ous elements. The reaction cell container is made from differ- ent rock materials, e.g. lithographic stone. The model of ideally plastic isotropic material [2] is used to determine its limiting state due to high plastic compression strain. Using the hypothesis of complete plasticity [3] we consider the problem to be statically determinable and apply the slip line method for its solution. We use the methods for a determination of constants in the equations of the limiting surface of ideal plasticity described by Coulomb's law [4]. Making use of the tempera- ture field obtained and the temperature depen- dence of the constants included in the condition of Coulomb's plasticity limiting state the problem for a container of predetermined shape and size has been numerically solved by means of a "plas- ticity" program package for computer-aided cal- culations [3, 4]. The calculations resulted in ob- taining the distribution of contact normal % and tangential % stresses at the container-matrix interface (fig. 2). These data are the initial ones for calculating the matrix strength. The value of stress jump at the media interface is influenced by a number of factors. Thus, allowing for the temperature dependence of the container materi- al properties results in a considerable reduction of the calculated value for stress jump approximat- ing the calculated model of straining to the real one which is physically valid. The obtained characteristics of the container 0378-4363 / 86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)