By Their Behavior Under Stress

ANALYSIS OF STRESS--STRAIN DIAGRAMS AND CLASSIFICATION OF LOW--DEFORMING MATERIALS BY THEIR BEHAVIOR UNDER STRESS G. A. Gogotsi UDC 666.7:620.1+621.438:666.3:620.1+539.7 Based on analytical data on stress--strain diagrams and the results of studies of fracture processes in ceramics, concretes, graphites, etc., a new characteristic of such materials was established earlier [1] -- a measure of brittleness “ and the classification of these materials was described in [2]. However, these works examined the behavior of the materials only during loading, and thus did not consider the behavioral features manifest during unloading. This somewhat approximate treatment of the problem requires refine- ment insofar as the study of the strength of materials used in making modern high-technology elements is con- cerned. The present work is a continuation of other investigations [1, 2, etal.] and is based on data obtained in a study of the behavior of low-deforming materials both under load and during unloading. Based on an examination of the results in [3-6] and our data and assuming that a change in conditions (to unloading) does not stipulate a fundamental change in the stress--strain diagrams, these diagrams may be divided into the following basic types (Fig. 1). The first (Fig. la) is characteristic, for example, of many single crystals, dense single-phase ceramics, window glass, etc., typified by linearly elastic behavior and the absence of any effects related to dissipation of the energy expended in its deformation. The second type (see Fig. lb) is similar to the first, but is for the case of nonlinear elasticity. Although we are not aware of any materials with such classical (from the point of view of nonlinear mechanics) behavior [7], the possibility that such diagrams exist will be considered for the generality of subsequent discussions. The third type of diagram (Fig. lc) is characteristic of certain glasses, ceramics, and composites which dis- sipate part of the strain energy during loading. The hysteresis seen here (the study of the mechanism of which has, indeed, been given more attention in connection with metals [8] and graphites [9] than with ceramics) is probably associated with phenomena such as internal friction, the opening of microcracks, and similar effects. A fourth type of diagram (Fig. ld) is characteristic of ceramics with heterogeneous structures (including reinforced ceramics), concretes, many graphites, etc., in which not only is stress nonlinearly dependent on strain, but inelasticity is the result of microscopic fractures in the material (this is treated in greater detail in [1, 2]) which may be accompanied by microplastic strains. In certain cases, this inelasticity may be con- nected with tw4nning effects -- e.g., in ferroelectrics such as perovskite -- and similar phenomena. We will write the brittleness measure [1], defined as the ratio of unit elastic energy* We (Fig. 2a) ac- cumulated in the material until the moment a critical state is attained to the total unit energy W t consumed in its deformation to this moment, in the following manner so that it may be calculated for any stress--strain diagram (see Fig. 1)