Open AccessProcessing the test results of the composite, which is a mechanical mixture of metal particles with a plastic polymer binder, has shown that its deformation and strength properties are substantially different from those of stable plastic material. The specimen tests for tensile and compression with measuring transverse deformations, as well as torsion tests of tubular samples have revealed that the process of its deformation is accompanied by a change in the original structure.
The composite instability is caused by the fact that during this process, it acquires considerable loosening that depends on the type of the stress-state. Hard metal particles are hardly deformed at any stress-state, but they form a layer of bonds that affect the mixture behavior under force action. The total deformation is the plastic flow of the binder on which deformation, caused both by sliding and by loss of the surface layer bonds, is superimposed.
The analysis shows that with destruction at tensile test the non-linear part of the bulk deformation (dilatancy) is 6 times more than "conditionally" elastic (3.5 times compressed). The objective of this work is to develop a technique for determining a dilatancy, define its influence on deformation and strength properties of the composite, and improve the mathematical model of the material. The proposed model based on the tensor-nonlinear equations describes loosening, as an additional component of the mean deformation and as a mean stress component, hereinafter referred to as: the first - by the deformation, the second – by the stress. A ratio value of the nonlinear part of deformation with the quadratic tensor argument to the linear part, which reaches 0.3, shows the need for such equations. It also shows the influence of deformation on the relationship between the deviators.
To enhance capabilities of mathematical model is possible after including therein the equations for the spherical part of the tensor of deformation and stress, derived from the initial M. Rayner equations (M. Rheology. - M.: Nauka (Science), 1965. 223 pp.). To bring together the non-linearity of the relationship between deviators with nonlinearity between the spherical tensor of stresses and deformations, parameters are introduced. To define them is developed a technique. The parameters as the functions of a stress-state angle are defined by the selection of their values when the theoretical curves in the best way overlay the experimental curves for secant moduli and coefficients of transverse deformations
This experimental data processing procedure allows us to find both the parameters and the bulk compression modulus. Parameters allow us to more accurately reflect the changing bulk deformation and mean (hydrostatic) stress.
Graphs present all the features and parameters found. Using them, we have obtained dependences for ratios of dilatancies to the value of maximum dilatancy in tension. As a result, dependence of ratios on deformations can be graphically shown for different types of stress-state. To check calculations are presented three theoretical curves for the mean stress - maximum stress ratio (mean stress module in compression) to compare them with the corresponding theoretical curves, which define the mean stress as the third part of the stress along the axis of the specimen in tension or compression. Their overlapping each other proves the non-contradiction of a relation equation of the spherical tensors and the accuracy of determining parameters, which define dilatancy, according to stress. The paper shows how the ratio of these dilatancies to the value of maximum dilatancy in tension depends on the deformation for different angles of the stress-state.
Using a mathematical model that takes into consideration the features of unstable media, the accounting for non-linearity with defining tensor dilatancy allows us to find a logical approach to defining the relationships between dilatancies and deformation and strength properties. This is achieved by using tensor - nonlinear equations which include the non-linear characteristics and parameters. The latter refine the calculation of the strength characteristics through the use of information about the additional bulk deformation and additional mean stress.
The main results of the work are as follows:
a) characteristics of deformation and characteristics in the main directions, taking into account the dependence of the composite properties on the level and type of stress-state, are defined;
b) is shown that to the tensor ratios of deviators relation are needed equations for bulk deformation and mean stress, with parameters depending on the type of stress-state, which allow to assess the effects of dilatancy caused by the loss of bonds at the surface of the metal filler;
c) a technique is developed to determine parameters intended to bring the theoretical curves into line with the experimental ones for the bulk deformation and the mean stress, taking into consideration the detected change of the composite structure;
d) limits of deformation and stress dilatancy as a function of the angle of the stress-state are investigated, and the possibility to use information about them ,as the convenient indicators to assess the applicability of the classical strength hypotheses, is shown.