CONGRUENCE LAW OF PROPERTIES
The law of congruence establishes that, with optimal structures between the properties of the binder and the conglomerate based on it, or between the properties of different conglomerates based on the common binder, or between the properties of different conglomerates based on various binders, there is an obligatory correspondence. This law means that when the quality of the binder is improved or reduced, the corresponding changes also occur with the quality of the conglomerate made on its basis, which is quantitatively estimated by means of design formulas (strength, elastic strains, etc.). Naturally, such a regularity is valid only for materials of the optimal structure. In non-optimal structures, conglomerates of inferior quality are often obtained even with the improvement of the binder, for example, with a higher grade of cement in concrete. This law once again emphasizes that only the optimization of the structure ensures the closest interconnection of measures to improve the binding agent (matrix) substance and to improve the quality of the conglomerate on its basis. In this relationship, the key linking element is the filling component, the significance of which is reflected in the exponents n and t of the general strength formula. The specific nature of the measures depends on the variety of binding material and aggregate, but a certain benefit always comes from: increasing the dispersity of the particles of the solid phase; the use of additives (additives) directed action; processing with the help of physical activators, etc.
A stable congruence of properties between ICS and its knitting part is expressed by the formulas
where x - (c// φ)/(c */φ); X2 = (C 2 /ph)/(c */f); La and Rb are the strengths of the two ICS of the optimal structure, made on the basis of the same binder (Figure 3.11, a, b).
A similar expression exists for the transition from one family of curves with a common astringent at the point M (R, cj/φ) to another family of curves with a new common astringent at the point c ' 2 /ph):
The corresponding notation is shown in Fig. 3.11, in.
Each homocentric bundle (a family of curves) originating from the points Mi, Mi, ..., Mn, is characterized by different initial materials, technological parameters, etc. But the points Mi, M2, ..., Mn can also refer to a single astringent substance, but with a difference in aggregates or major process parameters adopted for the manufacture of ICS. Consequently, the congruence law establishes the fundamental possibility of the relationship between the strength properties of various conglomerates.
Fig. 3.11. Graphs of the action of the congruence law:
a - with one binder and one filler; b - with one binder and two fill gels;
in - with two binders and two placeholders
In similar correspondences there are conglomerates of optimal structures and other indicators of mechanical and some physical properties that are sensitive to structural changes.
A side effect of the general strength formula and the congruence law is the relationship between the activity of the astringent matrix substance and its quantity in the ICS of the optimal structure. The numerical dependence is expressed by the formula obtained from the two proportionality equations: = kR * and R = kgM, in
which Rue * is the design strength of the optimal structure, k - the coefficient (dimensionless) that establishes the correspondence between the values of the design strength of the binding agent and the conglomerate; kg is the coefficient (dimensional, MPa), which establishes the correspondence of the consumption of the matrix substance to obtain the given strength of the ICS at a strict phase ratio and to ensure its optimal structure; M = c + φ - the amount of matrix (astringent) substance in fractions of a unit of mass of the binding component, determined with allowance for (3.5); type - exponents, determined from experimental data.
Multiplying both proportionality equations and the subsequent extraction of quasilongicons is obtained
where kg = l] to 1 -c 2 with (c/f) from the general strength formula.
From the formula (3.13) follows expediency of all-round increase of the calculated activity (strength) of the binder to reduce its consumption in the construction conglomerate of the optimal structure.
The law of congruence allows one to aim to improve production, to open new materials with predetermined and, moreover, extreme properties, to predict the parameters of the conglomerate according to the design strength of the binder, to find the calculated activity of the binder, that is, its future matrix substance optimal structure.
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