Issue 41

E. Nurullaev et alii, Frattura ed Integrità Strutturale, 41 (2017) 369-377; DOI: 10.3221/IGF-ESIS.41.48 371 where accumulation kinetics of internal composite damage as lamination between the polymer binder and filler particles is described in Gaussian function; n – quantity of volume fractions φ i of delaminated dispersed filler fractions (types);        / 0.5 t i i si – function parameter, α 0.5 i – sample elongation corresponding to the half volume of delaminated particles with i –type filler fraction (type),  si – mean-square dispersion for i –type filler fraction (type). Value α 0.5 i determines delimitation initiation,  si characterizes composite integrity violation rate. As long as there is no the interfacial Delamination in the elastomeric composite, limiting (rupturing) mechanical characteristics σ b , α b can be evaluated by considering of deformation rate and size of average polymer binder interlayer between filler solids:                            0 3 3 3 3 1 ; 0 f m m f b b m m where indexes « f » and « o » stand for filled and free state elastomeric, respectively. In terms of rupturing deformation the following relation results:         0 3 1 f m b b Value  0 b is derived out of the curve      0 f eff b which was obtained earlier by summarizing of multiple experimental data [1]. Effective concentration of transverse bonds is equal to the total concentrations of chemical (determinant for 3D- linking of initial linear polymers) and physical (intermolecular, depending on polymer structure and experiment temperature) bonds:                               1/3 1/3 3 2 (1 ) 1 29exp 0,225 10 ( ) T T g eff ch r ph ch r For example, if ν eff =1 mol/m 3 and T= 293 K rupturing deformation of 3D-linked elastomeric binder  0 b is almost 1000%. Stated curve is part of the computer program as a calibrating one [8]. If sample integrity has been damaged up to the rupture, limiting mechanical characteristics are maximum point values for hump-shaped tension diagrams (σ max , ε max ) or values of constrained maximum point assuring serviceability of partly disrupted composite, despite of possible sample tension. To evaluate dependence of material service time from internal damage level of filled polymer composite material by tension, we use envelopes of sample fracture points if no laminations (σ b , ε b ) or maximum points mentioned above (σ max , ε max ). These envelopes were introduced by Smith as following dependences “logσ b, max – logε b , max ” [9, 10]. Problem of fractional composition optimization for dispersed components of polymer material (for given average particle sizes) considering fulfillment of optimization conditions for other performance characteristics could be defined in the following nonlinear programming statement:          ( , , ) max; min; min; q d E m r r               ... ; 1 2 3 1 m j opt jv j j j j jm j v           min max 0 1, 1, 2, 3, ..., if ; v m I jv jv jv j j n       / , / opt x j opt j opt j x j j j I n where     , , q d are vectors of volume fractions, porosities and particle sizes of dispersed components in the polymer material, respectively,  opt j is optimal volume fraction of the filler in the composition, φ jv – volume fraction of v -th fraction with j -type filler in the composition, m j – fraction number of j -type dispersed component,   min max , jv jv are upper and lower limits for solids volume fractions in the composition, respectively, opt x j is optimum mass concentration of solid