Об учете масштабных эффектов при моделировании механических и трибологических свойств двухфазных микро- и наномодифицированных полимерных покрытий

This work presents simulated mechanical and frictional properties of polymer composite materials derived from the ultra-high molecular weight polyethylenes which are widely used as units of friction and sealing elements in different types of modern technology and medicine. There authors considered the two-phase polymer composites obtained by modifying the high molecular weight polymers by introducing micro- and nanoinclusions. Such materials tend to clear manifestation of scale effects, consisting of the non-monotonic dependence of the mechanical properties and tribological characteristics on the inclusion concentration and on characteristic size of inclusions. In order to register the scale effects it is proposed in this work to use first order gradient models which describe not only the non-local (gradient) effects in volume but also interfacial effects that affect the formation of transition zones in the vicinity of phase boundaries. Scale and surface parameters of gradient model of mechanical properties allow to take into account the peculiarities of the considered modified polymers, associated with the fact that the effect of fillers on properties is determined not with the own properties of the filler, but with the change of polymer morphology, i.e. with the forming of polymer crystallization zones in the vicinity of particles of filler distributed in volume. In order to simulate scale effects on the frictional properties, we proposed a model based on the analogy of the friction coefficient of inhomogeneous surface structures with mechanical characteristics of compliance of inhomogeneous material, when the "weak" phase defines the effective properties. It is shown that the use of this analogy simultaneously with the use of relations for effective compliances of periodic two-phase composite, found under the gradient model of elasticity in the one-dimensional approximation, allows a good description of typical non-monotonic dependences of the friction coefficient on the concentration of filler for the considered polymer composites. It appears that the proposed equations will be useful for the prediction of the properties of designed anti-friction polymer coatings.