Effect of normal load on the temperature and velocity dependence of the force of friction for high-elastic materials

The problem of the effect of normal load on the temperature and velocity dependence of the force of friction is examined for rubbers based on SKN-18, SKN-26, and SKN-40. In the temperature range from 18°–100°C the force of friction for these rubbers falls linearly with increase in temperature. The effect of loads up to 10⁷N/cm² on the temperature dependence of the force of friction for SKN-18, SKN-26, and SKN-40 rubbers reduces to a change in the real contact area or an increase in the temperature dependence with increase in load.The velocity dependence of the force of friction for SKN-18 rubber reveals a weak dependence of the activation energy and the average "jump distance" of the molecular chains on specific load. In the low-velocity region the force of friction depends linearly on the logarithm of velocity, at velocities above 0.44 cm/min and pressures of 30×10⁵ N/cm² the force of friction increases sharply due to an increase in uncontrolled heating of the friction surfaces.Mekhanika Polimerov, Vol. 1, No. 4, pp. 123–129, 1965     

Maximum force of friction in rubber-metal friction pairs under conditions of constant compressive deformation of the rubber

The maximum force of friction at the initial moment of slip has been investigated on rubber-metal friction pairs under conditions of constant compressive deformation of the rubber during transition from the high-elastic to the glassy state. Filled butadiene-nitrile rubber compounds were studied in the temperature range from +20 to –50°C. The temperature dependence of the maximum force of friction has a sharply expressed maximum near the glass transition temperature. As the temperature falls, the force of friction at first increases, in accordance with the molecular-kinetic theory. As the temperature continues to fall, in the transition region the maximum force of friction begins to rise more sharply owing to a sharp increase in the volume-mechanical friction component. The fall in the maximum force of friction below the glass transition point associated with a decrease in the deformed volume of rubber due to shrinkage and with the reduced mechanical loss factor.Mekhanika Polimerov, Vol. 3, No. 3, pp. 533–538, 1967     

Morphology of fractured polymer surfaces self-bonded below the glass transition temperature

Previosly noncontact surfaces of polystyrene (PS) and poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) were self-bonded in a lap shear joint geometry below the glass transition temperature T_g The joints were then fractured in tension at room temperature and the contact area was analyzed by means of scanning electron microscopy. Zones of plastic deformation were revealed on the surfaces of PS and PPO which had been bonded at T_g–33 and T_g–70°C, respectively, thus indicating interdiffusion across the interface. This result points to the lower T_g of the surface layer as compared with that of the bulk sample, in agreement with our previous studies. The unusually high self-bonding ability of PPO (at very low temperatures related to the bulk T_g) is presumably due to the low depth of penetration required to establish entanglements.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 665–672, September–October, 1998.     

Modification of glass-filled polyamide 66 by reactive oligoorganosilane

Properties of glass-filled polyamide 66 modified by reactive oligoorganosilane were investigated. It was found that modification led to the improvement of the rheological properties of polyamide. The addition of the modifier decreased the glass transition temperature T_g of the polyamide from 60 to 50–59°C, without affecting the melting point. Composites modified by oligoorganosilane are characterized by higher (10–40°C) temperatures of onset and 50% weight loss as compared to the initial composite. It was found that chemical reaction of oligoorganosilane with polyamide and glass fibers took place during coextrusion of the modifier and polyamide, which formed firm chemical bonds between the polyamide and filler and thus favored a considerable improvement in the physicomechanical properties of the composite. The change in the structure and properties of the polyamide observed during modification by oligoorganosilane significantly affected its behavior during friction. The modification made it possible to increase the wear resistance of the composite 1.5 to 2 times and to decrease its friction coefficient from 0.38 to 0.27–0.33. It was also found that the ability of oligoorganosilane to react during its processing with water in the polyamide allowed for a significant decrease in the intensity of hydrolytic processes in the polymer. Because of this, the physicomechanical, rheological, and antifrictional properties of modified composites with an increased content of moisture (up to 3%) in the initial polyamide surpass similar characteristics of the composites containing no modifier, with not only enhanced but also optimum (0.2%) humidity of polymer granules.Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 545–553, July–August, 1998.     

Temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region

The possibility of using temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region is demonstrated and an additional applicability criterion — similar slopes of the isotherms of the amplitude dependences of the dynamic functions — is formulated. In the case of heavily filled rubbers it may be necessary to determine the constants of the Williams-Landel-Ferry equation and the reference temperature T_S from the experimental data — they may not coincide with the universal values. Master curves of the dynamic functions are obtained for a series of shock-absorbing rubbers at a shear strain amplitude =0.01.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 751–754, July–August, 1973.     

Effect of temperature on the fracture surfaces of filled systems based on SKS-85 butadiene-styrene copolymer

The tear fracture surfaces of mixtures of SKS-85 butadiene — styrene copolymer (85% styrene) with ordinary (carbon black, chalk) and polymeric (Kapron and cellophane powder) fillers have been investigated on the interval from –60 to +40°C. As the temperature varies within the limits of the glassy state (T_g SKS-85=+24°C) of the filled polymer, the nature of the fracture surface of specimens of filled mixtures, like that of the unfilled polymer, changes; in the region of the temperature transition of the copolymer associated with the mobility of the phenyl groups (–10±5°C) there is a slowing of the fracture process. At temperatures below the T_g of the copolymer the tear fracture surfaces of specimens of mixtures containing ordinary and polymeric fillers differ sharply. The introduction of fillers (20 vol. %) with a coefficient of thermal expansion different from that of the filled polymer considerably reduces the resistance of the material to fracture and leads to a sharp increase in the rate of crack propagation; the introduction of polymeric fillers with coefficients of thermal expansion similar to that of the filled polymer leads to an increase in the resistance of the material to fracture and to a decrease in the rate of crack propagation.Moscow Technological Institute of the Meat and Dairy Industry; State Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 5, pp. 819–826, September–October, 1969.     

Influence of temperature on frictional properties of highly elastic materials in vacuum under high normal pressures

Experimental results obtained by the rubbing of cross-linked rubbers against smooth steel surfaces in vacuum under volume compression conditions at high normal pressures are examined. The influence of volume compression on the frictional properties of highly elastic materials at various temperatures is explained. Basic rules of temperature functions of specific frictional force at high normal pressures in vacuum and in atmosphere are established.V. I. Lenin Moscow State Pedagogical Institute, Problem Laboratory for Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 91–97, January–February, 1972.     

Nature and mechanism of friction of rubberlike polymers in different physical states

We have investigated the frictional properties of crosslinked butadiene-nitrile and butadiene-styrene copolymers and natural rubber in friction against polished steel under vacuum conditions in the temperature interval from –200 to +150° C, which embraces the glassy and high-elastic states, as well as the transition region between them. The temperature dependence of polymer friction is characterized by two maxima, a principal and a low-temperature maximum. The principal maximum, observed in the glass transition region, is not associated with the mechanical loss maximum observed in the polymers themselves. The temperature dependence of the force of friction is composed of three parts. In the high-elastic region there is an increase in the force of friction with fall in temperature, in accordance with the molecular-kinetic theory of friction of rubberlike polymers. In this region the nature of friction is associated with mechanical losses in the surface layer of polymer. The mechanical losses inside the polymer itself are unimportant. The deviation from the theoretical curve and the fall in the force of friction below a certain temperature in the transition region are chiefly associated with a decrease in the actual area of contact as the polymer passes into the glassy state. In the glassy region the friction is significantly determined by the mechanical losses in the polymer itself associated with the repeated elastic and forced-elastic deformation of the asperities in the layer of polymer in contact with the rigid surface. Therefore the low-temperature maximum is closely related to the mechanical loss maximum observed in the same temperature region in dynamic tests. Apart from this, the friction maximum is also associated with the increase in the forces of adhesion and the reduction of the actual area of contact at temperatures at which a forced-elastic mechanism of compression of the polymer asperities is not realized.Mekhanika Polimerov, Vol. 3, No. 1, pp. 123–135, 1967     

Discriminant analysis for locally stationary processes

In this paper, we discuss discriminant analysis for locally stationary processes, which constitute a class of non-stationary processes. Consider the case where a locally stationary process {X_t,T} belongs to one of two categories described by two hypotheses π₁ and π₂. Here T is the length of the observed stretch. These hypotheses specify that {X_t,T} has time-varying spectral densities f(u,λ) and g(u,λ) under π₁ and π₂, respectively. Although Gaussianity of {X_t,T} is not assumed, we use a classification criterion D( f:g), which is an approximation of the Gaussian likelihood ratio for {X_t,T} between π₁ and π₂. Then it is shown that D( f:g) is consistent, i.e., the misclassification probabilities based on D( f:g) converge to zero as T→∞. Next, in the case when g(u,λ) is contiguous to f(u,λ), we evaluate the misclassification probabilities, and discuss non-Gaussian robustness of D( f:g). Because the spectra depend on time, the features of non-Gaussian robustness are different from those for stationary processes. It is also interesting to investigate the behavior of D( f:g) with respect to infinitesimal perturbations of the spectra. Introducing an influence function of D( f:g), we illuminate its infinitesimal behavior. Some numerical studies are given.     

Effect of temperature on the chemical relaxation process in rubbers

The effect of temperature on the chemical relaxation of rubbers has been investigated. With reference to nine industrial rubbers it has been shown that during storage in the stressed state (at =const) chemical relaxation is chiefly determined by two processes proceeding at different rates. Furthermore, the chemical relaxation of rubbers is determined not only by the rate constants of these two processes but also by the pre-exponential constants C_0i, the relationship between which varies with increase in temperature. It is possible to extrapolate the rate constants (k_i) and pre-exponential constants (C_0i) from elevated temperatures (110–50° C) to temperatures in the range 20–25° C. An equation is proposed that makes it possible to calculate the change in the elastic properties of rubbers in the stressed state at storage temperatures (20–25° C) by means of results obtained at elevated temperatures.Mekhanika Polimerov, Vol. 3, No. 3, pp. 448–454, 1967     

Temperature reversal of the reinforcing effect of fillers

A previous investigation [4] of the tear strength of filled systems based on SKS-85 butadiene-styrene copolymer over a broad temperature interval revealed a reversal of the reinforcing effect of fillers with a coefficient of thermal expansion different from that of the filled polymer. At Tg the strength of mixtures containing polymer fillers [Kapron (polycaprolactam) and cellophane powder] exceeds that of mixtures containing chalk and carbon black. The temperature reversal effect is attributed to the severe weakening of the adhesion of the polymer to the surface of the filler particles as a result of the concentration of shrinkage stresses in the polymer-filler contact zone. The presence of shrinkage stresses around the filler particles at Tg is qualitatively demonstrated on model systems using a photoelastic technique. Moreover, it is shown that the unbalance, and hence the residual stresses, in filled systems at temperatures below the glass transition temperature of the filled polymer is determined by the difference in the coefficients of thermal expansion.Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 4, pp. 579–583, July–August, 1969.     

Coboundaries in

Let T be an ergodic automorphism of a probability space, f a bounded measurable function, . It is shown that the property that the probabilities μ(|S_n(f)|>n) are of order n^−p roughly corresponds to the existence of an approximation in L^∞ of f by functions (coboundaries) g−g○T, gL^p. Similarly, the probabilities μ(|S_n(f)|>n) are exponentially small iff f can be approximated by coboundaries g−g○T where g have finite exponential moments.

Résumé

Soit T un automorphisme ergodique d'un espace probabilisé, f une fonction bornée mesurable et . Une correspondance est établie entre l'existence de l'estimation des probabilités μ(|S_n(f)|>n) d'ordre n^−p et l'existence de l'approximation dans L^∞ de la fonction f par des cobords g−g○T où g est “presque” dans L^p. De manière similaire, les probabilités μ(|S_n(f)|>n) sont d'ordre e^−cn, pour un certain c>0, n=1,2… , si et seulement si f admet une approximation dans L^∞ par des cobords g−g○T avec g ayant des moments exponentiels.     

Adhesion of polysulfone—Liquid crystalline polymer blends to fibers

The effect of modifying a thermostable thermoplastic matrix with a liquid-crystalline (LC) polymer on its adhesion to fibers was investigated. Poly(arylene sulfone), LC polyether, and blends of them of varying composition were used as the matrices, and high-strength steel wire 150 m in diameter and alkali-free glass fibers 150–300 m in diameter were the substrates. The adhesive shear strength , measured by the pull-out method, was used as the measure of adhesion. The samples were formed at a temperature of T_f=300°C, and the heat treatment time t_f varied from 15 min to 2 h. It was found that when the values of t_f increased, the dependence –t_f was described by a curve with a maximum. The maximum was observed for t_f=30 min. The adhesive strength at the bonds of the poly(arylene sulfone) with the steel wire was sufficiently high (comparable to the adhesive strength of epoxy—4,4-isopropylidenediphenol matrices). The adhesive strength of the LC polyether with the steel wire was much lower. The strength of the interface of poly(arylene sulfone), LC polyether, and blends in bonds with the steel wire was much higher than in bonds with the glass fiber. The adhesive strength of the blends as a function of the concentration of LC polyether was described by a curve with a maximum. The maximum adhesive strength with fibers was provided by matrices containing 2–7% LC polyether.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 433–442, July–August, 1997.     

A note on differential operators of infinite order

A sufficient condition for entire functions f and g to be such that the series ∑_m=0^∞f^(m)(0)g^(m)/m! represents an entire function is established; and in that case, the growth of the resulting function is described.     

Some laws of plastics friction

The dependence of the actual contact area S of plastics on temperature, specific load, and sliding speed has been investigated. The value of S increases exponentially with the specific load, the maximum value at large specific loads being less than the nominal contact area. The temperature dependence of S under static conditions between 20 and 130° C is attributable to the decrease in the static modulus of elasticity of the plastic near the glass transition point and to the development of high-elastic and plastic deformations at elevated temperatures. There is practically no change in S as the sliding speed varies from 10^–3 to 10 cm/min; at the same time the force of friction increases slightly.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1078–1081, 1967     

Arithmetical identities of the Brauer-Rademacher type

Summary LetA be a regular arithmetical convolution andk a positive integer. LetA _k (r) = {d: d ^k A(r ^k )}, and letf A _k g denote the convolution of arithmetical functionsf andg with respect toA _k . A pair (f, g) of arithmetical functions is calledadmissible if(f A _k g)(m) 0 for allm and if the functions satisfy an arithmetical functional equation which generalizes the Brauer—Rademacher identity. Necessary and sufficient conditions are found for a pair (f, g) of multiplicative functions to be admissible, and it follows that, if(f A _k g)(m) 0 f(m) for allm, then (f, g) is admissible if and only if itsdual pair (f A _k g, g ^–1 ) is admissible.Iff andg ^–1 areA _k -multiplicative (a condition stronger than being multiplicative), and(f A _k g)(m) 0 for allm, then (f, g) is admissible, calledCohen admissible. Its dual pair is calledSubbarao admissible. If (f A _k g) ^–1 (m) 0 itsinverse pair (g ^–1 , f ^–1 ) is also Cohen admissible.Ifg is a multiplicative function then there exists a multiplicative functionf such that the pair (f, g) is admissible if and only if for everyA _k -primitive prime powerp ⁱ either (i)g(p ⁱ ) 0 or (ii)g(p ) = 0 for allp havingA _k -type equal tot. There is a similar kind of characterization of the multiplicative functions which are first components of admissible pairs of multiplicative functions. IfA _k is not the unitary convolution, then there exist multiplicative functionsg which satisfy (i) and are such that neitherg norg ^–1 isA _k -multiplicative: hence there exist admissible pairs of multiplicative functions which are neither Cohen admissible nor Subbarao admissible.An arithmetical functionf is said to be anA _k -totient if there areA _k -multiplicative functionsf _T andf _V such thatf = f _T A _k f _V ^-1 Iff andg areA _k -totients with(f A _k g)(m) 0 for allm, and iff _V = g _T , then the pair (f, g) is admissible. The class of such admissible pairs includes many pairs which are neither Cohen admissible nor Subbarao admissible. If (f, g) is a pair in this class, and iff(m), (f A _k g) ^–1 (m), g ^–1 (m),f ^–1 (m) andg(m) are all nonzero for allm, then its dual, its inverse, the dual of its inverse, the inverse of its dual and the inverse of the dual of its inverse are also admissible, and in many cases these six pairs are distinct.A number of related results, and many examples, are given.     

On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means

The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss–Weierstrass, Abel–Poisson, and Bochner–Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceB^s_{p, p}, 1<p<∞, 0<s<1, thenT_mtf (x)−f(x)=o_x(t^s) a.e. ast→0+.     

Effect of the physical state on tearing of amorphous polymers

The temperature dependence of the basic tear characteristics of deformation and failure of SKS-85 copolymer in the range from Tg to T>T_f is examined. It is established that the total work done in tearing the polymer in the brittle state is determined by the work of deformation up to separation of the specimen into two parts. In contrast to this, the total work done in tearing the polymer in the high-elastic state is determined mainly by the work of formation of the tear surface.Mekhanika Polimerov, Vol. 1, No. 5, pp. 71–77, 1965     

Interdiffusion and adhesion at the inteface of a polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blend below the glass transition temperature

Experiments on adhesion between the film surfaces of a polystyrene (PS)-poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) blend were carried out below the glass transition temperature of the bulk (T _g ), at T=T _g −13 and T=T _g −23°C. The contact time varied from 2 to 1440 min. The strength at the interface was then measured at room temperature. The strength at the blend-blend interface was calculated using an additive diffusion model which takes into account the strength at homopolymer-homopolymer interfaces (PS-PS, PS-PPO, and PPO-PPO), surface concentration of components, and its variation with depth. A fair agreement between the calculated and measured strength was found. The results of the study support the concept of decreasing glass transition temperature near the surface of polymer glasses as compared with T _g of the bulk. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 661–670, September–October, 1999.