Copyright © 202 2 V.V. Aulin, S.V. Lysenko, A.V. Hrynkiv, O.D. Derkach, D.O. Makarenko, This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Problems of Tribology, V. 27, No 2/104-2022, 71-79 Problems of Tribology Website: http://tribology.khnu.km.ua/index.php/ProbTrib E-mail: tribosenator@gmail.com DOI: https://doi.org/10.31891/2079-1372-2022-104-2-71-79 Influence of high-modulus filler content on critical load on tribocouples made of microheterophase polymer composite materials V.V. Aulin1* , S.V. Lysenko1 , A.V. Hrynkiv1 , O. D. Derkach2 , D.O. Makarenko2 1 Central Ukrainian National Technical University , Ukraine 2 Dnipro State Agrarian And Economic University, Ukraine * E-mail: AulinVV @ gmail.com Received: 10 April 2022: Revised: 15 May 2022: Accept: 05 June 2022 Abstract The influence of the content of high-modulus filler on the assessment of the critical load on the conjugation of polymeric composite materials is theoretically substantiated from the tribological point of view. Various cases of destruction of polymeric composite materials are considered. The conditions under which the setting of polymeric composite materials is observed, as well as the conditions of their destruction are formulated. Both viscous and brittle fracture of polymeric composite materials are considered. The main focus is on critical loads and stresses depending on the content of high-modulus filler, taking into account the modulus of elasticity of the polymer matrix and filler and the nature of their destruction. Key words: polymer composite material, microheterophase composite, high modulus filler, triad coupling of parts, critical load, setting, failure Introduction When the influence of the structure and composition of polymer composite materials (PCM) on the value of the critical pressure should be considered in the contacts of different types of microheterophase composites. In this case, the size of the structural components of PCM is much smaller than the size of the contact spot, and therefore we can consider the contact of two PCM as the contact of homogeneous materials [1]. In such PCM, the physico-mechanical and tribological properties of the friction surfaces depend on a number of factors. Conditions for efficient operation of triad couplings of parts with PCM at a critical setting load depend on the following factors [2]: – volume content of high-modulus filler of conjugated PCM of the same phase composition and with the same volume content; – differences in the volumetric content of the high-modulus filler when contacting conjugate parts with PCM of the same phase composition; – physical-mechanical and tribological properties of structural components of PCM conjugations with the same volume content of fillers; – physical-mechanical and tribological properties of structural components of PCM conjugations at different volume content of fillers; – bond strength of filler particles with the matrix in PCM; – particle size of fillers. Consideration of these factors will make it possible to design the PCM in accordance with the operating conditions of the moving couplings of machine parts, without reaching the critical values of the load and the observation of setting and failure. Literature review http://creativecommons.org/licenses/by/3.0/ http://tribology.khnu.km.ua/index.php/ProbTrib https://doi.org/10.31891/2079-1372-2022-104-2-71-79 72 Problems of Tribology By introducing particles of brittle high-modulus fillers into the plastic polymer matrix, the nature of deformation and destruction of PCM with increasing their bulk content f с will change [1,2]. The low content (concentration) of high-modulus filler particles indicates that the yield strength T  PCM increases with f с increase, and elongation at destruction R  – decreases. As the yield strength of PCM in contact increases, the critical T  setting pressure cp for a single microroughness on the conjugate surfaces of the parts increases in accordance with the equation I.V. Kragelsky [3-6]: Tuc Cp  . (1) Since the geometry of roughness slightly depends on the properties of PCM [7-9] at low roughness of friction surfaces of conjugation of parts, it can be assumed that the geometry of their contact with increasing volume fraction of filler f с remains unchanged. With increasing f с plastic properties of R  PCM decrease according to equation [10]: NNN m j jMM MM     1 2121 (2) It was found that f с > 0.15 value R  changes f с slightly with increasing. In this regard, for PCM with f с >0.15 the ability of the irregularities of the conjugate surfaces of the parts to plastic deformation can be assumed to be almost the same [11,12]. The diameter of the contact spot for such PCM is about 1...5 μm. This indicates that the dislocation processes will not change dramatically with the change in the diameter of the contact spot. For PCM with f с >0.15 the value of the coefficient of proportionality иС can be assumed to be constant and in accordance with the recommendations of I.V. Kragelsky at a value equal to 3...4. The value of the critical pressure pc in tribocouples with microheterophase PCM will mainly depend on the value of the yield strength of the material T  . When strengthening polymeric materials with spherical incoherent filler particles, the yield strength is equal to: n fPCMPMT c /1   , (3) where 6,1n ; PCM – coefficient that takes into account the shear modulus and Burgers vector of the polymer matrix, as well as the size and shape of the filler particles in PCM [13,14]. For PCM with a small value f с when contacting irregularities of the same composition, the critical pressure in the triad couplings of the parts is:  n fPCMPMuc cCp /1   . (4) From the last equation it follows that at n>1 the increase in critical pressure pc with increasing fс gradually slows down. Note that the slowdown occurs the faster the value of n [15]. Despite the decrease in PCM elongation with increasing f с , such composites have a viscous nature of fracture, and therefore setting when reaching the pressure in tribocouples pc will occur mainly by the mechanism of active centers [16-18]. The destruction of the micro-irregularities of the conjugate surfaces of the gripping parts, when shifting one of them relative to the other will be cohesive in nature with the formation of growths on one of the surfaces, which in some cases can scratch or plow another surface. Note that the formation of such growths is possible with equal probability on both contacting directed surfaces of the parts and there are also traces of the process of plowing on the surfaces of the triad. Purpose The aim of this work is tribophysical theoretical substantiation of the influence of changes in the content of high modulus filler in polymer composite material on the magnitude and nature of changes in the critical pressure on the tribocoupling of materials and their critical stress when varying the modulus of elasticity of Problems of Tribology 73 polymer matrix and filler. Results As the filler content f с in the polymer matrix of the material of the tribocouple parts with the considered type of contact of their working surfaces increases, the critical setting pressure will increase, and the wear at pressures close to рс will decrease slightly. The latter suggests that with increasing value, the fс efficiency of tribocoupling of parts with PCM should increase, which indicates an increase in their tribological efficiency . It is possible to predict that in PCM there is such a filler content when the value of its yield strength exceeds the value of the yield strength. In this case, the viscous nature of the destruction of PCM will turn into brittle fracture fracture [13]. In this case, equation (1) will change and take the form: сс Вр  , (5) where B – the coefficient that for fragile materials takes into account the same parameters as the coefficient u C ; c – tensile strength of PCM. Since for this class of materials with a change in the f с value of B is likely to change slightly, the value of pc , as in the previous case, will mainly be determined by the value c . The dependence c on fс for PCM can be represented by the Kramer-Griffiths-Orovan equation:   rfpc kcAE  1 2  , (6) where pМ E – the modulus of elasticity of the polymeric material (PM), A and kr are the coefficients characterizing the structural and phase state of PCM. At high contents of the filler ( f с 0.6), taking into account the data [10-12] with a high probability we can assume that the modulus of elasticity of PCM can be estimated by the formula: ffр сЕЕ  , (7) where  – the coefficient experimentally determined for PCM or calculated from condition (2) for the lower limit, at f с =0,6: pMfpMfppMfpMfMpМ EcEcEECEcHE  )1())1(( . (8) It is also possible to write the following equations:   rffpfc kссАЕ  1 2  ; (9)   2 1 1 rffpfc kссАЕВp   . (10) From equation (10) it follows that with increasing the f с value of pc critical pressure in the tribocouples of parts should decrease. The moment of transition from the viscous nature of the destruction of PCM to brittle with increasing content of filler theoretically can not be estimated. At the same time, the value of p c with increasing fс passes through the maximum. This gives grounds to introduce the criterion of maximum bearing capacity of triad couplings of parts made of PCM. At the optimal value of the filler content fopt c , at which Т  = c , and the value BС и  . Equating the right parts of equations (4) and (10), we obtain:   2/1/1 ])1([ rfoptpopt n foptT kcAEc   . (11) 74 Problems of Tribology Hence we can find fopt c at which pc has a conditional maximum value of pc.opt . Since the foptc values in Т  the environment В  change smoothly, the value of pc will also change smoothly and the effective performance of PCM in triad couplings of parts can be realized in some interval fopt c . At friction of microroughness of conjugate surfaces of details can be in the conditions of comprehensive uneven compression that promotes manifestation of plasticity and effective values f с should be a little more than fopt c . Depending on the composition and particle size of the filler should be effective PCM with f с =0.6...0.9. With a relatively high content of brittle filler on conjugate surfaces, it is possible to observe cracks, and with less – traces of setting. When contacting PCM with different contents of the same filler, as for single-phase materials, the value of pc will depend on the nature of deformation and destruction of contacting PCM, as well as their modulus of elasticity. When contacting PCM with f с > fopt c value of pc will be determined by the strength of the more fragile PCM and the ratio of their modulus of elasticity. At these values of pc, the modulus of elasticity of PCM, with increasing f с , increases in dependence close to rectilinear, and c decreases along a smooth curve. In the case of a small increase in the filler content f с compared to fopt c can be expected to even increase the value of pc . In this case, the probability of setting by the mechanism of active centers with increasing EM of one of the materials of the parts will decrease, and the strength will decrease slightly. This is especially observed in conditions when the micro-irregularities of the conjugate surfaces of the parts are in uneven all-round compression, ie at small values of equilibrium roughness. In cases where the material of one of the parts f с is much more fopt c and pc will be lower than the pressure when the PCM has foptc . When contacting PCM conjugate parts with f с < fopt c in case of increase f с in one of the materials of the part, the value of pc will increase in all cases, because the values of the modulus of elasticity Ep and Т PCM with large f с will be higher, and accordingly will be lower and the probability of setting materials. In tribocouple contacts of parts in which one of the PCM has f с > fopt c and conjugate – f с < fopt c , the value of pc for tribocoupling will be determined by the same conditions as in the contacts of brittle single-phase polymeric material with plastic material. Since the values Т  in В  these PCMs are higher than in the polymer matrix and the brittle filler, respectively, the pc in such contacts will be higher than in the contact of the filler with the matrix. In addition, high values of the modulus of elasticity Ep PCM at fс > foptc will reduce the probability of setting on the mechanism of active centers. Since the number of active centers increases with increasing f с PCM under the condition f с > foptc , the values of pc will be higher the higher the content of filler f с in this PCM. However, in PCM under the condition f с < foptc we have: with increasing fс the resistance of the dislocations will increase, and the number of dislocations in the cluster before the boundary of the contact surfaces will decrease. The maximum value of p c in this type of contact will be when the value fс in one of the conjugations of parts with PCM is slightly smaller, and in the other – slightly larger fopt c . Analyzing the results of the dependence of pc on the content of high-modulus filler fс in different materials of the tribocouple parts, it can be noted that the highest values of pc should be expected when contacting them, provided that conjugate PCM have different filler content f с . Moreover, in one of the PCM the value f с should be close to foptc , and in the second - should be greater foptc by a value at which the effect of increasing the modulus of elasticity Ep in the tribocontact prevails over the effect of reduction с . Approximately can be f с taken equal to half the range of effective values when contacting PCM of the same composition ( f с = 0.75...0.85). Mechanical and tribological properties of matrix and filler materials, other things being equal, will also affect the value of pc . In such PCMs, according to the Kramer-Griffiths-Orovan equation , the values of the modulus of elasticity and the с PCM as a whole increase as the modulus of elasticity of the filler Epf increases. The value of pc will also increase with increasing Epf . The maximum value of pc will be in the PCM contacts, in which the same f с modulus of elasticity of the filler is maximum. Contacts of two conjugate PCMs with a low Problems of Tribology 75 value of Epf will be the least efficient. When the PCM is strengthened by the Ansell and Lenel mechanism [3,13,16-18] , the value с of the three-coupled parts increases with increasing shear modulus of the reinforcing phase and the volume fraction of filler particles in this phase. Under conditions of uneven comprehensive compression PCM with small values of constant elasticity of the filler Ef will be more prone to setting. To reduce the adhesion of conjugate PCM it is necessary to increase f с in both PCM; in contacts with such PCM the value of pc with increasing fс outside fopt c will increase to large values f с than in PCM with large modulus of elasticity of the filler Epf. Values pc for contacts in which one of the PCM has a filler content with a higher, and in the other – with a lower value of the modulus of elasticity Epf, ie should acquire intermediate values. For this type of PCM contacts with a smaller modulus of elasticity, the values с are smaller and to increase the efficiency of these PCM contacts with a smaller modulus of elasticity, the filler content should be closer to fopt c . In the case of PCM with a large modulus of elasticity Ep can be taken with both smaller and larger fopt c . Due to the fact that the probability of adhesion by the mechanism of active centers with increasing Ep decreases, it is more appropriate in such contacts in PCM with large Epf should take the value fс > foptc . The limit value f с in these contacts may be greater than in the contacts of two conjugate PCM with a larger Ep. With a large difference between Ep2 and Ep1 for PCM with large Ep effective are the following values of filler f с =0.95...0.98. Assuming that basically, the setting of the friction surfaces is determined by the mechanism of formation of the general step of microroughnesses, the value of pc can be estimated by equations of the type:                                        2/1 0 2/1 0 2/12/1 21)3/exp( 3 )3/exp( 3 2 c д f f Т c д c l l rTU V rTВ rTU V rTВ l l   . (12) Taking pc proportional  , we have:                                        2/1 0 2/1 0 2/12/1 21)3/exp( 3 )3/exp( 3 2 c д f f u Т c д uuc l l rTU V rTВ CrTU V rTВ l l CCp   . (13) Lack of data on the value of u C , д l , B , 0 U і f U 0 impossible to determine a specific value c p . However, it is known that the value c p is greater the greater 0 U and f U 0 . If we take into account the results of the study of the evolution of the structure of multiphase PCM, we can conclude that the deformation processes during friction PCM with fillers with low and medium modulus of elasticity more accurately describes the Ansell-Lenel mechanism [4-6]. Knowing the values of the average PCM stresses and fillers by the equations: 2/1 2          pp fM TMT cL bGG  ; 2/1 2          pp ff f f Mf TM f Tf cL bGG  , (14) you can estimate the value of pc when contacting two conjugate PCM:                                                            2/12/12/12/1 2 21 2 2 pp ff f f Mf TM f c d pp f f M TM c df c f с cL bGG GB l l cL bGG G l l BBр  . (15) From equation (15) it follows that to increase pc tribocoupled parts with PCM it is necessary to choose matrices with high ТМ  and shear modules G M , and fillers – with high modulus of elasticity and such content that the distance between particles lp close to its minimum value , in which the Ansell-Lenel mechanism still works. The value of lp equal to 1.5...2.5·10 –2 μm, at dp = 0.5...2 μm, is observed if the volume fraction of binding is 1...5% . 76 Problems of Tribology For tribocouples of parts made of PCM with a fragile matrix, the amount of stress can be estimated by the formula: 2/1 0 3 exp 3                    T kU V kTB B n    . (16) In this case: 2/1 2          pp BfM TMf cl bGG  . (17) Then the value of the critical filler can be estimated by the equation:                                                         2/1 0 2/1 2 21 3 exp 3 2 pp BfM TM f c d Bc df c f c cl bGG B l l Tk U V kTB l l BBp     . (18) From equation (18) it follows that in triad couplings of parts with PCM with a fragile matrix must have a high value of U0 , and the filler is a high modulus of elasticity, ie high modulus. The volume fraction of binding should strive for its minimum allowable value (1...5%). At high values of U0, the given tribocouples of parts with PCM on the value of the critical setting load may be more effective than tribocouples with a metal matrix. But by the criterion of fragile destruction, they will be inferior to tribocouples with a metal matrix. The strength of PCM is significantly influenced by the strength of the interfacial boundaries. As noted, the destruction of the interfacial boundary leads to the development of cracks or chipping PCM, the formation of micropores, followed by their fusion in viscous fracture. During friction, due to the presence of sliding conjugate surfaces, the role of the boundaries will depend on the depth of the filler particles in the surface layer of the PCM material. All particles that do not come to the surface of the contact spot will perform the same role as under the volumetric load of PCM. The filler particles coming to the surface of the contact spot during friction will specifically affect the behavior of the material in the contact spot. In the case where the destruction of the interfacial boundaries leads to the appearance of cracking cracks, a network of microcracks will develop on the surface of the contact spot and the bearing capacity of PCM surfaces will be determined by brittle fracture rather than setting, which will reduce pc. If micropores are formed during the destruction of the interfacial boundary, then at d p ≈1 μm they can positively affect the process of friction of the conjugation of parts. The newly formed pores serve as reservoirs for lubrication, which improves the regeneration of the lubricating distribution film on the friction surfaces, reduce the coefficients of friction and heat release in the contact zone, and, accordingly, reduce the likelihood of setting materials of conjugated parts. In this regard, weak interfacial boundaries can be allowed in cases where the destruction of the boundaries do not develop cracking cracks, ie only when using plastic matrices and with such a content of filler particles, when contacts between them are absent. This structure of the material at dp ≈1μm can be provided in the manufacture of PCM with f с < fopt c . In addition to improving the lubrication, in case of loss of filler particles, their strengthening effect will be reduced and there will be a positive gradient of shear resistance, which will improve the performance of triad coupling parts with PCM. When using such PCM filler particles with a high modulus of elasticity in the event of loss of most particles from the surface layer on a high modulus substrate, a plastic coating with a thickness of 1 μm is formed, which reduces friction and improves the performance of three-coupled parts. The value of pc in this case should not be greatly reduced, because the presence of a solid substrate in PCM will limit the ability of Frank-Reed sources and generate dislocations in a thin surface layer, and, accordingly, removing filler particles from the surface layer In order to prevent setting on the mechanism of formation of the general step, from such PCM it is necessary to make only one detail of tribocoupling, and the second – with the high-modulus filler with strong interphase borders. If we limit ourselves to the effect of improving the lubrication of surfaces due to the formation of micropores on them when the filler particles fall, it is more appropriate to create a combined PCM, when one part has strong interfacial boundaries and the other - weak. In such a PCM, particles with a strong interfacial boundary must have a high modulus of elasticity, and particles with a fragile boundary can have any value of the modulus of elasticity. This expands the number of materials that can be used as filler particles with weak interfacial boundaries and allows you to enter such particles not in one part, but in both conjugate parts, because the development of the setting process by both mechanisms will prevent filler particles with high modulus and elasticity high strength of interfacial boundaries. The role of the size and shape of the filler particles can be determined by two factors [10-12]: cracking of Problems of Tribology 77 particles and their ability to inhibit the movement of dislocations. It was previously shown that on the spots of actual contact, larger filler particles crack at smaller values  . However, the mechanism of hardening Orovana at f с < foptc and at the same time fс more effectively increase the size Т of the smaller filler particles. Therefore, from the position of cracking and setting at f с < fopt c more effective should be PCM with smaller reinforcing particles. However, due to the facilitation of the possibility of transverse sliding of the dislocation with decreasing rp, with rp slightly larger size of the dislocation nucleus r0, too small particles will be an inefficient barrier to dislocation and will develop plastic deformation of irregularities on conjugate surfaces, and with it the probability of setting. Since r0= 4b [15,18], the lower value of r h should be of the order of 5 · 10 –3 μm. Such particles are very difficult to obtain, so we can assume fopt c that f c with a decrease in the particle size of the filler, the critical setting load will often increase in the case of modern technological methods. In PCM, the f с value c increases foptc when the plastic deformation that develops at the crack tip covers a large volume, ie with a large particle size of the filler. But here the value of rp has its limits. When rp increases to a certain value, the crack does not bypass this particle in the plastic phase, but goes through the body of a large particle of brittle material. As a result р  , the Griffiths-Orovan equation decreases and the value c decreases. The maximum particle diameter of the filler should be at the level of 10...50 μm. From this analysis it follows that to increase the value of pc in PCM with fс < foptc particle size should be reduced, and in PCM with f с > fopt c – increase to 1...2 μm. With large diameters of filler particles, the nature of contacting the surfaces changes, so the critical setting pressure will be subject to other laws close to the laws inherent in single-phase materials. All of the above applies to PCM with a plastic matrix. Further, the possibility of increasing the value of pc in contacts involving PCM with a brittle matrix should be analyzed, because at close values of the coefficient of thermal expansion of the matrix and filler, not very large difference Ep (not more than 5 times), low temperatures PCM, small diameter filler particles (about 3.5...11 μm) and their small content ( f с <0.3) can increase the strength of PCM. Conclusions 1 . Thus, based on the strength of the interfacial boundaries, the most effective should be considered three-coupled parts that are made of PCM with high-modulus filler particles with strong interfacial boundaries. When using filler particles with weak interfacial boundaries, good results can be expected in the case of using high-modulus filler particles or a mixture of high-modulus particles and particles with a small modulus of elasticity. 2. It was found that PCM of microheterophase type based on brittle matrices have a strength close to the strength of single-phase brittle materials. The critical setting pressure depends on the same parameters on which the critical pressure of single-phase brittle materials considered for different types of contacts depends. 3. According to the criterion of critical setting pressure, the most effective should be considered triad- coupling of parts in which PCM one of the working surfaces has f с > foptc and the size of the filler particles approaching the upper limit of the size of the reinforcing particles, and the other PCM has f с < fopt c and the particle size the size of the reinforcing particles of the filler. 4. The role and forms of particles of high-modulus filler, as well as its content in the polymer matrix in the formation of the value of the critical load on the moving conjugation of parts are theoretically substantiated. References 1. Aulin, VV (2014). Fizychni osnovy protsesiv i staniv samoorhanizatsii v trybotekhnichnykh systemakh: monohrafiia [ Kirovohrad: TOV "KOD" ] 369 c. 2. Aulin VV (2015). Trybofizychni osnovy pidvyshchennia zosostiikosti detalei ta robochykh orhaniv silskohospodarskoi tekhniky [ dys. ... Dr. Tech. Science: 05.02.04 ] 360 p. 3. Aulin VV, Derkach OD, Makarenko DO, Hrynkiv AV (2018). Vplyv rezhymiv ekspluatatsii na znoshuvannia detalei, vyhotovlenykh z polimerno-kompozytnoho materialu [ Problems of tribology. №4 ] - P.65-69. 4 . Kabat, O., Sytar, V., Derkach, O., Sukhyy, K. (2021). Polymeric composite materials of tribotechnical purpose with a high level of physical, mechanical and thermal properties [ Chemistry and Chemical Technology, 15 (4) ] pp. 543-550. 5. Kabat, O., Makarenko, D., Derkach, O., Muranov, Y. (2021). Determining the influence of the filler on 78 Problems of Tribology the properties of structural thermalresistant polymeric materials based on phenylone C1 [ Eastern-European Journal of Enterprise Technologies, 5 (6-113) ] pp. 24-29. 6. Dudin, V., Makarenko, D., Derkach, O., Muranov, Y. (2021). Determining the effect of a filler on the properties of composite materials based on polytetrafluoroethylene for tribological conjugations in machines and mechanisms [ Eastern-European Journal of Enterprise Technologies, 4 (12-112) ] pp. 61-70. 7. Kobets, AS, Derkach, OD, Kabat, OS, Volovyk, IA, Kovalenko, VL, Kotok, VA, Verbitskiy, VV (2020). Investigation friction and wear of constructional plastics based on aromatic polyamide [ ARPN Journal of Engineering and Applied Sciences, 15 (10) ] pp. 1189-1195. 8. Kobets, AS, Derkach, OD, Kabat, OS, Kovalenko, VL, Kotok, VA (2019) . Recycling of constructional plastics with additives of exhausted polyethylene [ ARPN Journal of Engineering and Applied Sciences, 14 (13) ] pp. 2397-2406. 9. Kabat, OS, Kharchenko, BG, Derkach, OD, Artemchuk, VV, Babenko, VG (2019). Polymer composites based on fluoroplastic and method for the production thereof (2019) . [ Voprosy Khimii i Khimicheskoi Tekhnologii (3) ] pp. 116-122. 10. Aulin VV (2006). Pole napruzhen v kompozytsiinomu materiali ta kompozytsiinomu pokrytti v umovakh tertia kovzannia. [Coll. science. prats LNAU. Series: Technical Sciences. №.65 (88)] P.13-20. 11. Aulin VV (2004). Vyznachennia obiemnoho vmistu napovniuvacha v antyfryktsiinomu kompozytsiinomu pokrytti. [Mashynoznavstvo №7 (85)] pp. 49-53. 12. Aulin VV (2006). Vplyv kharakterystyk komponentiv kontaktuiuchykh kompozytsiinykh materialiv i pokryttiv na parametry ta vlastyvosti zony tertia [Problems of tribology. Khmelnytskyi. KhNU, №4 (42)] pp. 110-112. 13. Aulin VV, Hrynkiv AV, Smal VV, Lysenko SV ta in. (2021). Basic approaches and requirements for the design of tribological polymer composite materials with high-modulus fillers [ Problems of Tribology, V. 26, No 4 / 102-2021 ] P. 51-60. 14. Aulin VV, Derkach OD, Hrynkiv AV, Makarenko DO (2021) Vyznachennia robochoi temperatury kompozytnykh elementiv rukhomykh ziednan v zoni tertia [ Naukovyi visnyk Tavriiskoho derzhavnoho ahrotekhnolohichnoho universytetu: Vronnekove . 11, vol. 1, stattia21 ] . 1 5. Aulin V., Derkach O., Makarenko D., Khrynkiv A., Krutous D., Muranov E. (2020). Development of a system for diagnosing bearing assemblies with polymer parts during operation [ Technology audit and production reserves № 5/1 (55) ] рр.18-20. 16. Aulin V., Derkach O., Makarenko D., Hrynkiv A. and in. (2019). Analysis of tribological efficiency of movable junctions "polymeric-composite materials - steel" [ Eastern-European Journal of Enterprise Technologies. Vol. 4 (12-100) ] P. 6-15. 17. Aulin VV , Derkach OD, Kabat OS, Makarenko DO, Hrynkiv AV, Krutous DI (2020). Application of polymer composites in the design of agricultural machines for tillage [ Problems of Tribology, V. 25, No 2 / 96 - 2020 ] - P. 49-58. 18. Aulin V., Kobets A., Derkach O., Makarenko D., Hrynkiv A. and in. (2020). Design of mated parts using polymeric materials with enhanced tribotechnical characteristics [ Eastern-European Journal of Enterprise Technologies. Vol.5 (12-107) ] P. 49-57. 19. Aulin VV (2016). Trybofizychni osnovy pidvyshchennia nadiinosti mobilnoi silskohospodarskoi ta avtotransportnoi tekhniky tekhnolohiiamy trybotekhnichnoho vidnovlennia: monohrafiia [Kropyvnytskyi: Lysenko VF] 303 s. Problems of Tribology 79 Аулін В.В., Лисенко С.В., Гриньків А.В., Деркач О.Д., Макаренко Д.О. Вплив вмісту високомодульного наповнювача на критичне навантаження на трибоспряження з мікрогетерофазних полімерних композиційних матеріалів В роботі теоретично з трибологічної точки зору обґрунтовано вплив вмісту високомодульного наповнювача на оцінку критичного навантаження на спряження полімерних композитних матеріалів. При цьому розглядаються різні випадки руйнування полімерних композитних матеріалів. Сформульовані умови, при яких спостерігаються схоплювання полімерних композитних матеріалів, а також умови їх руйнування. Розглядається як в'язке, так і крихке руйнування полімерних композитних матеріалів. Основна увага зосереджена на критичних навантаженні і напруження в залежності від вмісту високомодульного наповнювача з урахуванням модулів пружності полімерної матриці і наповнювача та характеру їх руйнування. Ключові слова: полімерний композитний матеріал, мікрогетерофазний композит, високомодульний наповнювач, трибоспряження деталей, критичне навантаження, схоплювання, руйнування.