2_Kaplun.doc Calculation of wear resistance and durability of structural elements with gradient diffusive coatings and metastable phases in the structure ... Проблеми трибології (Problems of Tribology) 2014, № 2 12 Kaplun V.,* Gonchar V.,* Kaplun P.,* Matviishyn P.** *Khmelnitsky National University, Khmelnitsky, Ukraine, **Berezhany Agrotechnical Institute, Berezhany, Ukraine E-mail: kaplun@datasvit.km.ua CALCULATION OF WEAR RESISTANCE AND DURABILITY OF STRUCTURAL ELEMENTS WITH GRADIENT DIFFUSIVE COATINGS AND METASTABLE PHASES IN THE STRUCTURE OF MATERIALS УДК. 621.891 Method of calculating of the durability and longevity of structural elements with gradient coatings and metastable phases in the structure of materials after ion nitriding and subsequent quenching to yield the residual nitrogen austenite is presented. Key words: residual austenite, wear, durability, nitriding, glow discharge Introduction Research by many authors [1; 2] shows that the presence of metastable residual austenite in the structure of material has a positive impact on improving of the durability of structural elements in abrasive environment. Under the influence of deformation the metastable austenite is converted into other phases, thus the energy of activation is absorbed, which leads to a slowdown of the fracture in wear. Methods of chemical and thermal processing – nitriding, carburizing, borating and others are widely used in order to improve the wear resistance and durability of structural elements in friction and wear. Thus the diffusive gradient coatings with improved tribological properties are formed on the surface. Operating experience of structural elements in friction shows that the most effective method of chemical and thermal processing is nitriding in a glow discharge [3; 7]. However, the literature is not driven the methodology of calculating of the durability of diffusive coatings with metastable phases in the structure of the material. Nitrided layers consist of nitride zone with stable structure and hardness and transitive zone (zone of internal nitriding) with variable hardness and nitrogen concentration in depth, which decreases from the surface to the base by the exponential dependence (1) and depends on technological parameters of the process of nitriding [8] (Fig. 1). 0 Hi H0 Hí Hv hhн hв hi hn 1 2 α P (h H1 н н, ) P (h H2 n 0, ) Fig. 1 – Distribution of hardness through the thickness of the nitrided layer: 1 – on linear dependence; 2 – by an exponential dependence ( ) )(04max0 321 in i hhkkk h i eHkHHН −⋅⋅⋅⋅−⋅+= , (1) mailto:kaplun@datasvit.km.ua Calculation of wear resistance and durability of structural elements with gradient diffusive coatings and metastable phases in the structure ... Проблеми трибології (Problems of Tribology) 2014, № 2 13 where 0H – the hardness of the base; maxH – surface hardness of the nitrided layer in optimally nitriding; iH – hardness of i-ty layer at a distance ih from the surface; nh – the thickness of the nitrided layer, which is the sum of the thickness of nitride zone нh and the zone of internal nitriding вh ; 4321 ,,, kkkk – coefficients that depend on the technological parameters of nitriding process (temperature, pressure, medium composition and time of diffusion saturation). Mean hardness of zone of internal nitriding can be found by the formula: нn h h i св hh dhH Н в н − = ∫ .. , (2) where нh and вh – thickness of the nitride zone and the zone of internal nitriding, respectively; iH – hardness of the nitrided layer at a distance ih from the surface In case when a change of hardness by depth zone of internal nitriding to approximate by linear dependence of hardness on thickness вh (Fig. 1), the average hardness cH of internal nitriding zone is defined by the formula: 2 0НHH нс + = , (3) Given the characteristics of the nitrided layer with nitride zone, a zone of internal nitriding and contain residual austenite, we obtain the generalized multifactor model of abrasive wear for each of the zones of the nitrided layer. Basic materіal The calculation of the intensity of wear materials with metastable phases in their structure and nitrided layers on the surface will be carried out in three stages. The first stage we make a list of all determining and determined quantities with their dimensions. Quantities that are determined will be: the intensity of wear of nitride zone – н н н J dL dU = and intensity of wear zone of internal nitriding в в в J dL dU = , where нU and нL – wear and the way of friction in nitride zone (μm), вU and вL – wear and friction path in the zone of internal nitriding (μm). Determining quantities or the main factors affecting the abrasive wear are: maxP – maximum pressure in the material cylinder, MPa; f – coefficient of friction; δ – clearance between the screw and the cylinder, μm; χ – diameter of cutting abrasive particle, μm; А – percentage of residual austenite in the material,%; aH – microhardness of abrasive, MPa; eT – temperature of extrusion, оС; qT – temperature of quenching, оС; нH – microhardness of nitride zone, MPa; вH – microhardness of zone of internal nitriding, MPa; 0H – microhardness of base, MPa; cH – average microhardness of zone of internal nitriding, MPa; In the second stage of the theory of similarity and dimension (TSD) we make dimensionless complexes from determining and determined quantities. In our case, taking into account the working conditions of the Calculation of wear resistance and durability of structural elements with gradient diffusive coatings and metastable phases in the structure ... Проблеми трибології (Problems of Tribology) 2014, № 2 14 extruder during processing feed grains with the addition of minerals containing abrasive particles, the intensity of wear for each of the zones can be expressed as the product of the following complexes: 11111 z T m Нн n A y см х нwнн н н ПППППkJ dL dU ⋅⋅⋅⋅⋅== , (4) 11111 z T m Нв n A y см х вwвв в в ПППППkJ dL dU ⋅⋅⋅⋅⋅== , (4, а) where 11111 ,,,,,, zmnyxkk wнwв – coefficients which are deterdmined from the experiment with regard to operating conditions. Complexes: н н H fР П ⋅ = max ; (5) с в H fР П ⋅ = max , (5, а) characterizing the stress state of contact and the dimensionless area of contact bodies. Complex: χ δ =смП , (6) which takes into account the influence of the size of clearance and the size of the abrasive. Dimensionless complex: AА KcAbАаП =+⋅+⋅= 2 , (7) where а, b, с – coefficients for each material from experiment on wear; AK – coefficient taking into account the influence of content of austenite А in the structure of the material on wear (parabolic dependence). Complex: H M a H KH H П == , (8) HK – coefficient which takes into account the effect of the hardness of the abrasive material on wear. Complex: Т q е T KT T П == , (9) TK – coefficient which takes into account the effect of temperature on wear. In the third stage of the method of TSD experiment we set relationships between dimensionless complexes that serve as similarity criteria: 11 1 11 max z q e m H an A yx н wнн T T H H K H fР kJ         ⋅      ⋅⋅      χ δ ⋅      ⋅ ⋅= ; (10) 11 1 11 max z q e m с an A yx с wвв T T H H K H fР kJ         ⋅      ⋅⋅      χ δ ⋅      ⋅ ⋅= , (10, а) For the conditions of abrasive wear 1x = 1 [9]; to avoid jamming between the screw and the cylinder we take constructively δ = χ; by [1] 1n = 1; 1m = 0,8 and 1z = 0,1 for steel Х12 (Table 1) according to the data [2]. Then: 2,085,0max ТHнA н wнн KKKH fР kJ ⋅⋅⋅      ⋅ ⋅= ; (11) 2,085,0max ТHвA с wвв KKKH fР kJ ⋅⋅⋅      ⋅ ⋅= , (11, а) Calculation of wear resistance and durability of structural elements with gradient diffusive coatings and metastable phases in the structure ... Проблеми трибології (Problems of Tribology) 2014, № 2 15 Table 1 Chemical composition of steel X12 Chemical composition, % Steel grade C Mn Cr Si Ni S P Cu X12 2,1 0,35 12 0,2 < 0,35 < 0,03 < 0,03 < 0,3 Coefficient wнwв kk , are found by the formula: н нн wн LfР НU k 1max 1 ⋅⋅ ⋅ = ; (12) в св wв LfР НU k 1max 1 ⋅⋅ ⋅ = , (12, а) where нU (μm) – wear in the nitride zone on the way нL (μm); вU (μm) – wear in the area of internal nitriding on the way of friction вL (μm). After the experiment, knowing ввнн LULU 1111 ,,, by formulas (12) and (12, a), we find wнwв kk , . For materials with gradient coatings the intensity of their wear is variable. Therefore, the durability of D coatings can be expressed: in linear units of the way of friction LD : в в н н L J h J h D += m, (13) Or in hours tD :       +⋅ ⋅⋅ = в в н н t J h J h V D 3106,3 1 hours, (13а) where V – sliding speed, m/s; нh and вh – thickness of the nitride zone and the zone of internal nitriding expressed in meters. In case when the value of allowable wear h is greater than the thickness of the nitrided layer, we calculate the durability of parts by the following dependencies: 0J hhh J h J h D вн в в н н L −− ++= m, (14) Or in hours tD :       −− ++⋅ ⋅⋅ = 0 3106,3 1 J hhh J h J h V D вн в в н н t hours, (14а) where 0J – the intensity of wear of the basic material. Summary To calculate the tribological characteristics and durability of structural elements with gradient coatings and metastable phases in the material structure the following method is recommended. We conduct calculations in the following sequence in accordance with the method of the theory of similarity and dimension (TSD): 1. We make up a list of quantities that determined with their dimensions. For materials without coating value, which is determined will be the intensity of wear:, where U – is wear and tear in μm, L – the way of friction in μm. For materials with gradient coatings obtained by nitriding, the values, which are determined will be the following figures: the intensity of wear of nitride zone – н н н J dL dU = and the intensity of wear zone of internal nitriding в в в J dL dU = , where нU and нL – wear and the way of friction in nitride zone (μm), вU and вL – wear and the way of friction in the zone of internal nitriding (μm). Calculation of wear resistance and durability of structural elements with gradient diffusive coatings and metastable phases in the structure ... Проблеми трибології (Problems of Tribology) 2014, № 2 16 2. We make up a list of determining quantities, or the main factors affecting the abrasive wear with their dimensions. From the experimental conditions we determine pressure maxP , coefficient of friction of sliding f, temperature of quenching qT and wear eT , size of the clearance δ and size of the abrasive particles χ and hardness aH . Based on metallographic studies of experimental models we find: percentage of residual austenite in the material, microhardness of nitride zone нH , microhardness of zone of internal nitriding вH , microhardness of basis 0H . 3. From determining and determined quantities we make up dimensionless complexes. 4. After the experiment we set the relationship between dimensionless complexes that serve as similarity criteria (4) and (4, а). 5. Knowing the basic values of determining quantities, we conduct tests for wear. On the basis of these tests and published data we find the coefficients 11111 ,,,,,, zmnyxkk wнwв and intensity of wear of the friction surface by dependencies (11) and (11, а). 6. Knowing the quantity of allowable wear we find the durability of structural elements strengthened by this technology (we find by dependencies): (13), (13, а), (14), (14, а). Deviations of calculated values of the intensity of wear and durability of materials with gradient coatings and metastable phases in their structure during abrasive wear are 11 % - 19 % of experimental data. References 1. Popov V.S. Durability of equipment of refractory production / V. S. Popov, N. N. Brуkov, N. S. Dmitrichenko, P. G. Pristupa // М. : Metalurgija. – 1978. – 232 s. 2. Brykov N.N. Effect of conditions on the degree of hardening and durability of metastable austenitic alloys / N. N. Brykov, G. A. Pugachev, M. N. Brykov // Problems of Tribology. – 2003. – № 3. – S.157–172. 3. Lahtin J. M. Nitriding of steel / J. M. Lahtin, J. D. Kogan. – M. : Mashinostrojenije, 1976. – 256 s. 4. Chemical and thermal treatment of metals and alloys. Handbook / ed. L. S. Lyahovicha. – M. : Mashinostrojenije, 1981. – 420 s. 5. Kaplun V.G. Advanced technologies of hardening of structural elements / V. G. Kaplun, P.V. Kaplun // Modern technology in engineering. – Har’kiv : NTU «HPI», 2007. – S. 388–403. 6. Kartinskij C.T. Technological parameters of the ion nitriding // Journal of engineering. – 1979. – №12. – S. 56–58. 7. Pastuh I.M. Theory and Practice of hydrogen-nitriding in a glow discharge. – Har’kiv : NEC HFTI. – 2006. – 364 s. 8. Kaplun V.G. Mathematical modeling of regularities of hardness distribution through the thickness of the nitrided layer with nitriding in a glow discharge / V. G. Kaplun, P. V. Kaplun, V. A. Gonchar // Herald of Khmelnitsky National University. – Engineering. – Khmelnyc’kij. – 2012. – №3. – S. 7–10. 9. Khrushchev M. M. Abrasive wear / M. M. Hrushhev, M. A. Babichev. – M. : Nauka. – 1970. – 252 s. Поступила в редакцію 03.03.2014 Каплун В, Гончар В., Каплун П., Матвіїшин П. Розрахунок зносостійкості і довговічністі структурних елементів конструкцій з градієнтними дифузійними покриттями і метастабільними фазами в структурі матеріалів. Представлено методика розрахунку зносостійкості і довговічності конструктивних елементів з метастабіль- ними фазами в структурі матеріалу і градієнтними покриттями на прикладі сталі Х12 після іонного азотування і на- ступного гартування з отриманням залишкового азотистого аустеніту. Ключові слова: залишковий аустеніт, знос, довговічність, азотування, тліючий розряд.