DOI: https://doi.org/10.15587/2312-8372.2019.156159

Continual description of polycrystalline systems taking into account their structure

Oleg Kuzin, Bohdan Lukiyanets, Nikolay Kuzin

Abstract


The object of research is the behavior of grain boundaries, the conditions for the formation of intergranular damage and intercrystalline destruction of polycrystalline alloys under the influence of force loads. The problem of creating internal boundary zones with given thermodynamic, physical and mechanical characteristics in alloys, the solution of which is the most promising way to improve their properties, requires the use of mathematical modeling methods. It is allow one to quantify the influence of chemical composition, heat treatment and external loads on the formation of intergranular damage to polycrystalline systems.

In the course of research based on the energy approach of describing continual media taking into account physical effects occurring on a scale commensurate with the structural components and their boundaries, the mathematical relationships of the model of polycrystalline systems are constructed. This model is the basis for calculations and establishing the stress-strain state of the material at the meso level. It is shown that the mechanical behavior of materials is influenced not only by the absolute values of the parameters of the properties of individual microvolumes of bodies, but also by their gradient.

The relationship between the presence of grain boundaries in improved steels with an increased level of energy and the ability to form intergranular damage when exposed to an external load is obtained. A conceptual approach has been developed to control the properties of the internal surfaces of the alloy section by changing their structural-energy state. This is due to the fact that the proposed model and experimental dependencies are based on a physically reasonable parameter – the relative property gradient, which determines the segregation of impurities and the separation of phases by the density of dislocations in the boundary zones of the grains.

The limiting values of the characteristics of local volumes of grains, at which the ability to form intergranular damage and intercrystallite destruction of alloys, is established. This ensures the possibility of introducing innovative technologies of grain-boundary design of the structure of metal products. It is makes possible to significantly increase the reliability parameters of machine parts in comparison with the known technologies – durability, service life, reliability with minimal economic costs.


Keywords


mathematical relationships of the model of polycrystalline systems; state of the grain boundaries of polycrystals; intergranular damage

References


Watanabe, T. (1988). Grain Boundary Design For Desirable Mechanical Properties. Le Journal de Physique Colloques, 49, 507–519. doi: http://doi.org/10.1051/jphyscol:1988562

Lejcek, P. (2010). Grain Boundary Segregation in Metals. Springer, 249. doi: http://doi.org/10.1007/978-3-642-12505-8

Makarov, P. V. (2004). Ob ierarkhicheskoy prirode deformatsii i razrusheniya tverdykh tel. Fizicheskaya mezomekhanika, 7 (4), 25–34.

Kozlov, E. V. (2003). Izmel'chenie zerna kak osnovnoy resurs povysheniya predela tekuchesti. Vestnik TGU, 8 (4), 509–513.

Entsiklopedicheskiy slovar' po metallurgii (2000). Moscow: Intermet Inzhiniring, 821.

Gottschalk, D., McBride, A., Reddy, B. D., Javili, A., Wriggers, P., Hirschberger, C. B. (2016). Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation. Computational Materials Science, 111, 443–459. doi: http://doi.org/10.1016/j.commatsci.2015.09.048

Kobayashi, R., Warren, J. A., Craig Carter, W. (2000). A continuum model of grain boundaries. Physica D: Nonlinear Phenomena, 140 (1-2), 141–150. doi: http://doi.org/10.1016/s0167-2789(00)00023-3

Shtremel', M. A. (1999). Prochnost' splavov. Chast' І. Defekty reshetki. Moscow: MISIS, 384.

Kozlov, E. V., Zhdanov, A. N., Koneva, N. A. (2006). Bar'ernoe tormozhenie dislokatsiy. Problema Kholla-Petcha. Fizicheskaya mezomekhanika, 9 (3), 81–92.

Korneva, N. A., Tishkina, L. I., Kozlov, E. V. (1998). Spektr i istochniki poley vnutrennikh napryazheniy v deformirovannykh metallakh i splavakh. Izvestiya RAN. Seriya fizicheskaya, 62 (7), 1350–1356.

Mughrabi, H. (1987). A two-parameter description of heterogeneous dislocation distributions in deformed metal crystals. Materials Science and Engineering, 85, 15–31. doi: http://doi.org/10.1016/0025-5416(87)90463-0

Kocks, U. F. (1970). The relation between polycrystal deformation and single-crystal deformation. Metallurgical and Materials Transactions B, 1 (5), 1121–1143. doi: http://doi.org/10.1007/bf02900224

Hirth, J. P. (1972). The influence of grain boundaries on mechanical properties. Metallurgical Transactions, 3 (12), 3047–3067. doi: http://doi.org/10.1007/bf02661312

Weinberg, F. (1958). Grain boundaries in metals. Canada Department of Mines and Technical Surveys, 79. doi: http://doi.org/10.4095/306660

Rabotnov, Yu. N. (1959). Mekhanizm dlitel'nogo razrusheniya. Voprosy prochnosti materialov i konstruktsiy. Moscow: Izd-vo AN SSSR, 5–7.

Kachanov, L. M. (1958). O vremeni razrusheniya v usloviyakh polzuchesti. Izv. AN SSSR. OTN. Mekhanika i mashinostroenie, 8, 26–31.

Burak, Ya. Y., Chapli, Ye. Ya. (Eds.) (2004). Fizyko-matematychne modeliuvannia skladnykh system. Lviv: Spolom, 264.

Peleshhak, R. M., Lukiyanets, B. A. (1998). Elektronnoe pereraspredelenie v okrestnosti yadra lineynoy dislokatsii. Pis'ma v zhurnal tekhnicheskoy fiziki, 24 (2), 37–41.

Kuzin, N. O. (2015). Ob odnoy matematicheskoy modeli izmeneniya svoystv materiala. Prikladnaya mekhanika, 51 (4), 125–132.

Afaghi-Khatibi, A., Ye, L., Mat, Y.-W. (1996). An Effective Crack Growth Model for Residual Strength Evaluation of Composite Laminates with Circular Holes. Journal of Composite Materials, 30 (2), 142–163. doi: http://doi.org/10.1177/002199839603000201

Chang, K.-Y., Llu, S., Chang, F.-K. (1991). Damage Tolerance of Laminated Composites Containing an Open Hole and Subjected to Tensile Loadings. Journal of Composite Materials, 25 (3), 274–301. doi: http://doi.org/10.1177/002199839102500303

Xia, S., Takezono, S., Tao, K. (1994). A nonlocal damage approach to analysis of the fracture process zone. Engineering Fracture Mechanics, 48 (1), 41–51. doi: http://doi.org/10.1016/0013-7944(94)90141-4

Legan, M. A. (1994). Correlation of local strength gradient criteria in a stress concentration zone with linear fracture mechanics. Journal of Applied Mechanics and Technical Physics, 34 (4), 585–592. doi: http://doi.org/10.1007/bf00851480

Kharlab, V. D. (1993). Gradientnyy kriteriy khrupkogo razrusheniya. Issledovanie po mekhanike stroitel'nykh konstruktsiy i materialov. Saint Petersburg: Sankt-Peterburgskiy gosudarstvennyy arkhitekturno-stroitel'nyy universitet, 4–16.

Lebedev, A. A., Shvets, V. P. (2008). Otsenka povrezhdennosti konstruktsionnykh staley po parametram rasseyaniya kharakteristik tverdosti materialov v nagruzhennom i razgruzhennom sostoyaniyakh. Problemy prochnosti, 3, 29–37.

Maugin, G. A. (1992). The thermomechanics of plasticity and fracture. Cambridge: Cambridge University Press, 350. doi: http://doi.org/10.1017/cbo9781139172400

Egorov, A. I. (1988). Optimal'noe upravlenie lineynymi sistemami. Kyiv: Vyshha shkola, 278.

Kuzin, O. A. (2018). Rol' izmeneniya svoystv lokal'nykh ob"emov zeren v protsessakh interkristallitnogo razrusheniya staley posle uluchsheniya. European multi science journal, 15, 27–29.

Ivanova, V. S. (1986). Mekhanika i sinergetika ustalostnogo razrusheniya. Fiziko khimicheskaya mekhanika materialov, 1, 62–68.

Ivanova, V. S. (1989). Sinergetika razrusheniya i mekhanicheskie svoystva. Moscow: Nauka, 167.

Volkov, I. A. (2008). Uravneniya sostoyaniya vyazkouprugo-plasticheskikh sred s povrezhdeniyami. Moscow: Fizmatlit, 424.


GOST Style Citations


Watanabe T. Grain Boundary Design For Desirable Mechanical Properties // Le Journal de Physique Colloques. 1988. Vol. 4. P. 507–519. doi: http://doi.org/10.1051/jphyscol:1988562 

Lejcek P. Grain Boundary Segregation in Metals. Springer, 2010. 249 p. doi: http://doi.org/10.1007/978-3-642-12505-8 

Makarov P. V. Ob ierarkhicheskoy prirode deformatsii i razrusheniya tverdykh tel // Fizicheskaya mezomekhanika. 2004. Vol. 7, Issue 4. P. 25–34.

Kozlov E. V. Izmel'chenie zerna kak osnovnoy resurs povysheniya predela tekuchesti // Vestnik TGU. 2003. Vol. 8, Issue 4. P. 509–513.

Entsiklopedicheskiy slovar' po metallurgii. Moscow: Intermet Inzhiniring, 2000. 821 p.

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation / Gottschalk D. et. al. // Computational Materials Science. 2016. Vol. 111. P. 443–459. doi: http://doi.org/10.1016/j.commatsci.2015.09.048 

Kobayashi R., Warren J. A., Craig Carter W. A continuum model of grain boundaries // Physica D: Nonlinear Phenomena. 2000. Vol. 140, Issue 1-2. 141–150. doi: http://doi.org/10.1016/s0167-2789(00)00023-3 

Shtremel' M. A. Prochnost' splavov. Chast' І. Defekty reshetki. Moscow: MISIS, 1999. 384 p.

Kozlov E. V., Zhdanov A. N., Koneva N. A. Bar'ernoe tormozhenie dislokatsiy. Problema Kholla-Petcha // Fizicheskaya mezomekhanika. 2006. Vol. 9, Issue 3. P. 81–92.

Korneva N. A., Tishkina L. I., Kozlov E. V. Spektr i istochniki poley vnutrennikh napryazheniy v deformirovannykh metallakh i splavakh // Izvestiya RAN. Seriya fizicheskaya. 1998. Vol. 62, Issue 7. P. 1350–1356.

Mughrabi H. A two-parameter description of heterogeneous dislocation distributions in deformed metal crystals // Materials Science and Engineering. 1987. Vol. 85. P. 15–31. doi: http://doi.org/10.1016/0025-5416(87)90463-0 

Kocks U. F. The relation between polycrystal deformation and single-crystal deformation // Metallurgical and Materials Transactions B. 1970. Vol. 1, Issue 5. P. 1121–1143. doi: http://doi.org/10.1007/bf02900224 

Hirth J. P. The influence of grain boundaries on mechanical properties // Metallurgical Transactions. 1972. Vol. 3, Issue 12. P. 3047–3067. doi: http://doi.org/10.1007/bf02661312 

Weinberg F. Grain boundaries in metals. Canada Department of Mines and Technical Surveys, 1958. 79 p. doi: http://doi.org/10.4095/306660 

Rabotnov Yu. N. Mekhanizm dlitel'nogo razrusheniya // Voprosy prochnosti materialov i konstruktsiy. Moscow: Izd-vo AN SSSR, 1959. P. 5–7.

Kachanov L. M. O vremeni razrusheniya v usloviyakh polzuchesti // Izv. AN SSSR. OTN. Mekhanika i mashinostroenie. 1958. Issue 8. P. 26–31.

Fizyko-matematychne modeliuvannia skladnykh system / ed. by Burak Ya. Y., Chapli Ye. Ya. Lviv: Spolom, 2004. 264 p.

Peleshhak R. M., Lukiyanets B. A. Elektronnoe pereraspredelenie v okrestnosti yadra lineynoy dislokatsii // Pis'ma v zhurnal tekhnicheskoy fiziki. 1998. Vol. 24, Issue 2. P. 37–41.

Kuzin N. O. Ob odnoy matematicheskoy modeli izmeneniya svoystv materiala // Prikladnaya mekhanika. 2015. Vol. 51, Issue 4. P. 125–132.

Afaghi-Khatibi A., Ye L., Mat Y.-W. An Effective Crack Growth Model for Residual Strength Evaluation of Composite Laminates with Circular Holes // Journal of Composite Materials. 1996. Vol. 30, Issue 2. P. 142–163. doi: http://doi.org/10.1177/002199839603000201 

Chang K.-Y., Llu, S., Chang F.-K. Damage Tolerance of Laminated Composites Containing an Open Hole and Subjected to Tensile Loadings // Journal of Composite Materials. 1991. Vol. 25, Issue 3. P. 274–301. doi: http://doi.org/10.1177/002199839102500303 

Xia S., Takezono S., Tao K. A nonlocal damage approach to analysis of the fracture process zone // Engineering Fracture Mechanics. 1994. Vol. 48, Issue 1. P. 41–51. doi: http://doi.org/10.1016/0013-7944(94)90141-4 

Legan M. A. Correlation of local strength gradient criteria in a stress concentration zone with linear fracture mechanics // Journal of Applied Mechanics and Technical Physics. 1994. Vol. 34, Issue 4. P. 585–592. doi: http://doi.org/10.1007/bf00851480 

Kharlab V. D. Gradientnyy kriteriy khrupkogo razrusheniya // Issledovanie po mekhanike stroitel'nykh konstruktsiy i materialov. Saint Petersburg: Sankt-Peterburgskiy gosudarstvennyy arkhitekturno-stroitel'nyy universitet, 1993. P. 4–16.

Lebedev A. A., Shvets V. P. Otsenka povrezhdennosti konstruktsionnykh staley po parametram rasseyaniya kharakteristik tverdosti materialov v nagruzhennom i razgruzhennom sostoyaniyakh // Problemy prochnosti. 2008. Issue 3. P. 29–37.

Maugin G. A. The thermomechanics of plasticity and fracture. Cambridge: Cambridge University Press, 1992. 350 p. doi: http://doi.org/10.1017/cbo9781139172400 

Egorov A. I. Optimal'noe upravlenie lineynymi sistemami. Kyiv: Vyshha shkola, 1988. 278 p.

Kuzin O. A. Rol' izmeneniya svoystv lokal'nykh ob"emov zeren v protsessakh interkristallitnogo razrusheniya staley posle uluchsheniya // European multi science journal. 2018. Issue 15. P. 27–29.

Ivanova V. S. Mekhanika i sinergetika ustalostnogo razrusheniya // Fiziko khimicheskaya mekhanika materialov. 1986. Issue 1. P. 62–68.

Ivanova V. S. Sinergetika razrusheniya i mekhanicheskie svoystva. Moscow: Nauka, 1989. 167 p.

Volkov I. A. Uravneniya sostoyaniya vyazkouprugo-plasticheskikh sred s povrezhdeniyami. Moscow: Fizmatlit, 2008. 424 p.







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ISSN (print) 2664-9969, ISSN (on-line) 2706-5448