Investigation of fragmentation statistics of natural materials in laboratory conditions
DOI:
https://doi.org/10.7242/2658-705X/2024.4.2Keywords:
fragmentation statistical analysis, quartzite, sandstone, andesiteAbstract
The results of study of the behavior of natural materials (quartzite, sandstone, andesite) under quasi-static, dynamic loading and low-speed indentation (10-3-103 1/s) are presented. The experimental conditions made it possible to preserve fragmented samples and to analyze the statistics of the preserved fragments by size (mass). During the research, a system of laboratory sieve and an HR202i electronic scales with a measurement error of 0.0001 g were used. The method of processing fragment photographs allowed us to establish the number and mass of fragments on sieves with cell sizes up to 0.063-0.05 mm, not less than 99% of the sample weight and minimize measurement error. The obtained cumulative distributions of fragments by mass N(mf) show a change in the shape of the inflection and a shift of the inflection point toward smaller scales with increasing strain rate. The data analysis reflects the similarity of the statistics of fragmentation according to the power law and asymptotic fracture modes with multiple ruptures obtained according to the brittle fracture scenario. It is shown that specimens fracture occurs according to different scenarios depending on loading conditions and is associated with a change in the rate of transition from one stage of crack appearance
(or accumulation of stress states, defective structure) to another (crack formation and complete fragmentation). It has been found that the formation of fragments is of an “automodel” nature.
References
Meibom A., Balslev I. Composite power laws in shock fragmentation // Physical Review Letters. – 1996. – V. 76. – No.14. – P. 2492–2494. https://doi.org/10.1103/PhysRevLett.76.2492
Chen W., Ravichandran G. Dynamic compressive failure of glass ceramic under lateral confinement // Journal of the Mechanics and Physics of Solids. – 1997. – V. 45. – No.8. – P. 1303–1328. https://doi.org/10.1016/S0022-5096(97)00006-9
Katsuragi H., Sugino D. and Honjo H. Scaling if impact fragmentation near the critical point // Physical Review E. – 2003. – V. 68. – No.4. – P. 046105(1–6). https://doi.org/10.1103/PhysRevE.68.046105
Katsuragi H., Ihara S., Honjo H. Explosive fragmentation of a thin ceramic tube using pulsed power // Physical Review Letters. – 2005. – V. 95. – No.9. – P. 095503(1–4). https://doi.org/10.1103/PhysRevLett.95.095503
Grady D. Fragmentation of rings and shells – Springer – Verlag Berlin Heidelberg, 2006. Printedin Germany. – 374 pp.
Davydova M.M., Uvarov S.V., Naimark O.B. Space-time scale invariance in dynamically fragmented quasi-brittle materials // Physical Mesomechanics. – 2016. – V.19. – No.1. – P. 86-92. https://doi.org/10.1134/S1029959916010094
Mott N.F. A theory of the fragmentation of shells and Bombs // Ministry of Supply. Past 3. – 1943. – No. A.C.4035. – P. 1–51. https://doi.org/10.1007/978-3-540-27145-1_11
Степанов Г.В., Бабуцкий А.И. Экспериментальное изучение дробления металлических колец // Проблемы Прочности. – 1984. – №8. – C. 108–110.
Wittel F.K., Kun F., Herrmann H.J., Kröplin B.H. Fragmentation of shells // Physical Review Letters. – 2004. – V. 93. – No.3. – P. 035504(1–4). https://doi.org/10.1103/PhysRevLett.93.035504
Bannikova I.A., Uvarov S.V., Naimark O.B. Experimental research of self-regularities of ceramics fracture under shock wave loading. PNRPU Mechanics Bulletin. – 2015. – No. 3. – Р. 25-37. https://doi.org/10.15593/perm.mech/2015.3.03
Банникова И.А. Автомодельные закономерности деформирования и разрушения сплошных сред при интенсивных воздействиях / Дисс. канд. физ.-мат. наук: 01.02.04. – Томск, ТГУ, 2017. – 168 с.
Ching Emily S.C., Lui S.L., Ke-Qing Xia. Energy dependence of impact fragmentation of long. Glass rods // Physical A. – 2000. – V. 287 – P. 83–90. https://doi.org/10.1016/S0378-4371(00)00446-5
Gladden J.R., Handzy N.Z., Belmonte A., Villermaux E. Dynamic buckling and fragmentation in brittle rods // Physical Review Letters. – 2005. – V. 94. – P. 035503(1–4). https://doi.org/10.1103/PhysRevLett.94.035503
Bannikova I.A., Uvarov S.V. Experimental study of fragmentation of fused quartz cylinders under quasi-static loading with the fractoluminescence recording // Proc. Struct. Int.. – 2021. – V. 32. – P.10-16. https://doi.org/10.1016/j.prostr.2021.09.003
Katsuragi H., Sugino D., Honjo H. Crossover of weighted mean fragment mass scaling in twodimensional brittle fragmentation // Physical Review E. – 2004. – V. 70. – No.62. – P. 065103(1–4). https://doi.org/10.1103/PhysRevE.70.065103
Grady D.E. Impact breach and fragmentation of glass plate // International Journal of Impact Engineering. – 2011. – V. 38. – Is.6. – P. 446–450. https://doi.org/10.1016/j.ijimpeng.2010.10.015
Greiner W., Stöcker H. Hot nuclear matter // Scientific American. – 1985. – V. 252. – No.1. – P. 76–87.
Grady D.E. Length scales and size distributions in dynamic fragmentation // International Journal of Fracture. – 2010. – V. 163. – P. 85–99. https://doi.org/10.1007/s10704-009-9418-4
Naimark O.B. Defect induced transitions as mechanisms of plasticity and failure in multifield continua // In: Advances in Multifield Theories of Continua with Substructure / Ed. G. Capriz and P. Mariano, Birkhäuser, Boston. – 2004. – P. 75–114.
Kurdyumov S.P. Evolution and self-organization laws of complex systems // International Journal of Modern Physics. – 1990. – V. 1(4). – P. 299–327. https://doi.org/10.1142/S0129183190000177
Lyapunova E.A., Davydova M.M., Zaitzev D.V., Panfilov P.E. Statistical regularities of alumina fragmentation under uniaxial compression at room and liquid nitrogen temperatures // AIP Conference Proceedings – 2016. – No.1785. – P. 040033. https://doi.org/10.1063/1.4967090
Naimark O.B., Uvarov S.V., Davydova M.M., Bannikova I.A. Multiscale statistical laws of dynamic fragmentation // Physical Mesomechanics. – 2017. – Vol. 20, No.1. – P. 90-101. https://doi.org/10.1134/S1029959917010088
Astrom J.A., Linna R.P., Timonen J. Exponential and power-law mass distributions in brittle fragmentation // Physical Review E. – 2004. – Vol. 70. – P. 026104(1–7). https://doi.org/10.1103/PhysRevE.70.026104
Bannikova I.A., Uvarov S.V. Scaling laws in fragmentation dynamics of rock materials // Proc. Struct.Int. – 2021. – V. 33. – P. 357–364. https://doi.org/10.1016/j.prostr.2021.10.043
Наймарк О.Б., Аглетдинов Э.А., Банников М.В., Баяндин Ю.В., Бурмистров Е.В., Лукин С.В., Никитюк А.С., Овчаренко Ю.В., Уваров С.В., Чудинов В.В. Механизмы разрушения горных пород в условиях множественных метастабильных состояний, индуцированных дефектами // Физика металлов и металловедение. – 2022. – Т. 123. – №12. – С. 1362-1370. https://doi.org/10.31857/S0015323022600988
Zaiser M. Scale invariance in plastic flow of crystalline solids // Advances in Physics. – 2006. – V. 55. – P. 185–245. https://doi.org/10.1080/00018730600583514
Bouchaud E. Scaling properties of cracks // J. Phys. Condens. Matter. – 1997. – V. 9. – No.21. – P.4319– 4344. https://doi.org/10.1088/0953-8984/9/21/002
Oborin V.A., Bayandin Y.V., Bilalov D.A., Sokovikov M.A., Chudinov V.V., Naimark O.B. Self-Similar Patterns of Damage Development and Reliability Assessment of AMg6 and D16T Aluminum Alloys under Consecutive Dynamic and Gigacycle Loading // Physical Mesomechanics. – 2019. – V. 22. – No. 2. – P. 141-151. https://doi.org/10.1134/S1029959919020048
Оборин В.А. Банников М.В., Баяндин Ю.В., Соковиков М.А., Билалов Д.А., Наймарк О.Б. Фрактальный анализ поверхности разрушения сплава АМг6 при усталостном и динамическом нагружении // Вестник Пермского национального исследовательского политехнического университета. Механика. – 2015. – №2. – С. 116–126. https://doi.org/10.15593/perm.mech/2015.2.07
Банникова И.А. «Метод фотографии» как инструмент исследования фрагментации // Заводская
лаборатория. Диагностика материалов. – 2017. – Т. 83. – №5. – С. 42–44.
Bannikova, I., Uvarov, S. Experimental study of fragmentation of fused quartz cylinders under quasistatic loading with the fractoluminescence recording // Procedia Structural Integrity. – 2021. – V. 32. – P. 10–16. https://doi.org/10.1016/j.prostr.2021.09.003
Банникова И.А., Савельева Н.В., Банников М.В., Чудинов В.В., Уваров С.В., Наймарк О.Б. Статистические закономерности разрушения и фрагментации горных пород при квазистатическом и динамическом воздействии // Актуальные проблемы современной механики сплошных сред и небесной механики – 2023: материалы XII Всероссийской научной конференции с международным участием. – Томск: ТГУ, 2023. – С. 19-22.
Bannikova I.A., Saveleva N.V., Uvarov S.V., Bannikov M.V., Panfilov P.E., Naimark O.B. Investigation of plasma spray ceramic fragmentation statistics in a wide range of strain rates // Russian Physics Journal. – 2023. – V.66. – No.9. – P. 990-997. https://doi.org/10.1007/s11182-023-03034-8
Uvarov S.V., Bannikova I.A., Naimark O.B., Gareev A.R. Dynamic indentation and low velocity impact of siliconized graphite // XXXIX Fortov International Conference on Equations of State for Matter (ELBRUS 2024) (http://www.ihed.ras.ru/elbrus24/program/restore.php?id=200).
