https://oldena.lpnu.ua/handle/ntb/39550| Title: | Propagation of plane elastic-tough-plastic waves in the materialwith yield delay |
| Authors: | Andrusyk, Yaroslav |
| Affiliation: | Lviv Polytechnic National University, Lviv, Ukraine |
| Bibliographic description (Ukraine): | Andrusyk Y. Propagation of plane elastic-tough-plastic waves in the materialwith yield delay / Yaroslav Andrusyk // Ukrainian Journal Of Mechanical Engineering Andmaterials Science. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 3. — No 1. — P. 9–26. |
| Is part of: | Ukrainian Journal Of Mechanical Engineering Andmaterials Science, 1 (3), 2017 |
| Issue: | 1 |
| Issue Date: | 1-Jan-2017 |
| Submitted date: | 24-Dec-2016 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| Keywords: | yield delay plane elastic-tough-plastic waves dynamic criterion of plasticity plastic state overstress medium “trembling” |
| Number of pages: | 18 |
| Page range: | 9-26 |
| Start page: | 9 |
| End page: | 26 |
| Abstract: | The use of electromechanical model of ideal elastic-tough-plastic material with yield delay while investigating the propagation of plane one-dimensional waves is being considered. The materials being investigated possesses the property of toughness only in the plastic region and is elastic up to the plastic state. The solving of the problem is being carried out in the conditions of one-parameter loading when the permanent (steady) uniformly distributed stress is being suddenly applied to the boundary surface of non-deformed half-space. The value of applied stress exceeds the limit level of elastic state in the case of static deformation and remains unchanged for the whole region of disturbed half-space. In order to conduct the corresponding calculation the dependence between the components the tensor of normal stress and linear deformations along the load axis is being determined. The defining equations of elastic-tough-plastic medium behind the front of the wave of transition from elastic to plastic state are being derived and the simple relationship for determination of the time (duration) of yield delay is deduced. The basic solution of these equations is obtained for the stresses in elastic and plastic region of the half-space. The special representation of the basic pattern of changing of lateral (transverse) stresses and longitudinal deformations for the region of active loading of material is defined. The distribution of velocities of the half-space points in the plastic region is obtained. The difference between the characters of propagation of plane elastic-plastic wave and the wave processes in the material with yield delay is shown. It is noted that two different solutions are obtained despite of the simple type of loading. The first one detects the strange character of medium’s behaviour when the material of disturbed halfspace in the plastic region is in the state of “trembling”, which causes the pulsations of lateral (transverse) stresses and the impulses of deformations along the axis that is normal to the boundary surface of the half-space. |
| URI: | https://ena.lpnu.ua/handle/ntb/39550 |
| ISSN: | 2411-8001 |
| Copyright owner: | © Національний університет "Львівська політехніка" © Andrusyk Ya., 2017 |
| References (Ukraine): | [1] Wood D. S. On longitudinal plane waves of elastic plastic strain in solids // J. Appl. Mech. – 1952. – P. 521–525. [2] Bleich H. H., Nelson I., Plane waves in an elastic-plastic half-space due to combined surface pressure and shear, Journal of Applied Mechanics, March 1966. [3] Bleich H. H., Mathews A. T., Wrigh J. P., Moving step load on the surface of a half – spase of granular material, Int. J. Solids and Struct., 4, 2, 1968. [4] Fong J. T., Elastic – plastic wave in a half – space of a linearly work – hardening material for coupled loading, Report No. 161, Stanford University, May 1966. [5] Kaliski S., Nowacki W. K., Wlodarczyk E., Plane biwaves in an elastic/viscoplastic semi – spase, Proc. Vibr. Probl., 8, 2, 1967. [6] Wlodarczyk E., Propagation of longitudinal – transverse loading and unloading waves in a nonhomogeneous elastic/viscoplastic medium, Proc. Vibr. Probl., 9, 2, 1968. [7] Ting T. C., Ning Nan, Plane waves due to combined compressive and shear stressses in a half space, J. June, 1969. [8] О распространении ударных волн в упруго-вязко-пластической среде / П. А. Безгласный, Н. Д. Вервейко // Изв. АН СССР. МТТ. – 1971. – № 5. – С. 71–76. [9] Динамика жестко-пластической балки с запаздыванием текучести / Ю. Н. Работнов, Ю. В. Суворова // Изв. АН СССР. Механика твердого тела. – 1968. – № 6. – С. 76–86. [10] Распространение волн в материале с запаздыванием текучести / Н. Г. Бураго, В. Н. Кукуджанов // Материалы V Всесоюзного симпозиума. – АЛМА-АТА: Наука. Казахской ССР, 1973. – С. 101–107. [11] Распространение упругопластических волн в материале с запаздыванием текучести / Е. В. Ломакин // Изв. АН СССР. МТТ. – 1970. – № 5. – С. 152–160. [12] Модель упругопластической среды с запаздыванием текучести / Ю. Н. Работнов // Прикладная механика и техническая физика. – 1968. – № 3. – С. 45–54. [13] Ще раз про зуб плинності та формулювання динамічної умови пластичності / Я. Ф. Андрусик // Вісник Вид-ва Львівської політехніки. Серія “Фізико-математичні науки”. – 2014. – № 804. – С. 120–126. [14] Propagation of Elastic-Tough-Plastic Wave in a Rod of Ideally Plastic Material which Possesses the Property of Yield Delay / Ya. Andrusyk // Ukrainian Journal of Mechanical Engineering and Materials Science, Vol. 1, No. 2, 2015, P. 51–66. [15] Механика сплошной среды, Т. I. / Л. И. Седов. – М.: Наука, 1976. – 536 с. [16] Механика деформируемого твердого тела / Ю. Н. Работнов. – М.: Наука, 1979. – 744 с. [17] Справочник по обыкновенным дифференциальным уравнениям / Э. Камке. – М.: Наука: Гл. ред. физ-мат. лит., 1971. – 576 с. [18] Пластическая деформация как волновой процесс / В. Е. Панин, Л. Б. Зуев, В. И. Данилов, Н. М. Мних // Докл. АН СССР. – 1989. – Т. 308, № 6. – С. 1375–1379. |
| References (International): | [1] Wood D. S. On longitudinal plane waves of elastic plastic strain in solids, J. Appl. Mech, 1952, P. 521–525. [2] Bleich H. H., Nelson I., Plane waves in an elastic-plastic half-space due to combined surface pressure and shear, Journal of Applied Mechanics, March 1966. [3] Bleich H. H., Mathews A. T., Wrigh J. P., Moving step load on the surface of a half – spase of granular material, Int. J. Solids and Struct., 4, 2, 1968. [4] Fong J. T., Elastic – plastic wave in a half – space of a linearly work – hardening material for coupled loading, Report No. 161, Stanford University, May 1966. [5] Kaliski S., Nowacki W. K., Wlodarczyk E., Plane biwaves in an elastic/viscoplastic semi – spase, Proc. Vibr. Probl., 8, 2, 1967. [6] Wlodarczyk E., Propagation of longitudinal – transverse loading and unloading waves in a nonhomogeneous elastic/viscoplastic medium, Proc. Vibr. Probl., 9, 2, 1968. [7] Ting T. C., Ning Nan, Plane waves due to combined compressive and shear stressses in a half space, J. June, 1969. [8] O rasprostranenii udarnykh voln v upruho-viazko-plasticheskoi srede, P. A. Bezhlasnyi, N. D. Verveiko, Izv. AN SSSR. MTT, 1971, No 5, P. 71–76. [9] Dinamika zhestko-plasticheskoi balki s zapazdyvaniem tekuchesti, Iu. N. Rabotnov, Iu. V. Suvorova, Izv. AN SSSR. Mekhanika tverdoho tela, 1968, No 6, P. 76–86. [10] Rasprostranenie voln v materiale s zapazdyvaniem tekuchesti, N. H. Buraho, V. N. Kukudzhanov, Materialy V Vsesoiuznoho simpoziuma, ALMA-ATA: Nauka. Kazakhskoi SSR, 1973, P. 101–107. [11] Rasprostranenie upruhoplasticheskikh voln v materiale s zapazdyvaniem tekuchesti, E. V. Lomakin, Izv. AN SSSR. MTT, 1970, No 5, P. 152–160. [12] Model upruhoplasticheskoi sredy s zapazdyvaniem tekuchesti, Iu. N. Rabotnov, Prikladnaia mekhanika i tekhnicheskaia fizika, 1968, No 3, P. 45–54. [13] Shche raz pro zub plynnosti ta formuliuvannia dynamichnoi umovy plastychnosti, Ya. F. Andrusyk, Visnyk Vyd-va Lvivskoi politekhniky. Seriia "Fizyko-matematychni nauky", 2014, No 804, P. 120–126. [14] Propagation of Elastic-Tough-Plastic Wave in a Rod of Ideally Plastic Material which Possesses the Property of Yield Delay, Ya. Andrusyk, Ukrainian Journal of Mechanical Engineering and Materials Science, Vol. 1, No. 2, 2015, P. 51–66. [15] Mekhanika sploshnoi sredy, T. I., L. I. Sedov, M., Nauka, 1976, 536 p. [16] Mekhanika deformiruemoho tverdoho tela, Iu. N. Rabotnov, M., Nauka, 1979, 744 p. [17] Spravochnik po obyknovennym differentsialnym uravneniiam, E. Kamke, M., Nauka: Hl. red. fiz-mat. lit., 1971, 576 p. [18] Plasticheskaia deformatsiia kak volnovoi protsess, V. E. Panin, L. B. Zuev, V. I. Danilov, N. M. Mnikh, Dokl. AN SSSR, 1989, V. 308, No 6, P. 1375–1379. |
| Content type: | Article |
| Appears in Collections: | Ukrainian Journal of Mechanical Engineering And Materials Science. – 2017. – Vol. 3, No. 1 |
| File | Description | Size | Format | |
|---|---|---|---|---|
| UJMEMS_2017v3n1_Andrusyk_Y-Propagation_of_plane_elastic_9-26.pdf | 1.01 MB | Adobe PDF | View/Open | |
| UJMEMS_2017v3n1_Andrusyk_Y-Propagation_of_plane_elastic_9-26__COVER.png | 484.4 kB | image/png | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.