Impact a circular cylinder with a flat on an elastic layer
DOI:
https://doi.org/10.31493/tit1812.0302Keywords:
impact, elastic, elastic-plastic, layer, plane problem, hard cylinderAbstract
In the work the comparison of the results of solving two plane problems is performed: the impact of a circular cylinder with a plane platform parallel to the cylinder axle (the flat) with an elastic layer and a second − plane strain state of nonstationary interaction of a circular cylinder with a flat with an elastic layer in a purely elastic and elastic-plastic mathematical formulation corresponding. The first contact occurs along the plane of the flat. A good coincidence of the results of the second problem at an elastic stage with the results of the first problem is shown. In the author's works a new approach was developed to solve plane and tree dimension problems of impact and non-stationary interaction in an elastoplastic formulation. The crack growing was simulated using an elastoplastic mathematical model. The numerical solution was obtained using the finite difference method scheme. The use of an elastic-plastic formulation makes it possible: 1) determine the stress-strain state at the points determined by the partitioning grid of the computational domain, not only on the surface; 2) to give a reliable description of the development of plastic deformations − the stage corresponding to plasticity is a continuation of the elastic stage; 3) reliably determine the destruction toughness. A method has been developed for calculating plastic strain fields and destruction toughness of the material using the solutions of dynamic plane problems of the stress-strain state in an elastoplastic formulation taking into account possible material unloading; 4) to verify and calibrate the solution of problems in an elastoplastic formulation for the first steps by time when the deformation process is elastic, it is convenient to use the solution of the corresponding elastic problem.References
Bogdanov V.R., 2017. Impact of a hard cylinder with flat surface on the elastic layer. Underwater Technologies, Vol.05, 8-15.
Bogdanov V.R., Lewicki H.R., Pryhodko T.B., Radzivill O.Y., Samborska L.R., 2009. The planar problem of the impact shell against elastic layer. Visnyk NTU, Kyiv, No.18, 281292 (In Ukrainian).
Kubenko V.D., Bogdanov V.R., 1995. Planar problem of the impact of a shell on an elastic half-space. International Applied Mechanics, 31, No.6, 483-490.
Kubenko V.D., Bogdanov V.R., 1995. Axisymmetric impact of a shell on an elastic halfspace. International Applied Mechanics, 31, No.10, 829-835. 5. Kubenko V.D., Popov S.N., Bogdanov V.R., 1995.The impact of elastic cylindrical shell with the surface of elastic half-space. Dop. NAN Ukrainy, No.7, 40-44 (in Ukrainian).
Kubenko V.D., Popov S.N., 1988. Plane problem of the impact of hard blunt body on the surface of an elastic half-space. Pricl. Mechanika, 24, No.7, 69-77 (in Russian).
Popov S.N., 1989. Vertical impact of the hard circular cylinder lateral surface on the elastic half-space.Pricl. Mechanika, 25, No.12, 41-47 (in Russian).
Bogdanov V.R., Sulim G.T., 2016. Determination of the material fracture toughness by numerical analysis of 3D elastoplastic dynamic deformation. Mechanics of Solids, 51(2), 206-215; DOI 10.3103/S0025654416020084.
Bogdanov V.R., 2015. A plane problem of impact of hard cylinder with elastic layer. Bulletin of University of Kyiv: Mathematics. Mechanics, No.34, 42-47 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2013. Plain deformation of elastoplastic material with profile shaped as a compact specimen (dynamic loading). Mechanics of Solids, May, 48(3), 329336; DOI 10.3103/S0025654413030096.
Bogdanov V.R., Sulym G.T., 2013. A modeling of plastic deformation's growth under impact, based on a numerical solution of the plane stress deformation problem. Vestnik Moskovskogo Aviatsionnogo Instituta, Vol.20, Iss.3, 196-201 (in Russian).
Bogdanov V.R., 2009. Three dimension problem of plastic deformations and stresses concentration near the top of crack. Bulletin of
University of Kyiv: Series: Physics & Mathematics, No.2, 51-56 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2012. The plane strain state of the material with stationary crack with taking in account the process of unloading. Mathematical Methods and Physicomechanical Fields, Lviv 55, No.3, 132-138 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2010. The crack growing in compact specimen by plastic-elastic model of planar stress state. Bulletin of University of Kyiv: Series: Physics & Mathematics, No. 4, 58-62 (In Ukrainian).
Bogdanov V.R., Sulym G.T., 2010. The crack clevage simulation based on the numerical modelling of the plane stress state. Bulletin of University of Lviv: Series: Physics & Mathematics, No. 73, 192-204 (in Ukrainian).
Bohdanov V.R., Sulym G.T., 2011. Evaluation of crack resistance based on the numerical modelling of the plane strained state. Material Science, 46, No.6, 723-732.
Bogdanov V.R., Sulym G.T., 2011. The clevage crack simulation based on the numerical modelling of the plane deformation state. Scientific collection Problems of Calculation Mechanics and Constructions Strength, Dnepropetrovsk, No.15, 33-44 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2010. Destruction toughness determination based on the numerical modelling of the three dimension dynamic problem. International scientific collection Strength of Machines and Constructions, Kyiv, No.43, 158-167 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2012. A three dimension simulation of process of growing crack based on the numerical solution. Scientific collection Problems of Calculation Mechanics and Constructions Strength, Dnepropetrovsk, No.19, 10-19 (in Ukrainian).
Bogdanov V.R., Sulym G.T., 2012. The crack clevage simulation in a compact specimen based on the numerical modeling of the three dimension problem. Scientific collection Methods of Solving Applied Problems in Solid Mechanics, Dnepropetrovsk, No.13, 60-68 (in Ukrainian).
Bogdanov V.R., 2011. About three dimension deformation of an elastic-plastic material with the profile of compact shape. Theoretical and Applied Mechanics, Donetsk, No.3 (49), 51-58 (in Ukrainian).
Zjukina E.L., 2004. Conservative difference schemes on non-uniform grids for a twodimensional wave equation. Trudy matematicheskogo centra imeni N.I. Lobachevskogo, Kazan', T.26, 151-160 (in Russian).
Weisbrod G., Rittel D., 2000. A method for dynamic fracture toughness determination using short beams. International Journal of Fracture, 104, 89-103.
Downloads
How to Cite
Issue
Section
License
Copyright (c) 2020 Transfer of Innovative Technologies
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Our journal abides by the CREATIVE COMMONS copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons Attribution License, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
