Mathematical and Experimental Analysis Tension of Steel in Bi-Polar Coordinates

• Autorzy: Jaroniek M.
• Języki publikacji: EN

Abstrakty

EN

A series of experiments was carried out to examine the effects of elastic–plastic deformation on the state of stress and the flow stress mechanism under static tension. The strain distribution determined from the fringe pattern using the Moire method allows one to determine the strain and the crack propagation of not–notched specimens an isotropic and elastic–plastic materials. In the analysis of stress the method of calculating using the bipolar coordinate is proposed. The theoretical model is divided into two elements and the condition of incompressibility is satisfied in each element. The proposed method is compared with the elastic-plastic FEM (ANSYS 12, 14) and it is satisfied approximately. The tensile test is aimed to verify the mathematical model that can be applied in the logarithmic stain in further computations.

Słowa kluczowe

EN

stress-strain relationship; bi-polar coordinates; moiré method; finite element method

PL

odkształcenia; współrzędne biegunowe; metoda elementów skończonych

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2016
• Tom: Vol. 20, nr 4
• Strony: 467--488
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Jaroniek M.

• Department of Strength of Materials Lodz University of Technology Stefanowskiego 1/15, 90-924 Łódź, Poland

Bibliografia

• [1] Bridgman, P. W.: Studies in large plastic flow and fracture, McGraw-Hill, New York, 1952.
• [2] Brinson, H. F. and Brinson, L. C.: Polymer Engineering Science and Viscoelasticity, Springer Science&Busines Media, New York, 2015.
• [3] Chakrabarty, J.: Theory of plasticity, Elsevier, Butterworth–Heinemann, 2006.
• [4] Hill, R.: The mathematical theory of plasticity, Oxford: The Clarendon Press, 1950.
• [5] Hutchinson, J. W.: Singular behaviour at the end of a tensile crack in a hardening material, J. Mech. Phys. Solids, Vol. 16, 13–31, 1968.
• [6] Hoffman, O. and Sachs, G.: Introduction to the Theory of Plasticity for Engineers, McGraw-Hill Book Company, 1953.
• [7] Jones, R. M.: Deformation Theory of Plasticity, Bull Ridge Publishing, Blacksburg, Virginia USA, 2009.
• [8] Khalil, A. M and Fazio P.: Moiré–fringe measurement Experimental Mechanics, 1973.
• [9] Khan, A. S. and Huang, S.: Continuum Theory of Plasticity, John Wiley&Sons New York, Chichester, Brisbane, Toronto, 1995.
• [10] Krzyś, W. and Z˙ yczkowski, M.: Elasticity and Plasticity – Problems and Examples, (in Polish), PWN, Warsaw, 1962.
• [11] Ludwik, P.: Elemente der technologischen Mechanik, Springer, Berlin, 1909.
• [12] Mróz, Z.: Non–associated flow laws in plasticity, Journal de Mecanique, 2, 1, 21, 1963.
• [13] Neimitz, A.: Mechanics of fracture, (in Polish), PWN, Warsaw, 1998.
• [14] Rice, J. R. and Rosengren, G. F: Plane Strain Deformation Near a Crack Tip in a Power–Law Hardening Material, Jurn. Mech. Phys. Solids, 16, 1968.
• [15] Rowlands, R. E., Vallem, H.: On replication for moir´e-fringe multiplication, Experimental Mechanics, 1980.
• [16] Sih, G. C.: Hanbook of Stress–Intensity Factors, Leigh University Press, Bethlehem, 1, 1973.
• [17] Seweryn, A.: Modelling of singular stress fields using finite element method, International Journal of Solids and Structures, 39, 4787–4804, 2002.
• [18] Shih, C. F. and Hutchinson, J.: W.: Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems, Journ. of Engineering Materials and Technology, 76, 1976.
• [19] Tada, H., Paris, P. and Irwin, G. R.: The stress analysis of cracks: Handbook, Hellertown: Del Research Corp., 385 1973.
• [20] Timoschenko, S.: Theory of Elasticity, John Wiley, New York, 1980.
• [21] Tvergaard, V. and Hutchinson, J. W.: Effect of strain–dependent cohesive zone model on prediction of crack growth resistance, Int. J. Solid Structures, 33, 3297–3308, 1996.
• [22] User’s Guide ANSYS, 12, 14, Ansys, Inc., Huston, USA, 2014.
• [23] Wegner, T.: Surface of limit state in nonlinear material and its relation with plasticity condition, The Archive of Mechanical Engineering, XLVII, 3, 205–223, 2000.
• [24] Wegner, T.: A method of material modelling with the use of strength hypothesis of inner equilibrium stability, Mechanics and Mechanical Engineering, 4, 2, p. 139–147, 2000.
• [25] Zienkiewicz, O. C.: The Finite Element Method in Engineering Science, McGraw-Hill, London, New York, 1971.