Modeling the Stress-Strain Curve of Elastic-Plastic Materials

Abstract:

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

• Periodical: Solid State Phenomena (Volume 316)
• Pages: 936-941
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.316.936
• Online since: April 2021
• Authors: Natalya Ya. Golovina*
• Keywords: Empirical Stress-Strain Curves, Functional Extremal, Processing of Experimental Data, Ramberg-Osgood's Law, Variational Principles of Mechanics

References

[1] W. Ramberg, W. R. Osgood, Description of stress–strain curves by three parameters, National Advisory Committee for Aeronautics,, Technical Note No. 902, Washington DC, (1943).

[2] Papirno, R. Goodness-of-Fit of the Ramberg-Osgood Analytic Stress-Strain Curve to Tensile Test Data. Journal of Testing and Evaluation 10, no. 6 (1982): 263-268.

DOI: 10.1520/jte10264j

[3] K. Rasmussen, Full-range stress-strain curves for stainless steel alloys,. Journal of Constructional Steel Research, no 59 (1), p.47–61, (2003).

DOI: 10.1016/s0143-974x(02)00018-4

[4] H.S. Gao, Modeling Stress Strain Curves for Nonlinear Analysis,. Materials Science Forum, p.575–578, 539–544, (2009).

DOI: 10.4028/www.scientific.net/msf.575-578.539

[5] Zhao, O., Rossi, B., Gardner, L., & Young, B. (2015). Behaviour of structural stainless steel cross-sections under combined loading - Part I: Experimental study. Engineering Structures, 89, 236–246.

DOI: 10.1016/j.engstruct.2014.11.014

[6] Walport, F., Gardner, L., Real, E., Arrayago, I., & Nethercot, D. A. (2019). Effects of material nonlinearity on the global analysis and stability of stainless steel frames. Journal of Constructional Steel Research, 152, 173–182.

DOI: 10.1016/j.jcsr.2018.04.019

[7] Arrayago, I., Real, E., & Gardner, L. (2015). Description of stress-strain curves for stainless steel alloys. Materials and Design, 87, 540–552.

DOI: 10.1016/j.matdes.2015.08.001

[8] N.Y. Golovina, Optimization of design parameters of bellows expansion joints. International Journal of Mechanical and Production Engineering Research and Development (IJMPERD), V. 9 (3) (2019): pp.1379-1392.

DOI: 10.24247/ijmperdjun2019148

[9] N.Y. Golovina, PhD thesis, Tyumen State Oil and Gas University, 2002, https://perma.cc/53VQ-2L2H (accessed 2019-05-04).

[10] N.Y. Golovina, S.Y. Krivosheeva, 2018 IOP Conf. Ser.: Earth Environ. Sci. 115 012043.

DOI: 10.1088/1755-1315/115/1/012043

[11] Belov, P.A., Golovina, N.Y. (2019). Generalization of the Ramberg–Osgood Model for Elastoplastic Materials: Journal of Materials Engineering and Performance.

[12] A. Mendelson, Plasticity: Theory, and Application, Malabar: Krieger, (1968).