Nonlinear-elastic behavior and effective parameters of materials containing pores and slit-like defects

Keywords

nonlinear elasticity, elastic potential, pores, slit-like defects.

Cite as

Kuzmov A. V., Vdovychenko O. V., Kirkova O. G., and Shtern M. B. Nonlinear-elastic behavior and effective parameters of materials containing pores and slit-like defects. Physico¬chemical Mechanics of Materials. 2024. 60(1), 034-041.

https://doi.org/10.15407/pcmm2024.01.034

Abstract

A nonlinear-elastic isotropic model is formulated and effective characteristics of the mate­rial containing defects in the form of cracks and pores are determined. The expres­sion for deformation specific energy, which is the second degree homogeneous function with respect to the invariants of the deformation tensor forms the model base. The relationship between the macroscopic parameters of the model, the content of defects and the morpho­logy of the material is established by the methods of computational microme­chanics. The model allows taking into account elastic dilatancy, and its limiting state corres­ponds to the Cam–Clay condition.

References

1. V. V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kyiv (1968).
2. Z. T. Nazarchuk, “Current aspects of nondestructive materials testing,” Mater. Sci., 29, No. 1, 87-92 (1993).
3. H. M. Nykyforchyn, and Z. O. Terlets’ka, “Computation model of corrosion-fatigue crack growth in thin metallic plates,” Mater. Sci., 30, No. 1, 25-30 (1995). https://doi.org/10.1007/BF00559012
4. Z. T. Nazarchuk, V. R. Skal’s’kyi, and O. M. Stankevych,”A method for the identification of the types of macrofracture of structural materials by the parameters of the wavelet transform of acoustic-emission signals,” Mater. Sci., 49, No. 6, 841-848 (2014). https://doi.org/10.1007/s11003-014-9682-y
5. Z. T. Nazarchuk, V. R. Skal’s’kyi, O. M. Serhienko, Yu. Ya. Matviiv, L. I. Hrechykhin, and E. D. Podlozny, “Estimation of the modulus of the vector of displacements in the process of simultaneous formation of cracks in the composites,” Mater. Sci., 47, No. 3, 375-385 (2011). https://doi.org/10.1007/s11003-011-9406-5
6. Y. G. Bezymannyi, “Use of acoustic methods to control the quality of layered materials”, Pow-der Metall. Met. Ceram., 38, 236-239 (1999). https://doi.org/10.1007/BF02675768
7. T. Nazarchuk, “Non-Destructive Testing and Technical Diagnostics,” in: Fracture Mechanics and Strength of Materials (V. V. Panasyuk editor) [in Ukrainian], Vol. 5, Spolom, Lviv (2009).
8. R. Skalskyi, I. M. Romanyshyn, O. M. Mokryi, and P. M. Semak, “Assessment of the degree of damage to materials by acoustic methods (A survey). Part 1,” Mater. Sci., 57, No. 5, 603-611 (2022). https://doi.org/10.1007/s11003-022-00586-x
9. I. Fedenko, “Deformation of tubular samples from sintered nickel powder under simple loading,” Visnyk Dnipropetrovskogo Universytety: Mechanics [in Ukrainian], 145-154. (1998).
10. He, P. Liu, Q. Tan, and G. Jiang, “Flexural and compressive mechanical behaviors of the porous titanium materials with entangled wire structure at different sintering conditions for load-bearing biomedical applications,” J. Mech. Behav. Biomed. Mater., 28, 309-319 (2013). https://doi.org/10.1016/j.jmbbm.2013.08.016
11. Y. Belrhiti, A. Gallet-Doncieux, A. Germaneau, P. Doumalin, J. C. Dupré, A. Alzina, Ph. Michaud, O. Pop, M. Huger, and T. Chotard, “Application of optical methods to investigate the non-linear asymmetric behavior of ceramics exhibiting large strain to rupture by four-points bending test,” J. Eur. Ceram. Soc., 32, 4073-4081 (2012). https://doi.org/10.1016/j.jeurceramsoc.2012.06.016
12. O. V. Vdovychenko, “Experimental studies of nonlinear behavior of porous aluminum oxide in the process of elastic oscillations,” Naukovi Notatky: Collection of Scientific Papers of Lutsk National Technical Universit [in Ukrainian]y, Issue 43, 41-45 (2013).
13. O. V. Vdovychenko, Identification of Mesostructure and Determination of Properties of Powder and Composite Materials by Methods of Acoustic Spectroscopy [in Ukrainian], Autor’s Abstract. of the Doc. Sci. Thesis (Technical Sciences), Kyiv (2020).
14. M. B. Shtern, “Elastic model of isotropic powder materials with different tensile and compres-sive properties,” Powder Metall. Met. Ceram., 48, 257-266 (2009). https://doi.org/10.1007/s11106-009-9137-4
15. V. V. Bozhydarnyk, and G.T. Sulym, Elements of the Theory of Elasticity [in Ukrainian], Svit, Lviv (2994).
16. R. I. Borja, and S. R. Lee, “Cam-clay plasticity, part 1: implicit integration of elasto-plastic constitutive relations,” Computer Methods in Appl. Mech. and Eng., 78, Is. 1, 49-72 (1990). https://doi.org/10.1016/0045-7825(90)90152-C
17. G. E. Mase, Theory and Problems of Continuum Mechanics, Schaum’s Outline Series, McGraw-Hill (1970).
18. A. V. Kuzmov, O. V. Vdovychenko, M. B. Shtern, and O. G. Kirkova, “Modeling of multimodulus elastic behavior of damaged powder materials using computational micromechanics,” Powder Metall. Met. Ceram., 59, 491-498 (2021). https://doi.org/10.1007/s11106-021-00192-7
19. R. M. Christensen, Mechanics of Composite Materials, Wiley-Interscience, New York (1979).
20. R. M. Jones, Mechanics of Composite Materials, CRC Press, Boca Raton (2018).
21. A. V. Vdovychenko, and Yu. N. Podrezov, “Evolution of Young’s dynamic modulus and damping ability of porous iron,” Metallofizika i Noveishiye Tekhnologii [in Russian], 27, Is. 11, 1429-1440 (2005).