PSI - Issue 13

A. Vedernikova et al. / Procedia Structural Integrity 13 (2018) 1165–1170 Author name / Structural Integrity Procedia 00 (2018) 000–000

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6. Conclusion This work is devoted to development of one of the possible explanations of nature the critical distance theory. Earlier, length scale parameter was introduced empirically, which made difficult to analyze its connection with material or fracture surface structures. In this work, we used the structural-sensitive parameter introduced in framework of the statistical theory of defect evolution. It allows us to propose the constitutive equations, which does not require explicit incorporation of the parameter with the dimension of length to the fracture model. As a result of theoretical and experimental study, we have shown that localization of the defect ensemble can be observed when two requirements are fulfilled: existence of the area where stresses are higher than ultimate tensile strength and the spatial size of this area is equal to the half of the critical distance. Consequently, critical distance can be considered as a length of dissipative structure growing in a blow-up regime. The structural analysis of fracture surfaces of specimens with notches confirms this hypothesis and shows the existence of two areas with different macro-relief on fracture surface. The central area has the rough structure with ridges and macrocracks. The annular area is characterized by relatively smooth macro-relief and has the characteristic size approximately equal to the critical distance. Acknowledgements The reported study was funded by RFBR according to the research projects №16-48-590148 and №18-31-00293. References Peterson, R. E., 1959. Notch sensitivity, in “ Metal Fatigue ”. In: Sines, G., Waisman, J.L. (Ed.). MacGraw-Hill, New York, pp. 293–306. Novozhilov, V.V., 1969. On a necessary and sufficient criterion for brittle strength. Journal of Applied Mathematics and Mechanics 33, 201–210. Neuber, H., 1958. Theory of Notch Stresses. Springer, Berlin. Whitney, J.M., Nuismer, R.J., 1974. Stress fracture criteria for laminated composites containing stress concentrations. Journal Of Composite Materials 8, 253–265. Taylor, D., 2008. The theory of critical distances. Engineering Fracture Mechanics 75, 1696–1705. Susmel L.,Taylor D., 2008. On the use of the Theory of Critical Distances to predict static failures in ductile metallic materials containing different geometrical features. Engineering Fracture Mechanics 75, 4410-4421. Susmel L.,Taylor D., 2010. The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Engineering Fracture Mechanics 77, 470-478. Plekhov, O.A., Naimark, O.B., 2009. Theoretical and experimental study of energy dissipation in the course of strain localization in iron. Journal of Applied Mechanics and Technical Physics 50, 127–136. Terekhina, A.I., Plekhov, O.A., Kpstina, A.A., Susmel, L., 2017. A comparison of the two approaches of the theory of critical distances based on linear-elastic and elasto-plastic analyses. IOP Conf. Series: Materials Science and Engineering 208, 012042. Naimark, O.B., 2003. Collective Properties of Defect Ensembles and Some Nonlinear Problems of Plasticity and Fracture. Physical Mesomechanics 6, 39–63. Murakami, S., 2012. Continuum Damage Mechanics – A Continuum Mechanics Approach to the Analysis of Damage and Fracture. Springer, Dordrecht, Heidelberg, London, New York. Glansdorff, P., Prigogine, I., 1971. Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley-Interscience, London. Lifshitz, E.M., Pitaevskii, L.P., 1981. Physical Kinetics. Vol. 10. Pergamon Press, Oxford. Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S. P., Mikhailov, A. P., 1995. Blow-up in Quasilinear Parabolic Equations. Walter de Gruyter, Berlin, New York.