Abstract
In frame of the self-consistent mathematical model, which includes the dynamics of a material and the state of its defects, the particular qualities of acoustic wave propagation in the material with damage is considered. In this study a constitutive equation of the damaged medium is derived and the similarity between the models for damaged materials and the medium with memory is confirmed. The dispersion analysis of the model is carried out, and it is shown that the damage of the material gives rise to frequency-dependent attenuation and anomalous dispersion of phase velocity of acoustic wave propagating through that material. This makes it possible to estimate the damage of the material by means of a nondestructive acoustic method.
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References
Berezina TG, Mints II (1976) Heat-strength and heat-resistant of metallic materials. Nauka, Moscow (in Russ.)
Collins JA (1993) Failure of materials in mechanical design: analysis, prediction, prevention, 2nd edn. Wiley, New York
Erofeev VI, Nikitina EA (2010) The self-consistent dynamic problem of estimating the damage of a material by an acoustic method. Acoust Phys 56(4):584–587
Erofeev VI, Nikitina EA, Sharabanova AV (2010) Wave propagation in damaged materials using a new generalized continuum. In: Maugin GA, Metrikine AV (eds) Mechanics of generalized continua. One hundred years after the Cosserats. Advances in mechanics and mathematics, vol 21. Springer, Heidelberg, pp 143–148
Hirao M, Ogi H, Suzuki N, Ohtani T (2000) Ultrasonic attenuation peak during fatigue of polycrystalline copper. Acta Mater 48(2):517–524
Kachanov LM (1986) Introduction to continuum damage mechanics. Springer, New York
Kartofelev D, Stulov A (2014) Propagation of deformation waves in wool felt. Acta Mech 225(11):3103–3113
Klepko VV, Lebedev EV, Kolupaev BB, Kolupaev BS (2007) Energy dissipation and modulus defect in heterogeneous systems based on flexible-chain linear polymers. Polym Sci, Ser B 49(1–2):18–21
Makhutov NA (1981) Deformation criteria of fracture and calculation of construction elements for strength. Mashinostroenie, Moscow (in Russ.)
Maugin GA (1992) The thermomechanics of plasticity and fracture. Cambridge University Press, Cambridge
Rabotnov YN (1969) Creep problems in structural members. North-Holland series in applied mathematics and mechanics. North-Holland Publishing Company, Amsterdam
Romanov AN (1988) Fracture under small-cycle loading. Nauka, Moscow (in Russ.)
Uglov AL, Erofeev VI, Smirnov AN (2009) Acoustic control of equipment during its manufacture and operation. Nauka, Moscow (in Russ.)
Volkov IA, Korotkikh YG (2008) Equations of state of viscoelastoplastic media with damages. Fizmatlit, Moscow (in Russ.)
Volkov VM, Mironov AA (2005) United model of fatigue crack formation and growth in stress concentrations. Probl Strength Plast 67:20–25
Wang J, Fang Q, Zhu Z (1998) Sensitivity of ultrasonic attenuation and velocity change to cyclic deformation in pure aluminum. Phys Status Solidi (a) 169(1):43–48
Zuev LB, Murav’ev VV, Danilova YS (1999) Criterion for fatigue failure in steels. Tech Phys Lett 25(5):352–353
Acknowledgments
This research was supported by the European Regional Development Fund (Project TK124 (CENS)), by the Estonian Ministry of Education and Research (Project IUT33-24), and by the Russian Science Foundation (Grant N 14-19-01637).
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Stulov, A., Erofeev, V.I. (2016). Frequency-Dependent Attenuation and Phase Velocity Dispersion of an Acoustic Wave Propagating in the Media with Damages. In: Altenbach, H., Forest, S. (eds) Generalized Continua as Models for Classical and Advanced Materials. Advanced Structured Materials, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-31721-2_19
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DOI: https://doi.org/10.1007/978-3-319-31721-2_19
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