Abstract
The aim of this paper is to develop a structural approach for the construction of statistical criterion of static and fatigue failure for the transversely isotropic piezoelectric materials. We use a probabilistic model of the mechanism of brittle microfracture. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. Daniel’s structural model of accumulation of microcracks is used for progressive microdamageability. Statistical criterion is convenient to use in the study of fatigue failure under cyclic loading. The reason for its applicability in such problems is experimentally established connection of fatigue failure mechanism with the phenomenon of accumulation of microdamages in the material. Statistical criterion relates macrodestruction beginning with a certain critical value of microcracks density. The model consists of derivation of constitutive equations for a damaged material, choosing the fracture criterion and the law of microdamage distribution; and determining effective electroelastic properties of the damaged medium and the model of accumulation of microdamages by the modified Eshelby method. The approach proposed makes it possible to find the residual ultimate strength of the material after n-fold loading and the conditional fatigue limit for the prescribed testing base N.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Suresh, S.: Fatigue of Materials. Cambridge University Press, Cambridge (1998)
Bolotin, V.V.: Prediction of Service Life of Machines and Structures. Mashinostroenie, Moscow (in Russian) (1984)
Suo, Z., Kuo, C.-M., Barnett, D.M., Willis, J.R.: Fracture mechanics for piezoelectric ceramics. J. Mech. Phys. Solids 40(4), 739–765 (1992)
Fuchs, H.O., Stephens, R.J.: Metal Fatigue in Engineering. Wiley, New York (1980)
Pook, L.: Metal Fatigue. Springer, New York (2009)
Luo, J., Bowen, P.: A probabilistic methodology for fatigue life prediction. Acta Materiala 51(12), 3537–3550 (2003)
Righiniotis, T.D., Chryssanthopoulos, M.K.: Probabilistic fatigue analysis under constant amplitude loading. J. Construct. Steel Res. 59(7), 867–886 (2003)
Xiao, Y.C., Li, S., Gao, Z.: A continuum damage mechanics model for high cycle fatigue. Int. J. Fatigue 20(7), 503–608 (1998)
Upadhyaya, Y.S., Sridhara, B.K.: Fatigue life prediction. A continuum damage mechanics and fracture mechanics approach. Mater. Des. 35, 220–224 (2012)
Babich, D.V., Bastun, V.N.: On dispersed microdamageability of elastic-brittle materials under deformation. J. Strain Anal. 45(1), 57–66 (2010)
Babich, D.V.: A statistical strength criterion for brittle materials. Strength Mater. 43(5), 573–582 (2011)
Babich, D.V.: Simulation of coupled processes of deformation and cracking in elastic brittle materials. Strength Mater. 36(2), 178–184 (2004)
Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241, 376–393 (1957)
Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity of Piezoelectric and Conductive Bodies, Moscow: Nauka, p. 470 (1988). (In Russian)
Babich, D.V., Bezverkhyi, O.I., Dorodnykh, T.I.: Continuum model of deformation of piezoelectric materials with cracks. Appl. Mech. Mater. 784, 161–172 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Babich, D., Bezverkhyi, O., Dorodnykh, T. (2016). Structural Probabilistic Modeling of Fatigue Fracture for Piezoceramic Materials Under Cyclic Loading. In: Awrejcewicz, J. (eds) Dynamical Systems: Modelling. DSTA 2015. Springer Proceedings in Mathematics & Statistics, vol 181. Springer, Cham. https://doi.org/10.1007/978-3-319-42402-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-42402-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42401-9
Online ISBN: 978-3-319-42402-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)