539.3

cyclic loading. pseudoelastic shape memory alloy, residual lifetime, Paris equation, modeling, fatigue crack, stress intensity factor.

Shape memory alloys are widely used in medicine, bioengineering, aerospace, mechanical, civil engineering and other areas. Though they haven’t been used for a long period of time, nevertheless, there are already known cases of SMA failure in structural elements. Therefore, there arises the question: how long can such structural elements be under operation. To answer this question, it is necessary to predict the residual lifetime of such alloys. The development of science and technology demands new increased requirements for the safety of such important structural elements, and, in particular, to the used devices. Fatigue crack growth (FCG) diagrams are generally significantly scattered, that can be taken into account, for instance, by building the distribution of parameters, which are involved in the equation describing the FCG diagram. Therefore, it is necessary to be able to predict FCG taking into account the scatter of mechanical properties, preliminary determined statistical distribution of crack growth resistance parameters, particularly, parameters of C and n of Paris equation. It is known, that the parameters of Paris equation are mutually dependent. Therefore, considering C as random variable, that changes from the specimen to specimen, it is possible to take into account the existing data scatter. The defects, which are found in the structural elements, have frequently the form of semi–elliptical cracks. FCG rate of pseudo–ellastic NiTi alloy was studied experimentally under uniaxial tension of cyllindrical specimens with a dimater of 8 mm at room temperature on air at servo-hydraulic testing machine STM-100. A methodology for predicting the residual lifetime of SMA cylindrical specimens with a semi-elliptical surface crack is proposed. The methodology is based on solving the system of differential equations describing crack propagation, load parameters and cyclic crack grow resistance, taking into account their statistical scatter and change of crack front shape. There were plotted the cumulative distribution functions of lifetime of specimens with a diameter of 2r for different initial crack depth (b/r = 0.25; 0.36; 0.5; 0.75) and the crack shape factor.

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1.   Yasniy P. et al. Calculation of constructive parameters of SMA damper. Sci. J. TNTU. 2017. Vol. 88, No. 4. P. 7–15.
2.   O’Brien B., Weafer F. M., Bruzzi M. S. Shape Memory Alloys for Use in Medicine. Comprehensive Biomaterials II / ed. Ducheyne P. Oxford: Elsevier, 2017. P. 50–78.
3.   Krejsa M. et al. Probabilistic prediction of fatigue damage based on linear fracture mechanics. Frat. ed Integrità Strutt. 2017. Vol. 11. No. 39. P. 43–159.
4.   HELLER R. A. Probabilistic Aspects of Fatigue, STP-511, American Society for Testing and Materials, Philadelphia. 1972. 203 p.
5.   Shatskyi I. P., Perepichka V. V., Ropyak L. Y. On the Influence of Facing on Strength of Solids with Surface Defects. Met. Noveishie Tekhnol. 2020. Vol. 42. No. 1. P. 69–76.
6.   Paris P., Erdogan F. A Critical Analysis of Crack Propagation Laws. J. Basic Eng. ASME, 1963. Vol. 85. No. 4. P. 528–533.
7.   Madsen H. O., Krenk S., Lind N. C. Methods of structural safety, Prentice-Hall Inc., Englewood Cliffs, New Jersey. 1986. 407 p.
8.   Yasniy O. P., Lapusta Y. Effect of the defect initial shape on the fatigue lifetime of a continuous casting machine roll. Comptes Rendus Mécanique. 2016. Vol. 344. No. 8. P. 596–602.
9.   Iasnii V. et al. Experimental study of pseudoelastic NiTi alloy under cyclic loading. Sci. J. TNTU. 2018. Vol. 92. No. 4. P. 7–12.
10. Anderson T. W., Darling D. A. A Test of Goodness of Fit. J. Am. Stat. Assoc. [American Statistical Association, Taylor & Francis, Ltd.], 1954. Vol. 49. No. 268. P. 765–769.
11. Wu S.-X. Shape change of surface crack during fatigue growth. Eng. Fract. Mech. 1985. Vol. 22. No. 5. P. 897–913.
12. Nishitani N., Chen D. Stress Intensity Factor for a Semi-Elliptic Surface Crack in a Shaft under Tension. Trans. Japan Soc. Mech. Eng. Ser. A. 1984. Vol. 50. No. 453. P. 1077–1082.