Chapter 12
Multi-mode Model and Calculation
Method for Fatigue Damage
Development
Ilia S. Nikitin , Nikolay G. Burago , Alexander D. Nikitin ,
and Boris A. Stratula
Abstract A multi-mode kinetic model of damage development under cyclic loading
is proposed to describe the process of fatigue failure. To determine the coefficients of
the kinetic equation of damage, the well-known criterion of multiaxial fatigue failure
is used. A procedure is proposed for calculating the kinetic equation coefficients for
various fatigue failure modes of the LCF-HCF and VHCF. A numerical method for
calculating crack-like zones up to macrofracture is developed. The model parameters are determined from the condition of matching the experimental and calculated
fatigue curve for a specimen of a certain geometry at a given load amplitude and
cycle asymmetry coefficient. Using the obtained values, the results of experiments
on specimens of a different geometry and asymmetry coefficients were reproduced
and the model and calculation algorithm performance were confirmed.
12.1 Introduction
Entire classes of criteria have been constructed that relate the number of cycles before
the initiation of fatigue damage (microcracks) with the amplitudes and maximum
values in the cycle (or average) that characterize the uniform stress-strain state of the
working part of the specimen in a fatigue test.
I. S. Nikitin (B) · N. G. Burago · A. D. Nikitin · B. A. Stratula
Institute for Computer Aided Design of the RAS, 19/18, Vtoraya Brestskaya ul., Moscow 123056,
Russian Federation
e-mail: i_nikitin@list.ru
N. G. Burago
e-mail: buragong@yandex.ru
A. D. Nikitin
e-mail: nikitin_alex@bk.ru
B. A. Stratula
e-mail: stratula@matway.net
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_12
157
Multi-mode Model and Calculation
Method for Fatigue Damage
Development
Ilia S. Nikitin , Nikolay G. Burago , Alexander D. Nikitin ,
and Boris A. Stratula
Abstract A multi-mode kinetic model of damage development under cyclic loading
is proposed to describe the process of fatigue failure. To determine the coefficients of
the kinetic equation of damage, the well-known criterion of multiaxial fatigue failure
is used. A procedure is proposed for calculating the kinetic equation coefficients for
various fatigue failure modes of the LCF-HCF and VHCF. A numerical method for
calculating crack-like zones up to macrofracture is developed. The model parameters are determined from the condition of matching the experimental and calculated
fatigue curve for a specimen of a certain geometry at a given load amplitude and
cycle asymmetry coefficient. Using the obtained values, the results of experiments
on specimens of a different geometry and asymmetry coefficients were reproduced
and the model and calculation algorithm performance were confirmed.
12.1 Introduction
Entire classes of criteria have been constructed that relate the number of cycles before
the initiation of fatigue damage (microcracks) with the amplitudes and maximum
values in the cycle (or average) that characterize the uniform stress-strain state of the
working part of the specimen in a fatigue test.
I. S. Nikitin (B) · N. G. Burago · A. D. Nikitin · B. A. Stratula
Institute for Computer Aided Design of the RAS, 19/18, Vtoraya Brestskaya ul., Moscow 123056,
Russian Federation
e-mail: i_nikitin@list.ru
N. G. Burago
e-mail: buragong@yandex.ru
A. D. Nikitin
e-mail: nikitin_alex@bk.ru
B. A. Stratula
e-mail: stratula@matway.net
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_12
157