A framework for fatigue reliability analysis of high-pressure turbine blades

  • Jie Zhou
  • Hong-Zhong HuangEmail author
  • Yan-Feng Li
  • Junyu Guo
S.I.: Reliability Modeling with Applications Based on Big Data


Fatigue evolution under continued stresses is a process of degradation of material performance with many uncertainties. In order to quantify the uncertainties of materials and working conditions, a probabilistic method is utilized to estimate the reliability of structures by considering scatter of the fatigue life prediction model, in which improvements are provided to model the accumulation of the damage. Firstly, the fatigue parameters are modeled by the Bayesian theory and the finite element analysis. Secondly, the distributions of parameters are transformed by the probabilistic method into the distribution of fatigue life by using the fatigue life prediction model, and a damage accumulation model is chosen to characterize regulation evolution of properties. Finally, the probability distribution function transformation approach is employed to expound distribution of fatigue damage by the known distribution of fatigue life, and a general probabilistic method is then used to estimate the reliability. By combining the above methods, the framework for reliability analysis is established and then is used to calculate the reliability for high-pressure turbine blades in a low cycle fatigue region under variable amplitude loadings.


Reliability analysis Bayesian theory Fatigue life Damage accumulation HP turbine blade 

List of symbols


Elastic Poisson’s ratio


Plastic Poisson’s ratio

τmax, τA, max

Maximum shear stress on the corresponding critical plane


Shear stress on the corresponding critical plane

σn, max, σmax, σB, max

Maximum normal stress on the corresponding critical plane


Normal stress on the corresponding critical plane


Normal stress amplitude

\( \sigma_{f}^{{\prime }} \)

Fatigue strength coefficient


Yield strength

Δγmax, ΔγA, max

Maximum shear strain range on the corresponding critical plane


Shear strain range on the corresponding critical plane

\( \Delta \varepsilon_{e} \)

Elastic strain

\( \Delta \varepsilon_{p} \)

Plastic strain


Normal strain range on the corresponding critical plane


Normal strain amplitude

Δεmax, ΔεB, max

Maximum normal strain range on the corresponding critical plane

\( \varepsilon_{f}^{{\prime }} \)

Fatigue ductility coefficient


Fatigue strength exponent


Fatigue ductility exponent

\( \tau_{f}^{{\prime }} \)

Shear fatigue strength coefficient


Shear fatigue strength exponent

\( \gamma_{f}^{{\prime }} \)

Shear fatigue ductility coefficient


Shear fatigue ductility exponent

\( \mu_{{N_{f} }} \)

Mean value of life cycles

\( \mu_{D} \)

Mean value of damage

\( \sigma_{{N_{f} }} \)

Variance of life cycles

\( \sigma_{D} \)

Variance of damage



\( a \)

Damage exponent


Young’s modulus


Shear modulus



\( N_{f} ,N_{f1} ,N_{f2} \)

Number of cycles to failure

\( T_{f} \)

Total life

\( S \)

Applied stress

\( k,C,m \)

Material parameter

\( \omega_{1} ,\omega_{2} ,\omega_{3} \)

Rotational speed





Finite element analysis






Modified energy-critical plane


Maximum shear strain range plane


Maximum normal strain range plane



This research was supported by the National Natural Science Foundation of China under the Contract Number 51875089. The authors would like to express special thanks to Prof. C. G. Soares at Universidade de Lisboa for his considerable help. The authors also appreciate the reviewers for their constructive comments on this paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jie Zhou
    • 1
    • 2
  • Hong-Zhong Huang
    • 1
    • 2
    Email author
  • Yan-Feng Li
    • 1
    • 2
  • Junyu Guo
    • 1
    • 2
  1. 1.School of Mechanical and Electrical EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.Center for System Reliability and SafetyUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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