Accelerated Stress Testing and Reliability Conference

Probabilistic Reliability Evaluation of Space System Considering Physics of Fatigue Failure

DR. M.Pour-Gol Mohammad Mechanical Engineering dep.

Sahand University of Technology

Tabriz-East Azerbaijan-Islamic Republic of Iran

pourgolmohammad@sut.ac.ir

ASTR 2016, Sep 28 - 30, Pensacola Beach, FL January-4-17 1

mailto:pourgolmohammad@sut.ac

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INTRODUCTION

Fatigue failure

Constant amplitude loading

Constant amplitude loading models

Variable amplitude loading (overload and underload)

Variable amplitude loading model

Uncertainty analysis

Reliability analysis

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FATIGUE FAILURE

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CONSTANT AMPLITUDE LOADING

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Walker model isnt able to describe third

phase of fatigue crack growth, but

completely could describe the second phase

of fatigue crack growth.

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CONSTANT AMPLITUDE LOADING

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Forman model opposite of Walker model

completely describe the third phase.

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VARIABLE AMPLITUDE LOADING

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RESULT (FATIGUE ANALYSIS)

Constant Amplitude loading: (SMAX=15lb/in R=0.5)

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WALKER CONSTANT AMPLITUDE LOADING

FORMAN CONSTANT AMPLITUDE LOADING

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RESULT (FATIGUE ANALYSIS)

Variable Amplitude loading: (SMAX=15lb/in stress ratio=0.5 Sol=22.5lb/in)

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WALKER VARIABLE AMPLITUDE LOADING

FORMAN VARIABLE AMPLITUDE LOADING

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UNCERTAINITY ANALYSIS

Uncertainty result for difference stress ratio (0, 0.1, 0.3, 0.5, 0.7, and 0.9)

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WALKER CONSTANT AMPLITUDE LOADING

FORMAN CONSTANT AMPLITUDE LOADING

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RELIABILITY (STOCHASTIC MODEL)

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Accelerated Stress Testing and Reliability Conference

RELIABILITY (STOCHASTIC MODEL)

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Accelerated Stress Testing and Reliability Conference

RELIABILITY (STOCHASTIC MODEL)

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Accelerated Stress Testing and Reliability Conference

RELIABILITY (STOCHASTIC MODEL)

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Accelerated Stress Testing and Reliability Conference

RELIABILITY (STOCHASTIC MODEL)

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Accelerated Stress Testing and Reliability Conference

RELIABILITY (STOCHASTIC MODEL)

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RELIABILITY (STOCHASTIC MODEL)

RESULT

EXPERIMENTAL DATA:

AFGROW software and MATLAB code:

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Error (%) R square Service time model

0.4 (under) 0.9731 54576 power

0.75 (over) 0.9637 53950 exponential

Error (%) R square Service time model

1.68 (under) 1 376524 Power

17.71 (over) 0.9436 304719 Exponential

2.3 (under) 0.9993 379000 Rational

0.99 (under) 1 373969 Global

Error (%) R square Service time model

3.49 (under) 1 371758 Power

12.35 (over) 0.956 314942 Exponential

5.44 (under) 0.9994 379000 Rational

2.03 (under) 0.9999 366716 Global

WALKER

MODEL

FORMAN

MODEL

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RELIABILITY (STOCHASTIC MODEL)

cumulative distribution function (CFD) versus number of cycles

Constant amplitude loading

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WALKER MODEL

POEWR FUNCTION

WALKER MODEL

GLOBAL FUNCTION

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RELIABILITY (STOCHASTIC MODEL)

Variable amplitude loading

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WALKER MODEL

VAL

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CONCLUSION

In uncertainty analyze, it is observed that by increasing in the cycle (crack size),

uncertainty range is widen.

Constant amplitude loading and the same stress intensity factor range but with a

different stress ratio, the uncertainty range was widen with increasing stress ratio.

Accuracy of Yang and Manning method depends on the approximation function.

By increasing accuracy of this relation, the result of stochastic analysis will be

increased.

In this study addition of power functions, three different functions is introduced.

These functions have more accuracy or less amount of computation than former

ones.

For constant amplitude loading a unique function (power function, rational

function, ) is introduced to obtain crack growth rate but for variable amplitude

loading couldnt define unique function and in this study Matlab developed code is

used instead of function.

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REFERENCES

[1] N. E. Dowling, Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue: Prentice hall, 1993.

[2] W. Cui, A state-of-the-art review on fatigue life prediction methods for metal structures, Journal of marine science and technology, vol. 7, no. 1, pp. 43-56, 2002.

[3] X. Huang, M. Torgeir, and W. Cui, An engineering model of fatigue crack growth under variable amplitude loading, International Journal of Fatigue, vol. 30, no. 1, pp. 2-10, 2008.

[4] P. Paris, and F. Erdogan, A critical analysis of crack propagation laws, Journal of Fluids Engineering, vol. 85, no. 4, pp. 528-533, 1963.

[5] K. Walker, The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum, Effects of environment and complex load history on fatigue life, vol. 462, pp. 1-14, 1970.

[6] R. G. Forman, V. Kearney, and R. Engle, Numerical analysis of crack propagation in cyclic-loaded structures, Journal of Fluids Engineering, vol. 89, no. 3, pp. 459-463, 1967.

[7] G. F. Abdelal, N. Abuelfoutouh, and A. H. Gad, Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture and Testing: Springer Science & Business Media, 2012.

[8] M. Sander, and H. Richard, Fatigue crack growth under variable amplitude loading Part I: experimental investigations, Fatigue & Fracture of Engineering Materials & Structures, vol. 29, no. 4, pp. 291-301, 2006.

[9] M. Yazdanipour, M. Pourgol-Mohammad, N.-A. Choupani, and M. Yazdani, Fatigue Life Prediction Based on Probabilistic Fracture Mechanics: Case Study of Automotive Parts, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, vol. 2, no. 1, pp. 011002, 2016.

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[10] W. Wu, and C. Ni, A study of stochastic fatigue crack growth modeling through experimental data, Probabilistic Engineering Mechanics, vol. 18, no. 2, pp. 107-118, 2003.

[11] X. Wang, M. Rabiei, J. Hurtado, M. Modarres, and P. Hoffman, A probabilistic-based airframe integrity management model, Reliability Engineering & System Safety, vol. 94, no. 5, pp. 932-941, 2009.

[12] J. Yang, and S. Manning, Stochastic crack growth analysis methodologies for metallic structures, Engineering Fracture Mechanics, vol. 37, no. 5, pp. 1105-1124, 1990.

[13] S. Beden, S. Abdullah, and A. Ariffin, Review of fatigue crack propagation models for metallic components, European Journal of Scientific Research, vol. 28, no. 3, pp. 364-397, 2009.

[14] A. Ray, and R. Patankar, Fatigue crack growth under variable-amplitude loading: Part IModel formulation in state-space setting, Applied Mathematical Modelling, vol. 25, no. 11, pp. 979-994, 2001.

[15] S. Khan, R. Alderliesten, J. Schijve, and R. Benedictus, On the fatigue crack growth prediction under variable amplitude loading, Computational and experimental analysis of damaged materials, pp. 77-105, 2007.

[16] L. Li, "MATLAB User Manual," Natick, MA: Matlab.

[17] J. A. Harter, AFGROW users guide and technical manual, D