Research Papers

A Probabilistic Design Method for Fatigue Life of Metallic Component

[+] Author and Article Information
Danial Faghihi

Institute for Computational Engineering
and Sciences,
The University of Texas at Austin,
Austin, TX 78712
e-mail: danial@ices.utexas.edu

Subhasis Sarkar, Mehdi Naderi, Nagaraja Iyyer

Technical Data Analysis, Inc.,
Falls Church, VA 22042

Jon E. Rankin, Lloyd Hackel

MIC-Laser Peening Division,
Livermore, CA 94551

1Corresponding author.

Manuscript received July 17, 2017; final manuscript received November 2, 2017; published online December 12, 2017. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 4(3), 031005 (Dec 12, 2017) (11 pages) Paper No: RISK-17-1079; doi: 10.1115/1.4038372 History: Received July 17, 2017; Revised November 02, 2017

In the present study, a general probabilistic design framework is developed for cyclic fatigue life prediction of metallic hardware using methods that address uncertainty in experimental data and computational model. The methodology involves: (i) fatigue test data conducted on coupons of Ti6Al4V material, (ii) continuum damage mechanics (CDM) based material constitutive models to simulate cyclic fatigue behavior of material, (iii) variance-based global sensitivity analysis, (iv) Bayesian framework for model calibration and uncertainty quantification, and (v) computational life prediction and probabilistic design decision making under uncertainty. The outcomes of computational analyses using the experimental data prove the feasibility of the probabilistic design methods for model calibration in the presence of incomplete and noisy data. Moreover, using probabilistic design methods results in assessment of reliability of fatigue life predicted by computational models.

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Fig. 3

Scatterplots illustrating a qualitative sensitivity analysis for the fatigue damage using 1000 Monte Carlo samples of the parameter space

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Fig. 4

Scatterplots illustrating a qualitative sensitivity analysis for the fatigue damage using 1000 Monte Carlo samples of the parameter space

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Fig. 1

Computational model as a black-box (input–output). The underlying physics of the fatigue damage model is hidden in order to develop a general uncertainty treatment process.

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Fig. 2

The proposed framework of uncertainty treatment in computational model and observational data. First, the computational fatigue damage model is subjected to sensitivity analysis to determine significant input parameters of the model. Next, using experimental data, the important parameters of model are calibrated. Utilizing statistical inverse methods (Bayesian approach) for model calibration results in encapsulating all the uncertainties due to fatigue test data and inadequacy of the fatigue damage model into the probability distribution function of the model parameters. Finally, the statistically calibrated model is used to make prediction or design decision with quantified uncertainty.

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Fig. 5

Total effect sensitivity index computed using 1000 Monte Carlo samples

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Fig. 6

Comparison between the KDEs of the number of cycles before failure resulting from fatigue damage model for the cases when (S, s) and (E, ν) considered as single (deterministic) values. Results obtained from 2000 Monte Carlo samples of the parameter space according to the distributions are presented in Table 1.

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Fig. 7

(a) Airfoil coupon of Ti6Al4V designed to generate fatigue test data used to calibrate lifetime predictions. (b) Fatigue test coupon instrumented for strain measurements on fatigue rig.

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Fig. 8

Stress analysis of fatigue test coupon including notch agrees with the 35 ksi loading and predicts 99 ksi load in the notch

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Fig. 9

Calibrated material parameters of the fatigue damage model. Posterior marginal density estimation of (a) damage denominator S and (b) damage exponent s.

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Fig. 10

Model prediction of fatigue strength of material (S–N diagram) with R = 0.1: mean values and 95% confidence interval

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Fig. 11

Probability density of the failure cycles under maximum stress of 100 ksi and R = 0.1 applied load and compressive residual plastic strain of 0.193. Results obtained from 100 Monte Carlo samples of posterior distributions of random parameters.




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