Fatigue data analysis with Weibull distribution function

Statistical analysis of fatigue data to define mean and characteristic parameters of a linear fatigue model using Weibull distribution

This function is prepared to analyse experimental fatigue data defining a mean curve using a linear fatigue model based on linear regression:

y = Ax + B

It also computes a characteristic value of the linear fatigue model corresponding to a probability of failure (p) based on Weibull distribution function:

y = [Ax + B] * beta [-ln(p)] ^ alfa

Alfa and beta are the scale and shape parameters, respectively, estimated by means of four estimation methods: Linear Least Squares Method, Weighted Linear Least Squares Method, Maximum Likelihood Method and Method of Moments. The most accurate estimation method is determined by aplying three goodness-of-fit tests: Kolmogorov-Smirnov, Anderson-Darling and Chi-Square.

INPUTS:

p - probability of failure [-]

cycles - experimental data: number of cycles

damage_parameter - experimental data: damage parameter

(stress,strain,etc.)

OUTPUTS:

A - Slope of linear fatigue model

B - Intersection of linear fatigue model with ordinate axis

r2 - Coefficient of determination

alfa - Scale parameter for Weibull distribution

beta - Shape parameter for Weibull distribution

detail_cat - Detail category

REFERENCES:

- J. Barbosa, R. Júnior, J. Correia, A. Jesus and R. Calçada, Analysis of the fatigue life estimators of the materials using small samples, Journal of Strain Analysis for Engineering Design, 53 (8): 699-710, https://doi.org/10.1177/0309324718782245

- B. Pedrosa, J. Correia, C. Rebelo and M. Veljkovic, Reliability of Fatigue Fatigue Strength Curves for Riveted Connections Using Normal and Weibull Distribution Functions, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, vol. 6, no. 3, (2020), https://doi.org/10.1061/AJRUA6.0001081

- B. Pedrosa, J. Correia, C. Rebelo, M. Veljkovic and H. Gervásio, Fatigue Experimental Characterization of Preloaded Injection Bolts in a Metallic Bridge Strengthening Scenario, Engineering Structures, vol. 234, 112005 (2021), https://doi.org/10.1016/j.engstruct.2021.112005

Developed by Bruno Pedrosa

ISISE - Institute for Sustainability

and Innovation in Structural Engineering

Department of Civil Engineering

University of Coimbra

Portugal

Bruno Pedrosa ([e-mail])

Ver.: 15-May-2023