Weibull strength distribution and reliability S-N percentiles for tensile tests

Manuel Baro Tijerina; Manuel Román Piña Monarrez; Jesús Barraza Contrera

doi:10.37636/recit.v5n3e230

Authors

Manuel Baro Tijerina Industrial and Technology Department https://orcid.org/0000-0003-1665-8379
Manuel Román Piña Monarrez Industrial and Manufacturing Department at IIT Institute https://orcid.org/0000-0002-2243-3400
Jesús Barraza Contreras Industrial and Manufacturing Department at IIT Institute https://orcid.org/0000-0002-1689-1245

DOI:

https://doi.org/10.37636/recit.v5n3e230

Keywords:

Mechanical design, True stress-strain, Weibull distribution., Fatigue reliability analysis, Stress/Strength, Reliability Engineering

Abstract

Based on the true stress, the ultimate material’s strength, and the fatigue slope b values, the probabilistic percentiles of the S-N curve of ductile materials are formulated. The Weibull β and η parameters used to determine the product’s reliability are determined directly from the material’s strength values corresponding to 103 and 106 cycles. And since in Table corresponding to the properties of this A538 A (b) steel and collected by table 23-A of Shigley Mechanical Engineering Design book; authors present the σt, Sut, and b values of several materials, then the Weibull parameters for each one of these materials as well as the 95% and 5% reliability percentiles of their S-N curves are given. A step-by-step application to the steel A538 A (b) material is presented. And based on the maximum and minimum applied stress values, the corresponding Weibull stress distribution was fitted and used with the Weibull strength distribution, in the stress/strength reliability function to determine the element’s reliability.

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References

M.R. Piña-Monarrez, “Weibull Stress Distribution for Static Mechanical Stress and its Stress/strength Analysis” Qual Reliab Engng Int. vol. 34, pp. 229–244. 2018. https://doi.org/10.1002/qre.18-0532. DOI: https://doi.org/10.1002/qre.2251

R. Budynas, and J. Nisbett, “Shigley’s Mechanical Engineering Design (Tenth edition)”. New York: McGraw Hill 2015. ISBN: 13-978-0-07-339820-4.

J. Gao, Z. An, and B. Liu, “A new method for obtaining P-S-N curves under the condition of small sample”. Proc IMechE, Part O: J Risk and Reliability vol. 231, no. 2, pp. 130-137. 2017. https://doi.org/10.1177/1748006X16686896. DOI: https://doi.org/10.1177/1748006X16686896

K.B. Rao, M.B. Anoop, G. Rahava, M. Prakash, and A. Rajadurai, “Probabilistic fatigue life analysis of welded steel plate railway bridge girders using S-N curve approach”. Proc IMechE, Part O: J Risk and Reliability vol. 227, no. 4, pp. 385-404. 2013. https://doi.org/10.1177/1748006X13480754. DOI: https://doi.org/10.1177/1748006X13480754

D.B. Kececioglu, “Robust Engineering Design‐By‐Reliability with Emphasis on Mechanical Components and Structural Reliability”. Pennsylvania: DEStech Publications Inc. 2003. ISBN:1-932078-07-X. DOI: https://doi.org/10.4271/2003-01-0141

S.R. Schmid, B.J. Hanrock, and B.O. Jacobson, “Fundamentals of Machine Elements SI Version”, Third Edition. CRC Press, Taylor and Francis Group Boca Raton FL 33487-2742. U.S. A. 2014. ISBN:13:978-1-4822-4750-3.

E. S. Lindquist, “Strength of materials and the Weibull distribution”. Prob. Eng. Mech. Vol. 9, no. 3, pp. 191-194. 1994. https://doi.org/10.1016/0266-8920(94)90004-3 DOI: https://doi.org/10.1016/0266-8920(94)90004-3

H. Rinne, “The Weibull distribution a handbook”, CRC press, Boca Ratón, FL, USA, 2009. ISBN: 13-978-1-4200-8743-7.

W. Weibull, “A statistical theory of the strength of materials”. Proceedings, R Swedish Inst Eng Res vol. 151, no. 45, 1939.

R. Jiang, “A novel parameter estimation method for the Weibull distribution on heavely censorated data”. Proc IMechE, Part O: J Risk and Reliability pp. vol. 236, no. 2, pp. 1-10. 2019. https://doi.org/10.1177/1748006X19887648. DOI: https://doi.org/10.1177/1748006X19887648

M.R. Piña-Monarrez, Weibull Analysis for Normal/Accelerated and Fatigue Random Vibration Test. Qual Reliab Engng Int. vol. 35, no. 7, pp. 2408-2428. 2019. https://doi.org/10.1002/qre.2532. DOI: https://doi.org/10.1002/qre.2532

C.R. Mischke, “A distribution-independent plotting rule for ordered failures”. J. Mech. Des. Vol. 104, pp. 593-597. 1979. https://doi.org/10.1115/1.3256391. DOI: https://doi.org/10.1115/1.3256391

M.R. Piña-Monarrez, J.F. Ortiz-Yañez, “Weibull and Lognormal Taguchi Analysis Using Multiple Linear Regression”. Reliab Eng Syst Saf. Vol. 144, pp. 244–53. 2015. https://doi.org/10.1016/j.ress.2015.08.004. DOI: https://doi.org/10.1016/j.ress.2015.08.004

M.R. Piña-Monarrez, “Conditional Weibull control charts using multiple linear regression”. Qual Reliab Eng Int vol. 33, no. 4, pp. 785‐791. 2016. https://doi.org/10.1002/qre.2056. DOI: https://doi.org/10.1002/qre.2056

E.E. Franz Boehm, and E.E. Lewis. “A stress-strength interference approach to reliability analysis of ceramics: Part I — fast fracture Probabilistic Engineering Mechanics”, vol. 7, no. 1, pp. 1-8. 1992. https://doi.org/10.1016/0266-8920(92)90002-Y. DOI: https://doi.org/10.1016/0266-8920(92)90002-Y

R.L.M. Sales Filho, E. López Droguett, ID. Lins, M.C. Moura, M. Amiri, R.V. Azevedo, “Stress‐strength reliability analysis with extreme values based on q‐exponential distribution”. Qual Reliab Engng Int. vol. 33, no. 3, pp. 457‐477. 2017. https://doi.org/10.1002/qre.2020. DOI: https://doi.org/10.1002/qre.2020

Z.A. Al-Hemyari, “Some estimators for the scale parameter and reliability function of Weibull lifetime data”. Proc IMechE, Part O: J Risk and Reliability. Vol. 224, pp. 197-205. 2010. https://doi.org/10.1243/1748006XJRR299. DOI: https://doi.org/10.1243/1748006XJRR299

A. Kleyner, “Effect of field stress variance n test to field correlation in accelerated reliability demonstration testing”. Qual Reliab Engng Int. vol. 31, no. 5, pp. 783‐788. 2015. https://doi.org/10.1002/qre.1635. DOI: https://doi.org/10.1002/qre.1635