journal article·2023-04Open access

A framework for automating the parameter determination of crack growth models

Athanasios Iliopoulos, John G. Michopoulos, Rhys Jones, Anthony J. Kinloch, Daren Peng

Abstract

Motivated by the need for an efficient fatigue crack growth prediction infrastructure for both legacy and novel materials, we have initiated the development of an automated computational framework capable of determining crack growth model parameters for an equationally defined model. As a first step in addressing this need, the present paper focuses on the Hartman-Schijve crack growth variant of the NASGRO equation by exploring and comparing various global optimization methods for parameter determination and evaluating their performance by using both synthetic and actual data. It also introduces the concept of the total least-squares minimization criterion within the context of crack growth modeling. The development of an open-source software library and an application implementing the approach are also described and are available for distribution to the technical community.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Statistical and numerical algorithms · Soil Geostatistics and Mapping · Scientific Measurement and Uncertainty Evaluation

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (50)

Show source-provided references
1. A Critical Analysis of Crack Propagation Laws10.1115/1.3656900 ↗
2. A review of effective-strain based and multi R-ratio crack propagation models and a comparison of simulated results using the two approaches10.1016/j.ijfatigue.2020.105920 ↗
3. Blasón S, Correia J, Apetre N, Arcari A, De Jesus A, Moreira P, Fernández-Canteli A. Proposal of a fatigue crack propagation model taking into account crack closure effects using a modified CCS crack growth model. In: Procedia Structural Integrity, vol. 1, 2016, p. 110–7.10.1016/j.prostr.2016.02.016 ↗
4. A comparative analysis of driving force models for fatigue crack propagation of CFRP-reinforced steel structure10.1016/j.ijfatigue.2019.105266 ↗
5. Forman R, Shivakumar V, Cardinal J, Williams L, McKeighan P. Fatigue crack growth database for damage tolerance analysis. Office of Aviation Research, U.S. Department of Defense, DOT/FAA/AR-05/15, Washington, DC, 2005.
6. Kłysz S, Leski A. Good Practice for Fatigue Crack Growth Curves Description. In: Applied Fracture Mechanics, A. Belov, Ed., InTech, 2012.10.5772/52794 ↗
7. NASGRO® Fracture Mechanics and Fatigue Crack Growth Analysis Software, vol. 9.2, NASA-JSC and Southwest Research Institute, 2020.
8. Interpreting fatigue test results using a probabilistic fracture approach10.1016/j.ijfatigue.2005.01.006 ↗
9. Experimental and analytical investigation of fatigue10.1016/S0951-8339(02)00004-7 ↗
10. Huang X, Cui W, Leng J. A model of fatigue crack growth under various load spectra. In: Proc of Sih GC, 7th Int conf of MESO, August 1–4, 2005, Montreal, Canada, 2005.
11. Crack Growth in a Range of Additively Manufactured Aerospace Structural Materials10.3390/aerospace5040118 ↗
12. Representing crack growth in additively manufactured Ti-6Al-4V10.1016/j.ijfatigue.2018.07.019 ↗
13. An analysis of the total least squares problem10.1137/0717073 ↗
14. Senning M. Process parameter identification: A total least square approach. In: Proceedings of the Third IFAC/IFIP Symposium, 5–8 October 1982, Madrid,Spain, 1983.10.1016/B978-0-08-029352-3.50047-7 ↗
15. Overview of total least-squares methods10.1016/j.sigpro.2007.04.004 ↗
16. Bisection is optimal10.1007/BF01459080 ↗
17. Yamamoto T. Historical Developments in Convergence Analysis for Newton's and Newton-like Methods. In: Numerical Analysis : Historical Developments in the 20th Century, C. Brezinski and L. Wuytack, Eds., Elsevier, 2001, p. 241–63.10.1016/B978-0-444-50617-7.50011-2 ↗
18. On the convergence of Halley's method10.1080/00029890.1981.11995308 ↗
19. A Note on Alternative Regressions10.2307/1907024 ↗
20. Bivariate line-fitting methods for allometry10.1017/S1464793106007007 ↗
21. Draper N, Smith H. Applied Regression Analysis, Wiley-Interscience, 1998.10.1002/9781118625590 ↗
22. Tofallis C. Model Fitting for Multiple Variables by Minimising the Geometric Mean Deviation. In: Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications, Dordrecht: Kluwer Academic Publ., 2002.10.1007/978-94-017-3552-0_23 ↗
23. Johnson SG. The NLopt nonlinear-optimization package, 2021. [Online]. Available: http://github.com/stevengj/nlopt. [Accessed September 2021].
24. Lipschitzian Optimization without the Lipschitz Constant10.1007/BF00941892 ↗
25. A locally-biased form of the DIRECT algorithm10.1023/A:1017930332101 ↗
26. Price WL. A controlled random search procedure for global optimization. In: Towards Global Optimization 2, L. C. W. D. a. G. P. Szego, Ed., Amsterdam, North-Holland Press, 1978, p. 71–84.
27. Global optimization by controlled random search10.1007/BF00933504 ↗
28. Some variants of the controlled random search algorithm for global optimization10.1007/s10957-006-9101-0 ↗
29. Application of deterministic low-discrepancy sequences in global optimization10.1007/s10589-005-4615-1 ↗
30. Runarsson TP, Y. X. Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evolut Comput. 2000; 4(3):284–94.10.1109/4235.873238 ↗
31. Search biases in constrained evolutionary optimization10.1109/TSMCC.2004.841906 ↗
32. Designing Novel Photonic Devices by Bio-Inspired Computing10.1109/LPT.2010.2051222 ↗
33. da Silva Santos CH. Parallel and Bio-Inspired Computing Applied to Analyze Microwave and Photonic Metamaterial Strucutures (Ph.D. thesis), University of Campinas, 2010.
34. Evolution Strategies: A Comprehensive Introduction10.1023/A:1015059928466 ↗
35. Rechenberg I. Evolutionsstrategie – Optimierung technischer Systeme nach Prinzipien der biologischen Evolution (Ph.D Thesis), Reprinted by Fromman-Holzboog (1973), 1971.
36. Minimization of multiextremal functions under nonconvex constraints10.1007/BF01075079 ↗
37. ISO/IEC 14882:2020 - Programming languages - C++, Geneva: International Organization for Standardization, 2020.
38. Iliopoulos A, Michopoulos JG. CGROW: A framework for fatigue crack growth model parameter determination. U.S. Naval Research Laboratory, 21 Sep 2021. [Online]. Available: https://github.com/USNavalResearchLaboratory/cgrow. [Accessed 21 Sep 2022].
39. Iliopoulos A, Michopoulos JG. CGROW - Releases: A framework for fatigue crack growth model parameter determination. U.S. Naval Research Laboratory, 21 Sep 2021. [Online]. Available: https://github.com/USNavalResearchLaboratory/cgrow/releases. [Accessed 22 Sep. 2022].
40. Martin K, Hoffman B. Mastering CMake: A Cross-Platform Build System, New York: Kitware, Inc., 2008.
41. “Qt: Cross platform software development for embedded and desktop,” The Qt Company, Sep 2021. [Online]. Available: https://www.qt.io/. [Accessed 29 Sep 2021].
42. Stroustrup B. The C++ Programming Language, Boston, MA: Addison-Wesley, 2013.
43. Iliopoulos A, Michopoulos JG. CXXPLOT: A simple to use C++ 2D plotting library. U.S. Naval Research Laboratory, 29 Sep 2021. [Online]. Available: https://github.com/USNavalResearchLaboratory/cxxplot. [Accessed 21 Sep 2022].
44. Eichhammer E. Qt Plotting Widget QCustomPlot. Sep 2021. [Online]. Available: https://www.qcustomplot.com/. [Accessed 21 Sep 2022].
45. Modelling the Variability and the Anisotropic Behaviour of Crack Growth in SLM Ti6Al4V10.3390/ma14061400 ↗
46. Further Studies into Crack Growth in Additively Manufactured Materials10.3390/ma13102223 ↗
47. Fatigue crack propagation behaviour of epoxy resins modified with silica-nanoparticles10.1016/j.polymer.2015.01.036 ↗
48. Murri G. Evaluation of Delamination Onset and Growth Characterization Methods under Mode I Fatigue Loading. NASA/TM-2013-217966, Langley Research Center, Hampton, Virginia, 2013.
49. Delamination growth in polymer-matrix fibre composites and the use of fracture mechanics data for material characterisation and life prediction10.1016/j.compstruct.2017.07.097 ↗
50. Vugrin KW, Swiler LP, Roberts RM, Mack NJS, Sullivan SP. Confidence Region Estimation Techniques for Nonlinear Regression: Three Case Studies. Sandia National Laboratories, Albuquerque, 2005.10.2172/877714 ↗