Identifying crack tip position and stress intensity factors from displacement data
Source abstract
Abstract
Fracture prognosis and characterization efforts require knowledge of crack tip position and the Stress Intensity Factors (SIFs) acting in the vicinity of the crack. Here, we present an efficient numerical approach to infer both of these characteristics under a consistent theoretical framework from noisy, unstructured displacement data. The novel approach utilizes the separability of the asymptotic linear elastic fracture mechanics fields to expedite the search for crack tip position and is particularly useful for noisy displacement data. The manuscript begins with an assessment of the importance of accurately locating crack tip position when quantifying the SIFs from displacement data. Next, the proposed separability approach for quickly inferring crack tip position is introduced. Comparing to the widely used displacement correlation approach, the performance of the separability approach is assessed. Cases involving both noisy data and systematic deviation from the asymptotic linear elastic fracture mechanics model are considered, e.g. inelastic material behavior and finite geometries. An open source python implementation of the proposed approach is available for use by those doing field and laboratory work involving digital image correlation and simulations, e.g. finite element, discrete element, molecular dynamics and peridynamics, where the crack tip position is not explicitly defined.
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Research context
OpenAlex topics: Non-Destructive Testing Techniques · Numerical methods in engineering · Rock Mechanics and Modeling
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References (41)
Show source-provided references
1. Ayatollahi M, Nejati M (2011) An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue Fract Eng Mater Struct 34(3):159–17610.1111/j.1460-2695.2010.01504.x ↗
2. Baker K, Warner D (2012) Extended timescale atomistic modeling of crack tip behavior in aluminum. Modell Simul Mater Sci Eng 20(6):06500510.1088/0965-0393/20/6/065005 ↗
3. Bertsekas D, Tsitsiklis JN (2008) Introduction to probability, vol 1. Athena Scientific, Nashua
4. Buehler MJ, Van Duin AC, Goddard WA III (2006) Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field. Phys Rev Lett 96(9):09550510.1103/PhysRevLett.96.095505 ↗
5. Carroll J, Efstathiou C, Lambros J, Sehitoglu H, Hauber B, Spottswood S, Chona R (2009) Investigation of fatigue crack closure using multiscale image correlation experiments. Eng Fract Mech 76:2384–239810.1016/j.engfracmech.2009.08.002 ↗
6. Diniz-Ehrhardt M, Ferreira D, Santos S (2019) Combining pattern search and implicit filtering for solving linearly constrained minimization problems with noisy objective functions. Optim Methods Softw 34(4):827–85210.1080/10556788.2018.1464570 ↗
7. Freund LB (1998) Dynamic fracture mechanics. Cambridge University Press, Cambridge
8. Gonzáles GL, González JA, Castro JT, Freire JL (2017) A j-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects. Theoret Appl Fract Mech 90:14–2110.1016/j.tafmec.2017.02.008 ↗
9. Gu W, Warner DH (2021) Dissolution at a ductile crack tip. Phys Rev Lett 127(14):14600110.1103/PhysRevLett.127.146001 ↗
10. Hamam R, Hild F, Roux S (2007) Stress intensity factor gauging by digital image correlation: application in cyclic fatigue. Strain 43(3):181–19210.1111/j.1475-1305.2007.00345.x ↗
11. Hansen R, Waldram D, Thai T, Berke R (2021) Super resolution digital image correlation (SR-DIC): an alternative to image stitching at high magnifications. Exp Mech 61(9):1351–136810.1007/s11340-021-00729-2 ↗
12. Hooke R, Jeeves TA (1961) “Direct search’’ solution of numerical and statistical problems. J ACM 8(2):212–22910.1145/321062.321069 ↗
13. Hughes TJ (2012) The finite element method: linear static and dynamic finite element analysis. Courier Corporation, Chelmsford
14. Jiang L, Xie H, Pan B (2015) Speeding up digital image correlation computation using the integral image technique. Opt Lasers Eng 65:117–12210.1016/j.optlaseng.2014.07.001 ↗
15. Lewis RM, Torczon V, Trosset MW (2000) Direct search methods: then and now. J Comput Appl Math 124(1–2):191–20710.1016/S0377-0427(00)00423-4 ↗
16. Liang T, Ye W (2014) An efficient hybrid DSMC/MD algorithm for accurate modeling of micro gas flows. Commun Comput Phys 15(1):246–26410.4208/cicp.141112.160513a ↗
17. Lim I, Johnston I, Choi S (1992) Comparison between various displacement-based stress intensity factor computation techniques. Int J Fract 58(3):193–21010.1007/BF00015615 ↗
18. Mai NT, Choi ST (2018) Atomic-scale mutual integrals for mixed-mode fracture: abnormal fracture toughness of grain boundaries in graphene. Int J Solids Struct 138:205–21610.1016/j.ijsolstr.2018.01.013 ↗
19. Pataky GJ, Sangid MD, Sehitoglu H, Hamilton RF, Maier HJ, Sofronis P (2012) Full field measurements of anisotropic stress intensity factor ranges in fatigue. Eng Fract Mech 94:13–2810.1016/j.engfracmech.2012.06.002 ↗
20. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–1910.1006/jcph.1995.1039 ↗
21. Reed RP (1983) The Economic Effects of Fracture in the United States: a report to NBS by Batelle Columbus Laboratories. National Bureau of Standards, US Department of Commerce
22. Réthoré J, Gravouil A, Morestin F, Combescure A (2005) Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral. Int J Fract 132:65–7910.1007/s10704-004-8141-4 ↗
23. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35(2):379–38610.1115/1.3601206 ↗
24. Rice JR (1974) Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids 22(1):17–2610.1016/0022-5096(74)90010-6 ↗
25. Sanford RJ, Dally JW (1979) A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns. Eng Fract Mech 11(4):621–63310.1016/0013-7944(79)90123-1 ↗
26. Seitl S, Malíková L, Sobek J, Frantík P, Lopez-Crespo P (2017) Williams expansion-based approximation of the stress field in an al 2024 body with a crack from optical measurements. Frattura ed Integrità Strutturale 11(41):323–33110.3221/IGF-ESIS.41.43 ↗
27. Smith D, Ayatollahi M, Pavier M (2001) The role of t-stress in brittle fracture for linear elastic materials under mixed-mode loading. Fatigue Fract Eng Mater Struct 24(2):137–15010.1046/j.1460-2695.2001.00377.x ↗
28. Stenström C, Eriksson K (2019) The j-contour integral in peridynamics via displacements. Int J Fract 216(2):173–18310.1007/s10704-019-00351-3 ↗
29. Stepanova L, Roslyakov P (2016) Complete williams asymptotic expansion of the stress field near the crack tip: analytical solutions, interference-optic methods and numerical experiments. In: AIP Conference Proceedings, AIP Publishing LLC, vol 1785, p 03002910.1063/1.4967050 ↗
30. Suresh S (1998) Fatigue of materials. Cambridge University Press, Cambridge10.1017/CBO9780511806575 ↗
31. Tada H, Paris PC, Irwin GR (1973) The stress analysis of cracks. Handbook, Del Research Corporation 34
32. Thompson AP, Aktulga HM, Berger R, Bolintineanu DS, Michael Brown W, Crozier PS, in’t Veld PJ, Kohlmeyer A, Moore SG, Nguyen TD, Shan R, Stevens M, Tranchida J, Trott C, Plimpton SJ (2021) LAMMPS—a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput Phys Commun 271:10817110.1016/j.cpc.2021.108171 ↗
33. Wang B, Oterkus S, Oterkus E (2020) Determination of horizon size in state-based peridynamics. Continuum Mech Thermodyn 1–2410.1007/s00161-020-00896-y ↗
34. Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–11410.1115/1.4011454 ↗
35. Wilson MA, Grutzik SJ, Chandross M (2019) Continuum stress intensity factors from atomistic fracture simulations. Comput Methods Appl Mech Eng 354:732–74910.1016/j.cma.2019.05.050 ↗
36. Wu R, Kong C, Li K, Zhang D (2016) Real-time digital image correlation for dynamic strain measurement. Exp Mech 56(5):833–84310.1007/s11340-016-0133-6 ↗
37. Yoda M (1980) The j-integral fracture toughness for mode II. Int J Fract 16:R175–R17810.1007/BF00018247 ↗
38. Yoneyama S, Arikawa S, Kusayanagi S, Hazumi K (2014) Evaluating j-integral from displacement fields measured by digital image correlation. Strain 50(2):147–16010.1111/str.12074 ↗
39. Zanganeh M, Lopez-Crespo P, Tai Y, Yates J (2013) Locating the crack tip using displacement field data: a comparative study. Strain 49(2):102–11510.1111/str.12017 ↗
40. Zehnder AT (2012) Fracture mechanics, vol 62. Springer, New York10.1007/978-94-007-2595-9 ↗
41. Zhao M, Gu W, Warner DH (2022) Atomic mechanism of near threshold fatigue crack growth in vacuum. Nat Commun 13(1):81210.1038/s41467-022-28481-8 ↗