journal article·2024-12Open access

Failure assessment of eccentric circular holes under compressive loading

Francesco Ferrian, Alberto Sapora, Rafael Estevez, Aurélien Doitrand

International Journal of Fracture· Volume 248· Issue 1-3

Abstract

Abstract The present work aims to investigate the failure size effect on flattened disks containing an eccentric circular hole under mode I loading conditions. For this purpose, uniaxial compression tests are carried out on polymethyl methacrylate (PMMA) samples with holes. Depending on the hole radius and eccentricity, the energy release rate is either an increasing or decreasing function of the crack length, thus affecting the stability of crack propagation. Experimental results are interpreted and discussed through the coupled stress and energy criterion of Finite Fracture Mechanics. The approach lies on the assumption of a finite crack advance and it is implemented through the numerical estimation of the stress field and the Incremental Energy Release Rate functions. Finally, stability and crack speed propagation are discussed under the assumption of Linear Elastic Fracture Mechanics. Theoretical predictions reveal in agreement with experimental results thus demonstrating that the Coupled Criterion effectively captures the failure condition.
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Research context

OpenAlex topics: Fatigue and fracture mechanics · Mechanical Behavior of Composites · Structural Response to Dynamic Loads

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References (59)

Show source-provided references
1. Awerbuch J, Madhukar MS (1985) Notched strength of composite laminates: predictions and experiments—a review. J Reinf Plast Compos 4:3–159. https://doi.org/10.1177/07316844850040010210.1177/073168448500400102 ↗
2. Baldassari M, Monaco A, Sapora A, Cornetti P (2023) Size effect on flexural strength of notched and un-notched concrete and rock specimens by finite fracture mechanics. Theor Appl Fract Mech 125:103787. https://doi.org/10.1016/j.tafmec.2023.10378710.1016/j.tafmec.2023.103787 ↗
3. Berto F, Campagnolo A, Elices M, Lazzarin P (2013) A synthesis of polymethylmethacrylate data from U-notched specimens and V-notches with end holes by means of local energy. Mater Des 49:826–833. https://doi.org/10.1016/j.matdes.2013.01.07410.1016/j.matdes.2013.01.074 ↗
4. Carrère N, Doitrand A, Martin E, Leguillon D (2021) Theoretical study based on 2D assumptions of the influence of small pores on crack initiation in adhesively bonded joints. Int J Adhes Adhes 111:102979. https://doi.org/10.1016/j.ijadhadh.2021.10297910.1016/j.ijadhadh.2021.102979 ↗
5. Chao Correas A, Sapora A, Reinoso J et al (2023) Coupled versus energetic nonlocal failure criteria: a case study on the crack onset from circular holes under biaxial loadings. Eur J Mech A/Solids 101:105037. https://doi.org/10.1016/j.euromechsol.2023.10503710.1016/j.euromechsol.2023.105037 ↗
6. Chao Correas A, Reinoso J, Cornetti P, Corrado M (2024) On the (lack of) representativeness of quasi-static variational fracture models for unstable crack propagation. J Mech Phys Solids 186:105573. https://doi.org/10.1016/j.jmps.2024.10557310.1016/j.jmps.2024.105573 ↗
7. Chen X, Doitrand A, Godin N, Fusco C (2023) Crack initiation in PMMA plates with circular holes considering kinetic energy and nonlinear elastic material behavior. Theor Appl Fract Mech 124:103783. https://doi.org/10.1016/j.tafmec.2023.10378310.1016/j.tafmec.2023.103783 ↗
8. Choi SR, Salem JA (1993) Fracture toughness of PMMA as measured with indentation cracks. J Mater Res 8:3210–3217. https://doi.org/10.1557/JMR.1993.321010.1557/JMR.1993.3210 ↗
9. Cicero S, Madrazo V, Carrascal IA (2012) Analysis of notch effect in PMMA using the theory of critical distances. Eng Fract Mech 86:56–72. https://doi.org/10.1016/j.engfracmech.2012.02.01510.1016/j.engfracmech.2012.02.015 ↗
10. Cicero S, Torabi AR, Madrazo V, Azizi P (2018) Prediction of fracture loads in PMMA U-notched specimens using the equivalent material concept and the theory of critical distances combined criterion. Fatigue Fract Eng Mater Struct 41:688–699. https://doi.org/10.1111/ffe.1272810.1111/ffe.12728 ↗
11. Cornetti P, Pugno N, Carpinteri A, Taylor D (2006) Finite fracture mechanics: a coupled stress and energy failure criterion. Eng Fract Mech 73:2021–2033. https://doi.org/10.1016/j.engfracmech.2006.03.01010.1016/j.engfracmech.2006.03.010 ↗
12. Doitrand A, Estevez R, Leguillon D (2019) Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression. Eur J Mech A/Solids 76:290–299. https://doi.org/10.1016/j.euromechsol.2019.04.01310.1016/j.euromechsol.2019.04.013 ↗
13. Doitrand A, Sapora A (2020) Nonlinear implementation of finite fracture mechanics: a case study on notched Brazilian disk samples. Int J Non Linear Mech 119:103245. https://doi.org/10.1016/j.ijnonlinmec.2019.10324510.1016/j.ijnonlinmec.2019.103245 ↗
14. Doitrand A, Leguillon D (2021) Asymptotic analysis of pore crack initiation near a free edge. Theor Appl Fract Mech 116:103125. https://doi.org/10.1016/j.tafmec.2021.10312510.1016/j.tafmec.2021.103125 ↗
15. Doitrand A, Cornetti P, Sapora A, Estevez R (2021a) Experimental and theoretical characterization of mixed mode brittle failure from square holes. Int J Fract 228:33–43. https://doi.org/10.1007/s10704-020-00512-910.1007/s10704-020-00512-9 ↗
16. Doitrand A, Henry R, Lube T, Meille S (2021b) Size effect assessment by weibull’s approach and the coupled criterion. Eng Fract Mech 256:107979. https://doi.org/10.1016/j.engfracmech.2021.10797910.1016/j.engfracmech.2021.107979 ↗
17. Doitrand A, Molnár G, Leguillon D et al (2022) Dynamic crack initiation assessment with the coupled criterion. Eur J Mech A/Solids 93:104483. https://doi.org/10.1016/j.euromechsol.2021.10448310.1016/j.euromechsol.2021.104483 ↗
18. Duminy T, Doitrand A, Meille S (2024) Fracture parameter identification by digital image correlation and finite fracture mechanics for millimeter-scale samples. Eng Fract Mech 295:109770. https://doi.org/10.1016/j.engfracmech.2023.10977010.1016/j.engfracmech.2023.109770 ↗
19. Dunn ML, Suwito W, Cunningham S (1997) Fracture initiation at sharp notches: correlation using critical stress intensities. Int J Solids Struct 34:3873–3883. https://doi.org/10.1016/S0020-7683(96)00236-310.1016/S0020-7683(96)00236-3 ↗
20. Felger J, Stein N, Becker W (2017) Mixed-mode fracture in open-hole composite plates of finite-width: an asymptotic coupled stress and energy approach. Int J Solids Struct 122–123:14–24. https://doi.org/10.1016/j.ijsolstr.2017.05.03910.1016/j.ijsolstr.2017.05.039 ↗
21. Freund LB (1998) Dynamic fracture mechanics. Cambridge University Press, Cambridge
22. Griffith AA (1921) VI. The phenomena of rupture and flow in solids. Philos Trans R Soc London Ser a Contain Pap a Math or Phys Character 221:163–198. https://doi.org/10.1098/rsta.1921.000610.1098/rsta.1921.0006 ↗
23. Hashin Z (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. J Mech Phys Solids 44:1129–1145. https://doi.org/10.1016/0022-5096(95)00080-110.1016/0022-5096(95)00080-1 ↗
24. Kim S-R, Nairn JA (2000) Fracture mechanics analysis of coating/substrate systems. Eng Fract Mech 65:573–593. https://doi.org/10.1016/S0013-7944(99)00141-110.1016/S0013-7944(99)00141-1 ↗
25. Kirsch G (1898) Die Theorie der elastizitat und die bedurfnisse der festigkeitslehre. Zantralblatt Verlin Deutscher Ingenieure
26. Kurguzov V, Kuznetsov D (2024) Fracture analysis of Brazilian circular hole disk under mixed mode loading. Eng Fract Mech 297:109875. https://doi.org/10.1016/j.engfracmech.2024.10987510.1016/j.engfracmech.2024.109875 ↗
27. Lampman S (2003) Characterization and failure analysis of plastics. ASM International, Materials Park, OH10.31399/asm.tb.cfap.9781627082815 ↗
28. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A/Solids 21:61–72. https://doi.org/10.1016/S0997-7538(01)01184-610.1016/S0997-7538(01)01184-6 ↗
29. Leguillon D, Martin E (2013) The strengthening effect caused by an elastic contrast—part I: the bimaterial case. Int J Fract 179:157–167. https://doi.org/10.1007/s10704-012-9787-y10.1007/s10704-012-9787-y ↗
30. Leite A, Mantič V, París F (2021) Crack onset in stretched open hole PMMA plates considering linear and non-linear elastic behaviours. Theor Appl Fract Mech 114:102931. https://doi.org/10.1016/j.tafmec.2021.10293110.1016/j.tafmec.2021.102931 ↗
31. Li J, Zhang XB (2006) A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials. Eng Fract Mech 73:505–523. https://doi.org/10.1016/j.engfracmech.2005.09.00110.1016/j.engfracmech.2005.09.001 ↗
32. Lin H, Xiong W, Yan Q (2016) Modified formula for the tensile strength as obtained by the flattened brazilian disk test. Rock Mech Rock Eng 49:1579–1586. https://doi.org/10.1007/s00603-015-0785-z10.1007/s00603-015-0785-z ↗
33. Mantič V (2009) Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion. Int J Solids Struct 46:1287–1304. https://doi.org/10.1016/j.ijsolstr.2008.10.03610.1016/j.ijsolstr.2008.10.036 ↗
34. Marsavina L, Sapora A, Susmel L, Taylor D (2023) The application of the theory of critical distances to nonhomogeneous materials. Fatigue Fract Eng Mater Struct 46:1314–1329. https://doi.org/10.1111/ffe.1392210.1111/ffe.13922 ↗
35. Neuber H (1936) Theorie der technischen formzahl. Forsch Auf Dem Gebiete Des Ingenieurwesens 7:271–274. https://doi.org/10.1007/BF0258490810.1007/BF02584908 ↗
36. Peterson RE (1938) Methods of correlating data from fatigue tests of stress concentration specimens. In: Macmillan (ed) Stephen Timoshenko Anniversary Volume. New York, pp. 179
37. Pipes RB, Wetherhold RC, Gillespie JW (1979) Notched strength of composite materials. J Compos Mater 13:148–160. https://doi.org/10.1177/00219983790130020610.1177/002199837901300206 ↗
38. Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture: I. Crack initiation and arrest. Int J Fract 25:247–262. https://doi.org/10.1007/BF0096346010.1007/BF00963460 ↗
39. Rosendahl PL, Weißgraeber P, Stein N, Becker W (2017) Asymmetric crack onset at open-holes under tensile and in-plane bending loading. Int J Solids Struct 113–114:10–23. https://doi.org/10.1016/j.ijsolstr.2016.09.01110.1016/j.ijsolstr.2016.09.011 ↗
40. Sakha M, Nejati M, Driesner T (2023) On the initiation of hydraulic fractures in anisotropic rocks. Int J Rock Mech Min Sci 169:105429. https://doi.org/10.1016/j.ijrmms.2023.10542910.1016/j.ijrmms.2023.105429 ↗
41. Sapora A, Cornetti P (2018) Crack onset and propagation stability from a circular hole under biaxial loading. Int J Fract 214:97–104. https://doi.org/10.1007/s10704-018-0315-610.1007/s10704-018-0315-6 ↗
42. Sapora A, Torabi AR, Etesam S, Cornetti P (2018) Finite fracture mechanics crack initiation from a circular hole. Fatigue Fract Eng Mater Struct 41:1627–1636. https://doi.org/10.1111/ffe.1280110.1111/ffe.12801 ↗
43. Sapora A, Ferrian F, Cornetti P et al (2023) Ligament size effect in largely cracked tensile structures. Theor Appl Fract Mech 125:103871. https://doi.org/10.1016/j.tafmec.2023.10387110.1016/j.tafmec.2023.103871 ↗
44. Seldén R (1987) Fracture energy measurements in polycarbonate and PMMA. Polym Test 7:209–222. https://doi.org/10.1016/0142-9418(87)90032-810.1016/0142-9418(87)90032-8 ↗
45. Seweryn A (1994) Brittle fracture criterion for structures with sharp notches. Eng Fract Mech 47:673–681. https://doi.org/10.1016/0013-7944(94)90158-910.1016/0013-7944(94)90158-9 ↗
46. Seweryn A, Sł P, Mróz Z (1997) Brittle fracture in plane elements with sharp notches under mixed-mode loading. J Eng Mech 123:535–543. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:6(535)10.1061/(ASCE)0733-9399(1997)123:6(535) ↗
47. Seweryn A, Łukaszewicz A (2002) Verification of brittle fracture criteria for elements with V-shaped notches. Eng Fract Mech 69:1487–1510. https://doi.org/10.1016/S0013-7944(01)00138-210.1016/S0013-7944(01)00138-2 ↗
48. Tan SC (1987) Fracture strength of composite laminates with an elliptical opening. Compos Sci Technol 29:133–152. https://doi.org/10.1016/0266-3538(87)90053-410.1016/0266-3538(87)90053-4 ↗
49. Taylor D (2004) Predicting the fracture strength of ceramic materials using the theory of critical distances. Eng Fract Mech 71:2407–2416. https://doi.org/10.1016/j.engfracmech.2004.01.00210.1016/j.engfracmech.2004.01.002 ↗
50. Taylor D (2006) The theory of critical distances applied to the prediction of brittle fracture in metallic materials. Struct Durab Heal Monit 1:145–154. https://doi.org/10.3970/sdhm.2005.001.14510.3970/sdhm.2005.001.145 ↗
51. Taylor D (2007) The theory of critical distances. Elsevier, London
52. Torabi AR, Etesam S, Sapora A, Cornetti P (2017) Size effects on brittle fracture of Brazilian disk samples containing a circular hole. Eng Fract Mech 186:496–503. https://doi.org/10.1016/j.engfracmech.2017.11.00810.1016/j.engfracmech.2017.11.008 ↗
53. Vedernikova A, Kostina A, Plekhov O, Bragov A (2019) On the use of the critical distance concept to estimate tensile strength of notched components under dynamic loading and physical explanation theory. Theor Appl Fract Mech 103:102280. https://doi.org/10.1016/j.tafmec.2019.10228010.1016/j.tafmec.2019.102280 ↗
54. Wang Q-Z, Xing L (1999) Determination of fracture toughness KIC by using the flattened Brazilian disk specimen for rocks. Eng Fract Mech 64:193–201. https://doi.org/10.1016/S0013-7944(99)00065-X10.1016/S0013-7944(99)00065-X ↗
55. Wang Q, Jia X, Kou S et al (2004) The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results. Int J Rock Mech Min Sci 41:245–253. https://doi.org/10.1016/S1365-1609(03)00093-510.1016/S1365-1609(03)00093-5 ↗
56. Weißgraeber P, Hell S, Becker W (2016) Crack nucleation in negative geometries. Eng Fract Mech 168:93–104. https://doi.org/10.1016/j.engfracmech.2016.02.04510.1016/j.engfracmech.2016.02.045 ↗
57. Whitney JM, Nuismer RJ (1974) Stress fracture criteria for laminated composites containing stress concentrations. J Compos Mater 8:253–265. https://doi.org/10.1177/00219983740080030310.1177/002199837400800303 ↗
58. Wu S, Ma J, Cheng Y et al (2018) Numerical analysis of the flattened Brazilian test: failure process, recommended geometric parameters and loading conditions. Eng Fract Mech 204:288–305. https://doi.org/10.1016/j.engfracmech.2018.09.02410.1016/j.engfracmech.2018.09.024 ↗
59. Zhang X, Sun Z, Hu X (2014) Low temperature fracture toughness of PMMA and crack-tip conditions under flat-tipped cylindrical indenter. Polym Test 38:57–63. https://doi.org/10.1016/j.polymertesting.2014.06.00910.1016/j.polymertesting.2014.06.009 ↗