Elasto-plastic fracture criterion for structural components with sharp V-shaped notches
Source abstract
Abstract
Mode I fracture of plate specimens with sharp V-shaped notches is studied analytically and numerically. Within computations, elastic-perfectly plastic constitutive behaviour is assumed. The crack initiation from the tip of the V-shaped notch is described with the help of a modified Leonov–Panasyuk–Dugdale model using an additional parameter, namely, the diameter of the plasticity zone. Under small-scale yielding conditions in the presence of a singularity of the stress field in the vicinity of the V-shaped notch tip, a coupled fracture criterion is proposed. A strain-based fracture criterion is formulated at the real notch tip, and a force-based criterion operating with averaged normal stresses is considered at the fictitious crack tip. The diagrams of quasi-brittle fracture of specimens from structured material are constructed. The propagation of the plastic zone in the notched plates under quasi-static loading is simulated numerically. The plastic zone size in the vicinity of the V-shaped notch tip is assessed; in the limiting case, the V-notch degenerates into an edge crack. The generalized stress intensity factor for a crack growing from a sharp V-shaped notch is obtained by the finite element method. It is shown that under small-scale yielding, the analytical predictions of the critical load agree with the numerical results for a wide range of opening angles.
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Research context
OpenAlex topics: Fatigue and fracture mechanics · Material Properties and Failure Mechanisms · High-Velocity Impact and Material Behavior
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References (63)
Show source-provided references
1. Anderson TL (2005) Fracture mechanics: fundamentals and applications. CRC Press, London10.1201/9781420058215 ↗
2. Astapov NS, Kurguzov VD (2016) Modeling the delamination of a bi-material with different elastic constants under normal rupture. Mech Compos Mater Struct 22:548–566 (in Russian)
3. Astapov NS, Kornev VM, Kurguzov VD (2016) Delamination model for a composite with a crack. Phys Mesomech 19:49–57 (in Russian)
4. Atzori B, Lazzarin P, Meneghetti G (2005) Unified treatment of fatigue limit of components weakened by notches and defects subjected to prevailing mode I stresses. Int J Fract 133(1):61–87. https://doi.org/10.1007/s10704-005-2183-010.1007/s10704-005-2183-0 ↗
5. Awaji H, Sakaida Y (1990) V-notch technique for single-edge notched beam and chevron notch methods. J Am Ceram Soc 73(11):3522–3523. https://doi.org/10.1111/j.1151-2916.1990.tb06490.x10.1111/j.1151-2916.1990.tb06490.x ↗
6. Bazant ZP, Jirasek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech 128:1119–1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)10.1061/(ASCE)0733-9399(2002)128:11(1119) ↗
7. Berto F, Lazzarin P (2009) A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theor Appl Fract Mech 52(3):183–194. https://doi.org/10.1016/j.tafmec.2009.10.00110.1016/j.tafmec.2009.10.001 ↗
8. Berto F, Lazzarin P (2014) Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches. Mater Sci Eng R Rep 75(1):1–48. https://doi.org/10.1016/j.mser.2013.11.00110.1016/j.mser.2013.11.001 ↗
9. Bouledroua O, Elazzizi A, Meliani MH, Pluvinage G, Matvienko YG (2017) T-stress estimation by the two-parameter approach for a specimen with a V-shaped notch. J Appl Mech Tech Phys 58(3):546–55510.1134/S0021894417030208 ↗
10. Carpinteri A, Stern M, Soni ML (1976) On the computation of stress intensities at fixed-free corners. Int J Solid Struct 12(5):331–337. https://doi.org/10.1016/0020-7683(76)90023-810.1016/0020-7683(76)90023-8 ↗
11. Carpinteri A, Cornetti P, Pugno N, Sapora A, Taylor D (2008) A finite fracture mechanics approach to structures with sharp V-notches. Eng Fract Mech 75(7):1736–1752. https://doi.org/10.1016/j.engfracmech.2007.04.01010.1016/j.engfracmech.2007.04.010 ↗
12. Chen D (1995) Stress intensity factors for V-notched strip under tension or in-plane bending. Int J Fract 70:81–97. https://doi.org/10.1007/BF0001813710.1007/BF00018137 ↗
13. Cherepanov GP (1979) Mechanics of brittle fracture. McGraw-Hill, New York
14. Ciavarella M, Meneghetti G (2004) On fatigue limit in the presence of notches: classical versus recent unified formulations. Int J Fatig 26(3):289–298. https://doi.org/10.1016/S0142-1123(03)00106-310.1016/S0142-1123(03)00106-3 ↗
15. 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 ↗
16. Damani R, Gstrein R, Danzer R (1996) Critical notch-root radius effect in SENB-S fracture toughness testing. J Eur Ceram Soc 16(7):695–702. https://doi.org/10.1016/0955-2219(95)00197-210.1016/0955-2219(95)00197-2 ↗
17. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solid 8(2):100–104. https://doi.org/10.1016/0022-5096(60)90013-210.1016/0022-5096(60)90013-2 ↗
18. Dunn ML, Suwito W (1997) Fracture initiation at sharp notches: correlation using critical stress intensities. Int J Solid Struct 34(29):3873–3883. https://doi.org/10.1016/S0020-7683(96)00236-310.1016/S0020-7683(96)00236-3 ↗
19. Dunn ML, Suwito W, Cunningham S, May CW (1997) Fracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading. Int J Fract 84(4):367–38110.1023/A:1007346203407 ↗
20. Eleces M, Guinea GV, Gomez J, Planas J (2002) The cohesive zone model: advantages, limitations and challenges. Eng Fract Mech 69:137–163. https://doi.org/10.1016/S0013-7944(01)00083-210.1016/S0013-7944(01)00083-2 ↗
21. Fett T (2005) Influence of a finite notch root radius on fracture toughness. J Eur Ceram Soc 25(5):543–547. https://doi.org/10.1016/j.jeurceramsoc.2004.01.01010.1016/j.jeurceramsoc.2004.01.010 ↗
22. Gogotsi GA (2000) Fracture toughness studies on v-notched ceramic specimens. Strength Mater 32:81–85. https://doi.org/10.1007/BF0251151010.1007/BF02511510 ↗
23. Griffith AA (1920) The phenomena of flow and rupture in solids. Philos Trans Math Phys Eng Sci 221:163–198
24. Gross D, Seelig T (2006) Fracture mechanics. Springer, Berlin
25. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–36410.1115/1.4011547 ↗
26. Kornev VM, Demeshkin AG (2018) Quasi-brittle fracture of compact specimens with sharp notches and u-shaped cuts. J Appl Mech Tech Phys 59:120–131. https://doi.org/10.1134/S002189441801015710.1134/S0021894418010157 ↗
27. Kornev VM, Kurguzov VD (2005) Modification of the fracture criterion for V-shaped notches (plane problem). relationship between toughness and strength and structural parameters. J Appl Mech Tech Phys 46:85–93. https://doi.org/10.1007/s10808-005-0043-310.1007/s10808-005-0043-3 ↗
28. Kornev VM, Kurguzov VD (2008) Multiparametric sufficient criterion of quasi-brittle fracture for complicated stress state. Eng Fract Mech 75(5):1099–1113. https://doi.org/10.1016/j.engfracmech.2007.04.02310.1016/j.engfracmech.2007.04.023 ↗
29. Kornev VM, Kurguzov VD (2010) Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone. J Appl Mech Tech Phys 51:904–912. https://doi.org/10.1007/s10808-010-0112-010.1007/s10808-010-0112-0 ↗
30. Kotousov A, Lazzarin P, Berto F, Pook LP (2013) Three-dimensional stress states at crack tip induced by shear and anti-plane loading. Eng Fract Mech 108:65–74. https://doi.org/10.1016/j.engfracmech.2013.04.01010.1016/j.engfracmech.2013.04.010 ↗
31. Kurguzov VD (2016) Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks. J Appl Mech Tech Phys 57:1198–1207. https://doi.org/10.1134/S002189441607008710.1134/S0021894416070087 ↗
32. Kurguzov VD, Kornev VM (2013) Construction of quasi-brittle and quasi-ductile fracture diagrams based on necessary and sufficient criteria. J Appl Mech Tech Phys 54:156–169. https://doi.org/10.1134/S002189441301019710.1134/S0021894413010197 ↗
33. Kurguzov VD, Kornev VM (2020) Simulation of fracture of elastoplastic materials in mode III: from brittle to ductile. Meccanica 55:161–175. https://doi.org/10.1007/s11012-019-01090-410.1007/s11012-019-01090-4 ↗
34. Kurguzov VD, Astapov NS, Astapov IS (2014) Fracture model for structured quasibrittle materials. J Appl Mech Tech Phys 55:1055–1065. https://doi.org/10.1134/S002189441406018210.1134/S0021894414060182 ↗
35. Kurguzov VD, Kornev VM, Moskvichev VV, Kozlov AA (2014) Influence of periodic change in the yield strength in a plate on the development of plastic zones near a crack tip. J Appl Mech Tech Phys 55:137–144. https://doi.org/10.1134/S002189441406016910.1134/S0021894414060169 ↗
36. Lazzarin P, Zambardi R (2001) A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches. Int J Fract 112:275–298. https://doi.org/10.1023/A:101359593061710.1023/A:1013595930617 ↗
37. Lazzarin P, Lassen T, Livieri P (2003) A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry. Fatig Frac Eng Mater Struct 26(1):49–58. https://doi.org/10.1046/j.1460-2695.2003.00586.x10.1046/j.1460-2695.2003.00586.x ↗
38. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A Solids 21(1):61–72. https://doi.org/10.1016/S0997-7538(01)01184-610.1016/S0997-7538(01)01184-6 ↗
39. Leonov MY, Panasyuk VV (1959) Small cracks growth in the solids. Appl Mech 5:391–401 (in Russian)
40. Livieri P (2008) Use of J-integral to predict static failures in sharp V-notches and rounded U-notches. Eng Fract Mech 75(7):1779–1793. https://doi.org/10.1016/j.engfracmech.2007.01.02210.1016/j.engfracmech.2007.01.022 ↗
41. MARC 2018 (2018) Volume A: theory and user information. MSC Software Corporation, Santa Ana
42. Meliani HM, Azari Z, Pluvinage G, Matvienko YuG (2010) The effective T-stress estimation and crack paths emanating from U-notches. Eng Fract Mech 77(11):1682–1692. https://doi.org/10.1016/j.engfracmech.2010.03.01010.1016/j.engfracmech.2010.03.010 ↗
43. Morozov NF (1984) Mathematical problems in the theory of cracks. Nauka, Moscow (in Russian)
44. Mugadu A, Hills DA (2002) Characterising the process zone in complete fretting contacts using plain fatigue sharp V-notch specimens. J Mech Phys Solids 50(7):1417–1429. https://doi.org/10.1016/S0022-5096(01)00123-510.1016/S0022-5096(01)00123-5 ↗
45. Murakami Y (1990) Stress intensity factors handbook. Pergamon Press, New York (Edited by Y. Murakami)
46. Neuber G (1960) Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung. Springer, Berlin
47. Novozhilov VV (1969) On the necessary and sufficient criteria for brittle strength. J Appl Math Mech 33(2):212–222 (in Russian)10.1016/0021-8928(69)90025-2 ↗
48. Picard D, Leguillon D, Putot C (2006) A method to estimate the influence of the notch-root radius on the fracture toughness measurement of ceramics. J Eur Ceram Soc 26(8):1421–1427. https://doi.org/10.1016/j.jeurceramsoc.2005.02.01610.1016/j.jeurceramsoc.2005.02.016 ↗
49. Pook LP (2013) A 50-year retrospective review of three-dimensional effects at cracks and sharp notches. Fatig Frac Eng Mater Struct 36:699–723. https://doi.org/10.1111/ffe.1207410.1111/ffe.12074 ↗
50. Pook LP, Berto F, Campagnolo F, Lazzarin P (2014) Coupled fracture mode of a cracked disc under anti-plane loading. Eng Fract Mech 128:22–36. https://doi.org/10.1016/j.engfracmech.2014.07.00110.1016/j.engfracmech.2014.07.001 ↗
51. Pook LP, Campagnolo A, Berto F, Lazzarin P (2015) Coupled fracture mode of a cracked plate under anti-plane loading. Eng Fract Mech 134:391–403. https://doi.org/10.1016/j.engfracmech.2014.12.02110.1016/j.engfracmech.2014.12.021 ↗
52. Radaj D (2014) State-of-the-art review on extended stress intensity factor concepts. Fatig Fract Eng Mater Struct 37(1):1–28. https://doi.org/10.1111/ffe.1212010.1111/ffe.12120 ↗
53. Radaj D, Lehrke HP, Greuling S (2001) Theoretical fatigue-effective notch stresses at spot welds. Fatig Fract Eng Mater Struct 24(5):293–308. https://doi.org/10.1046/j.1460-2695.2001.00378.x10.1046/j.1460-2695.2001.00378.x ↗
54. Rice JR (1968) Mathematical analysis in the mechanics of fracture. Chapter 3 of fracture: an advanced treatise (Vol. 2, Mathematical Fundamentals) (ed. H. Liebowitz). Academic Press, New York, pp 191–311
55. Savruk MP, Kazberuk A (2017) Stress concentration at notches. Springer, Geneva10.1007/978-3-319-44555-7 ↗
56. Seweryn A (1994) Brittle fracture criterion for structures with sharp notches. Eng Fract Mech 47(50):673–68110.1016/0013-7944(94)90158-9 ↗
57. Seweryn A, Łukaszewicz A (2002) Verification of brittle fracture criteria for elements with V-shaped notches. Eng Fract Mech 69(13):1487–1510. https://doi.org/10.1016/S0013-7944(01)00138-210.1016/S0013-7944(01)00138-2 ↗
58. Shutov AV, Kreißig R (2008) Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration. Comp Meth Appl Mech Eng 197(21):2015–2029. https://doi.org/10.1016/j.cma.2007.12.01710.1016/j.cma.2007.12.017 ↗
59. Shutov AV, Silbermann CB, Ihlemann J (2015) Ductile damage model for metal forming simulations including refined description of void nucleation. Int J Plast 71:195–217. https://doi.org/10.1016/j.ijplas.2015.03.00310.1016/j.ijplas.2015.03.003 ↗
60. Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York
61. Sinclair GB, Okajima M, Griffin JH (1984) Path independent integrals for computing stress intensity factors at sharp notches in elastic plates. Int J Numer Meth Eng 20(6):999–1008. https://doi.org/10.1002/nme.162020060310.1002/nme.1620200603 ↗
62. Vasil’ev VV, Lurie SA (2016) New solution of the plane problem of an equilibrium crack. Mech Solids 51:557–561. https://doi.org/10.3103/S002565441605007110.3103/S0025654416050071 ↗
63. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech 19(4):526–528. https://resolver.caltech.edu/CaltechAUTHORS:20140730-11174417010.1115/1.4010553 ↗