Abstract
The Brazilian disk specimen weakened by a central dumbbell-shaped slit with two key-shaped ends and made of PMMA is employed to perform mixed mode I/II brittle fracture experiments on key-hole notches for various notch lengths and radii and, also, different mode mixity ratios. The load-carrying capacity of the specimen resulting from the test machine at the onset of sudden fracture is theoretically predicted by means of a well-known brittle fracture criterion, namely the local strain energy density criterion. A good agreement is found to exist between the theoretical and the experimental results.
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References
Lauterbach B., Gross D.: The role of nucleation and growth of micro cracks in brittle solids under compression: a numerical study. Acta Mech. 159, 199–211 (2002)
Shindo Y., Narita F., Sato T.: Analysis of mode II interlaminar fracture and damage behavior in end notched flexure testing of GFRP woven laminates at cryogenic temperatures. Acta Mech. 187, 231–240 (2006)
Guo J.H., Lu Z.X., Feng X.: The fracture behavior of multiple cracks emanating from a circular hole in piezoelectric materials. Acta Mech. 215, 119–134 (2010)
Brighenti R., Carpinteri A., Spagnoli A.: Influence of material microvoids and heterogeneities on fatigue crack propagation. Acta Mech. 225, 3123–3135 (2014)
Sih G.C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10, 305–321 (1974)
Lazzarin P., Zambardi R.: 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 (2001)
Lazzarin P., Berto F.: Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches. Int. J. Fract. 135, 161–185 (2005)
Berto F., Lazzarin P.: Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches. Mater. Sci. Eng. R Rep. 75, 1–48 (2014)
Lazzarin P., Berto F., Elices M., Gòmez J.: Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite-size volumes. Fatigue Fract. Eng. Mater. Struct. 32, 671–684 (2009)
Ayatollahi M.R., Berto F., Lazzarin P.: Mixed mode brittle fracture of sharp and blunt V-notches in polycrystalline graphite. Carbon 49, 2465–2474 (2011)
Berto F., Lazzarin P., Marangon C.: Brittle fracture of U-notched graphite plates under mixed mode loading. Mater. Des. 41, 421–432 (2012)
Berto F., Ayatollahi M.R.: Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy. Mater. Des. 32, 2858–2869 (2011)
Lazzarin P., Campagnolo A., Berto F.: A comparison among some recent energy- and stress-based criteria for the fracture assessment of sharp V-notched components under mode I loading. Theor. Appl. Fract. Mech. 71, 21–30 (2014)
Torabi A.R., Berto F.: Notch fracture toughness evaluation for a brittle graphite material. Mater. Perform. Charact. 3, 398–413 (2014)
Torabi A.R., Berto F.: Strain energy density to assess mode II fracture in U-notched disk-type graphite plates. Int. J. Damage Mech. 23, 917–930 (2013)
Torabi A.R., Berto F.: Mixed mode fracture assessment of U-notched graphite Brazilian disk specimens by means of the local energy. Struct. Eng. Mech. 50, 723–740 (2014)
Torabi A.R., Berto F.: Fracture assessment of blunt V-notched graphite specimens by means of the strain energy density. Strength Mater. 45, 635–647 (2013)
Berto F., Campagnolo A., Elices M., Lazzarin P.: 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 (2013)
Berto F., Lazzarin P., Ayatollahi M.R.: Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading. Carbon 50, 1942–1952 (2012)
Berto F., Lazzarin P., Ayatollahi M.R.: Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading. Carbon 63, 101–116 (2013)
Ayatollahi M.R., Torabi A.R.: Brittle fracture in rounded-tip V-shaped notches. Mater. Des. 31, 60–67 (2010)
Ayatollahi M.R., Torabi A.R.: Tensile fracture in notched polycrystalline graphite specimens. Carbon 48, 2255–2265 (2010)
Torabi A.R.: Fracture assessment of U-notched graphite plates under tension. Int. J. Fract. 181, 285–292 (2013)
Torabi A.R., Fakoor M., Pirhadi E.: Tensile fracture in coarse-grained polycrystalline graphite weakened by a U-shaped notch. Eng. Fract. Mech. 111, 77–85 (2013)
Torabi A.R.: Estimation of tensile load-bearing capacity of ductile metallic materials weakened by a V-notch: the equivalent material concept. Mater. Sci. Eng. A 536, 249–255 (2012)
Torabi A.R.: On the use of the equivalent material concept to predict tensile load-bearing capacity of ductile steel bolts containing V-shaped threads. Eng. Fract. Mech. 97, 136–147 (2013)
Torabi A.R.: Ultimate bending strength evaluation of U-notched ductile steel samples under large-scale yielding conditions. Int. J. Fract. 180, 261–268 (2013)
Ayatollahi M.R., Torabi A.R.: Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen. Int. J. Solids Struct. 47, 454–465 (2010)
Torabi A.R., Fakoor M., Darbani M.: Pure shear fracture study in a brittle graphite material containing a U-notch. Int. J. Damage Mech. 23, 839–854 (2013)
Ayatollahi M.R., Torabi A.R.: A criterion for brittle fracture in U-notched components under mixed mode loading. Eng. Fract. Mech. 76, 1883–1896 (2009)
Ayatollahi M.R., Torabi A.R.: Investigation of mixed mode brittle fracture in rounded-tip V-notched components. Eng. Fract. Mech. 77, 3087–3104 (2010)
Ayatollahi M.R., Torabi A.R.: Failure assessment of notched polycrystalline graphite under tensile-shear loading. Mater. Sci. Eng. A 528, 5685–5695 (2011)
Ayatollahi M.R., Torabi A.R.: Experimental verification of RV-MTS model for fracture in soda-lime glass weakened by a V-notch. J. Mech. Sci. Technol. 25, 2529–2534 (2011)
Ayatollahi M.R., Torabi A.R., Azizi P.: Experimental and theoretical assessment of brittle fracture in engineering components containing a sharp V-notch. Exp. Mech. 51, 919–932 (2011)
Torabi A.R.: Sudden fracture from U-notches in fine-grained isostatic graphite under mixed mode I/II loading. Int. J. Fract. 181, 309–316 (2013)
Torabi A.R., Fakoor M., Pirhadi E.: Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading. Int. J. Solids Struct. 51, 1287–1298 (2014)
Gómez F.J., Elices M.: A fracture criterion for sharp V-notched samples. Int. J. Fract. 123, 163–175 (2003)
Gómez F.J., Elices M., Valiente A.: Cracking in PMMA containing U-shaped notches. Fatigue Fract. Eng. Mater. Struct. 23, 795–803 (2000)
Gómez F.J., Elices M.: A fracture criterion for blunted V-notched samples. Int. J. Fract. 127, 239–264 (2004)
Planas J., Elices M., Guinea G., Gómez F., Cendón D., Arbilla I.: Generalizations and specializations of cohesive crack models. Eng. Fract. Mech. 70, 1759–1776 (2003)
Carpinteri A., Cornetti P., Pugno N., Sapora A., Taylor D.: A finite fracture mechanics approach to structures with sharp V-notches. Eng. Fract. Mech. 75, 1736–1752 (2008)
Sapora A., Cornetti P., Carpinteri A.: A finite fracture mechanics approach to V-notched elements subjected to mixed-mode loading. Eng. Fract. Mech. 97, 216–226 (2013)
Susmel L., Taylor D.: The theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading. Eng. Fract. Mech. 75, 534–550 (2008)
Livieri P.: A new path independent integral applied to notched components under mode I loadings. Int. J. Fract. 123, 107–125 (2003)
Matvienko Y.U.G., Morozov E.M.: Calculation of the energy J-integral for bodies with notches and cracks. Int. J. Fract. 125, 249–261 (2004)
Berto F., Lazzarin P.: Relationships between J-integral and the strain energy evaluated in a finite volume surrounding the tip of sharp and blunt V-notches. Int. J. Solids Struct. 44, 4621–4645 (2007)
Livieri P.: Use of J-integral to predict static failures in sharp V-notches and rounded U-notches. Eng. Fract. Mech. 75, 1779–1793 (2008)
Barati E., Alizadeh Y., Aghazadeh J., Berto F.: Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending. Mater. Des. 31, 2964–2971 (2010)
Barati E., Alizadeh Y.: A numerical method for evaluation of J-integral in plates made of functionally graded materials with sharp and blunt V-notches. Fatigue Fract. Eng. Mater. Struct. 34, 1041–1052 (2011)
Becker T.H., Mostafavi M., Tait R.B., Marrow T.J.: An approach to calculate the J-integral by digital image correlation displacement field measurement. Fatigue Fract. Eng. Mater. Struct. 35, 971–984 (2012)
Kullmer G., Richard H.A.: Influence of the root radius of crack-like notches on the fracture load of brittle components. Arch. Appl. Mech. 76, 711–723 (2006)
Lazzarin P., Berto F., Ayatollahi M.R.: Brittle failure of inclined key-hole notches in isostatic graphite under in-plane mixed mode loading. Fatigue Fract. Eng. Mater. Struct. 36, 942–955 (2013)
Torabi A.R.: Closed-form expressions of mode I apparent notch fracture toughness for key-hole notches. J. Strain Anal. Eng. Des. 49, 583–591 (2014)
Torabi A.R., Pirhadi E.: Stress-based criteria for brittle fracture in key-hole notches under mixed mode loading. Eur. J. Mech. A Solids 49, 1–12 (2015)
Torabi, A.R., Abedinasab, S.M.: Fracture study on Key-hole notches under tension: two brittle fracture criteria and notch fracture toughness measurement by the disk test. Exp. Mech. (2014, in press)
Lazzarin P., Berto F., Zappalorto M.: Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications. Int. J. Fatigue 32, 1559–1567 (2010)
Pook L.P., Berto F., Campagnolo A., Lazzarin P.: Coupled fracture mode of a cracked disc under anti-plane loading. Eng. Fract. Mech. 128, 22–36 (2014)
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Torabi, A.R., Campagnolo, A. & Berto, F. Experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode I/II loading. Acta Mech 226, 2313–2322 (2015). https://doi.org/10.1007/s00707-015-1323-5
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DOI: https://doi.org/10.1007/s00707-015-1323-5