The aim of this study was to examine the effect of size on the mixed-mode fracture toughness of quasi-brittle nanocomposites with the help of modified maximum tangential stress criterion. The literature reveals that the effect of size on mixed-mode fracture behavior of brittle nanocomposites has not been well investigated previously using modified maximum tangential stress criterion. The studied nanocomposites were made of epoxy resin reinforced with 7 wt%, 20–30 nm nanosilica. The accuracy of the method was assessed by taking into account the high-order terms of Williams series expansion along with finite element over-deterministic method. To investigate the effect of size on fracture toughness, a number of three-point semi-circular bending tests with different radii and four angles of edge–crack orientation were conducted and subjected to mixed-mode loading. The size of fracture process zone and apparent fracture toughness (Kc) were also evaluated as a function of sample size. Experimental results showed that the proposed approach can accurately predict the fracture behavior of studied nanocomposites.
Al-ShayeaNA. Crack propagation trajectories for rocks under mixed mode I–II fracture. Eng Geol2005; 81(1): 84–97.
2.
WeibullW. The phenomenon of rupture in solids, Royal Swedish Institute of Engineering Research (Ingenioersvetenskaps Akad. Handl.), Stockholm, 1939; 153: I–55.
3.
LeicesterRH. The size effect of notches. In: Proceedings of the second Australasian conference on the mechanics of structures and materials, Melbourne, Australia, July 1969: 4.1–4.20. (Also Division of Forest Products Reprint No. 817 CSIRO, Australia, 1969).
4.
BazantZP. Crack band model for fracture of geomaterials. In: Proceedings of the 4th international conference of numerical methods in geomechanics, EisensteinZ. (ed.), Edmonton, Alberta, Canada, May 31–June 4, 1982; 3: 1137–1152.
5.
BazantZP. Size effect in blunt fracture: concrete, rock, metal. J Eng Mech1984; 110(4): 518–535.
6.
KimJKYiST. Application of size effect to compressive strength of concrete members. Sadhana2002; 27(4): 467–484.
7.
MorelS. Size effect in quasibrittle fracture: derivation of the energetic size effect law from equivalent LEFM and asymptotic analysis. Int J Fracture2008; 154(1–2): 15–26.
BarenblattG. Self-similarity: dimensional analysis, and intermediate asymptotics. J Appl Math Mech1980; 44(2): 267–272.
10.
HillerborgAModéerMPeterssonPE. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res1976; 6(6): 773–781.
11.
HuXDuanK. Size effect and quasi-brittle fracture: the role of FPZ. Int J Fracture2008; 154: 3–14.
12.
AyatollahiMRAkbardoostJ. Size effects on fracture toughness of quasi-brittle materials—a new approach. Eng Fract Mech2012; 92: 89–100.
13.
AyatollahiMRAkbardoostJ. Size and geometry effects on rock fracture toughness: mode I fracture. Rock Mech Rock Eng2014; 47: 677–687.
14.
GaloueiMFakhimiA. Size effect, Material ductility and shape of fracture process zone in quasi-brittle materials. Comput Geotech2015; 65: 126–135.
15.
FantilliPAFrigoBChiaiaB. Size effect in crack spacing of quasi-brittle materials. Procedia Engineer2015; 109: 390–394.
16.
ZamanianMMortezaeiMSalehniaB. Fracture toughness of epoxy polymer modified with nanosilica particles: particle size effect. Eng Fract Mech2013; 97: 193–206.
17.
WilliamsML. On the stress distribution at the base of a stationary crack. J Appl Mech1957; 24: 109–114.
18.
AlihaMRMAyatollahiMRPakzadR. Brittle fracture analysis using a ring-shape specimen containing two angled cracks. Int J Fracture2008; 153(1): 63–68.
19.
AlihaMRMAyatollahiMRSmithDJ. Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng Fract Mech2010; 77(11): 2200–2212.
20.
AyatollahiMRAlihaMRM. Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Comp Mater Sci2007; 38(4): 660–670.
21.
AyatollahiMRAlihaMRMSaghafiH. An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Eng Fract Mech2011; 78(1): 110–123.
22.
FettT. Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions. Eng Fract Mech2001; 68(9): 1119–1136.
23.
ErdoganFSihG. On the crack extension in plates under plane loading and transverse shear. J Basic Eng: T ASME1963; 85(4): 519–525.
24.
BoccaPCarpinteriAValenteS. Size effects in the mixed mode crack propagation: softening and snap-back analysis. Eng Fract Mech1990; 35(1–3): 159–170.
25.
Di LeonardoG. Fracture toughness characterization of materials under multiaxial loading. Int J Fracture1979; 15(6): 537–552.
26.
BažantZPGettuRKazemiM. Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. Int J Rock Mech Min1991; 28(1): 43–51.
27.
BazantZPPlanasJ. Fracture and size effect in concrete and other quasibrittle materials, vol. 16. Boca Raton, FL: CRC Press, 1997.
28.
KarihalooBL. Tension softening diagrams and longitudinally reinforced beams. In: BakerGKarihalooBL (eds) Fracture of brittle disordered materials: concrete, rock and ceramic. E & FN Spon, 2–6 Boundary Row, London SE1 8HN, UK, 1995, pp.35–50.
EftekhariMBaghbananAHashemolhosseiniH. Fracture propagation in a cracked semicircular bend specimen under mixed mode loading using extended finite element method. Arab J Geosci2015; 8: 9635–9646.
31.
AyatollahiMRNejatiM. An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue Fract Eng M2011; 34: 159–176.
32.
AyatollahiMRAkbardoostJBertoF. Size effects on mixed-mode fracture behavior of polygranular graphite. Carbon2016; 103: 394–403.
33.
AyatollahiMRAlihaMRM. Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. Int J Rock Mech Min2007; 44(4): 617–624.
