A theoretical model is developed to study the fiber debonding and pull-out in hybrid-fiber-reinforced brittle-matrix composites. By adopting the shear-lag model which includes the matrix shear deformation in the bonding region and friction in the debonding region, the relationship between the pull-out length and the debonding length of fiber is obtained by treating the interface debonding as a particular crack propagation problem along the interface. The interface debonding criterion for the hybrid-fiber-reinforced composites is obtained by applying the energy release rate relation in an interface debonding process. The analysis is applied to hybrid carbon/glass fiber-reinforced epoxy composites, and the theoretical results have a reasonable agreement with the experimental data. The hybrid effect is studied and the effect of material parameters is discussed.
PanNPostleR. The tensile strength of hybrid fibre composites: a probabilistic analysis of the hybrid effects. Phil Trans R Soc Lond A1996; 354: 1875–1897.
2.
MandersPWBaderMG. The strength of hybrid glass/carbon fibre composites Part 1 failure strain enhancement and failure mode. J Mater Sci1981; 16: 2233–2245.
3.
AvestonJKellyA. Tensile first cracking strain and strength of hybrid composites and laminates. Phil Trans R Soc Lond A1980; 294: 519–534.
4.
SwolfsYGorbatikhLRomanovV. Stress concentrations in an impregnated fibre bundle with random fibre packing. Compos Sci Technol2013; 74: 113–120.
5.
RossollAMoserBMortensenA. Tensile strength of axially loaded unidirectional Nextel 610™ reinforced aluminium: a case study in local load sharing between randomly distributed fibres. Compos A2012; 43: 129–137.
6.
BunsellARHarrisB. Hybrid carbon and glass fibre composites. Composites1974; 5: 157–164.
7.
AvestonJSillwoodJM. Synergistic fibre strengthening in hybrid composites. J Mater Sci1976; 11: 1877–1883.
8.
ZwebenC. Tensile strength of hybrid composites. J Mater Sci1977; 12: 1325–1337.
9.
FukudaH. An advanced theory of the strength of hybrid composites. J Mater Sci1983; 19: 974–982.
10.
KirkJNMunroMBeaumontPWR. The fracture energy of hybrid carbon and glass fibre composites. J Mater Sci1978; 13: 2197–2204.
11.
KakemiMHannantDJ. Mathematical model for tensile behaviour of hybrid continuous fibre cement composites. Composites1995; 26: 637–643.
12.
LuanSFLiHZJiaYX. Analysis of micro-failure behaviors in hybrid fiber model composites. Polymer2006; 47: 6218–6225.
13.
LiHZJiaYXLuanSF. Influence of inter-fiber spacing and interfacial adhesion on failure of multi-fiber model composites: experiment and numerical analysis. Polym Compos2008; 29: 964–971.
14.
AnHLiYXLiM. Interfacial adhesion and micro-failure phenomena in multi-fiber micro-composites using fragmentation test. Compos Interfaces2012; 19: 385–396.
15.
WangMCZhangZGSunZJ. The hybrid model and mechanical properties of hybrid composites reinforced with different diameter fibers. J Reinf Plast Compos2009; 28: 257–264.
16.
PaviaFLetertreACurtinWA. Prediction of first matrix cracking in micro/nanohybrid brittle matrix composites. Compos Sci Technol2010; 70: 916–921.
17.
PandyaKSVeerrajuCNaikNK. Hybrid composites made of carbon and glass woven fabrics under quasi-static loading. Mater Des2011; 32: 4094–4099.
18.
BurksBMiddletonJKumosaM. Micromechanics modeling of fatigue failure mechanisms in a hybrid polymer matrix composite. Compos Sci Technol2012; 72: 1863–1869.
19.
SwolfsYGorbatikhLVerpoestI. Stress concentrations in hybrid unidirectional fibre-reinforced composites with random fibre packings. Compos Sci Technol2013; 85: 10–16.
AvestonJCooperGAKellyA. The properties of fibre composites: conference proceedings, National Physical Laboratory, Guildford: IPC Science and Technology Press Ltd., 1971, pp. 15–26.
22.
AvestonJKellyA. Theory of multiple fracture of fibrous composites. J Mater Sci1972; 8: 352–362.
CoxHL. The elasticity and strength of paper and other fibrous materials. Br J Appl Phys1995; 3: 72–79.
25.
LawrenceP. Some theoretical considerations of fibre pull-out from an elastic matrix. J Mater Sci1972; 7: 1–6.
26.
HsuehCH. Interfacial debonding and fiber pull-out stresses of fiber-reinforced composites. Mater Sci Engng A1990; 123: 1–11.
27.
HsuehCH. Interfacial debonding and fiber pull-out stresses of fiber-reinforced composites II: non-constant interfacial bond strength. Mater Sci Engng A1990; 125: 67–73.
28.
HsuehCH. Evaluation of interfacial shear strength, residual clamping stress and coefficient of friction for fiber-reinforced ceramic composites. Acta Meta Mater1990; 38: 403–409.
29.
StangHShahSP. Failure of fibre-reinforced composites by pull-out fracture. J Mater Sci1986; 21: 953–957.
30.
GaoYCMaiYWCotterellB. Fracture of fiber-reinforced materials. J Appl Math Phys (ZAMP)1988; 39: 550–572.
31.
GaoYC. Damage theory of fiber-reinforced materials. Sci China Ser A1989; 32: 953–961.
32.
HutchinsonJWJensenHW. Models of fiber debonding and pullout in brittle composites with friction. Mech Mater1990; 9: 139–163.
33.
CurtinWA. Theory of mechanical properties of ceramic-matrix composites. J Am Ceram Soc1991; 74: 2837–2845.
34.
ZhouLMKimJKMaiYW. Interfacial debonding and fibre pull-out stresses Part II A new model based on the fracture mechanics approach. J Mater Sci1992; 27: 3155–3166.
35.
LiuYFKagawaY. The energy release rate for an interfacial debond crack in a fiber pull-out model. Compos Sci Technol2000; 60: 167–171.
36.
ChiangYC. On fiber debonding and matrix cracking in fiber-reinforced ceramics. Compos Sci Technol2001; 61: 1743–1756.
37.
GaoXLLiK. A shear-lag model for carbon nanotube-reinforced polymer composites. Int J Solids Struct2005; 42: 1649–1667.
38.
HaqueARamasettyA. Theoretical study of stress transfer in carbon nanotube reinforced polymer matrix composites. Comp Struct2005; 71: 68–77.
39.
QingH. A new theoretical model of the quasistatic single-fiber pullout problem: analysis of stress field. Mech Mater2013; 60: 66–79.
40.
YaoYChenSHChenPJ. The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite. Mech Mater2013; 58: 35–54.
41.
YaoYChenSH. The effects of fiber’s surface roughness on the mechanical properties of fiber-reinforced polymer composites. J Compos Mater2013; 47: 2909–2923.
42.
WellsJKBeaumontPWR. Debonding and pull-out processes in fibrous composites. J Mater Sci1985; 20: 1275–1284.
