A micromechanical model for short fiber-reinforced composites (SFRCs) with functionally graded interphases and a systematic prediction scheme to determine the effective properties are presented. The matrix and the fibers are regarded to be linear elastic, isotropic, and homogeneous. Fibers are assumed to be ellipsoids coated perfectly by functionally graded interphases, which is supposed to be formed chemically or physically by the constituents near the interface. First, to analyze the grading interphase effect, layer-wise concept is followed to divide the functionally graded interphases into multi-homogeneous sub-layers. Next, to take the effect of functionally graded interphases into account, a combination of multi-inclusion method and Mori–Tanaka method is applied to predict effective elastic properties of this unidirectional SFRCs with respect to the content and aspect ratio of the inclusions. By employing coordinate transformation, spatially elastic moduli are obtained. Finally, Voigt homogenization scheme is used to obtain the overall, averaged, symmetrical elastic properties of the SFRCs. Numerical examples and analyses demonstrate the applicability of the proposed method and indicate the influences of graded interphase, orientation, and aspect ratio of inclusions as well as properties and contents of the constituents on the overall properties of SFRCs.
PapanicolaouGCPaipetisSATheocarisPS. The concept of boundary interphase in composite mechanics. Colloid Polym Sci1978; 256: 625–630.
2.
MatzenmillerAGerlachS. Parameter identification of elastic interphase properties in fiber composites. Composites Part B2006; 37: 117–126.
3.
SpringDWPaulinoGH. Computational homogenization of the debonding of particle reinforced composites: The role of interphases in interfaces. Comput Mater Sci2015; 109: 209–224.
4.
Karger-KocsisJMahmoodHPegorettiA. Recent advances in fiber/matrix interphase engineering for polymer composites. Prog Mater Sci2015; 73: 1–43.
5.
KarpurPMatikasTEKrishnamurthyS. Ultrasonic characterization of the fiber–matrix interphase/interface for mechanics of continuous fiber reinforced metal matrix and ceramic matrix composites. Compos Eng1995; 5: 697–711.
6.
WarrierSGMajumdarBSGundelDB, et al.Implications of tangential shear stress induced failure during transverse loading of SiCTi-6Al-4V composites. Acta Mater1997; 45: 3469–3480.
7.
TorresFGCubillasML. Study of the interfacial properties of natural fibre reinforced polyethylene. Polym Test2005; 24: 694–708.
8.
TzounisPNGergidisLNMatikasTE, et al.Mathematical investigation of interfacial property in fiber reinforced model composites. Composites Part B2012; 43: 2605–2612.
9.
MogilevskayaSGCrouchSL. A Galerkin boundary integral method for multiple circular elastic inclusions with uniform interphase layers. Int J Solids Struct2004; 41: 1285–1311.
10.
JiangYTohgoKShimamuraY. A micro-mechanics model for composites reinforced by regularly distributed particles with an inhomogeneous interphase. Comput Mater Sci2009; 46: 507–515.
11.
XuYDuSXiaoJ, et al.Evaluation of the effective elastic properties of long fiber reinforced composites with interphases. Comput Mater Sci2012; 61: 34–41.
12.
WangXZhangJWangZ, et al.Effects of interphase properties in unidirectional fiber reinforced composite materials. Mater Des2011; 32: 3486–3492.
13.
MalignoARWarriorNALongAC. Effects of interphase material properties in unidirectional fibre reinforced composites. Compos Sci Technol2010; 70: 36–44.
14.
AndrianovIVDanishefskyVVKalamkarovAL. Micromechanical analysis of fiber-reinforced composites on account of influence of fiber coatings. Composites Part B2008; 39: 874–881.
15.
ArtioliEBisegnaP. Effective longitudinal shear moduli of periodic fibre-reinforced composites with functionally-graded fibre coatings. Int J Solids Struct2013; 50: 1154–1163.
16.
LiuYJXuNLuoJF. Modeling of interphases in fiber-reinforced composites under transverse loading using the boundary element method. J Appl Mech2000; 67: 41–49.
17.
ChenXLiuY. Multiple-cell modeling of fiber-reinforced composites with the presence of interphases using the boundary element method. Comput Mater Sci2001; 21: 86–94.
18.
WangJCrouchSLMogilevskayaSG. Numerical modeling of the elastic behavior of fiber-reinforced composites with inhomogeneous interphases. Compos Sci Technol2006; 66: 1–18.
19.
TuckerCLIIILiangE. Stiffness predictions for unidirectional short-fiber composites: Review and evaluation. Compos Sci Technol1999; 59: 655–671.
20.
TonGPWengGJ. The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites. Polym Compos1983; 5: 327–333.
21.
QiuYPWengGJ. A theory of plasticity for porous materials and particle-reinforced composites. J Appl Mech1992; 59: 261–268.
22.
ZhaoYHWengGJ. Plasticity of a two-phase composite with partially debonded inclusions. Int J Plast1996; 12: 781–804.
23.
HashemiRWengGJKargarnovinMH, et al.Piezoelectric composites with periodic multi-coated inhomogeneities. Int J Solids Struct2010; 47: 2893–2904.
24.
VietNVWangQKuoWS. Effective Young’s modulus of carbon nanotube/epoxy composites. Composites Part B2016; 94: 160–166.
25.
YaoYChenSChenP. The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite. Mech Mater2013; 58: 35–54.
26.
MoriTTanakaK. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall Sin1973; 21: 571–574.
27.
TanHHuangYLiuC, et al.The Mori–Tanaka method for composite materials with nonlinear interface debonding. Int J Plast2005; 21: 1890–1918.
28.
ChouTWNomuraSTayaM. A self-consistent approach to the elastic stiffness of short-fiber composites. J Compos Mater1980; 14: 178–188.
29.
HuangYHuKXWeiX, et al.A generalized self-consistent mechanics method for composite materials with multiphase inclusions. J Mech Phys Solids1994; 42: 491–504.
30.
HuangWRokhlinSI. Generalized self-consistent model for composites with functionally graded and multilayered interphases. Transfer matrix approach. Mech Mater1996; 22: 219–247.
31.
LeeYMYangRBGauSS. A generalized self-consistent method for calculation of effective thermal conductivity of composites with interfacial contact conductance. Int Commun Heat Mass Transfer2006; 33: 142–150.
32.
LurieSMinhatM. Application of generalized self-consistent method to predict effective elastic properties of bristled fiber composites. Composites Part B2014; 61: 26–40.
33.
HoriMNemat-NasserS. Double-inclusion model and overall moduli of multi-phase composites. Mech Mater1993; 14: 189–206.
34.
Nemat-NasserSHoriM. Micromechanics: Overall properties of heterogeneous materials, North Holland: Elsevier, 2013.
35.
LuPLeongYWPallathadkaPK, et al.Effective moduli of nanoparticle reinforced composites considering interphase effect by extended double-inclusion model–Theory and explicit expressions. Int J Eng Sci2013; 73: 33–55.
36.
LiJY. Thermoelastic behavior of composites with functionally graded interphase: A multi-inclusion model. Int J Solids Struct2000; 37: 5579–5597.
37.
PierardOFriebelCDoghriI. Mean-field homogenization of multi-phase thermo-elastic composites: A general framework and its validation. Compos Sci Technol2004; 64: 1587–1603.
38.
ShabanaYM. A micromechanical model for composites containing multi-layered interphases. Compos Struct2013; 101: 265–273.
39.
LiuLSongYJFuHJ, et al.The effect of interphase modification on carbon fiber/polyarylacetylene resin composites. Appl Surf Sci2008; 254: 5342–5347.
40.
LiuLJiaCYHeJM, et al.Interfacial characterization, control and modification of carbon fiber reinforced polymer composites. Compos Sci Technol2015; 121: 56–72.
41.
KuttnerCHanischASchmalzH, et al.Influence of the polymeric interphase design on the interfacial properties of (fiber-reinforced) composites. ACS Appl Mater Interfaces2013; 5: 2469–2478.
42.
ZhangXQFanXYYanC, et al.Interfacial microstructure and properties of carbon fiber composites modified with graphene oxide. ACS Appl Mater Interfaces2012; 4: 1543–1552.
43.
DaiHLRaoYN. Vibration and transient response of a FGM hollow cylinder. Mech Adv Mater Struct2014; 21: 468–476.
44.
FuSYLaukeB. An analytical characterization of the anisotropy of the elastic modulus of misaligned short-fiber-reinforced polymers. Compos Sci Technol1998; 58: 1961–1972.
45.
KenagaDDoyleJFSunCT. The characterization of boron/aluminum in the nonlinear range as an orthotropic elastic plastic material. J Compos Mater1987; 21: 516–531.
46.
HashinZRosenBW. The elastic moduli of fiber-reinforced materials. J Appl Mech1964; 31: 223–232.
47.
SunCTChenJL. A micromechanical model for plastic behavior of fibrous composites. Compos Sci Technol1990; 40: 115–129.
48.
Caruso JJ, Chamis CC. Assessment of simplified composite micromechanics using threedimensional finite-element analysis. J Compos Tech Res 1986; 8: 77–83.
49.
SunCTVaidyaRS. Prediction of composite properties from a representative volume element. Compos Sci Technol1996; 51: 171–179.
50.
BrisardSDormieuxLKondoD. Hashin–Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects. Comput Mater Sci2010; 48: 589–596.
51.
HuangJH. Some closed-form solutions for effective moduli of composites containing randomly oriented short fibers. Mater Sci Eng, A2001; 315: 11–20.
