This work deals with the fiber ends debonding-induced elastic moduli degradation of a short fiber reinforced composite (SFRC). The strain fields of the matrix in a representative volume element (RVE) of the SFRC are determined from an imaginary fiber technique. By using the debonding boundary conditions, the debonded modulus of the composite is derived, which is affected by not only the far-field but also the transient solutions for the longitudinal strain of the matrix. Particularly, the imaginary fiber technique provides unbounded solution for a moderately large fiber aspect ratio. This is resolved by separating the RVE along the fiber direction into two domains. Combining the longitudinal strains in both domains, the longitudinal modulus is determined, and the longitudinal bridging tensor element in the micromechanics Bridging Model is amended. Five elastic moduli of an SFRC after the fiber end debonding are obtained on the amended Bridging Model. The effects of the fiber volume fraction, fiber aspect ratio, and fiber-to-matrix modulus ratio on the end-debonded longitudinal modulus, transverse modulus, and longitudinal Poisson’s ratio are investigated.
AbedianAMondaliMPahlavanpourM (2007)
Basic modifications in 3D micromechanical modeling of short fiber composites with bonded and debonded fiber end. Computational Materials Science40(3): 421–433. https://doi.org/10.1016/j.commatsci.2007.01.021
2.
AlvesMCarlstedtDOhlssonF, et al. (2020)
Ultra-strong and stiff randomly-oriented discontinuous composites: Closing the gap to quasi-isotropic continuous-fibre laminates. Composites Part A: Applied Science and Manufacturing132: 105826.
3.
ArifMMeraghniFChemiskyY, et al. (2014)
In situ damage mechanisms investigation of PA66/GF30 composite: Effect of relative humidity. Composites Part B: Engineering58: 487–495.
4.
ArifMFSaintierNMeraghniF, et al. (2014)
Multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66. Composites Part B: Engineering61: 55–65.
5.
AzotiWElmarakbiA (2017)
Constitutive modelling of ductile damage matrix reinforced by platelets-like particles with imperfect interfaces: Application to graphene polymer nanocomposite materials. Composites Part B: Engineering113: 55–64.
6.
BanHYaoYChenS, et al. (2019)
A new constitutive model of micro-particle reinforced metal matrix composites with damage effects. International Journal of Mechanical Sciences152: 524–534.
7.
BenSZhaoJZhangY, et al. (2015)
The interface strength and debonding for composite structures: Review and recent developments. Composite Structures129: 8–26.
8.
BonfohNLipinskiP (2007)
Ductile damage micromodeling by particles’ debonding in metal matrix composites. International Journal of Mechanical Sciences49(2): 151–160.
9.
BrassartLInglisHMDelannayL, et al. (2009)
An extended Mori–Tanaka homogenization scheme for finite strain modeling of debonding in particle-reinforced elastomers. Computational Materials Science45(3): 611–616.
10.
ChenJHuangZYuanM (2008)
A constitutive theory of particulate-reinforced viscoelastic materials with partially debonded microvoids. Computational Materials Science41(3): 334–343.
11.
ChristmanTNeedlemanASureshS (1989) An experimental and numerical study of deformation in metal-ceramic composites. Acta Metallurgica37(11): 3029–3050.
12.
CoxHL (1952)
The elasticity and strength of paper and other fibrous materials. British Journal of Applied Physics3(3): 72–79.
13.
DespringreNChemiskyYBonnayK, et al. (2016)
Micromechanical modeling of damage and load transfer in particulate composites with partially debonded interface. Composite Structures155: 77–88.
14.
DingXDJiangZHSunJ, et al. (2002)
Stress–strain behavior in initial yield stage of short fiber reinforced metal matrix composite. Composites Science and Technology62(6): 841–850.
15.
DoghriIFriebelC (2005)
Effective elasto-plastic properties of inclusion-reinforced composites. Study of shape, orientation and cyclic response. Mechanics of Materials37(1): 45–68.
16.
DoghriIOuaarA (2003)
Homogenization of two-phase elasto-plastic composite materials and structures. International Journal of Solids and Structures40(7): 1681–1712.
17.
EshelbyJD (1957)
The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society A - Mathematical Physical and Engineering Sciences
241: 376–396.
18.
FuS-YYueC-YHuX, et al. (2000)
Analyses of the micromechanics of stress transfer in single- and multi-fiber pull-out tests. Composites Science and Technology60(4): 569–579.
19.
GaoY-CMaiY-WCotterellB (1988)
Fracture of fiber-reinforced materials. Zeitschrift Für Angewandte Mathematik Und Physik39(4): 550–572.
20.
GentieuTCatapanoAJumelJ, et al. (2019)
A mean-field homogenisation scheme with CZM-based interfaces describing progressive inclusions debonding. Composite Structures229: 111398.
21.
GörthoferJSchneiderMHrymakA, et al. (2022)
A convex anisotropic damage model based on the compliance tensor. International Journal of Damage Mechanics31(1): 43–86.
22.
HanhanISangidMD (2021)
Damage propagation in short fiber thermoplastic composites analyzed through coupled 3D experiments and simulations. Composites Part B: Engineering218: 108931.
23.
HashemianBShodjaH (2021)
Effective anti-plane moduli of couple stress composites containing elliptic multi-coated nano-fibers with interfacial damage and variational bounds. International Journal of Damage Mechanics30(9): 1351–1376.
24.
HeXSongSLuoX, et al. (2020)
Predicting ductility of Mg/SiCp nanocomposite under multiaxial loading conditions based on unit cell modeling. International Journal of Mechanical Sciences184: 105831.
25.
HenryJPimentaS (2018)
Virtual testing framework for hybrid aligned discontinuous composites. Composites Science and Technology159: 259–272.
26.
HuXFangJXuF, et al. (2016)
Real internal microstructure based key mechanism analysis on the micro-damage process of short fibre-reinforced composites. Scientific Reports6: 34761.
27.
HuangHHuangZ (2021)
Tensile failure prediction of a short fiber or particle composite. Polymer Composites42(2): 774–790.
28.
HuangH-BHuangZ-M (2020)
Micromechanical prediction of elastic-plastic behavior of a short fiber or particle reinforced composite. Composites Part A: Applied Science and Manufacturing134: 105889.
29.
HuangZ-M (2021)
Constitutive relation, deformation, failure and strength of composites reinforced with continuous/short fibers or particles. Composite Structures262: 113279.
30.
HuangZ-M (2001)
Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model. Composites Part A: Applied Science and Manufacturing32(2): 143–172.
31.
HuangZ-MZhangC-CXueY-D (2019)
Stiffness prediction of short fiber reinforced composites. International Journal of Mechanical Sciences161–162: 105068.
32.
IiiCLTLiangE (1999)
Stiffness predictions for unidirectional short-fiber composites: Review and evaluation. Composites Science and Technology17: 655–671.
33.
IqbalNAliYLeeS (2020)
Mechanical degradation analysis of a single electrode particle with multiple binder connections: a comparative study. International Journal of Mechanical Sciences188: 105943.
34.
JainA (2019)
Micro and mesomechanics of fibre reinforced composites using mean field homogenization formulations: a review. Materials Today Communications21: 100552.
35.
JainAAbdinYVan PaepegemW, et al. (2015)
Effective anisotropic stiffness of inclusions with debonded interface for Eshelby-based models. Composite Structures131: 692–706.
36.
JiangZLiuXLiG, et al. (2004)
A new analytical model for three-dimensional elastic stress field distribution in short fibre composite. Materials Science and Engineering: A366(2): 381–396.
37.
JuJWLeeHK (2001)
A micromechanical damage model for effective elastoplastic behavior of partially debonded ductile matrix composites. International Journal of Solids and Structures38(36–37): 6307–6332.
38.
KangG-ZGaoQ (2002)
Tensile properties of randomly oriented short d-Al2O3 fiber reinforced aluminum alloy composites: II. Composites Part A: Applied Science and Manufacturing33(5): 657–667.
39.
KoyamaSKatanoSSaikiI, et al. (2011)
A modification of the Mori–Tanaka estimate of average elastoplastic behavior of composites and polycrystals with interfacial debonding. Mechanics of Materials43(10): 538–555.
40.
LancioniGAlessiR (2020)
Modeling micro-cracking and failure in short fiber-reinforced composites. Journal of the Mechanics and Physics of Solids137: 103854.
41.
LeeDJ (2016)
Fracture mechanical model for tensile strength of particle reinforced elastomeric composites. Mechanics of Materials102: 54–60.
42.
LeeSLeeJRyuS (2019)
Modified Eshelby tensor for an anisotropic matrix with interfacial damage. Mathematics and Mechanics of Solids24(6): 1749–1762.
43.
LegarthBN (2003)
Debonding of particles in anisotropic materials. International Journal of Mechanical Sciences45(6–7): 1119–1133.
44.
LinGGeubellePHSottosNR (2001)
Simulation of fiber debonding with friction in a model composite pushout test. International Journal of Solids and Structures38(46–47): 8547–8562.
45.
LongbiaoL (2020)
A time-dependent tensile constitutive model for long-fiber-reinforced unidirectional ceramic-matrix minicomposites considering interface and fiber oxidation. International Journal of Damage Mechanics29(7): 1138–1166.
46.
LoveBMBatraRC (2010)
Effect of particulate/matrix debonding on the formation of adiabatic shear bands. International Journal of Mechanical Sciences52(2): 386–397.
47.
MehdipourHCamanhoPPBelingardiG (2019)
Elasto-plastic constitutive equations for short fiber reinforced polymers. Composites Part B: Engineering165: 199–214.
48.
MoriTTanakaK (1973)
Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica21(5): 571–574.
49.
MullerVBrylkaBDillenbergerF, et al. (2016)
Homogenization of elastic properties of short-fiber reinforced composites based on measured microstructure data. Journal of Composite Materials50(3): 297–312.
50.
NailiCDoghriIKanitT, et al. (2020)
Short fiber reinforced composites: Unbiased full-field evaluation of various homogenization methods in elasticity. Composites Science and Technology187: 107942.
51.
NgoDParkKPaulinoGH, et al. (2010)
On the constitutive relation of materials with microstructure using a potential-based cohesive model for interface interaction. Engineering Fracture Mechanics77(7): 1153–1174.
52.
NodaN-AChenDZhangG, et al. (2020)
Single-fiber pull-out analysis comparing the intensities of singular stress fields (ISSFs) at fiber end/entry points. International Journal of Mechanical Sciences165: 105196.
53.
Notta-CuvierDLauroFBennaniB (2015)
Modelling of progressive fibre/matrix debonding in short-fibre reinforced composites up to failure. International Journal of Solids and Structures66: 140–150.
54.
NouriHGuessasmaSRogerF, et al. (2017)
Exploring damage kinetics in short glass fibre reinforced thermoplastics. Composite Structures180: 63–74.
55.
OkabeTNishikawaMTakedaN (2010)
Micromechanics on the rate-dependent fracture of discontinuous fiber-reinforced plastics. International Journal of Damage Mechanics19(3): 339–360.
56.
OthmaniYDelannayLDoghriI (2011)
Equivalent inclusion solution adapted to particle debonding with a non-linear cohesive law. International Journal of Solids and Structures48(24): 3326–3335.
57.
QuJ (1993)
Eshelby tensor for an elastic inclusion with slightly weakened interface. Journal of Applied Mechanics60(4): 1048–1050.
58.
SadeghpourEGuoYChuaD, et al. (2020)
A modified Mori–Tanaka approach incorporating filler-matrix interface failure to model graphene/polymer nanocomposites. International Journal of Mechanical Sciences180: 105699.
59.
SchemmannMGorthoferJSeeligT, et al. (2018)
Anisotropic meanfield modeling of debonding and matrix damage in SMC composites. Composites Science and Technology161: 143–158.
60.
SchneiderMWichtDBohlkeT (2019)
On polarization-based schemes for the FFT-based computational homogenization of inelastic materials. Computational Mechanics64(4): 1073–1095.
61.
ShahSZHChoudhryRSMahadzirS (2020)
A new approach for strength and stiffness prediction of discontinuous fibre reinforced composites (DFC). Composites Part B: Engineering183: 107676.
62.
SharmaADaggumatiS (2020)
Computational micromechanical modeling of transverse tensile damage behavior in unidirectional glass fiber-reinforced plastic composite plies: Ductile versus brittle fracture mechanics approach. International Journal of Damage Mechanics29(6): 943–964.
63.
ShokriehMMMoshrefzadeh-SaniH (2017)
A novel laminate analogy to calculate the strength of two-dimensional randomly oriented short-fiber composites. Composites Science and Technology147: 22–29.
64.
ShokriehMMMoshrefzadeh-SaniH (2016)
An optimized representative volume element to predict the stiffness of aligned short fiber composites. Journal of Composite Materials50(23): 3301–3310.
65.
SunQLuoXYangYQ, et al. (2015)
Micromechanical analysis of fiber and titanium matrix interface by shear lag method. Composites Part B: Engineering79: 466–475.
66.
TanHHuangYLiuC, et al. (2005)
The mori–tanaka method for composite materials with nonlinear interface debonding. International Journal of Plasticity21(10): 1890–1918.
67.
TanHHuangYLiuC, et al. (2007)
The uniaxial tension of particulate composite materials with nonlinear interface debonding. International Journal of Solids and Structures44(6): 1809–1822.
68.
TayaMMuraT (1981)
On stiffness and strength of an aligned short-fiber reinforced composite containing Fiber-End cracks under uniaxial applied stress. Journal of Applied Mechanics48(2): 361–367.
69.
TianWLQiLHZhouJM, et al. (2015)
Representative volume element for composites reinforced by spatially randomly distributed discontinuous fibers and its applications. Composite Structures131: 366–373.
70.
TohgoKFujiiTKatoD, et al. (2014)
Influence of particle size and debonding damage on an elastic–plastic singular field around a crack-tip in particulate-reinforced composites. Acta Mechanica225(4–5): 1373–1389.
71.
VisweswaraiahSBSeleznevaMLessardL, et al. (2018)
Mechanical characterisation and modelling of randomly oriented strand architecture and their hybrids – A general review. Journal of Reinforced Plastics and Composites37(8): 548–580.
72.
WangKPeiSLiY, et al. (2019)
In-situ 3D fracture propagation of short carbon fiber reinforced polymer composites. Composites Science and Technology182: 107788.
73.
WangQBianLLiH (2012)
Effective elastic modulus and micro-structure damage of particle-reinforced composites. Composite Structures94(7): 2218–2226.
74.
WeiXZhuHChenQ, et al. (2023)
A micromechanical crack bridging model considering the slip-softening interface with the residual shear stress for SFRCC. International Journal of Damage Mechanics32(1): 103–131.
75.
XiongXSShenSZHuaL, et al. (2018)
Predicting tensile behaviors of short flax fiber-reinforced polymer-matrix composites using a modified shear-lag model. Journal of Composite Materials52(27): 3701–3713.
76.
XuBWeiAYeJ, et al. (2022)
Transverse creep induced by interfacial diffusion in fiber-reinforced composites: a micromechanics model and computational validation. International Journal of Mechanical Sciences213: 106877.
77.
YangWPanYPelegriAA (2013)
Multiscale modeling of matrix cracking coupled with interfacial debonding in random glass fiber composites based on volume elements. Journal of Composite Materials47(27): 3389–3399.
78.
YangWCZhangXFChenYL, et al. (2019)
Strength analysis of bio-inspired composites reinforced by regularly and randomly staggered platelets. Composite Structures216: 415–426.
79.
YangYChenJHuangZ (2020)
Damage evolution in fibrous composites caused by interfacial debonding. International Journal of Damage Mechanics29(1): 67–85.
80.
YaoYChenSChenP (2013)
The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite. Mechanics of Materials58: 35–54.
81.
YuHLonganaMLJalalvandM, et al. (2015)
Pseudo-ductility in intermingled carbon/glass hybrid composites with highly aligned discontinuous fibres. Composites Part A: Applied Science and Manufacturing73: 35–44.
82.
YuHPotterKDWisnomMR (2014)
A novel manufacturing method for aligned discontinuous fibre composites (high performance-discontinuous fibre method). Composites Part A: Applied Science and Manufacturing65: 175–185.
83.
ZaïriFNaït-AbdelazizMGloaguenJM, et al. (2008)
Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage. International Journal of Solids and Structures45(20): 5220–5236.
84.
ZhangGSuwatnodomPJuJ (2013)
Micromechanics of crack bridging stress-displacement and fracture energy in steel hooked-end fiber-reinforced cementitious composites. International Journal of Damage Mechanics22(6): 829–859.
85.
ZhangMHChenJKZhaoF, et al. (2016)
A new model of interfacial adhesive strength of fiber-reinforced polymeric composites upon consideration of cohesive force. International Journal of Mechanical Sciences106: 50–61.
86.
ZhangYJuJWZhuH, et al. (2020)
A novel multi-scale model for predicting the thermal damage of hybrid fiber-reinforced concrete. International Journal of Damage Mechanics29(1): 19–44.
87.
ZhaoYHWengGJ (1997)
Transversely isotropic moduli of two partially debonded composites. International Journal of Solids and Structures34(4): 493–507.
88.
ZhuHWeiXJuJW, et al. (2021)
Statistical micromechanical damage model for SH-SFRC under tensile load considering the interfacial slip-softening and matrix spalling effects. International Journal of Damage Mechanics30(9): 1423–1449.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
