This paper introduces new rule-of-thumb equations for estimating the effective elastic modulus of randomly oriented short fiber reinforced composites (SFRCs), developed using the Tandon and Weng method combined with the simplifications from the Tsai-Pagano model. These types of rule-of-thumb equations are useful for a quick first approximation when designing SFRCs. The analysis reveals a linear relationship between the effective Young’s modulus of randomly oriented SFRCs and the effective axial and transverse elastic moduli of unidirectional SFRCs, highlighting that the slope of this relationship is sensitive to the axial-to-transverse modulus ratio. Equations are provided to estimate this slope. Additionally, the study utilizes a two-step homogenization analysis, applied theoretically in this work, which proved to be a practical method for predicting the elastic modulus of randomly oriented SFRCs. Finally, a comprehensive comparative analysis with similar theoretical models demonstrates that the proposed approach delivers comparable prediction performance in two-dimensional random fiber distribution cases and slightly superior performance in three-dimensional random fiber distribution cases. Notably, the rule-of-thumb model developed in this work outperformed other two-step homogenization rule-of-thumb models, achieving better predictions of Young’s modulus.
MirkhalafSMEggelsEHvan BeurdenTJH, et al.A finite element based orientation averaging method for predicting elastic properties of short fiber reinforced composites. Compos B Eng2020; 202: 108388. DOI: 10.1016/j.compositesb.2020.108388.
2.
MonfaredV. 31 - problems in short-fiber composites and analysis of chopped fiber-reinforced materials. In: SamuiPKimDIyerNR, et al. (eds). New materials in civil engineering. Massachusetts, USA: Butterworth-Heinemann, 2020, pp. 919–1043.
3.
FuS-YLaukeBMaiY-W. Science and engineering of short fibre-reinforced polymer composites. Cambridge: Woodhead Publishing, 2019.
4.
NailiCDoghriIKanitT, et al.Short fiber reinforced composites: Unbiased full-field evaluation of various homogenization methods in elasticity. Compos Sci Technol2020; 187: 107942. DOI: 10.1016/j.compscitech.2019.107942.
5.
SchneiderM. A review of nonlinear FFT-based computational homogenization methods. Acta Mech2021; 232: 2051–2100. DOI: 10.1007/s00707-021-02962-1.
6.
SchneiderM. On the effectiveness of the Moulinec–Suquet discretization for composite materials. Int J Numer Methods Eng2023; 124: 3191–3218. DOI: 10.1002/nme.7244.
7.
OmaireySLDunningPDSriramulaS. Development of an ABAQUS plugin tool for periodic RVE homogenisation. Eng Comput2019; 35: 567–577. DOI: 10.1007/s00366-018-0616-4.
8.
BudarapuPRZhuangXRabczukT, et al.Chapter One - multiscale modeling of material failure: theory and computational methods. In: HusseinMI (ed). Advances in applied mechanics. Amsterdam, The Netherlands: Elsevier, 2019, pp. 1–103.
9.
TsaiSWPaganoNJ. Invariant properties of composite materials. Technical Report, Air Force Materials Lab. Ohio: Wright-Patterson AFB, 1968.
10.
HalpinJCPaganoNJ. The laminate approximation for randomly oriented fibrous composites. J Compos Mater1969; 3: 720–724. DOI: 10.1177/002199836900300416.
11.
ChenCYTuckerCL. Mechanical property predictions for short fiber/Brittle matrix composites. J Reinforc Plast Compos1984; 3: 120–129. DOI: 10.1177/073168448400300202.
12.
TandonGPWengGJ. Average stress in the matrix and effective moduli of randomly oriented composites. Compos Sci Technol1986; 27: 111–132. DOI: 10.1016/0266-3538(86)90067-9.
13.
HuangJH. Some closed-form solutions for effective moduli of composites containing randomly oriented short fibers. Materials Science and Engineering: A2001; 315: 11–20. DOI: 10.1016/S0921-5093(01)01212-6.
14.
LavengoodRGoettlerL. Stiffness of non-aligned fiber reinforced composites. In: US government R&D reports. Springfield: National Technical Information Service, 1971, vol AD886372.
15.
TahaIAbdinYF. Modeling of strength and stiffness of short randomly oriented glass fiber—polypropylene composites. J Compos Mater2011; 45: 1805–1821. DOI: 10.1177/0021998310389089.
16.
ManeraM. Elastic properties of randomly oriented short fiber-glass composites. J Compos Mater1977; 11: 235–247. DOI: 10.1177/002199837701100208.
17.
FornesTDPaulDR. Modeling properties of nylon 6/clay nanocomposites using composite theories. Polymer2003; 44: 4993–5013. DOI: 10.1016/S0032-3861(03)00471-3.
18.
van EsMXiqiaoFvan TurnhoutJvan der GiessenE. Chapter 21 - Comparing polymer-clay nanocomposites with conventional composites using composite modeling. In: Al-Malaika S, Golovoy AW, et al (eds). Specialty polymer additives: principles and applications. Malden (MA): Blackwell Science, 2001, pp. 391–413.
19.
PanN. The elastic constants of randomly oriented fiber composites: a new approach to prediction. Sci Eng Compos Mater1996; 5: 63–72. DOI: 10.1515/SECM.1996.5.2.63.
20.
FuS-YLaukeB. The elastic modulus of misaligned short-fiber-reinforced polymers. Compos Sci Technol1998; 58: 389–400. DOI: 10.1016/S0266-3538(97)00129-2.
21.
KariSBergerHGabbertU. Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites. Comput Mater Sci2007; 39: 198–204. DOI: 10.1016/j.commatsci.2006.02.024.
22.
MortazavianSFatemiA. Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites. Compos B Eng2015; 72: 116–129. DOI: 10.1016/j.compositesb.2014.11.041.
23.
NelsonJWRiddleTW. Comparison of analytical assessment of composite properties utilizing short discontinuous bamboo fibers. Composites Part C: Open Access2022; 8: 100262. DOI: 10.1016/j.jcomc.2022.100262.
24.
AriawanDSurojoETriyonoJ, et al.Micromechanical analysis on tensile properties prediction of discontinuous randomized zalacca fibre/high-density polyethylene composites under critical fibre length. Theoretical and Applied Mechanics Letters2020; 10: 57–65. DOI: 10.1016/j.taml.2020.01.009.
25.
ChatzigeorgiouGMeraghniFCharalambakisN. Multiscale modeling approaches for composites. Amsterdam, The Netherlands: Elsevier, 2022.
26.
SeidelGDLagoudasDC. Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mech Mater2006; 38: 884–907. DOI: 10.1016/j.mechmat.2005.06.029.
27.
Rivas-MenchiAHerrera-FrancoPJValadez-GonzálezA, et al.Enhancing interfacial shear strength with tailored carbon nanotube orientations: a micromechanical hierarchical model of single fiber fragmentation tests. Mater Today Commun2024; 38: 108104. DOI: 10.1016/j.mtcomm.2024.108104.
28.
FisherFT. Nanomechanics and the viscoelastic behavior of carbon nanotube-reinforced polymers. Evanston, IL: Northwestern University, 2002.
29.
BradshawRDFisherFTBrinsonLC. Fiber waviness in nanotube-reinforced polymer composites—II: modeling via numerical approximation of the dilute strain concentration tensor. Compos Sci Technol2003; 63: 1705–1722. DOI: 10.1016/S0266-3538(03)00070-8.
30.
ZhangPAbediRSoghratiS. A finite element homogenization-based approach to analyze anisotropic mechanical properties of chopped fiber composites using realistic microstructural models. Finite Elem Anal Des2024; 235: 104140. DOI: 10.1016/j.finel.2024.104140.
31.
HalpinJC. Stiffness and expansion estimates for oriented short fiber composites. J Compos Mater1969; 3: 732–734. DOI: 10.1177/002199836900300419.
32.
KrenchelH. Fibre reinforcement; theoretical and practical investigations of the elasticity and strength of fibre-reinforced materials. Copenhagen: Akademisk forlag, 1964.
33.
LoosM. Chapter 5 - fundamentals of polymer matrix composites containing CNTs. In: LoosM (ed). Carbon nanotube reinforced composites. Oxford: William Andrew Publishing, 2015, pp. 125–170.
34.
ColemanJNKhanUBlauWJ, et al.Small but strong: a review of the mechanical properties of carbon nanotube–polymer composites. Carbon2006; 44: 1624–1652. DOI: 10.1016/j.carbon.2006.02.038.
35.
ThomasonJL. The influence of fibre length and concentration on the properties of glass fibre reinforced polypropylene: 5. Injection moulded long and short fibre PP. Compos Appl Sci Manuf2002; 33: 1641–1652. DOI: 10.1016/S1359-835X(02)00179-3.
36.
ThomasonJL. The influence of fibre length and concentration on the properties of glass fibre reinforced polypropylene. 6. The properties of injection moulded long fibre PP at high fibre content. Compos Appl Sci Manuf2005; 36: 995–1003. DOI: 10.1016/j.compositesa.2004.11.004.
37.
ThomasonJLVlugMA. Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: 1. Tensile and flexural modulus. Compos Appl Sci Manuf1996; 27: 477–484. DOI: 10.1016/1359-835X(95)00065-A.
38.
LiuHZengDLiY, et al.Development of RVE-embedded solid elements model for predicting effective elastic constants of discontinuous fiber reinforced composites. Mech Mater2016; 93: 109–123. DOI: 10.1016/j.mechmat.2015.10.011.
39.
KavvadiasIETsongasKBantilasKE, et al.Mechanical characterization of MWCNT-reinforced cement paste: experimental and multiscale computational investigation. Materials2023; 16: 5379. DOI: 10.3390/ma16155379.
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