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Erschienen in: Colloid and Polymer Science 4/2019

12.02.2019 | Original Contribution

A re-formulation of the Mori–Tanaka method for predicting material properties of fiber-reinforced polymers/composites

verfasst von: Jing Pan, Lichun Bian

Erschienen in: Colloid and Polymer Science | Ausgabe 4/2019

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Abstract

In this investigation, a re-formulation has been developed to investigate the effect of fiber aspect ratio on the effective elastic moduli of fiber-reinforced polymers/composites. The matrix and inclusions are considered as isotropic materials. The five independent elastic constants are derived based on a modified Mori–Tanaka theory. The relationship between composite elastic constants and inclusion aspect ratio is also established. Three types of composites containing unidirectional aligned fiber and two-dimensional and three-dimensional random orientated inclusions are explicitly analyzed. Moreover, three extreme cases involving long fibers, spheres, and thin discs are taken into account. It is found that the longitudinal elastic properties are very sensitive to fiber-like inclusions, whereas the transverse elastic properties are closely related to disc-like inclusions.

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Literatur
1.
Zurück zum Zitat Rodríguez-Ramos R, Guinovart-Díaz R, Bravo-Castillero J, Sabina FJ, Berger H, Kari S, Gabbert U (2009) Variational bounds for anisotropic elastic multiphase composites with different shapes of inclusions. Arch Appl Mech 79(8):695–708CrossRef Rodríguez-Ramos R, Guinovart-Díaz R, Bravo-Castillero J, Sabina FJ, Berger H, Kari S, Gabbert U (2009) Variational bounds for anisotropic elastic multiphase composites with different shapes of inclusions. Arch Appl Mech 79(8):695–708CrossRef
2.
Zurück zum Zitat Wang J, Pyrz R (2004) Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part I: basic theory and formulas. Compos Sci Technol 64(7):925–934CrossRef Wang J, Pyrz R (2004) Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part I: basic theory and formulas. Compos Sci Technol 64(7):925–934CrossRef
3.
Zurück zum Zitat Pan J, Bian LC (2017) Influence of agglomeration parameters on carbon nanotube composites. Acta Mech 228(6):2207–2217CrossRef Pan J, Bian LC (2017) Influence of agglomeration parameters on carbon nanotube composites. Acta Mech 228(6):2207–2217CrossRef
4.
Zurück zum Zitat Pan J, Bian LC, Zhao HC et al (2016) A new micromechanics model and effective elastic modulus of nanotube reinforced composites. Comput Mater Sci 113:21–26CrossRef Pan J, Bian LC, Zhao HC et al (2016) A new micromechanics model and effective elastic modulus of nanotube reinforced composites. Comput Mater Sci 113:21–26CrossRef
5.
Zurück zum Zitat Lee KY, Paul DR (2005) A model for composites containing three-dimensional ellipsoidal inclusions. Polymer 46(21):9064–9080CrossRef Lee KY, Paul DR (2005) A model for composites containing three-dimensional ellipsoidal inclusions. Polymer 46(21):9064–9080CrossRef
6.
Zurück zum Zitat Kashtalyan M, Sinchuk Y, Piat R, Guz I (2016) Analysis of multiple cracking in metal/ceramic composites with lamellar microstructure. Arch Appl Mech 86(1–2):177–188CrossRef Kashtalyan M, Sinchuk Y, Piat R, Guz I (2016) Analysis of multiple cracking in metal/ceramic composites with lamellar microstructure. Arch Appl Mech 86(1–2):177–188CrossRef
7.
Zurück zum Zitat Kordkheili SAH, Toozandehjani H (2014) Effective mechanical properties of unidirectional composites in the presence of imperfect interface. Arch Appl Mech 84(6):807–819CrossRef Kordkheili SAH, Toozandehjani H (2014) Effective mechanical properties of unidirectional composites in the presence of imperfect interface. Arch Appl Mech 84(6):807–819CrossRef
8.
Zurück zum Zitat Lee JK, Kim JG (2013) Model for predicting effective thermal conductivity of composites with aligned continuous fibers of graded conductivity. Arch Appl Mech 83(11):1569–1575CrossRef Lee JK, Kim JG (2013) Model for predicting effective thermal conductivity of composites with aligned continuous fibers of graded conductivity. Arch Appl Mech 83(11):1569–1575CrossRef
9.
Zurück zum Zitat Zhao YH, Tandon GP, Weng GJ (1989) Elastic moduli for a class of porous materials. Acta Mech 76(1–2):105–130CrossRef Zhao YH, Tandon GP, Weng GJ (1989) Elastic moduli for a class of porous materials. Acta Mech 76(1–2):105–130CrossRef
10.
Zurück zum Zitat Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574CrossRef Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574CrossRef
11.
Zurück zum Zitat Benveniste Y (1987) A new approach to the application of Mori-Tanaka's theory in composite materials. Mech Mater 6(2):147–157CrossRef Benveniste Y (1987) A new approach to the application of Mori-Tanaka's theory in composite materials. Mech Mater 6(2):147–157CrossRef
12.
Zurück zum Zitat Walpole LJ (1981) Elastic behavior of composite materials: theoretical foundations. Adv Appl Mech 21:169–242CrossRef Walpole LJ (1981) Elastic behavior of composite materials: theoretical foundations. Adv Appl Mech 21:169–242CrossRef
13.
Zurück zum Zitat Choi MO, Kim YJ (2018) Effect of poly (3-hydroxybutyrate-co-3-hydroxyvalerate) /gelatin ratios on the characteristics of biomimetic composite nanofibrous scaffolds. Colloid Polym Sci 296(5):917–926CrossRef Choi MO, Kim YJ (2018) Effect of poly (3-hydroxybutyrate-co-3-hydroxyvalerate) /gelatin ratios on the characteristics of biomimetic composite nanofibrous scaffolds. Colloid Polym Sci 296(5):917–926CrossRef
14.
Zurück zum Zitat Panda S, Reddy NH, Kumar ASP (2015) Design and finite element analysis of a short piezoelectric fiber-reinforced composite actuator. Arch Appl Mech 85(5):691–711CrossRef Panda S, Reddy NH, Kumar ASP (2015) Design and finite element analysis of a short piezoelectric fiber-reinforced composite actuator. Arch Appl Mech 85(5):691–711CrossRef
15.
Zurück zum Zitat Bian LC, Zhao HC (2015) Elastic properties of a single-walled carbon nanotube under a thermal environment. Compos Struct 121:337–343CrossRef Bian LC, Zhao HC (2015) Elastic properties of a single-walled carbon nanotube under a thermal environment. Compos Struct 121:337–343CrossRef
16.
Zurück zum Zitat Sindu BS, Sasmal S (2015) Evaluation of mechanical characteristics of nano modified epoxy based polymers using molecular dynamics. Comput Mater Sci 96:146–158CrossRef Sindu BS, Sasmal S (2015) Evaluation of mechanical characteristics of nano modified epoxy based polymers using molecular dynamics. Comput Mater Sci 96:146–158CrossRef
17.
Zurück zum Zitat Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222CrossRef Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222CrossRef
18.
Zurück zum Zitat Chang CI, Conway HD, Weaver TC (1972) The elastic constants and bond stresses for a three-dimensional composite reinforced by discontinuous fibers. Fibre Sci Technol 5(2):143–162CrossRef Chang CI, Conway HD, Weaver TC (1972) The elastic constants and bond stresses for a three-dimensional composite reinforced by discontinuous fibers. Fibre Sci Technol 5(2):143–162CrossRef
19.
Zurück zum Zitat Russel WB (1973) On the effective moduli of composite materials: effect of fiber length and geometry at dilute concentrations. Zeitschrift Für Angewandte Mathematik Und Physik Zamp 24(4):581–600CrossRef Russel WB (1973) On the effective moduli of composite materials: effect of fiber length and geometry at dilute concentrations. Zeitschrift Für Angewandte Mathematik Und Physik Zamp 24(4):581–600CrossRef
20.
Zurück zum Zitat Tandon GP, Weng GJ (1986) Average stress in the matrix and effective moduli of randomly oriented composites. Compos Sci Technol 27(2):111–132CrossRef Tandon GP, Weng GJ (1986) Average stress in the matrix and effective moduli of randomly oriented composites. Compos Sci Technol 27(2):111–132CrossRef
21.
Zurück zum Zitat Jarali CS, Patil SF, Pilli SC, Lu YC (2013) Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix. J Mater Sci 48(8):3160–3172CrossRef Jarali CS, Patil SF, Pilli SC, Lu YC (2013) Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix. J Mater Sci 48(8):3160–3172CrossRef
22.
Zurück zum Zitat Tian W, Qi L, Zhou J, Guan J (2014) Effects of the fiber orientation and fiber aspect ratio on the tensile strength of C sf/Mg composites. Comput Mater Sci 89(12):6–11CrossRef Tian W, Qi L, Zhou J, Guan J (2014) Effects of the fiber orientation and fiber aspect ratio on the tensile strength of C sf/Mg composites. Comput Mater Sci 89(12):6–11CrossRef
23.
Zurück zum Zitat Halpin JC, Tsai SW (1967) Environmental factors in composite materials design. Air force technical. Report:67–423 Halpin JC, Tsai SW (1967) Environmental factors in composite materials design. Air force technical. Report:67–423
24.
Zurück zum Zitat Thomason JL (2008) The influence of fibre length, diameter and concentration on the modulus of glass-fibre reinforced polyamide 6, 6. Compos A Appl Sci Manuf 39(11):1732–1738CrossRef Thomason JL (2008) The influence of fibre length, diameter and concentration on the modulus of glass-fibre reinforced polyamide 6, 6. Compos A Appl Sci Manuf 39(11):1732–1738CrossRef
25.
Zurück zum Zitat Tucker Iii CL, Liang E (1999) Stiffness predictions for unidirectional short-fiber composites: review and evaluation. Compos Sci Technol 59(5):655–671CrossRef Tucker Iii CL, Liang E (1999) Stiffness predictions for unidirectional short-fiber composites: review and evaluation. Compos Sci Technol 59(5):655–671CrossRef
26.
Zurück zum Zitat Ferrari M, Johnson GC (1989) The effective elasticities of short-fiber composites with arbitrary orientation distribution. Mech Mater 8:67–73CrossRef Ferrari M, Johnson GC (1989) The effective elasticities of short-fiber composites with arbitrary orientation distribution. Mech Mater 8:67–73CrossRef
27.
Zurück zum Zitat Chen CH, Cheng CH (1996) Effective elastic moduli of misoriented short-fiber composites. Int J Solids Struct 33:2519–2539CrossRef Chen CH, Cheng CH (1996) Effective elastic moduli of misoriented short-fiber composites. Int J Solids Struct 33:2519–2539CrossRef
28.
Zurück zum Zitat Böhm HJ (2004) Modeling the mechanical behavior of short fiber reinforced composites, in “Mechanics of Microstructured Materials” (Ed. H.J.Böhm). Springer–Verlag, Vienna 41–56 Böhm HJ (2004) Modeling the mechanical behavior of short fiber reinforced composites, in “Mechanics of Microstructured Materials” (Ed. H.J.Böhm). Springer–Verlag, Vienna 41–56
29.
Zurück zum Zitat Giordano S (2005) Order and disorder in heterogeneous material microstructure: electric and elastic characterisation of dispersions of pseudo-oriented spheroids. Int J Eng Sci 43:1033–1058CrossRef Giordano S (2005) Order and disorder in heterogeneous material microstructure: electric and elastic characterisation of dispersions of pseudo-oriented spheroids. Int J Eng Sci 43:1033–1058CrossRef
30.
Zurück zum Zitat Marzari N, Ferrari M (1992) Textural and micromorphological effects on the overall elastic response of macroscopically anisotropic composites. J Appl Mech 59:269–275CrossRef Marzari N, Ferrari M (1992) Textural and micromorphological effects on the overall elastic response of macroscopically anisotropic composites. J Appl Mech 59:269–275CrossRef
31.
Zurück zum Zitat Berryman JG, Berge PA (1996) Critique of two explicit schemes for estimating elastic properties of multiphase composites. Mech Mater 22:149–164CrossRef Berryman JG, Berge PA (1996) Critique of two explicit schemes for estimating elastic properties of multiphase composites. Mech Mater 22:149–164CrossRef
32.
Zurück zum Zitat Allen DH, Lee JW (1990) The effective thermoelastic properties of whisker-reinforced composites as functions of material forming parameters. In: Weng GJ, Taya M, Abé H (eds) Micromechanics and Inhomogeneity. Springer-Verlag, New York, pp 17–40CrossRef Allen DH, Lee JW (1990) The effective thermoelastic properties of whisker-reinforced composites as functions of material forming parameters. In: Weng GJ, Taya M, Abé H (eds) Micromechanics and Inhomogeneity. Springer-Verlag, New York, pp 17–40CrossRef
33.
Zurück zum Zitat Pettermann HE, Böhm HJ, Rammerstorfer FG (1997) Some direction dependent properties of matrix–inclusion type composites with given reinforcement orientation distributions. Composites B 28:253–265CrossRef Pettermann HE, Böhm HJ, Rammerstorfer FG (1997) Some direction dependent properties of matrix–inclusion type composites with given reinforcement orientation distributions. Composites B 28:253–265CrossRef
34.
Zurück zum Zitat Mlekusch B (1999) Thermoelastic properties of short-fibre-reinforced thermoplastics. Compos Sci Technol 59:911–923CrossRef Mlekusch B (1999) Thermoelastic properties of short-fibre-reinforced thermoplastics. Compos Sci Technol 59:911–923CrossRef
35.
Zurück zum Zitat Hong GK, Kwac LK (2009) Evaluation of elastic modulus for unidirectionally aligned short fiber composites. J Mech Sci Technol 23(1):54–63CrossRef Hong GK, Kwac LK (2009) Evaluation of elastic modulus for unidirectionally aligned short fiber composites. J Mech Sci Technol 23(1):54–63CrossRef
36.
Zurück zum Zitat Richard TG (1975) The mechanical behavior of a solid microsphere filled composite. J Compos Mater 9(2):108–113CrossRef Richard TG (1975) The mechanical behavior of a solid microsphere filled composite. J Compos Mater 9(2):108–113CrossRef
37.
Zurück zum Zitat Norris AN (1990) The mechanical properties of platelet reinforced composites. Int J Solids Struct 26(5):663–674CrossRef Norris AN (1990) The mechanical properties of platelet reinforced composites. Int J Solids Struct 26(5):663–674CrossRef
38.
Zurück zum Zitat Pettermann HE, Böhm HJ, Alcalá J (2002) Normalized diagrams for micromechanical estimates of the elastic response of composite materials. Metall Mater Trans A 33(10):3187–3199CrossRef Pettermann HE, Böhm HJ, Alcalá J (2002) Normalized diagrams for micromechanical estimates of the elastic response of composite materials. Metall Mater Trans A 33(10):3187–3199CrossRef
Metadaten
Titel
A re-formulation of the Mori–Tanaka method for predicting material properties of fiber-reinforced polymers/composites
verfasst von
Jing Pan
Lichun Bian
Publikationsdatum
12.02.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Colloid and Polymer Science / Ausgabe 4/2019
Print ISSN: 0303-402X
Elektronische ISSN: 1435-1536
DOI
https://doi.org/10.1007/s00396-019-04472-y

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