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Research Papers

Mechanical Evaluation of Hydroxyapatite Nanocomposites Using Finite Element Modeling

[+] Author and Article Information
Ani Ural

e-mail: ani.ural@villanova.edu
Department of Mechanical Engineering
Villanova University
800 Lancaster Avenue
Villanova, PA 19085

A Please provide complete page range for Ref. [32].

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received January 13, 2012; final manuscript received October 24, 2012; published online January 23, 2013. Editor: Hussein Zbib.

J. Eng. Mater. Technol 135(1), 011007 (Jan 23, 2013) (9 pages) Paper No: MATS-12-1010; doi: 10.1115/1.4023187 History: Received January 13, 2012; Revised October 24, 2012

Hydroxyapatite (HA) has been proposed as a candidate material for bone implants because of its similarity to the inorganic phase in bone. However, due to its lower mechanical properties compared to bone, it has not been used in load bearing bone implants. Inclusion of second phase reinforcements in HA such as carbon nanotubes (CNT) and graphene nanosheets is expected to significantly improve its mechanical properties. In this study, a computational framework that will improve the understanding of the mechanical behavior of graphene nanosheet and CNT-reinforced HA-nanocomposites is proposed. The variation of elastic modulus of HA-nanocomposites is assessed based on the nanofiller type, volume fraction, alignment, area, thickness, and aspect ratio using the finite element modeling. The results of the simulations show that graphene nanosheets are more effective in improving the elastic modulus of nanocomposites than CNTs at similar volume fractions. HA-nanocomposites reinforced by graphene nanosheets exhibit transversely isotropic material properties and provide the highest elastic modulus when aligned along a direction or randomly distributed in a plane, whereas CNTs provide the best reinforcement when aligned along an axis. Variation in graphene nanosheet area, thickness, aspect ratio, and carbon nanotube length have negligible effect on elastic modulus of the HA-nanocomposite. In addition, comparison between the finite element simulations and theoretical calculations show that clustering of nanoinclusions reduces the effectiveness of the reinforcement they provide. The simulation results and the computational framework presented in this study are expected to help in determining the best design and manufacturing parameters that can be adapted for developing HA-nanocomposite bone implant materials.

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Figures

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Fig. 5

Variation of elastic modulus along all axes with the nanofiller orientation for (a) carbon nanotubes and (b) graphene nanosheets. Note that Orientation 1 and Orientation 2 refer to the in-plane alignment and axis alignment, respectively, whereas xy and z indicate the direction for which the elastic modulus was evaluated. All other variables except alignment is kept constant (graphene nanosheets: volume fraction: 1%, area: 1 μm2, aspect ratio: 2, thickness: 1 nm; carbon nanotubes: volume fraction: 4%, diameter: 1.5 nm, wall thickness: 0.335 nm, length: 40 nm). For HA-graphene nanosheets, the polynomial fits in Orientation 1 are Ex,y = 10−5x3 − 0.0019x2 − 0.0072 x + 110.08 (R2 = 0.995), Ez = 0.0013x2 − 0.0777 x + 102.35 (R2 = 0.971) and in Orientation 2, Ex,y = −10−5x3 + 0.0015x2 − 0.0441 x + 103.87 (R2 = 0.930) and Ez = (2 × 10−5)x3 − 0.0022x2 − 0.0009 x + 109.96 (R2 = 0.980). For HA-carbon nanotubes, the polynomial fits in Orientation 1 are Ex,y = 1 × 10−5x3 − 0.001x2 − 0.0361 x + 108.42 (R2 = 0.992), Ez = 0.001x2 − 0.0614 x + 102.18 (R2 = 0.931) and in Orientation 2, Ex,y = 0.0009x2 − 0.0619 x + 102.12 (R2 = 0.968) and Ez = (6 × 10−5)x3 − 0.0065x2 − 0.1214 x + 126.4 (R2 = 0.998). Note that the variable, x, in the equations denotes the angle of rotation in degrees.

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Fig. 4

Variation of elastic modulus with nanofiller volume fraction for graphene nanosheets and carbon nanotubes. Note that all other variables except volume fraction is kept constant (Graphene nanosheets: area: 1 μm2, aspect ratio: 2, thickness: 1 nm, random orientation; carbon nanotubes: diameter: 1.5 nm, wall thickness: 0.335 nm, length: 100 nm, random orientation)

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Fig. 3

(a) Sample finite element mesh showing the different components of the model. The finite element models were generated by combining the graphene nanosheets/CNTs with HA matrix to create the nanocomposite. (b) Nanosheet volume fraction versus elastic modulus for different mesh sizes. Note that Mesh 1 corresponds to the element size used in all the simulations reported in this study. Mesh 2 is a finer mesh with element size that is half of the element size in Mesh 1. Mesh 3 is an even finer mesh that has an element size that is one third of the element size in Mesh 1.

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Fig. 2

Sample nanofiller networks used in the finite element simulations showing different nanofiller orientations. Graphene nanosheets (a) aligned with z-axis, (b) aligned with xy-plane, (c) random distribution. Carbon nanotubes (d) aligned with z-axis, (e) aligned with xy-plane, and (f) random distribution. The orientations that ranged between completely aligned and random cases were investigated in the finite element simulations.

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Fig. 1

Sample nanosheet networks used in the finite element simulations showing the effect of the variation of nanosheet network parameters on the models (a) volume fraction, (b) aspect ratio, and (c) nanosheet area

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Fig. 6

Variation of elastic modulus with (a) aspect ratio of graphene nanosheets (volume fraction: 0.67%, area: 1 μm2; thickness: 1 nm; random orientation) (b) thickness of graphene nanosheets (volume fraction: 1%, area: 1 μm2, aspect ratio: 2, random orientation) (c) area of graphene nanosheets (volume fraction: 1%, aspect ratio: 2, thickness: 1 nm, random orientation) (d) length of carbon nanotubes (volume fraction: 4%, diameter: 1.5 nm, wall thickness: 0.335 nm, aligned along z-axis).

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Fig. 7

Comparison of theoretical predictions with finite element simulations for randomly distributed carbon nanotubes and graphene nanosheets. The solid lines for the finite element show the results obtained directly from simulations. Dotted lines extending from the solid lines were included to show the trendline for volume fractions for which simulations were not performed for better comparison with theoretical calculations.

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