Modeling and Analysis of Strengthening Mechanism of MWCNT Reinforced Copper Matrix Nanocomposites by using Shear Lag Model

Modeling and Analysis of Strengthening Mechanism of MWCNT Reinforced Copper Matrix Nanocomposites by using Shear Lag Model

Mahesh

Department of Mechanical Engineering

M. S. Ramaiah Institute of Technology Bangalore, INDIA

Dr. Raji George

Professor

Vishwanth Koti

Assistant Professor Department of mechanical Engineering

1. Ramaiah Institute of Technology Bangalore, India

   Department of mechanical Engineering

   M.S. Ramaiah Institute of Technology Bangalore, India

   Abstract—Young's modulus of carbon nanotubes is approximately 1 TPa. Hence an ideal reinforcement material for composites. In order to achieve better mechanical properties in CNTs reinforced metal matrix nanocomposites, understanding of strengthening mechanism is very important. One such model is shear lag model. The model explains load transfer mechanism between matrix and reinforcement. Here Shear lag model is analyzed along with experimental results.

   Keywords—-Powder metallurgy route, MWCNT/Cu nanocomposite, Shear Lag model.

   1. INTRODUCTION

      Since the discovery of carbon nanotubes lot of research work has been carried out by researchers and scientists due to their best mechanical properties such as strength, stiffness, electrical conductivity and thermal conductivity. No material is available till today known to mankind, which can match these above mentioned mechanical properties for carbon nanotubes, for both experimental and theoretical results [1 – 6]. From literature Survey and scientists experimental data it is evident that Young's modulus of single walled carbon nanotubes and multiwalled carbon nanotubes is in the range of 1 to 5 TPa. This is one of the major reason for using carbon nanotubes as reinforcement material in composites. Another reason is density. Density of multiwalled carbon nanotubes is nearly

      1.8 g/cc which makes them lighter and stronger. But very less research work has been done in metal matrix nanocomposites when compared to polymer and ceramic matrix nanocomposites due to various reasons associated with metal matrix nanocomposites preparation. One among them is wettability of CNTs with metal matrix. To overcome this problem it is very much necessary to understand load transfer mechanism between reinforcement and matrix. Strengthening of metal matrix nanocomposites can be done by understanding load transfer mechanism between matrix and reinforcement, which is well explained by shear lag model. The present work addresses the

      processing of MWCNT/Cu nanocomposites, measurement of hardness of processed nanocomposites, providing an evidence of existence of wettability problem and explaining strengthening mechanism of nanocomposites by using shear lag model.

   2. EXPERIMENTAL

      1. Material Used

         Multiwalled carbon nanotubes were procured from United Nanotech Laboratory Ltd.. Mechanical characterization XRD and SEM is done to check purity and quality of procured MWCNT. Average diameter of procured MWCNT is 5 – 20 nm and length is 10 microns.

         Copper powder is procured and its purity is checked by using XRD characterization technique. Copper particle size is approximately in the range of 35 – 45 nm.

      2. Fabrication Of MWCNT/Cu Nanocomposite

      Powder metallurgy route technique is used to fabricate MWCNT/Cu nanocomposites. A mixture of MWCNT as reinforcement and copper powder as matrix were ball milled at 200rpm for 2 hrs consisting of 8 cycles each of 15 minutes with 5 minutes gap between each cycle. Along with mixture, few drops of ethanol is used for dispersion of MWCNT reinforcement in copper matrix and to avoid agglomeration of MWCNT. The milled powder was compacted in a circular die. And a 10 ton force is used to compact powder mixture. Then green compacted billet is sintered in an oven at 850 °C for 3 hours. No secondary operation is carried out. But turning and facing is done to remove oxide layer formed during sintering process and to get accurate required dimensions. Oxide layer is formed because sintering is carried out in an open air oven. EDX and SEM characterization technique provide proof for presence of MWCNT in sintered MWCNT/Cu nanocomposites.

   3. RESULTS AND DISCUSSION

Quality and purity of procured MWCNT is validated by XRD and SEM given in figure 3.1 and 3.2 respectively. Copper quality is ensured by XRD given figure 3.3.

1000

800

Counts

Counts

600

400

200

0

0 20 40 60 80 100

A

Figure 3.1 XRD of MWCNT

(Procured form United Nanotech Laboratory Ltd.)

Figure 3.2 SEM of MWCNT

(Procured form United Nanotech Laboratory Ltd.)

2000

1800

1600

Counts

Counts

1400

1200

1000

800

600

400

200

0

0 50 100

2()

Figure 3.3 XRD of Procured Pure Copper

Density of prepared MWCNT/Cu nanocomposites samples were calculated by measuring weight and volume of the samples manually and from manually calculated density porosity of the samples calculated which given in Table 3.4 and respective graph is given in graph 3.5. Porosity is resulted because no secondary operation is carried out.

Density of MWCNT/Cu in g/cc

Density of MWCNT/Cu in g/cc

Table 3.4 Showing Density of MWCNT/Cu nanocomposite and Porosity of Prepared MWCNT/Cu nanocomposite

9.5

9

8.5

8

7.5

Theoretical

Experimental

9.5

9

8.5

8

7.5

Theoretical

Experimental

0

0.5

1

1.5

0

0.5

1

1.5

Weight Fraction of MWCNT in %

Weight Fraction of MWCNT in %

7

6.5

7

6.5

Graph 3.5 Theoretical Density vs. Experimental Density

Shear Lag Model

This model explains the load transfer between matrix and reinforcement by interfacial shear stress as shown in figure

3.6. High aspect ratios are favored with this model but aspect ratio higher than 500, no significant effect on the strength of nanocomposites. Aspect ratio of MWCNT are in the range of ~100. From experimental results as sown in Table 3.7 and Graph 3.8 it is evident that the results were not up to the mark and not as expected by this model. And from the analysis of experimental results shown in Table

3.7 and Graph 3.8 it is evident that wetting of the MWCNT is the reason behind low experimental results of nanocomposites. From analysis it is evident that wetting is reason and it is found that the wettability problem is caused due to huge difference betwen surface tension of matrix and reinforcement. Surface tension for aluminum and copper is 600 and 750 mN/m.

Figure 3.6 Configuration of Shear Lag Model

The Young's modulus of nanocomposites by Shear Lag Model is given by

Ec=Vf*Ef*(1 – (tanh(n*s))/(n*s)) + (1 – Vf) * Em Where,

Ec – Young's modulus of nanocomposites in GPa Em – Young's modulus of matrix material in GPa

Ef – Young's modulus of reinforcement material in GPa Vf – Reinforcement material volume fraction

S – Aspect ratio of reinforcement n – Constant and is given by

n = ((2*Em)/(Ef*(1+vm)*ln(1/Vf)))1/2

Calculation from the above theoretical model and experimental data are shown in below Table 3.7.

Commercial purity copper under the same processing and testing conditions shown lesser results than the MWCNT/Cu nanocomposites. Yield strength of nanocomposites is high than pure copper which is calculated from the measured hardness. 1% weight fraction reinforcement shown highest strength. From experimental results, Young's modulus of nanocomposites is less compared to theoretical values. This is mainly due to wetting problem of MWCNT.

Table 3.7 Shear Lag and Experimental Young's Modulus of MWCNT/Cu nanocomposite

200

180

160

Aspect Ratio 50

200

180

160

Aspect Ratio 50

Weight Fraction of MWCNT in %

Weight Fraction of MWCNT in %

140

120

140

120

Aspect Ratio 100

Aspect Ratio 100

100

80

60

100

80

60

Aspect Ratio 500

Aspect Ratio 500

40

20

0

40

20

0

0

0

0.5

0.5

1 1.5

1 1.5

Experimental Result for Aspect Ratio 100

Experimental Result for Aspect Ratio 100

Young's Modulus of MWCNT/Cu in GPa

Young's Modulus of MWCNT/Cu in GPa

Graph 3.8 Shear Lag vs. Experimental Young's modulus

IV. CONCLUSION

In this chapter the conclusions are made by the result obtained by investigation of MWCNT/Cu nanocomposite. Investigations are carried out by hardness test, prediction of yield strength, Shear Lag model.

• From results it is evident that the experimental Young's modulus of nanocomposites did not met theoretical Young's modulus, calculated by using shear lag model.

• This is mainly due to inefficient transfer of load from matrix to reinforcement material. Mainly caused due to wettability problem of MWCNT. But strength of nanocomposites is increased as MWCNT reinforcement is increased. Strength is higher than pure copper and this can be used as light material in various applications.

• There is no significant effect on strength of MWCNT/Cu for higher aspect ratio

• Density of nanocomposites decreases as reinforcement increases because of density of MWCNT resulting decreased weight of nanocomposites.

• Agglomeration plays an important role in increasing strength of nanocomposites.

• Wettability problem can be improved by coating MWCNT with other materials which are having same crystal structure

• It is evident that aspect ratio higher than or equal to 500 is ineffective on the strength of the MWCNT/Cu nanocomposites.

Finally it is evident that strength of MWCNT/Cu was increased as the addition of MWCNT as reinforcement. But the experimental results were not up to the mark due to inefficient load transfer between matrix and reinforcement explained by Shear Lag model.

ACKNOWLEDGEMENT

The author would like to thank the management, Principal and HOD of their respective Institute for their constant support in carrying out the research.

REFERENCES

1. Srinivas R. Bhakshi, Arvind Agarwal. "An analysis of the factors affecting strengthening in carbon nanotubes reinforced aluminum composite" Carbon 49 (2011) 533 544

2. S. R. Bhakshi, D. Lahiri, A. Agarwal. " Carbon nanotubes metal matrix composites a review"

3. Kyung Tae Kim, Seung II Cha, Seong Hyeon Hong, Soon Hyung Hong. "Microstructures and tensile behavior of carbon nanotube reinforced Cu matrix nanocomposites"

   Materials Science and Engineering A 430 (2006) 27 33

4. J. P. Tu, Y. Z. Yang, L. Y. Wang X. C. Ma, X. B. Zhang. "Tribological properties of carbon nanotube reinforcement copper composites" Tribology Letters Vol. 10 (2001) 225 228

5. Chulju Kim, Byengsoo Lim, Bumjoon Kim, Untae Shim, Seyoung Oh, Byungho Sung, Jeehoon Choi, Jaehyung Ki, Seunghyun Baik. "Strengthening of copper matrix composites by nickel coated single walled carbon nanotubes reinforcement" Synthetic Metals 159 (2009) 424 429

6. I. Sridhar, Khartic R. Narayan. "Processing and characterization of MWCNT reinforced aluminum matrix composites" J Mater Sci 44 (2009) 1750 1756

7. R. George, K. T. Kashyap, R. Rahul, S. Yamadagni. "Strengthening in carbon nanotube/aluminum composites"

   Scripta Materialia 53 (2005) 1159 1163

8. J.R. Davis, Copper and Copper Alloys, ASM International, 2001

9. C.S. Goh, J. Wei, L.C. Lee, M. Gupta, Compos. Sci.

   Technol. 68 (2008) 14321439

10. B.S. Lim, C.J. Kim, B.J. Kim, U.T. Shim, S.Y. Oh, B.H.

    Sung, et al., Nanotechnology 17 (2006) 57595764

11. K.T. Kim, J. Eckert, S.B. Menzel, T. Geming, S.H. Hong,

    Appl. Phys. Lett. 92 (2008) 121901

12. K.T. Kim, S.I. Cha, S.H. Hong, S.H. Hong, Mater. Sci. Eng.

    A. 430 (2006) 27 33

13. T. Laha, A. Agarwal, T. McKechnie, S. Seal, Mater. Sci.

    Eng. A. 381 (1) (2004) 249 258

14. A.M.K. Esawi, M.A. El Borady, Compos. Sci. Technol. 68 (2008) 486 492

15. P. Kim, L. Shi, A. Majumdar, P.L. McEuen, Phys. Rev. Lett. 87 (2001) 215502