Chinedum Ogonna MGBEMENA, Department of Mechanical Engineering, Federal University of Petroleum Resources, P.M.B 1221, Eurun, Delta State, Nigeria

ThankGod Enatimi BOYE, Ikuobase EMOVON, Department of Mechanical Engineering, Federal University of Petroleum Resources, P.M.B 1221, Eurun, Delta State, Nigeria

Tiếng Anh

### Tóm tắt

This paper is on the prediction of stress limits and strain distributions of an automobile tire sidewall developed from Natural Rubber (NR)/Tea Seed Oil (TSO) modified kaolin composites. The stress-strain data report of NR/TSO modified kaolin at filler loading of 10phr was used to establish parameters characterizing the elastic behavior of the rubber vulcanizates. The tire model investigated was developed from MATLAB PDE Toolbox. The study was developed on maximum inflation pressure of 0.220632 MPa. The 2D Finite Element (FE) model computations for static loading of the tire sidewall gave a reasonable prediction of the stress limits and strain distributions, as the shear stresses obtained were within the range of −10 MPa to 10 MPa. The strain energy distributions were found to be within the range of −1500 J·m−3 to 1500 J·m−3. The stress limits for the first principal stress with respect to their magnitudes and orientations was obtained as 10 MPa for tensile stress and −20 MPa for compressive stress respectively while the stress limits for the second principal stress was obtained as 20 MPa for tensile stress and −10 MPa for compressive stress. The plane stress analysis with MATLAB PDE Toolbox gave stress limits distribution in terms of von-Mises stresses in the range 5 MPa - 25 MPa. The results indicate that NR/TSO modified kaolin composites can be employed in automobile tire sidewall applications.

### Từ khoá

Kaolin, natural rubber, strain, stress, tire von-Mises.

### Tài liệu tham khảo

[1] SADEK, S. and M. OLSSON. New models

for prediction of high cycle fatigue failure

based on highly loaded regions. International

Journal of Fatigue. 2014, vol. 66,

iss. 1, pp. 101110.

[2] GROSS, A. J. and K. RAVI-CHANDAR.

Prediction of ductile failure using a local

strain-to-failure criterion. International

Journal of Fracture. 2014, vol. 186, iss. 12,

pp. 6691.

[3] MOHOTTI, D., M. ALI, T. NGO, J. LU

and P. MENDIS. Strain rate dependent

constitutive model for predicting material

behaviour of polyurea under high strain

rate tensile loading. Materials and Design.

2014, vol. 53, iss. 1, pp. 830837.

[4] IHUEZE, C. C., C. E. OKAFOR and C.

I. OKOYE. Natural Fibers Composites Design

and Characterization for Limit Stress

Prediction in Multiaxial Stress State. Journal

of King Saud University - Engineering

Sciences. 2015, vol. 27, iss. 2, pp. 193206.

[5] CRAWFORD, R. J. Plastic Engineering.

3rd ed. Oxford: Elsevier ButterworthHeinamann,

1998.

[6] STEINMANN, P., M. HOSSAIN and G.

POSSART. Hyperelastic models for rubberlike

materials: consistent tangent operators

and suitability for Treloar's data. Archive

of Applied Mechanics. 2012, vol. 82, iss. 9,

pp. 135.

[7] NUNES, L. C. S. Mechanical characterization

of hyperelastic polydimethylsiloxane

by simple shear test. Materials Science and

Engineering. 2011, vol. 528, iss. 3, pp. 1799

1804.

[8] HAMZA, M. N. and H. M. ALWAN. Hyperelastic

constitutive modeling of Rubber and

Rubberlike materials under nite strain. International

Journal of Solids and Structures.

2010, vol. 41, iss. 18, pp. 53275350.

[9] SUSSMAN, T. and K. J. BATHE. A model

of incompressible isotropic hyperelastic material

behavior using spline interpolations

of tension-compression test data. Communications

in numerical methods in engineering.

2009, vol. 25, iss. 1, pp. 5363.

[10] MIEHE, C., S. GOKTEPE and F. LULEI.

A micro-macro approach to rubber-like

materials-Part I: The non-ane microsphere

model of rubber elasticity. Journal of

the Mechanics and Physics of Solids. 2004,

vol. 52, iss. 11, pp. 26172660.

[11] BOYCE, M. C. and E. M. ARRUDA. Constitutive

models of rubber elasticity: A Review.

Rubber Chemistry and Technology.

2000, vol. 73, no. 3, pp. 504523.

[12] MOONEY, M. A. A theory of large elastic

deformation. Journal of Applied Physics.

1940, vol. 11, iss. 9, pp. 582592.

[13] OGDEN, R. W. Large deformation

isotropic elasticity - on the correlation of

theory and experiment for the incompressible

rubber-like solids. Proceedings of theRoyal Society of London. 1972, vol. 326,

iss. 1567, pp. 565584.

[14] OGDEN, R. W. Large deformation

isotropic elasticity - on the correlation of

theory and experiment for the compressible

rubberlike solids. Proceedings of the Royal

Society of London. 1972, vol. 328, iss. 1575

pp. 567583.

[15] OGDEN, R. W. Non-linear elastic deformation.

1st ed. New York: Dover Publications,

1984.

[16] OGDEN, R. W. Non-linear Elasticity.

1st ed. Cambridge: Cambridge University

Press, 2001.

[17] MGBEMENA, C. O., S. RUGMINI and

A. R. R. MENON. Cure Characteristics,

Filler Dispersion and Mechanical Properties

of Natural Rubber/ Organomodied

Kaolin Nanocomposites. International

Conference on Rubber & Rubber-Like Materials.

Kharagpur, 2013.

[18] MGBEMENA, C. O., N. O. IBEKWE,

A. P. MOHAMED, A. R. R. MENON

and S. RUGMINI. Characterization of

Kaolin intercalates of Oleochemicals derived

from Rubber Seed (Hevea brasiliensis)

and Tea Seed (Camelia sinensis) Oils. Journal

of King Saud University-Science. 2013,

vol. 25, iss. 2, pp. 149155.

[19] RUGMINI, S. and A. R. R. MENON.

Organomodied Kaolin as Filler for Natural

Rubber. Journal of Applied Polymer Science.

2008, vol. 107, iss. 6, pp. 34763483.

[20] SPIEGEL, L. and G. F. LIMBRUNNER.

Applied Statics and Strength of materials.

3rd ed. New Jersey: Prentice Hall, 1998.

for prediction of high cycle fatigue failure

based on highly loaded regions. International

Journal of Fatigue. 2014, vol. 66,

iss. 1, pp. 101110.

[2] GROSS, A. J. and K. RAVI-CHANDAR.

Prediction of ductile failure using a local

strain-to-failure criterion. International

Journal of Fracture. 2014, vol. 186, iss. 12,

pp. 6691.

[3] MOHOTTI, D., M. ALI, T. NGO, J. LU

and P. MENDIS. Strain rate dependent

constitutive model for predicting material

behaviour of polyurea under high strain

rate tensile loading. Materials and Design.

2014, vol. 53, iss. 1, pp. 830837.

[4] IHUEZE, C. C., C. E. OKAFOR and C.

I. OKOYE. Natural Fibers Composites Design

and Characterization for Limit Stress

Prediction in Multiaxial Stress State. Journal

of King Saud University - Engineering

Sciences. 2015, vol. 27, iss. 2, pp. 193206.

[5] CRAWFORD, R. J. Plastic Engineering.

3rd ed. Oxford: Elsevier ButterworthHeinamann,

1998.

[6] STEINMANN, P., M. HOSSAIN and G.

POSSART. Hyperelastic models for rubberlike

materials: consistent tangent operators

and suitability for Treloar's data. Archive

of Applied Mechanics. 2012, vol. 82, iss. 9,

pp. 135.

[7] NUNES, L. C. S. Mechanical characterization

of hyperelastic polydimethylsiloxane

by simple shear test. Materials Science and

Engineering. 2011, vol. 528, iss. 3, pp. 1799

1804.

[8] HAMZA, M. N. and H. M. ALWAN. Hyperelastic

constitutive modeling of Rubber and

Rubberlike materials under nite strain. International

Journal of Solids and Structures.

2010, vol. 41, iss. 18, pp. 53275350.

[9] SUSSMAN, T. and K. J. BATHE. A model

of incompressible isotropic hyperelastic material

behavior using spline interpolations

of tension-compression test data. Communications

in numerical methods in engineering.

2009, vol. 25, iss. 1, pp. 5363.

[10] MIEHE, C., S. GOKTEPE and F. LULEI.

A micro-macro approach to rubber-like

materials-Part I: The non-ane microsphere

model of rubber elasticity. Journal of

the Mechanics and Physics of Solids. 2004,

vol. 52, iss. 11, pp. 26172660.

[11] BOYCE, M. C. and E. M. ARRUDA. Constitutive

models of rubber elasticity: A Review.

Rubber Chemistry and Technology.

2000, vol. 73, no. 3, pp. 504523.

[12] MOONEY, M. A. A theory of large elastic

deformation. Journal of Applied Physics.

1940, vol. 11, iss. 9, pp. 582592.

[13] OGDEN, R. W. Large deformation

isotropic elasticity - on the correlation of

theory and experiment for the incompressible

rubber-like solids. Proceedings of theRoyal Society of London. 1972, vol. 326,

iss. 1567, pp. 565584.

[14] OGDEN, R. W. Large deformation

isotropic elasticity - on the correlation of

theory and experiment for the compressible

rubberlike solids. Proceedings of the Royal

Society of London. 1972, vol. 328, iss. 1575

pp. 567583.

[15] OGDEN, R. W. Non-linear elastic deformation.

1st ed. New York: Dover Publications,

1984.

[16] OGDEN, R. W. Non-linear Elasticity.

1st ed. Cambridge: Cambridge University

Press, 2001.

[17] MGBEMENA, C. O., S. RUGMINI and

A. R. R. MENON. Cure Characteristics,

Filler Dispersion and Mechanical Properties

of Natural Rubber/ Organomodied

Kaolin Nanocomposites. International

Conference on Rubber & Rubber-Like Materials.

Kharagpur, 2013.

[18] MGBEMENA, C. O., N. O. IBEKWE,

A. P. MOHAMED, A. R. R. MENON

and S. RUGMINI. Characterization of

Kaolin intercalates of Oleochemicals derived

from Rubber Seed (Hevea brasiliensis)

and Tea Seed (Camelia sinensis) Oils. Journal

of King Saud University-Science. 2013,

vol. 25, iss. 2, pp. 149155.

[19] RUGMINI, S. and A. R. R. MENON.

Organomodied Kaolin as Filler for Natural

Rubber. Journal of Applied Polymer Science.

2008, vol. 107, iss. 6, pp. 34763483.

[20] SPIEGEL, L. and G. F. LIMBRUNNER.

Applied Statics and Strength of materials.

3rd ed. New Jersey: Prentice Hall, 1998.