Sains Malaysiana 42(11)(2013): 1647–1654

 

The Use of Inter-conversion Equations on Bituminous Binder Data

(Penggunaan Persamaan Antara-Penukaran ke Atas Data Pengikat Berbitumen)

 

NUR IZZI MD. YUSOFF1*, MOHD ROSLI HAININ2, DAMIEN MOUNIER3

& GORDON D. AIREY4

 

1Department of Civil and Structural Engineering, Faculty of Engineering and Build Environment

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

 

2Faculty of Civil Engineering and Construction Research Alliance, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia

 

3Civil Aviation Technical Centre (STAC), CS 30012, 31 Avenue du Maréchal Leclerc

94385 Bonneuil-Sur-Marne Cedex, France

 

4Nottingham Transportation Engineering Centre, University of Nottingham

University Park, NG7 2RD Nottingham, United Kingdom

 

Diserahkan: 19 Disember 2012/Diterima: 9 April 2013

 

 

ABSTRACT

According to the classical theory of viscoelasticity, a linear viscoelastic (LVE) function can be converted into another viscoelastic function even though they emphasize different information. In this study, dynamic tests were conducted on different conventional penetration grade bitumens using a dynamic shear rheometer (DSR) in the LVE region. The results showed that the dynamic data in the frequency domain can be converted into the time domain functions using a numerical technique. This was done with the aid of the non-linear regularization (NLREG) computer program. The NLREG software is a computer program for solving nonlinear ill-posed problem and is based on non-linear Tikhonov regularization method. The use of data interconversion equation is found suitable for converting from the frequency domain into the time domain of conventional penetration grade bitumens.

 

Keywords: Complex modulus; creep compliance; master curve; relaxation modulus

 

 

ABSTRAK

Menurut teori klasik likat kenyal, satu fungsi linear likat kenyal (LVE) boleh ditukar kepada fungsi likat kenyal yang lain walaupun ia menekankan maklumat yang berbeza. Dalam kajian ini, ujian dinamik dijalankan ke atas bitumen biasa yang berlainan gred penembusan dengan menggunakan reometer ricih dinamik (DSR) di dalam sempadan LVE. Keputusan menunjukkan bahawa data dinamik dalam domain frekuensi boleh ditukar kepada fungsi-fungsi dalam domain masa dengan menggunakan teknik berangka. Ini dilakukan dengan menggunakan bantuan perisian komputer pengaturan tidak linear (NLREG). Perisian NLREG adalah satu program komputer yang digunakan untuk menyelesaikan masalah tidak linear yang buruk yang timbul dan ia berdasarkan kaedah pengaturan Tikhonov tidak linear. Penggunaan persamaan antara-penukaran data adalah didapati sesuai untuk menukarkan domain frekuensi kepada domain masa terhadap bitumen bergred penembusan biasa.

 

Kata kunci: Lengkung utama; modulus kelonggaran; modulus kompleks; pematuhan rayap

 

RUJUKAN

Airey, G.D. 1997. Rheological Characteristics of Polymer Modified and Aged Bitumens. PhD Thesis, University of Nottingham, UK (unpublished).

Airey, G.A. 2002. Use of Black diagrams to identify inconsistencies in rheological data. Road Materials and Pavement Design 3: 403-424.

Anderson, M. 2010. Spring 2010 lab corner–master curves. The Asphalt Institute Magazine. http://www.asphaltinstitute.org/ singlenews.asp?item_ID= 2018&comm=0. Accessed on

Baumgaertal, M. & Winter, H.H. 1989. Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheologica Acta 28: 511-519.

Dealy, J.M. & Larson, R.G. 2006. Structure and Rheology of Molten Polymers, from Structure to Flow Behaviour and Back Again. Munich: Hanser Publisher.

Einaga, Y., Osaki, K., Kurata, M. & Tamura, M. 1971. Creep behaviour of polymer solutions. III. creep compliance concentrated polystyrene solutions. Macromolecules 5: 635-640.

Emri, I., Von Bernstorff, B.S., Cvelbar, R. & Nikonov, A. 2005. Re-examination of the approximate methods for inter-conversion between frequency and time dependent material function. Journal of Non-Newtonian Fluid Mechanics 129: 75-84.

Ferry, J.D. 1980. Viscoelastic Properties of Polymers. 3rd ed. New York: John Wiley & Sons.

Goodwin, J.W. & Hughes, R.W. 2000. Rheology for Chemists: An Introduction. Cambridge: The Royal Society of Chemistry.

Honerkamp, J. & Weese, J. 1990. Tikhonov regularization method for ill-posed problems. Continuum Mechanics and Thermodynamics 2: 17-30.

Honerkamp, J & Weese, J. 1993. A non-linear regularization method for the calculation of Relaxation Spectra. Rheologica Acta 32: 65-73.

Mayama, M. 1997. The evaluation of heavy duty binders in bituminous road materials. Proceedings of Institution of Civil Engineers-Transport 123: 39-52.

Mun, S., Chehab, G.R. & Kim, Y.R. 2007. Determination of time-domain viscoelastic functions using optimized inter-conversion techniques. Road Material and Pavement Design 8: 351-365.

Park, S.W. & Schapery, S.A. 1999. Methods of inter-conversion between linear viscoelastic material functions. Part I - A numerical method based on Prony series. International Journal of Solid and Structures 36: 1653-1675.

Park, S.W. & Kim, Y.R. 2001. Inter-conversion between relaxation modulus and creep compliance for viscoelastic solid. Journal of Materials in Civil Engineering 11: 76-82.

Plazek, J.D. & Echeverria, I. 2000. Don’t cry for me Charlie Brown, or compliance comes comprehension. Journal of Rheology 44: 831-841.

Provencher, S.W. 1982. CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations. Computer Physics Communications 27: 229-242.

Rowe, G.M. & Sharrock, M.J. 2000. The measurement and analysis system to accurately determine asphalt concrete properties using the indirect tensile mode. The 1st International Symposium on Binder Rheology and Pavement Performance the University of Calgary, August 14-15, Alberta, Canada.

 

 

*Pengarang untuk surat-menyurat; email: izzi@vlsi.eng.ukm.my

 

 

 

sebelumnya