Dear all,
How can I draw a black diagram for my rheological binder evaluation data obtained from a dynamic shear rheometer? I have the complex modulus and the phase angle obtained at four different temperatures.
Thank you
Plot the phase angle on the y-axis versus the log of the complex modulus |G*| on the x-axis and that will be the Black diagram.
If a log-log plot is made of the loss modulus G” on the y-axis versus the storage modulus G’ on the x-axis then what is obtained is a Cole-Cole diagram.
In case dynamic mechanical data is obtained on solid samples, then a log-log plot of loss modulus E” on the y-axis versus the storage modulus E’ on the x-axis gives an Argand diagram. Some idea of how these plots look can be seen in the following paper:
D. R. Saini, A. V. Shenoy and V. M. Nadkarni, Dynamic mechanical properties of highly loaded ferrite-filled thermoplastic elastomers, J. Appl. Polym. Sci., Vol. 29, p. 4123 (1984).
Most of the attempts for making different diagrams are in order to seek methods to get plots which could be independent of either frequency or temperature. There are various methods of unifications and one such unification method is discussed in detail in the following books:
1. A. V. Shenoy and D. R. Saini, Thermoplastic Melt Rheology and Processing, Marcel Dekker Inc., New York (1996).
2. Aroon V. Shenoy, Rheology of Filled Polymer Systems, Kluwer Academic Publishers, Netherlands (1999).
When the word “binder” is mentioned in the question, it is not clear whether this refers to a polymeric binder for filled systems or to an asphalt binder. If it is a polymeric binder for filled systems, then such systems are shown in the book number 2 mentioned above. If it is asphalt binder, then some idea of unifying data can be got from the following papers.
1. Aroon Shenoy, Developing unified rheological curves for polymer-modified asphalts. Part I: Theoretical analysis, Materials and Structures, Vol. 33(231), p. 425-429 (2000).
2. Aroon Shenoy, Developing unified rheological curves for polymer-modified asphalts. Part II: Experimental verification, Materials and Structures, Vol. 33(231), p. 430-437 (2000).
Thank you very much for your prompt reply Dr. Aroon Shenoy.
The thing is that i am studying EVA modified asphalt binders. I have obtained the phase angle and the complex modulus over a frequency range of 0.1 to 10 Hz at four different temperatures ranging from 45 to 75. while plotting the complex modulus vs the phase angle, should I include the data at each temperature separately, or should i include all the data obtained at all temperatures in one plot?
thank you very much for the reference. I am sure they will come in handy.
Thank you
High regards,
While plotting the phase angle versus the log of the complex modulus |G*| for the rheological data of EVA-modified asphalt binder, put all data points for the four different temperatures ranging from 45 to 75 °C on the same plot. However, use different symbols for each temperature so that it becomes clear how the data at the different temperatures have laid out.
Data on EVA-modified asphalt binder has been dealt with in the following paper and may be of help to you:
Aroon Shenoy, Model-fitting the master curves of the dynamic shear rheometer data to extract a rut controlling term for asphalt pavements, ASTM - J. of Testing and Evaluation, Vol. 30, No. 2, pp. 95-102 (March 2002).
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