Dear Imran,
Master curve is drawn to study the asphalt binder behavior under wide range of frequency at a particular temperature. Since, very low frequency (eg. 0.000001Hz) and very high frequency (eg. 10000Hz) is practically not possible to perform in the laboratory. Master curve helps in this regard to study the behavior of the visco-elastic material under the wide range of frequency.
You need to carry out Time-Temperature sweep test for the development of master curve. Essentially you need to cover minimum 4-5 temperatures (eg. 40, 50, 60, 70, 80 °C) and a wide range of frequency (eg. 0.1 rad/sec to 100 rad/sec) to draw a reliable master curve. You need to cover wide range of stated frequency at each temperature level.
Please note that master curve is drawn at a particular reference temperature. Hence it is preferred that your reference temperature is in the range of different tested temperature. It is more realistic to consider prevalent field temperature as a reference temperature. Let's say the prevalent temperature in the field is 30 °C in your country, then, you should carry out DSR test at various temperatures such as 10, 20, 30, 40, and 50 °C. This will help in carrying out finding out reduced frequency.
Further while finding out reduced frequency, use of WLF equation(for shifting purpose) is preferred for reference temperature in intermediate to high-temperature condition. However, Arrhenius equation is better if you wish to draw the master curve at a reference temperature in low-temperature condition (eg. -10 °C). Please note that for low-temperature condition, Bending Beam Rheometer (BBR) data is used for this purpose, not the DSR.
Further, selection of a particular model (Sigmoidal, CAM, modified CAM, Double logistic model) is very much important to get appropriate master curve as each model is having their own advantages and limitations.
There are many pieces of literature available in this regard. Let me know if you need further help in this regard.
Good luck.
Here is my paper about Prony' series model parameters determination, but first steps are about master curve creation. If you need assistance feel free to ask.
https://www.researchgate.net/publication/263544550_APPLICATION_OF_NON-LINEAR_OPTIMIZATION_METHODS_FOR_DETERMINATION_OF_PRONY_SERIES_PARAMETERS_OF_VISCO-ELASTIC_MATERIALS
Chapter APPLICATION OF NON-LINEAR OPTIMIZATION METHODS FOR DETERMINA...
Master curves for DSR results can be plotted by using the Rheoplus software.
Dear Imran,
Master curve is drawn to study the asphalt binder behavior under wide range of frequency at a particular temperature. Since, very low frequency (eg. 0.000001Hz) and very high frequency (eg. 10000Hz) is practically not possible to perform in the laboratory. Master curve helps in this regard to study the behavior of the visco-elastic material under the wide range of frequency.
You need to carry out Time-Temperature sweep test for the development of master curve. Essentially you need to cover minimum 4-5 temperatures (eg. 40, 50, 60, 70, 80 °C) and a wide range of frequency (eg. 0.1 rad/sec to 100 rad/sec) to draw a reliable master curve. You need to cover wide range of stated frequency at each temperature level.
Please note that master curve is drawn at a particular reference temperature. Hence it is preferred that your reference temperature is in the range of different tested temperature. It is more realistic to consider prevalent field temperature as a reference temperature. Let's say the prevalent temperature in the field is 30 °C in your country, then, you should carry out DSR test at various temperatures such as 10, 20, 30, 40, and 50 °C. This will help in carrying out finding out reduced frequency.
Further while finding out reduced frequency, use of WLF equation(for shifting purpose) is preferred for reference temperature in intermediate to high-temperature condition. However, Arrhenius equation is better if you wish to draw the master curve at a reference temperature in low-temperature condition (eg. -10 °C). Please note that for low-temperature condition, Bending Beam Rheometer (BBR) data is used for this purpose, not the DSR.
Further, selection of a particular model (Sigmoidal, CAM, modified CAM, Double logistic model) is very much important to get appropriate master curve as each model is having their own advantages and limitations.
There are many pieces of literature available in this regard. Let me know if you need further help in this regard.
Good luck.
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