Development of Standard Techniques for the Calculation of ...

1 Development of Standard Techniquesfor the Calculation of Master Curvesfor Linear-Visco Elastic Rowe and SharrockThe 1st International Symposium onBinder Rheology And Pavement Performance at The University of CalgaryAugust 13 - 15, 2000 Software Objectives Master Curve Production Discrete Relaxation and Retardation SpectraCalculation Conversions - time to frequency and vice-versa Advanced graphing and ease of use toperform complex calculationsWhy master curves? Powerful tool to understand how asphalttype and chemical makeup affects the visco-elastic behavior of binders Enables easy interpolation of properties andavenue for extrapolationMaster Curve ProductionShifting Techniques (Gordon/Shaw) Determine an initial estimate of the shift using WLFparameters and Standard constants.

2 Refine the fit by using a pairwise shifting technique andstraight lines representing each data set. Further refine the fit using pairwise shifting with apolynomial representing the data being shifted. The orderof the polynomial being taken as the minimum valuebetween number of the augment n+1, where n is thenumber of data points - or - f (the number of decades offrequency - or time).Normalized for density - vertical shift To enable all properties to be reported at thedensity corresponding to the referencetemperature (Rouse, 1953)Spectra CalculationsBaumgaertel and Winter (1989) Relaxation and Retardation Spectra Calculated for example Enables conversion of time to frequency (and vice-versa) and yields information about molecularstructure (Rouse)Voigt ElementMaxwell ElementBasic Visco-Elastic Model - The Maxwell ModelBasic Visco-Elastic Model - The Maxwell ModelnnRelaxation Spectra ModelRetardation Spectra ModelTypical Results from DifferentTypical Results from DifferentEquipmentEquipmentTwo example used1.

3 BBR2. DSRBBR1. Bending Beam Rheometer - Typical Data Set1. Bending Beam Rheometer - Typical Data Set1. Raw Data - 5 isotherms2. Stiffness Master Curve, S(t)3. Compliance Master Curve, D(t)4. Computed E , E from spectra calculations1. Raw Data - 5 isotherms2. Stiffness Master Curve, S(t)3. Compliance Master Curve, D(t)4. Computed E , E from spectra calculationsDSR1. Raw Data - 8 isotherms2. Stiffness Master Curve, G , G 3. Master Curve, G*, 4. Master Curve, G* versus 2. Dynamic Shear Rheometer - Typical Data Set2. Dynamic Shear Rheometer - Typical Data Set1. Raw Data - 8 isotherms2. Stiffness Master Curve, G , G 3. Master Curve, G*, 4. Master Curve, G* versus 3 formats for master curve G , G versus frequency G*, versus frequency G* versus (Black space)ErrorTypical ErrorTypical error -BBR - new spec - < DSR etc < 5%Error need to be determined for variousapplications.

4 Fit needs to consider noise andgoodness of Criteria Root mean square errorERROR to modified bindersBlack spaceConclusions Software developed for rapid production ofmaster curves Shifting based on Gordon and Shaw Inter-conversions enabled Interpolation rapid and easy to perform Graphs in different formats allows understandingof data RMS error criteria - a measure of goodness of fit Works well with modified binders and mixtures