Rheology is the science that studies the internal response of materials when they deform as a result of an applied stress. To learn about the rheological properties of any material, one must measure the deformation resulting from an applied stress or the force required to produce a given deformation (1).

1 Dynamic Cutoff Rheometer (DSR)

Dynamic shear rheometers are used to study the rheological behavior of various materials, including asphalt. The two most common methods used by the team to determine the viscoelastic properties of asphalts are transient (constant rate stress/strain) and dynamic (oscillatory) methods (2). The typical configuration of these equipments consists of a fixed lower plate and a mobile upper plate, between which an asphalt sample is placed, to which a shear stress is applied.

Dynamic or oscillatory tests cover a wide range of stresses in relatively short times, offering very valuable results (3). The operation of the equipment can be by controlled tension or by controlled deformation. In a tension controlled arrangement, a fixed torque is applied to the top plate to generate the oscillating motion. Because the applied stress level is fixed, the distance the plate moves in its oscillatory path can vary between cycles. When the strain-controlled test is defined, the upper platen is accurately moved between the amplitude extremities at the specified frequency and the torque required to maintain oscillation is measured. Since the DSR only takes three measurements; torque, angular rotation and time, all results are calculated from these variables. The following equations are used to calculate the strain () and stress () in the equipment:

( 1 )

Where:

g is the deformation of the sample, dimensionless or expressed in%.

q is the angular rotation, in radians (rad).

R is the radius of the plate, in millimeters (mm).

h is the space between the plates, in mm.

( 2 )

Where:

t is the shear stress, in Pa.

T is the recorded torque, in Newton meter (Nm).

From these definitions the absolute complex cut modulus is derived, whose expression is the following:

( 3 )

Where:

G * (ω) is the complex shear modulus, expressed in Pa.

ω is the angular frequency, in radians per second (rad / s).

Note: in this work the angular velocity will be referred to as angular frequency or simply frequency, therefore the frequency variable may present units of rad/s or Hertz (Hz). Both are related as .

Note: in this work the angular velocity will be referred to as angular frequency or simply frequency, therefore the frequency variable may present units of rad/s or Hertz (Hz). Both are related as .

For viscoelastic materials such as asphalt, the shear modulus is composed of a loss modulus (viscous component, G'') and a storage modulus (elastic component, G'), the relative magnitude of which determines how the material responds to loads. applied. The two components are linked to the complex modulus by the phase angle in a vector sum as shown in Figure 1. Therefore, the different components can be related using equation 4:

For viscoelastic materials such as asphalt, the shear modulus is composed of a loss modulus (viscous component, G'') and a storage modulus (elastic component, G'), the relative magnitude of which determines how the material responds to loads. applied. The two components are linked to the complex modulus by the phase angle in a vector sum as shown in Figure 1. Therefore, the different components can be related using equation 4:

For viscoelastic materials such as asphalt, the shear modulus is composed of a loss modulus (viscous component, G'') and a storage modulus (elastic component, G'), the relative magnitude of which determines how the material responds to loads. applied. The two components are linked to the complex modulus by the phase angle in a vector sum as shown in Figure 1. Therefore, the different components can be related using equation 4:

Where:

For viscoelastic materials such as asphalt, the shear modulus is composed of a loss modulus (viscous component, G'') and a storage modulus (elastic component, G'), the relative magnitude of which determines how the material responds to loads. applied. The two components are linked to the complex modulus by the phase angle in a vector sum as shown in Figure 1. Therefore, the different components can be related using equation 4:

G ’’ (ω) is the loss modulus, in Pa.

CITEVI has an Anton Para DSR SmartPave 102 shown in Figure 2. Due to the high stiffness of asphalt cements at room temperature, high shear stresses are required to reach a certain level of deformation, which can be limited by the minimum torque recordable by the equipment (2). To overcome this, the 8 mm diameter geometry is used to perform tests at temperatures below 35 °C and the 25 mm diameter geometry is used for tests where the temperature is equal to or greater than 35 °C. To maintain the specified temperature for each test, the equipment has a Peltier temperature control device and a water circulator to cool the pieces. In addition, an air compressor is used to help the rotation of the frictionless geometry in what is called an air bearing, allowing for high levels of precision. The operation of the rheometer and temperature control unit, along with data acquisition and analysis, are controlled by a computer.

Figure 2. SmartPave 102 dynamic shear rheometer. Taken from Anton Paar's website (4)

2 Linear viscoelastic region

The relationship between stress and strain in asphalt can be approximated as linear to small strains. Within this region, the relationship between stress and strain is influenced only by temperature and load time (frequency) and not by the magnitude of stress or strain. By increasing the amplitude of the stresses, the relationship is no longer linear and a decrease in the modulus of rigidity is caused (2).

There are three important reasons why the linear viscoelastic region of asphalt should be defined. First of all, it is advisable to limit the characterization of asphalt to its linear viscoelastic response to simplify the mathematical modeling of the material, since the nonlinear response, particularly for viscoelastic materials, is extremely difficult to characterize and model in the laboratory. Second, the rheological measurements and analysis methods are defined under the linear viscoelastic region. Finally, in the field of pavement design, it is necessary to study the asphalt and the asphalt mixture in the same domain in order to define the applicability limits of the linear viscoelastic theory (2).