Cone and Plate Geometry for the DHR/AR Rheometer

General Information

A schematic diagram of the cone and plate measuring system is shown in the figure below. During testing, the cone (the upper geometry) remains stationary while the parallel plate (the lower geometry) moves to deform the sample. The cones have an angle of less than or equal to 4° and are arranged such that they are parallel to the plate during testing.

To avoid contact between the cone and plate, and to prevent damage to either, the tip of the cone is removed. The length of material that is removed from the tip of the cone is referred to as the truncation distance. When testing a sample, the cone is positioned so that the virtual tip of the cone (i.e. if it was not machined away) would be in contact with the plate. At this location, the gap is equal to the truncation distance of the cone. The stress and strain calculations for a cone are geometrically driven and are based on the gap between the cone and plate being exactly the truncation distance of the cone. For this reason, it is critical to test samples with a cone and plate at and only at the truncation distance of the cone. The truncation distances for different cones vary and range from approximately 50 to 100 microns.

The conical angle and truncation distance for each cone are individually determined. These values are included on a calibration certificate that is supplied with each geometry. In addition, these values, as well as the serial number of the geometry, are inscribed on each geometry stem.

Testing Samples

The cone and plate geometry is used to test a wide variety of materials including polymer melts, suspensions and emulsions. Because of the geometry of the cone, there is no velocity gradient across the cone diameter during testing. The cone and –plate configuration is the desired configuration for normal stress measurements. For the cone and plate geometry, the normal force, N, corresponds to the first normal stress difference, N₁.

Unlike parallel plates, the gap for a cone and plate is fixed, and defined by the truncation distance of the cone. Because of the necessity to operate specifically at the truncation distance, a cone is normally used for isothermal testing only, as temperature changes may lead to changes in gap due to thermal expansion. Invar geometries may be used for tests in which the temperature is varied. Because of Invar's exceptional thermal expansion properties, Invar geometries are used for applications where temperature ramps or sweeps are necessary.

 Back to top

Testing at Other than Ambient Temperatures

The cone and plate geometry should be used for isothermal testing, as temperature changes may cause thermal expansion of the test fixture. For example, a cone and plate geometry with a 50-micron gap may undergo thermal expansion of 10 microns during testing at various temperatures. This thermal expansion would result in a 20 percent error in the measured gap, and would result in erroneous test data.

Following equilibration, the gap should be zeroed at the working temperature and then set to the testing gap. For applications in which a cone and plate is required and the test temperatures are varied, Invar tools can be used. Invar has a coefficient of thermal expansion that is 10 times less than steel between 0 and 230°C. Outside this range, Invar's thermal expansion properties are similar to steel's. If temperature ramps or sweeps must be performed using the cone and plate geometry, Invar should be used in the temperature range specified above.

Loading the Sample

1. Ensure that the gap has been zeroed, and raise the upper geometry so that there is sufficient work space to load the sample.
2. Place the sample on the lower plate. Ensure that the sample is centered on the tool.
3. Adjust the sample gap until the upper plate is close to the sample. Set the gap using the Set Gap function in TRIOS or the Touch Screen, entering the appropriate parameters. The gap should be approximately 0.10 mm above the truncation gap to facilitate sample trimming. Use the normal force limits to avoid damaging samples during loading. The normal force limits will not allow the normal force to rise above a specified level, so that sample relaxation is allowed to occur during the loading process.
4. Trim the sample flush with the edges of the plates.
5. Lower the stage to achieve the gap specified on the Certificate of Calibration. This may be done manually, or by using the Set Gap function. The sample should bulge slightly from the edges of the test geometry.
6. Allow samples to relax before beginning testing by monitoring the normal force and waiting for it to decay to close to zero.
7. Start the test. The sample gap is measured throughout the experiment.

Back to top

Equations

© 2014 TA Instruments–Waters LLC | 159 Lukens Drive | New Castle, DE 19720