Contained Compression Testing using a Texture Analyser – Calculating Bulk Modulus

Bulk modulus is a defined as the relative change in a sample’s volume when a unit compressive or tensile stress acts uniformly over its surface. 

It is a measure of how resistant a substance is to pure compression. Its measurement is possible by the use of a Texture Analyser, providing care is taken over the sample setup.

How to measure bulk modulus

The cylinder probe and the container must have very similar diameters for performing a bulk modulus test, as the whole sample must be in compression. If the probe is much smaller than the container, it becomes a penetration test.

When the sample is compressed, the cross-sectional area stays constant, but the height of sample decreases from L_initial to L_final, decreasing the volume:

All lengths are in m, all areas are in m², all forces are in N and all pressures are in Pa. Parameters saved in Exponent must have these units.

The following equations allow the calculation of bulk modulus from a force-distance graph.
Definition of bulk modulus, K:

where V₀ is initial sample volume and dP/dV is the change in pressure with respect to volume.

Pressure on the sample:

where F is the force applied by the texture analyser and A is the cross-sectional area of the sample and probe (stored in the Parameters tab of the Test Configuration window in Exponent).

Sample volume:

where L is the sample height as shown in the diagram above.

For the dP/dV part of the bulk modulus equation:

So substituting values for P and V into the bulk modulus equation:

where dF/dL is the gradient of the force-distance curve in the initial linear region.

So the final bulk density equation to use in an Exponent macro is:

There is a Texture Analysis test for virtually any physical property. Contact Stable Micro Systems today to learn more about our full range of solutions.

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For more information on how to measure texture, please visit the Texture Analysis Properties section on our website.

The TA.XTplus texture analyser is part of a family of texture analysis instruments and equipment from Stable Micro Systems. An extensive portfolio of specialist attachments is available to measure and analyse the textural properties of a huge range of food products. Our technical experts can also custom design instrument fixtures according to individual specifications.

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