# Obtaining Modulus Values from Thermal Mechanical Analyzer (TMA)

We mentioned using DMA to measure modulus in the previous blog. In this blog, we will discuss the usefulness of using TMA to measure modulus.

The TMA film set up is especially useful for tensile modulus measurement of plastic films. This set up is similar to typical tensile testing set up such as an Instron machine. A film sample is clamped at top and bottom at a constant temperature and the film sample is subjected to a controlled elongation strain or tensile force. The main difference being that in the TMA set up sample is not pulled till rupture. A stress-strain curve of the film sample is plotted and the tensile modulus is calculated from the initial slope of the graph where linear viscoelastic response is observed.

The Young’s modulus of a polymer sample can also be measured by TMA using the penetration probe set up. See equation below:

E = 3 F / (4 D d)

where:
E = modulus, MPa,
F = force, N,
D = diameter of a circular, flat tipped probe, mm, and
d = penetration depth, mm.

ASTM E2347 utilizes this equation to calculate the indentation softening temperature (similar to Vicat softening temperature) when the sample reaches a certain modulus value. For this TMA penetration set up sample is placed under a constant force while temperature increases at a constant heat rate.

# Obtaining Modulus Values from Dynamic Mechanical Analyzer (DMA)

Dynamic mechanical measurement of plastics is a very useful technique in viscoelastic behavior characterizations. Historically, scientists have been studying DMA thermographs to detect thermal transitions resulting from molecular motions and evaluate process-structure-property relationships. In recent years, however, there has been an increased application in DMA testing to mainly measure elastic modulus values of plastics. I wonder if this recent interest might be correlated with the increase usage of finite element analysis simulations, where people require mechanical data to be inputted into the simulation software, such as AutoCAD.

One advantage of using DMA testing is the sample size. DMA testing uses a much smaller sample size than the dog bone coupons for tensile testing or the large rectangular size for flexure testing. The smaller sample size is preferable as it is easier to fabricate a smaller piece without flaws that may affect the test results. However, the dimensional accuracy of the sample becomes more demanding in order to achieve accurate modulus values. Another advantage of using DMA testing is the ease to obtain modulus values at different temperatures. Only one sample is required in this case during a temperature ramp test.

Calculating modulus from DMA testing can be done easily as the test uses a small strain on the sample. However, strength data is not always possible to obtain. This is because DMA is designed as a tool to study polymer molecular behavior where resolution and sensitivity are important. So most commercial available DMA models have a very limited z-direction travelling distance and a small force range.

DMA thermograph is typically presented in storage modulus (E’), loss modulus (E’’), and tan delta, with respect to time or temperature. The dynamic modulus values are converted to elastic modulus value by the approximation

Elastic Modulus ~ |E*| = [E’2 + E’’2] 1/2

In an ideal elastic material, elastic modulus becomes E’ as tan delta approaches zero and E’’ becomes negligible.