Category Archives: TMA

thermal mechanical analysis

Frequently Asked Questions about TMA CTE Measurement

The linear coefficient of thermal expansion (CLTE, or CTE or α) is often measured by a thermomechanical analyzer (TMA).  There are two standard test methods that we are often asked to follow: one is the ASTM E 831 test method and the other is the IPC-TM-650 2.4.24 test method.  To help clients prepare samples for testing and interpret test results, I compile a FAQ for your references in this blog.

Q.  Can you describe briefly how the test is done?
A.  In a TMA, the specimen is placed in the sample holder at ambient temperature. The sample height is measured by the probe with a minimal amount of force to maintain contact throughout the experiment. The furnace is closed around the sample stage to control temperature.  The initial temperature is usually 20 oC below the lowest temperature of interest. The specimen is then heated at a specified heating rate, for example, 5 oC/min, over the desired temperature range.  A thermograph is produced where the sample height dimensional change is tracked over the entire temperature range of interest.

Q.  What are the specimen dimension requirements for testing?
A.  Each specimen is a cube or a cylindrical shape. The base (i.e., x – y dimensions) should be 5 to 8 mm by 5 to 8 mm.  The measuring direction (may be called height, or length, or z-direction) should be 5 to 8 mm and flat and parallel.  The ASTM test method specifies length to be between 2 and 10 mm.  The IPC test method specifies thickness to be greater than 0.51mm.

Q.  Why a wide range in specimen height is allowed in test method?
A.  There are several reasons for this. One reason is dependent on the sample shape.  For example, the IPC method is specific for printed circuit boards which is flat and thin.  Another reason is the expected thermal expansion of the sample.  For samples with low thermal expansion, a longer length is preferable to improve measurement accuracy.  However, specimen longer than 10 mm is discouraged to minimize specimen temperature gradients.

Q.  Can I use a different heating rate than specified in the standard test method?
A.  Yes. A different heating rate is allowed as long as any deviation from the standard test method be reported in the test report.

Q.  How many specimens should be tested of the same material?
A.  It all depends… The ASTM test method recommends at least three specimens.  The IPC test method recommends two specimens.  Each test should use a fresh specimen.  Bottom line, do at least one!

Q.  What is the precision of the TMA CTE test?
A.  5 to 10% is typical. The precision depends on imprecisions of measurements (i.e., temperature and length measurements from the TMA equipment), sample preparations (i.e., surface parallelism), and sample type (i.e., specimen thickness and expected thermal expansion).

Q.  What is the dimensional unit for values of CTE, α
A.  The unit for α is length change over total length per temperature scale. The following expressions in SI units are frequently used:

ppm/ oC
10-6/ oC

Q.  How is CTE calculated
A.  The coefficient of linear thermal expansion (CLTE or CTE or a) is length change over temperature change over total initial length. In math expression,

α = (ΔL/ΔT) x (1 / Lo)

Determine CTE values from TMA thermograph; graph from ASTM E831 test method

CTE values are expressed either as “mean” value over a temperature range or as “instantaneous” value at a specific temperature.  The mean CTE value is the slope of direct line between two points on a TMA thermograph.  For example, in the TMA thermograph shown below, the mean CTE value between temperature of interest 0 to 100 oC is 24.26 mm/m.oC.  The instantaneous value is the right y-axis a value at a temperature.  This right y-axis (the blue line) is the derivative values of the left y-axis (the green line).  For example, the instantaneous CTE value at 150 oC is 26.3 mm/m.oC.

A typical TMA thermograph from TMA CTE testing

Measuring in-plane direction thermal expansion and shrinkage of a film or a sheet on a TMA

Thermal mechanical analyzer (TMA) is frequently used for coefficient of thermal expansion (CTE) measurement.  In a previous blog  CTE by TMA I mentioned that the expansion probe is used to measure linear CTE of a solid block of sample and the through-thickness expansion of a film sample.  To measure in-plane behaviors such as thermal expansion and shrinkage of a film sample, the tension probe with film sample assembly is used, see the photograph below.

TMA - film probe set up

TMA – film probe set up

Depending on how a film or a sheet is made it is likely to have directional differences in its machine direction (MD) and transverse direction (TD).  One common example that everyone can relate to is the shrinkage of a T-shirt after wash and dry.  I’ve had T-shirts that did not change size or shape after wash and dry, and I’ve had T-shirts that became smaller all around afterwards.  There was one T-shirt I had that became shorter but not narrower after wash and dry.  All these differences point to the various materials and processes that can be used to weave a fabric and to make a T-shirt which cause a difference in how the shirt behaves after wash and dry cycles.

This means the film or sheet sample should be tested in both directions and care should be taken to align directions during sample preparation.  One problem that can happen when sample is not aligned or when a sample is particularly heterogeneous is that the thermal stress differences in directions might cause the sample to twist during thermal testing.

Measuring Linear Thermal Expansion of Solid Materials by TMA

The thermal mechanical analyzer (TMA) with an expansion probe can be used to determine linear thermal expansion (aka CTE) of solid materials. The standard test method ASTM E 831 describes the instrumentation and how the testing is performed and analyzed.  A sample is cut to a small cube or cylinder to fit on the sample stage with the two faces flat and parallel in the direction of interest for CTE measurement, see picture below.  The sample length should be long enough to provide adequate resolution but not too long to cause thermal gradient within the sample.  A small load or force is placed on the sample from the contacting probe to ensure good contact but not inhibit sample expansion during heating.

To measure the through-thickness CTE of a film sample it is sometimes necessary to stack multiple sheets to increase overall sample length/thickness in order to improve resolution of the measurement.

TMA expansion probe with sample

TMA expansion probe with sample

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)

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.

TMA Penetration Probe

One of the probes for the thermomechanical analyzer (TMA) is the penetration probe.  Penetration probe is sometimes called the micro-indentation probe or micro-indenter.  The penetration probe is useful in determining softening temperature (aka softening point) and hardness of a bulk material.  For example, ASTM E2347 details test procedures and calculations to determine the indentation softening temperature that is very similar to Vicat softening temperature.  With this probe, the indentation hardness can also be measured and Young’s modulus calculated successfully provided the Poisson’s ratio is known.

The penetration probe is also useful for coatings and films.  It can be used to compare the same organic coating of various thicknesses or to compare various organic coating formulations.  By carefully designing experiment and testing samples side by side it is possible to compare and choose the most suitable material combinations for an application. There are things to consider when designing your experiment.  For example, it is known that hardness is dependent on coating thickness and substrate material when the coating is less than ~100 microns.  Another thing to consider is that penetration experiment requires a load and therefore it may be a creep experiment over time at a constant temperature.