Determination of the modulus of elasticity in a tensile test (tensile modulus)

The modulus of elasticity describes the stiffness of a plastic. This value is very dependent on various factors such as, loading speed, temperature and specimen history. It corresponds to the slope of a stress-strain curve. Since this slope is not linear for many plastics, the result of this value depends on at which strain it is taken.


Method to ISO 527-1

The position of the modulus of elasticity is standardized in ISO 527-1 by defining that the value is to be

determined between the extension values 0.0005 and 0.0025. This corresponds to a specimen strain of 0.05 % and 0.25 %. The calculation can be performed as a secant, therefore, as a calculation between two points. A calculation as linear regression, which considers all measurement points in the area being considered, and which prevails in the modern PC controlled test machines, will give a statistically more secure value.

Method to ASTM D 638

In this Standard there are no fixed strain limits for the determination of the modulus. However, the Standard differentiates between a modulus of elasticity, which is determined in the linear area of the stress-strain diagram, and a secant modulus.


Modulus of elasticity:

For materials which display a linear portion, a slope line with maximum pitch is applied to this area and the modulus of elasticity is determined via this line. This is the preferred method.


Secant modulus:

Only if no linear area can be determined, is a secant modulus between the extension zero point and a freely selected point on the stress-strain curve determined. It is not allowed to declare the tangent slope, which is used for determining the zero point, as the secant modulus.

Test speeds in the ASTM

While slower test speeds are prescribed in the ISO Standard for determination of the tensile modulus, the ASTM allows the same speeds to be used, which are also used for the further values. The only limitation is given by the maximum data acquisition rate of the measurement system being used. (see: required measuring frequency of the measurement electronics).

Comparability of modulus of values according to ISO and ASTM

For materials showing a linear slope area, the evaluations of ISO and ASTM lead to similar values as long as they are determined under identical test speeds. Differences during the measurements on moulding material come from the different manufacturing histories of the specimen. Materials which display no linear area can show values which vary from each other in double digit percent ranges, depending on which test Standard is being used.

One or two specimen?

Since, in the ISO, the determination of the tensile modulus is performed at a slower test speed than the determination of the further tensile characteristics, it should not be measured during the same test as the tensile characteristics. In the ASTM however, it is allowed to determine the modulus of elasticity as well as the further tensile characteristics in one test.

In practice, various methods have become common:

a) Two tests, two specimen

If the tensile modulus determination is performed as a completely independent test, then it exactly corresponds to the ISO 527 standard. The effort is very high however, since the number of specimen to be made is doubled. For this reason, this method is seldom used.

b) Two tests, one specimen

This variant is much less expensive because the same specimen is used for both tests. The specimen must not be removed from the grips between the tests. Since the pre-straining of the specimen is a maximum of 0.25%, and this becomes even smaller because of resetting during unloading, the measurement error for elongation at yield and elongation at break usually does not exceed 0.1%.

c) One test, one specimen

This method is allowed in the ASTM. It is often used in tests to ISO also, although it does not conform to the Standard. This is because of the simplicity, but also because, depending on the visco-elastic characteristic of the material, the measurement error for elongation at yield and elongation at break does not exceed 0.2% elongation.