YOUNG MODULUS FOR RUBBER

Geschriben am 29-01-2013

We thank Mr. GRUAND Méca SARL Cy for his redaction.
"Ut tensio sic vis" latin sentence from Robert Hooke (1678) means "such extension, such  strength" (proportionality rule: elongation is proportional to applied strength).

Thomas Young his British fellow countryman will leave his name associated to this linear behavior of many materials .
In a low deformations range, materials behavior (Stress relation to strain) can be often compared to a straight line from the origin (in red, on the following graph).
This behavior range gap is traditionally called "linear elastic domain".
Young’s modulus is defined as E = Stress / Strain.
As strains are without any dimension, Young's modulus as same dimensions than stress; that's to write effort by surface unity  (for example: N / mm ² or Mega Pascal MPa).

Elastomers do not escape to this rule and for low strains we can assimilate their behaviour to a linear one.

So Young's modulus is knowledge's departure point for materials.
This parameter is indicating materials' stiffness. For metals, it's use is much more current than for elastomers because this module is only recommended for low deformations where materials behaviour is linear.

Some authors were able to establish a relation between hardness and tangent of the curve "strain"  / to "the origin stress"  :

Also, in elastomers case, we can read in materials data (cf.materials CHEVALIER data sheets), the following informations: module in 100 %, module in 200 % or module in 300 %, it's not mean that it is Young’s sense modulus.
We should rather write that it is about stress for strain levels of 100 % 200 % or 300 %.
We note that even if two materials have the same modulus values in 100 %, 200 % or 300 %, then a similar hardness, these have not systematically a same break tensile or a same behaviour unloading.
According to the basic elastomer and the composition (for example) if this one is constituted with carbon black or with different substances, we can get a different behaviour with same Hardness / Rigid ity.
The measure of this tensile strength against the break is made on a same type sample as that used for the measure in rigidity behaviour, with strength machine assistance which allows simultaneous effort measure (dynamometer) and movement (extensometer).
During the sample strength, this one lengthens until the break. With extensometer use, we follow elongation progress, and we can note the necessary strength to obtain: 10 %, 20 %, 50 %, 100 %, 200 %, and of elongation for example.

SAMPLE
The sample is defined by the NF standard T 46-002. It appears us a barbell or a ring with 4 sizes for the barbell (H1 to H4), and two for the ring.
Most usually use is a barbell of size H2 die cut from a 2 mm thickness sheet. His central side presents a rectangular section of 4 x 2 mm on a 25 mm length.
It is the lowest section and that break will take place.
It is also on this area that is situated 2 marks distant from 20 mm for the elongation measure.
(sample drawing):

The strength speed is 500 mm per minute. The tensile strength is expressed in MPa.
Following the strength machine, and its electronic assistance, we can obtain automatically modulus for x % or y % or a strength curve "strain" / "stress" which we can read the necessary effort to get any elongation between stretching origin and breaking sample.

(example of curve "strength" / "elongation" with modulus
reading in 100 %, 200 % and 300 %)

And to give some practical indications, modulus levels in 100 % for:
- Silicone 30 shore A:  0,7 MPa approximately
- Silicone 70 shore A:  3,3 MPa approximately
- Nitrile 50 shore A:     1,5 MPa approximately
- Nitrile 75 Shore A:     5,8 MPa approximately