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What is the Shore A hardness used for?

The Shore A and D hardness tests are widely used by the rubber industry.  However, I'm not sure what practical use these numbers can be put to during design.  My current feeling is that Shore hardness numbers can at best give you a feel for the texture of the rubber - a Shore A value of 5 = gummy bear texture, Shore A = 40 implies erasure texture etc.

Can someone explain how Shore hardness values can be used in the design of mechanical components made of rubber?

Thanks in advance,


Zhigang Suo's picture

I have never heard of this test, and followed up on the link on the test that you provided with interest.  From the description, the test looks like a version of indentation.  It seems likely that the Shore hardness values do not quantitatively relate to any foundamental properties.  Then one may ask, what does a similar indentation test offer?

Now for metals indentation hardness relates to yield strength.  A few years back people were debating whether it was possible to infer hardening exponent from the indentation test.  Not sure what came out of that debate.

Your question also reminded me of a very neat piece of mechanics pointed out in a paper by YT Cheng and CM Cheng.  For a conical indentor, by dimensional considerations, they showed that the force scales with the depth squared.  The prefactor is of the dimension of stress.  They then used the finite element method to calculate the prefactor for metals.  For a rubber-like materia, I believe that the prefactor should scale withh the elastic modulus.  I have not looked up in the literature to see if the idea of Cheng and Cheng has been followed up for rubber-like materials.

Your question has pointed to the general issue of how to use the information obtained from an indentation test.  Let's hope Michelle Oyen and others will shed some light on this topic. 

MichelleLOyen's picture

The history of the "hardness" test is an interesting one; the quantity (really the mean supported stress under contact) grew to become popular due to the Tabor relation, where in soft metals the hardness under sharp contact could be easily related to the yield stress of a material.  Somehow in the intervening years, and especially in the age of nanoindentation, the fallacy has spread that hardness is a material property.  It is not, but it is a measure of the total deformation under a given load and as such it does have some usefulness in many contexts outside of its primary association with plastic deformation resistance in soft metals.  In fact, since the plastic deformation resistance of something like rubber is very large, but it's measured "hardness" in terms of load divided by inferred contact area is small (since it's elastic modulus is small) the ideas actually diverge if you're not careful.  Only in metals is the "measured hardness" a measure of plastic deformation resistance and you could argue that this is its most useful interpretation.

We followed up Sakai's original work on hardness as a series sum of plastic and elastic deformation components, and extended the ideas to soft polymers and rubbers and also biological materials in the following two papers:

Oyen ML and Ko C-C,  Examination of Local Variations in Viscous, Elastic, and Plastic Indentation Responses in Healing Bone , Journal of Materials Science: Materials in Medicine, 18 (2007) 623-8.
Oyen ML, Nanoindentation Hardness Measurements of Mineralized Tissues , Journal of Biomechanics, 39 (2006) 2699-702.

In general, the mean supported stress under contact is definitely a useful measure of mechanical properties, in terms of the total resistance to deformation under a given load (and in the case of viscoelastic or poroelastic polymers or tissues, within a given experiemental measurement time-frame) but that's all it is--a quick and dirty engineering test that gives a rough estimate of something that is not actually a material property.  I am not surprised that relating it back to a specific property such as elastic modulus is not trivial, nor that nonlinear elasticity would come up in polymeric or biological materials in terms of the interpretation.  


As a computational mechanics/numerical modeler of materials, the major stumbling block that I've faced has been the determination of material properties - particularly, but not exclusively, for nonlinear materials.  A simulation is arguably as accurate as the inputs that go into it. 

One way to get properties is via ab-initio simulations and coarse-graining up in length scales.  But the cost of that can be prohibitive and the accuracy depends strongly on whether the "correct" intermolecular potential has been used.  The other option is to perform detailed experiments to determine properties.  That's also too expensive most of the situations that I've run into in the recent past.

The lowest cost alternative is a hardness-like test which doesn't require expensive equipment and specimen preparation, and skilled operators.  But such tests are barely useful when it comes to fitting good materials models.

Does that mean that computational methods of analysis are essentially useless for industrial research projects which are cash poor?  Is a back of the envelope hand calculation the best we can do in such situations? 

-- Biswajit 

As mentioned these test have no accepted relation to fundamental properties.  They are mainly used in two contexts:

(1) Quality control.  It a very rapid test and can be used to assess in a very approximate manner if a material has been properly cured or not.  (It is afterall a hardness test.)

 (2) If you have some experience with these numbers you can roughly correlate Shore Hardness to Elastic modulus.  This is useful in preliminary design work and model building.  Note that when buying rubber from supply catalogs, the material properties are often given in terms of Shore Hardness and not modulus like most would prefer.


Prof. Dr. Sanjay Govindjee
University of California, Berkeley

Thanks Zhigang and Sanjay.

Reading Sanjay's second point, I wonder what sort of Shore hardness would work for rubber O-rings in solid rocket boosters - a la the Challenger.  Design is clearly as much of an art as a science.

After the little push from Zhigang I went ahead and searched Google scholar for papers on possible relations between Shore hardness values and elastic properties and found this paper by Qi, Joyce and  Boyce called " Durometer hardness and the stress-strain behavior of elastomeric materials", Rubber chemistry and technology, 2003, vol. 76, n2, pp. 419-435.  Could someone with easy access to a library send me a copy of the paper?

The abstract says:

"The Durometer hardness test is one of the most commonly used measurements to qualitatively assess and compare the mechanical behavior of elastomeric and elastomeric-like materials. This paper presents nonlinear finite element simulations of hardness tests which act to provide a mapping of measured Durometer Shore A and D values to the stress-strain behavior of elastomers. In the simulations, the nonlinear stress-strain behavior of the elastomers is first represented
using the Gaussian (neo-Hookean) constitutive model. The predictive capability of the simulations is verified by comparison of calculated conversions of Shore A to Shore D values with the guideline conversion chart in ASTM D2240. The simulation results are then used to determine
the relationship between the neo-Hookean elastic modulus and Shore A and Shore D values. The simulation results show the elastomer to undergo locally large deformations during hardness testing. In order to assess the potential role of the limiting extensibility of the elastomer on the hardness measurement, simulations are conducted where the elastomer is represented by the non-Gaussian Arruda-Boyce constitutive model. The limiting extensibility is found to predict a
higher hardness value for a material with a given initial modulus. This effect is pronounced as the limiting extensibility decreases to less than 5 and eliminates the one-to-one mapping of hardness to modulus. However, the durometer hardness test still can be used as a reasonable
approximation of the initial neo-Hookean modulus unless the limiting extensibility is known to be small as is the case in many materials, such as some elastomers and most soft biological tissues

-- Biswajit 

This is a bit complicated since it depends on the exact interference of the joint but I would say anywhere from Shore A 50 to 80.



Prof. Dr. Sanjay Govindjee
University of California, Berkeley

Sounds a bit like black magic :)  Thanks Sanjay.

-- Biswajit many cases yes.  But if you know what you are doing, then a bit less so.  -sanjay


Prof. Dr. Sanjay Govindjee
University of California, Berkeley


In academia, during the numerical analysis of elastomeric materials, I always assumed that some stress-strain data would be available.  I could then fit a model to those data and do my analysis.  Academia allows for the time that's needed to do that.

Industrial research has been quite different in some respects.  I now have to do numerical simulations of elastomers using data from hardness tests and rheometer traces, of plastics from supplier data on  the powdered form, and so on.  I wonder if such simulations tell me anything useful at all except when the strains are quite small.  

-- Biswajit 

Not to sound too fuzzy but it really depends.  if you are working exclusively on a certain class of materials then a company with good practices will over time have a knowledge database on the correlations of the fast easy tests to the more involved tests.  The correlations will never be perfect but will give you a certain amount of confidence.  If this database does not exist then it is your job (over time) to compile it.  Otherwise you can not even say that your computations are even meaningful in the small strain regime.



Prof. Dr. Sanjay Govindjee
University of California, Berkeley

Since I'm now into rubber I won't be able to rest until I've figured out another issue that's been bothering me.

I distinctly recall being told in a materials science class that natural rubber has a negative coefficient of thermal expansion.  However, a search of the literature throws up only positive values of the CTE with a few interspersed papers claiming a negative thermal expansion coefficient.  There also appears to be a "thermoelastic inversion effect" which separates the positive and negative expansion regimes.  A couple of papers on the effect claim that negative CTEs are observed only at strains greater than 10%.

Can anyone clear up this mess for me?

Thanks in advance.

-- Biswajit 


Have you looked in Treloar's classic monograph The Physics of Rubber Elasticity?  It is nicely explained there.


Prof. Dr. Sanjay Govindjee
University of California, Berkeley

Thanks Sanjay.  The book is not in our company library but I've sent my spies to a nearby university to track it down and get it for me.  I'll post my feedback as soon as I get my hands on the book.

Also, I have received a copy of the paper on mapping Shored hardness values to elastic moduli from one of our readers on iMechanica.  I am truly grateful for that and will comment on the contents soon.

-- Biswajit 

"I wonder if such simulations tell me anything useful at all except when the strains are quite small.  " - Biswajit

Dr. Banerjee,

My experience is that when the material model (approx. material model) for the elastomer is developed from the modulus obtained from the elastomer hardness, the results are quiet good for comparison purpose. However, in terms of the absolute values, such a material model may result in a considerable different values. E.g. I had compared the peak contact pressure developed by an o-ring at different lubricant pressures using the approx. material model & using the accurate material model developed from the stress-strain data of the elastomer. I found that the percentage increase in the peak contact pressure - due to increased lubricant pressure - obtained by the approx. material model was close to the one obtained from the accurate material model till ~1000 psi. After ~1000 psi, however, results obtained from the two material models could not be correlated.

~ Nimish.

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