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## Convert Durometer to Young’s Modulus

July 14th, 2011

If you work with rubber and plastic materials frequently, you more than likely have access to a stress-strain curve for use in Simulation.  What can you do, though, if you don’t have all the required material properties for analysis?  If you’ve ever searched for material properties via MatWeb, IDES or other sources, you’ll likely find the hardness of plastics and rubbers listed in Shore-A or Shore-D – and no Young’s Modulus.  Fear not!  There is a simple calculation to convert a Shore durometer to Young’s Modulus, which is sufficient to get you started with your analysis work.

Before I show you the calculation, you should be aware that there is not a direct relationship between a Shore scale and Young’s Modulus!  The calculation allows you to approximate ‘E’ based on a range of Shore-A (20 to 80) or Shore-D (30 to 85) durometers for simple static analysis.**  If you routinely work with plastic and rubber materials, you should be using SolidWorks Simulation Premium with the actual stress-strain curve for the material(s) you design with!

For a durometer given in Shore-A, multiply this value by 0.0235.  Then subtract 0.6403 from this result.  The next step is to find the inverse base-e logarithm of this new result.  The answer is an approximation for Young’s Modulus in megapascals (MPa).  To convert this to pounds per square inch (psi), simply multiply this number by 145.0377.  If you’re like me, word problems were never a strong suit!  Here are the equations to input into Excel for a Shore-A or Shore-D durometer – or download the Excel spreadsheet here.

Shore-A to Young’s Modulus (in MPa):
=EXP((Shore-A Durometer)*0.0235-0.6403)

Shore-D to Young’s Modulus (in MPa):
=EXP((Shore-D Durometer + 50)*0.0235-0.6403)

Replace the ‘Shore-A Durometer’ or ‘Shore-D Durometer’ with either a number or the cell location of the value.

** Making Engineering decisions based upon analysis results with this “material property conversion” is not recommended.

### Bill Reuss

Elite Application Engineer CAE Technical Specialist 3DVision Technologies

### 2 Responses to “Convert Durometer to Young’s Modulus”

1. Carl Ingalls says:

Hello Bill,

I noticed a discrepancy between your version of the equation (for converting from Shore A or Shore D to Young’s Modulus), and the version that appears in Wikipedia (http://en.wikipedia.org/wiki/Shore_durometer).

Your version uses base e for the log and exp functions. Wikipedia uses base 10. The results will be significantly different.

Wikipedia could be wrong, but they do quote the original source of the equation. Do you have access to the original version? If so, can you check to see whether it is base e or base 10?

Thank you, Carl Ingalls

2. Bill Reuss says:

Hello Carl,
I cannot find my original document that used base-e in the calculation. The eHow website has a conversion that matches what I wrote, though. (http://www.ehow.com/how_7941189_convert-durometer-youngs-modulus.html)

I’ll expand on my caveat’s that I included in this blog article. Shore values are only an indication of that material’s ability to respond to a very small, localized force on the surface. This is not the same as Young’s Modulus, which is basically the ability of the entire part/material to respond to a load. Further, the chemical makeup of the elastomer will affect Young’s Modulus, even for materials that have the same Shore value for surface hardness. Regardless of the calculation or approximation you use, there is absolutely no substitute for having the accurate material properties from physical test data!

Good luck with your analysis work, Carl, and thank you for reading the 3DVision blog!

Best regards, Bill Reuss

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