How to Calculate Young's Modulus and Poisson Ratio if not given in Material Specs.

[DAVIDMALOY]

Hi All,

I could use some help.

I am a one man business and I do design and engineering for small companies.

As an engineer, I often have to work with these clients and often they will provide me with material data sheet for plastics that they want to use.

I have to perform FEA (ProMechanica) strucural simulation for them to show validatity of the design. So sometimes I have to show or record Young's Modulus, Tensile Modulus, Possion Ratio, Density, etc in my reports. Also I keep copies for ISO 9000 reasons.

A client has has me a question and I gave him an answer as below you will see my method of finding Young's Modulus and Poisson Ratio.

The question from client: "How do you or someone tell me how to calculate Young's modulus and Poisson Ratio if not given in the Material Specs."

I would appreciate if someone could validate my formula and use of numbers from Material Data Spec sheets.

One method I have used over the years.

Young's Modulus = Stress / Strain ( Standard Text Book Answer)

Example: I have a material data sheet, attached. see "ABS_Data_Sheet.pdf"

Tensile Stress = 42.5Mpa

Strain at 50 percent yield = 23% (sometimes these values are stated; Strain at 50% elongation / 50mm/1minute

Young's Modulus =

math: 42.5Mpa / (23%/100) = (Not knowing the forces but given a maximum strain I use the maximum strain as control factor)

math: 42.5Mpa / 0.23 =

math: 184,782,608.696 Pas.

math:: round 184.8e6 Mpa

Poisson ratio.

Possion Ratio is rarely given.

Could someone help me this this method given that most material suppliers never provide this value.

There must be values given from the material data sheets that can be plugged into a formula and then caluclate the resulting Possion Ratio.

If I remember correct Possion Ratio may not be a required value in ProMechanica (Could some confirm this as true or false)

Poisson's Ratio can be expressed as

υ = - ε_t / ε_l (1)

where

υ = Poisson's ratio

ε_t = transverse strain

ε_l = longitudinal or axial strain

Strain can be expressed as

ε = dl/L (2)

where

dl = change in length

L = initial length

For most common materials the Poisson's ratio is in the range 0 - 0.5.

What values do I use from the Material Data Sheet do I use to calucate the Poisson Ratio - not given any axial or transversial strain values. Or am I missing it and the values are there. Yeah, I can be tht stupid sometimes.

I have attached some Spec sheet that I often have to deal with

Thank in advance to all.

Dave

This thread is inactive and closed by the PTC Community Management Team. If you would like to provide a reply and re-open this thread, please notify the moderator and reference the thread. You may also use "Start a topic" button to ask a new question. Please be sure to include what version of the PTC product you are using so another community member knowledgeable about your version may be able to assist.

[dschenken]

The reason those values aren't published is they aren't easy to establish and are subject to a large number of influences that metals, for example, are not. If you need such information, you'll either have to contract to have samples tested at a materials lab or try to get the information from your suppliers.

[DenisJaunin]

Hello, David,

You should be able to find information on the sites of fabcriquants of these materials.

I am attaching a few links that will help you, but some are in French.

I think Wikipedia should have its equivalent in English.

Cordially.

Denis.

See page 45.

http://mediamef.utt.fr/modules/P1/M1-2/EXPORTS_S124.publi/web/res/Caracteristiques_materiaux.pdf

http://mediamef.utt.fr/modules/P1/M1-2/EXPORTS_S124.publi/web/res/Caracteristiques_materiaux.pdf

http://fr.wikipedia.org/wiki/Coefficient_de_Poisson

http://fr.wikipedia.org/wiki/Module_de_Young

http://www.kayelaby.npl.co.uk/general_physics/2_2/2_2_2.html

http://www.campusplastics.com/

[346gnu]

David,

As other replies,

1. Google for typical values, info often buried within papers.

2. Matweb etc

3. Material info from manufacturers

4. Measurement

But would add that ABS and Polycarbonates are going to have a 0.3<=nu<=0.45 and if unable to pin it down further, you have to bound to likely solution by running more than one study and list the references that provided the bounding info in the report.

Asking the customer to pay for measurements is usually sufficient an incentive to have resonable assumptions accepted. Ask the customer to accept the assumptions/methodology before carrying out the main part of the work.

Regards

[sdensberger]

One method I have used over the years.

Young's Modulus = Stress / Strain ( Standard Text Book Answer)

Example: I have a material data sheet, attached. see "ABS_Data_Sheet.pdf"

Tensile Stress = 42.5Mpa

Strain at 50 percent yield = 23% (sometimes these values are stated; Strain at 50% elongation / 50mm/1minute

Young's Modulus =

math: 42.5Mpa / (23%/100) = (Not knowing the forces but given a maximum strain I use the maximum strain as control factor)

math: 42.5Mpa / 0.23 =

math: 184,782,608.696 Pas.

math:: round 184.8e6 Mpa

This method works, provided your material is linear and elastic. Furthermore, the strain of 23% is at the fracture point, not the yield point.

If your material is linear, isotropic, and elastic, then there are four key points on a stress-strain curve:

1. True Elastic Limit: Point at which dislocations start to occur.
2. Proportionality Limit: Point with Hooke's Law is (technically) no longer valid.
3. Elastic Limit: Point at which further strains are plastic.
4. Offset Yield Strength: This is a somewhat arbitrary point. Common values are 0.1% and 0.2%. This point is well within the plastic region.

To use your method, you'll need the strain for the Proportionality Limit. For example, A-36 steel has a yield strength of 250 MPa, and an elongation at break of 20%. Using your method, you'd calculate a Young's Modulus of 1.25 GPa (250 MPa / (20%/100)), but we know that the Young's Modulus is 200 GPa. If we use the Proportionality Limit of 0.125%, then you'll see we get the correct value of 200 GPa (250 MPa / (0.125%/100)).

As for the Poisson's Ratio (nu), it depends on the material model. For linear, isotropic, and elastic, the Poisson's Ratio can be calculated from the Young's (E) and Shear (G) Modulus:

G = E/(2(1+nu))

[DavidMalicky]

As Shaun alluded, you can't get Young's Modulus (E) from Tensile Strength, unless the material is extremely brittle.

For ABS, if you need to work from that datasheet, the line you want is the "Flexural Modulus". This is E found from a bending test. It is usually the same as the uniaxial E, unless the material is anisotropic (composites, wood, directional plastics, usually in which case you would need an orthotropic material model and many more properties). For plastics, the flexural modulus is often a little different than the tensile modulus. If your part is mostly in bending stress, then the Flexural Modulus is actually most appropriate for E.

For plastics, keep in mind that E (tensile and flexural) is highly dependent on temperature.

Poisson's ratio is required in FEA. A great many materials have a Poisson's ratio of about 0.35, +/- 0.05. Common exceptions include rubbers, bio-tissues, ceramics, cast metals, and a few polymers. Google will find it for almost any material. Stress and strain are not very sensitive to Poisson's ratio in the range of 0.3-0.4 (around 5-10% variance). But be very careful when it approaches 0.5 (above 0.45, esp above 0.48) the mechanics change drastically there.