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:
- True Elastic Limit: Point at which dislocations start to occur.
- Proportionality Limit: Point with Hooke's Law is (technically) no longer valid.
- Elastic Limit: Point at which further strains are plastic.
- 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))