Estimate tensile modulus and Poisson’s ratio from axial loading and measured deformation. Choose a single-point secant estimate or fit slopes through a selected set of linear tensile-test readings.
Stress, strain and modulus
Engineering stress σ = F/A₀, using tensile force F and original area A₀. Axial strain εa = (L − L₀)/L₀; transverse strain εt = (t − t₀)/t₀. The single-point mode gives Esecant = σ/εa and ν = −εt/εa.
A point referenced to the unloaded origin is a secant estimate. The fitted mode uses ordinary least squares with a free intercept: stress = E × axial strain + intercept. Poisson’s ratio is the negative fitted slope of transverse versus axial strain using the same selected rows.
Use gauge-region measurements and a justified linear elastic interval. Crosshead movement can include fixture compliance. A high fit R² measures consistency, not whether the interval is elastic or the test procedure is appropriate.
Worked example
A 10,000 N force acting on an original 50 mm² area gives 200 MPa stress. A gauge length increasing from 50 to 50.05 mm gives 0.001 axial strain. A transverse dimension decreasing from 10 to 9.997 mm gives −0.0003 strain. The secant estimate is 200/0.001 = 200 GPa, and ν = −(−0.0003)/0.001 = 0.3.
Frequently asked questions
Can one point establish Young’s modulus?
It gives a secant estimate under the stated assumptions. A test modulus requires the appropriate measurement procedure and elastic interval.
Can transverse expansion be entered?
Yes. It produces a negative Poisson ratio. Check whether the material, loading and measurements support an auxetic response.
Why fit a nonzero intercept?
Offsets can occur in test data. The fitted mode estimates the intercept rather than forcing every dataset through zero; inspect that offset before interpreting the slope.
References: NIST guide to elastic-modulus measurement; MIT OpenCourseWare: stress-strain and Poisson relationships.
