Scatter Plot for Material Stress-Strain — Young's Modulus & Hooke's Law
A stress-strain scatter plot maps engineering strain ($\epsilon = \Delta L / L_0$) on the horizontal axis against tensile stress ($\sigma = F / A_0$) on the vertical axis, where the linear elastic slope equals Young's Modulus ($E = \sigma / \epsilon$).
Tip: Paste Excel or Google Sheets rows (Ctrl+V / ⌘V) directly into any cell.
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Hooke's Law: sigma = E * epsilon. If strain is entered in %, Young's Modulus in GPa = (Slope m in MPa/%) / 10.
Chart Design & Use-Case Tips
- 01Hooke's Law: sigma = E * epsilon. If strain is entered in %, Young's Modulus in GPa = (Slope m in MPa/%) / 10.
- 02In the proportional elastic region, Stress is strictly proportional to Strain ($\sigma = E \epsilon$), yielding an $R^2$ near 0.999.
- 03When high-strain points begin curving below the linear regression line (as in Load Steps 6–7), the specimen has crossed its proportional yield limit into plastic deformation.
- 04Export as Vector SVG for mechanical engineering lab reports and materials science papers.
Frequently Asked Questions
How do I calculate Young's Modulus (E) from the regression slope?+
If X is Strain in percent (%) and Y is Stress in MPa, divide the OLS slope m by 10 to obtain Young's Modulus E in Gigapascals (GPa). For the elastic steps above (~2050 MPa/%), E ≈ 205 GPa (structural steel).
What causes R² to drop below 1.00 on a full tensile test?+
Once stress exceeds the yield strength, the metal deforms plastically and the curve flattens toward Ultimate Tensile Strength (UTS), departing from Hooke's linear law.
Can I isolate just the linear elastic region?+
Yes—remove the post-yield rows in the Data Workbench to fit the exact OLS slope on the purely elastic points.