Authoritative engineering context
Data Source and Methodology
Primary standard: ASTM E111-17(2022) — Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus. ASTM International, 2022. Direct link
Reference text: Mechanics of Materials by R. C. Hibbeler, 10th ed., Pearson, 2017. Publisher page
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
ε = ΔL / L_0
E = σ / ε
These are engineering (nominal) definitions using the original area A and original gauge length L0. The E relation holds within the linear-elastic range.
Glossary of Variables
- F (Force): Axial load applied to the specimen (N or lbf).
- A (Area): Original cross-sectional area (m² or in²).
- L0 (Original length): Gauge length before load (m or in).
- ΔL (Elongation): Change in length under load; positive in tension, negative in compression (m or in).
- σ (Stress): Engineering stress; internal force per unit area (Pa, MPa or psi, ksi).
- ε (Strain): Engineering strain; unitless ratio of deformation to original length (often shown as % or microstrain).
- E (Young’s modulus): Slope of the stress–strain curve in the linear-elastic region (Pa, GPa or psi, Mpsi).
Come Funziona: Un Esempio Passo-Passo
Suppose a tensile test reports the following SI measurements:
- F = 10,000 N
- A = 200 mm² = 2.0 × 10⁻⁴ m²
- L0 = 1.0 m
- ΔL = 0.001 m
- Compute stress: σ = F/A = 10,000 / 0.0002 = 50,000,000 Pa = 50 MPa.
- Compute strain: ε = ΔL/L0 = 0.001 / 1.0 = 0.001 = 0.1% = 1000 µε.
- Compute modulus: E = σ/ε = 50 MPa / 0.001 = 50,000 MPa = 50 GPa.
These values are within the elastic region for many aluminum alloys but below typical steels (≈200 GPa).
Frequently Asked Questions (FAQ)
Is this calculator using engineering or true measures?
It uses engineering stress and strain, based on the original area and gauge length. For large plastic strains, true measures should be considered.
Can I enter negative force or elongation?
Yes. Negative values represent compression. Stress and strain will have matching signs.
Which units should I choose?
Pick SI for N, m, Pa, or US for lbf, in, psi. Results also show convenient magnitudes like MPa/GPa and ksi/Mpsi.
Why is Young’s modulus blank?
E is shown only when σ and ε are both available and ε ≠ 0. Enter ΔL and L0 to compute ε.
What accuracy should I expect?
Numerical accuracy is high; real-world fidelity depends on test compliance with standards such as ASTM E111 and precise measurements of A and L0.
What’s a typical E value?
Typical values: aluminum ≈ 69 GPa; steel ≈ 200 GPa; titanium ≈ 110 GPa; polymers vary widely.
How do I interpret microstrain (µε)?
1 µε = 1×10⁻⁶ strain. It’s a convenient unit for small elastic deformations measured via strain gauges.