KEVOS® MAKEOS · Materials
True Stress, True Strain and Flow Curve
What are the nominal and true stress and strain at this point in a tensile test, and what does the flow curve predict?
Nominal (engineering) and true stress and strain from a tensile test load, original and current area and gauge length, the flow stress from the strain-hardening law σ = K εⁿ, elongation and reduction of area — the metalworking quantities used for forming calculations.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load | kN | Load at the point of interest. |
| Original cross-section area | mm² | Original cross-section area of the specimen. |
| Current (or fracture) area, 0 = constant volume | mm² | Measured current area (or at fracture); 0 assumes constant volume, A = A₀ l₀ ÷ l. |
| Original gauge length | mm | Original gauge length. |
| Current (or fracture) gauge length | mm | Current gauge length (or the length between gauge marks after fracture). |
| Strength coefficient K | MPa | Strength coefficient of the flow curve (true stress at true strain 1) from material data. |
| Strain-hardening exponent n | Strain-hardening exponent (typically 0.10–0.50 for metals). |
Method and formulas
- Nominal stress = F ÷ A₀; nominal strain = (l − l₀) ÷ l₀.
- True stress = F ÷ A; true strain ε = ln(l ÷ l₀).
- Flow curve σ = K εⁿ.
- Elongation = (l_f − l₀) ÷ l₀ × 100%; reduction of area = (A₀ − A_f) ÷ A₀ × 100%.
- Example: 30 kN with the gauge stretched from 50 to 60 mm gives a true stress of 458.37 MPa at a true strain of 0.18232.
Limitations
- Constant-volume area holds only before necking; measure the area after necking starts.
- The power-law flow curve is an approximation over the plastic range.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Convert tensile test data to true stress and strain for forming
- Estimate flow stress at a forming strain
- Report elongation and reduction of area
Who it is for
- Materials engineers
- Forming engineers
- Test laboratory technicians
What you get
- Nominal stress and strain
- True stress and strain
- Flow stress, elongation and reduction of area
Interpreting the result
- n roughly equals the true strain at the onset of necking: high n means good stretch formability.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1331–1334. Topic reference; no source tables or recommended settings are reproduced.
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