BIZOMAT 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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load
- What it is
- The tensile load on the specimen at the moment you want stress and strain for, read from the test machine.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Nominal and true stress both rise in direct proportion to the load.
- Get it right
- In kilonewtons: 12,500 N is 12.5 kN.
What this means: Original cross-section area
- What it is
- The cross-section area of the specimen within the gauge length before testing.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² to 1000000 mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 78.54 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger original area lowers nominal stress, and under constant volume also true stress.
- Get it right
- For a round bar this is π d² ÷ 4 of the original diameter; do not type the diameter itself.
What this means: Current (or fracture) area, 0 = constant volume
- What it is
- The measured cross-section area at the same moment as the load and length, or at fracture for the reduction of area. With 0 the tool assumes constant volume, A = A₀ l₀ ÷ l.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0 mm² to 1000000 mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use 0 only before necking starts; once the specimen necks, measure the smallest area, because constant volume no longer gives the local area.
What this means: Original gauge length
- What it is
- The distance between the gauge marks on the specimen before any load is applied.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the marked gauge length, not the total specimen length or the distance between grips.
What this means: Current (or fracture) gauge length
- What it is
- The distance between the same gauge marks at the moment of the load, or after fracture with the broken pieces fitted together.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- True strain is ln(l ÷ l₀), so it grows more slowly than nominal strain as the length increases.
- Get it right
- It must not be less than the original length: this tool covers tension only.
What this means: Strength coefficient K
- What it is
- The strength coefficient of the material’s flow curve σ = K εⁿ: the true stress the curve gives at a true strain of 1.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 530 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow stress is directly proportional to K; true stress and strain do not use it.
- Get it right
- Take K and n as a matched pair from the same material data or curve fit.
What this means: Strain-hardening exponent n
- What it is
- The strain-hardening exponent of the flow curve σ = K εⁿ, describing how quickly the material strengthens as it is stretched.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.26 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the value fitted together with K. With 0 the flow stress equals K at any strain.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Counting strain and thickness
In Hand Forming Sheet Metal by the Numbers
What it covers: Measure stretch and shrink as engineering and true strain, predict thickness from constant volume, read a circle grid on a trial dome, and catch grid lines that started the cracks.
Method explained here · BIZOMAT original book
True stress, true strain and work hardening
In Yield and Plastic Flow by the Numbers
What it covers: Why engineering stress misleads after yield, how true stress and strain and the flow curve describe work hardening, when necking starts, and what cold drawing does to the HC-63's barrel.
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