Calculate True Strain Calculator
True Strain Calculator
Enter the initial and final lengths to calculate true strain (also known as logarithmic strain) and engineering strain.
Chart comparing True Strain and Engineering Strain as final length changes (initial length fixed at 100).
Engineering Strain vs. True Strain Comparison
| Final Length (L) | Engineering Strain (εₑ) | True Strain (εₜ) | Difference (εₑ – εₜ) | % Difference |
|---|
Comparison table for Initial Length L₀ = 100.
What is True Strain?
True strain, also known as logarithmic strain or natural strain, is a measure of deformation that accounts for the continuous change in length of a material as it is being deformed. Unlike engineering strain, which is based on the original length, true strain is calculated based on the instantaneous length of the material during deformation. This makes it a more accurate measure of strain, especially for large deformations where the change in length is significant. To calculate true strain, we integrate the incremental strains over the entire deformation process.
Materials scientists, engineers (particularly in mechanical and civil engineering), and researchers use true strain when analyzing the behavior of materials under large deformations, such as in metal forming processes (rolling, forging, drawing), crash analysis, and understanding material failure. When you need to calculate true strain, you are looking for a measure that reflects the actual strain experienced by the material at any point during the deformation.
A common misconception is that engineering strain and true strain are always very similar. While they are close for small deformations (typically strains less than 0.1 or 10%), they diverge significantly at larger strains. Engineering strain overestimates the strain for tension and underestimates it for compression compared to true strain at large deformations.
True Strain Formula and Mathematical Explanation
The formula to calculate true strain (εₜ) is derived by considering the deformation as a sum of infinitesimal increments of strain, each based on the current length.
If a material element of instantaneous length l undergoes an infinitesimal change in length dl, the infinitesimal strain is dl/l. The total true strain from an initial length L₀ to a final length L is the integral:
εₜ = ∫L₀L (1/l) dl = [ln(l)]L₀L = ln(L) – ln(L₀) = ln(L/L₀)
So, the true strain εₜ is given by:
εₜ = ln(L / L₀)
Where:
- ln is the natural logarithm.
- L is the final length.
- L₀ is the initial length.
We can also relate true strain to engineering strain (εₑ = (L – L₀) / L₀). Since L/L₀ = 1 + (L – L₀)/L₀ = 1 + εₑ, we have:
εₜ = ln(1 + εₑ)
This shows that for small values of εₑ, εₜ ≈ εₑ (using the Taylor expansion ln(1+x) ≈ x for small x). When you need to calculate true strain from engineering strain, this relationship is very useful.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| L₀ | Initial Length | mm, cm, m, in, etc. | > 0 |
| L | Final Length | Same as L₀ | > 0 |
| ΔL | Change in Length (L – L₀) | Same as L₀ | Any real number (positive for tension, negative for compression) |
| εₑ | Engineering Strain | Dimensionless | -1 to ∞ (practically -0.9 to large positive values) |
| εₜ | True Strain | Dimensionless | -∞ to ∞ (practically -2.3 to large positive values) |
Practical Examples (Real-World Use Cases)
Example 1: Tensile Test of a Metal Rod
A metal rod with an initial length (L₀) of 50 mm is subjected to a tensile test and stretches to a final length (L) of 60 mm before necking starts.
- Initial Length (L₀) = 50 mm
- Final Length (L) = 60 mm
Change in Length (ΔL) = 60 – 50 = 10 mm
Engineering Strain (εₑ) = 10 / 50 = 0.2
To calculate true strain: εₜ = ln(60 / 50) = ln(1.2) ≈ 0.1823
The true strain is 0.1823, which is slightly less than the engineering strain of 0.2.
Example 2: Compression of a Cylinder
A cylindrical sample with an initial height (L₀) of 100 mm is compressed to a final height (L) of 70 mm in a forging process.
- Initial Length (L₀) = 100 mm
- Final Length (L) = 70 mm
Change in Length (ΔL) = 70 – 100 = -30 mm
Engineering Strain (εₑ) = -30 / 100 = -0.3
To calculate true strain: εₜ = ln(70 / 100) = ln(0.7) ≈ -0.3567
In compression, the true strain (-0.3567) is more negative than the engineering strain (-0.3), indicating a larger compressive strain when considered instantaneously.
How to Use This Calculate True Strain Calculator
- Enter Initial Length (L₀): Input the original length of the material before any deformation in the “Initial Length (L₀)” field. Ensure this value is positive and use consistent units.
- Enter Final Length (L): Input the length of the material after deformation in the “Final Length (L)” field, using the same units as the initial length. This value must also be positive.
- View Results: The calculator will automatically update and display the True Strain (εₜ) as the primary result, along with intermediate values like Engineering Strain (εₑ), Change in Length (ΔL), and the Length Ratio (L/L₀). The formulas used are also shown.
- Interpret Results: The true strain value gives a more accurate measure of the deformation, especially if the change in length is large relative to the original length. Compare it with the engineering strain to see the difference. The chart and table also help visualize this comparison.
- Reset: Click the “Reset” button to return the input fields to their default values.
- Copy: Click “Copy Results” to copy the main result and intermediate values to your clipboard.
This tool helps you quickly calculate true strain for various scenarios in material testing and deformation analysis.
Key Factors That Affect True Strain Results
The calculated true strain value is directly dependent on the initial and final lengths. However, several physical factors influence how a material reaches that final length under load:
- Material Properties: The material’s elastic modulus, yield strength, and ductility determine how much it deforms under a given stress. Different materials will reach different final lengths (and thus true strains) under the same load.
- Temperature: Temperature can significantly affect a material’s mechanical properties. Higher temperatures generally increase ductility and decrease strength, potentially leading to larger deformations and true strains before failure.
- Strain Rate: The speed at which the deformation occurs (strain rate) can influence material behavior. Some materials become stronger and less ductile at high strain rates, affecting the final true strain achieved.
- Original Dimensions and Geometry: The initial length (L₀) is a direct input, but the cross-sectional area and shape can influence how stress is distributed and how the material deforms, especially in non-uniform deformation like necking.
- Type of Loading: Whether the material is under tension, compression, shear, or a combination affects the deformation mode and the resulting true strain components.
- Presence of Notches or Defects: Stress concentrations at notches or defects can lead to localized deformation and higher local true strains, potentially initiating failure earlier.
Understanding these factors is crucial when interpreting the results of a test or process where you need to calculate true strain.
Frequently Asked Questions (FAQ)
Engineering strain is calculated using the original length, while true strain is calculated using the instantaneous length throughout the deformation. True strain is more accurate for large deformations. When you calculate true strain, you’re getting a measure based on the current dimensions.
Use true strain for large deformations (typically when engineering strain exceeds 0.1 or 10%), in metal forming analysis, and when dealing with material behavior beyond the elastic region, especially in tensile testing at high strains.
Yes, for tensile deformation (L > L₀), true strain is always less than engineering strain because the denominator (instantaneous length) in the incremental strain is increasing.
Yes, for compressive deformation (L < L₀), true strain is more negative (larger in magnitude) than engineering strain because the denominator is decreasing.
Yes, true strain is negative during compression (when the final length is less than the initial length).
True strain, like engineering strain, is dimensionless as it’s a ratio of lengths (or ln of a ratio).
True stress is calculated by dividing the applied load by the instantaneous cross-sectional area. It’s often used in conjunction with true strain to get a true stress-strain curve.
Because its calculation involves the natural logarithm (ln) of the ratio of final length to initial length. If you need to calculate true strain, the logarithm is key.
Related Tools and Internal Resources
- Engineering Strain Calculator: Calculate the conventional engineering strain based on original dimensions.
- Stress Analysis Tools: Explore tools for calculating stress in various materials and structures.
- Material Properties Database: Find mechanical properties of different engineering materials.
- Tensile Test Guide: Learn about the procedures and interpretation of tensile tests.
- Deformation Mechanics: Understand the principles of how materials deform under load.
- Plasticity Explained: An introduction to the plastic behavior of materials beyond the elastic limit.