equation for true strain

Guri Bee

2 min read

·

21-10-2024

1

0

Share

Unraveling the Mystery of True Strain: A Comprehensive Guide

Understanding strain is fundamental in materials science and engineering. While engineering strain is a simple measure of deformation, it often fails to accurately capture the actual strain experienced by a material, especially at large deformations. This is where true strain comes into play.

True strain, also known as logarithmic strain, provides a more accurate representation of the actual deformation experienced by a material. It accounts for the changing cross-sectional area as the material is deformed, making it a more reliable measure for analyzing material behavior under stress.

What is the Equation for True Strain?

The equation for true strain is:

ε_t = ln(l_t/l₀)

where:

• ε_t is the true strain
• ln is the natural logarithm
• l_t is the instantaneous length of the material
• l₀ is the original length of the material

Here's a breakdown of why this equation works:

• Logarithmic Nature: True strain uses a logarithmic function to account for the continuous change in cross-sectional area as the material deforms.
• Instantaneous Length: True strain considers the length of the material at any given instant during deformation, providing a more accurate representation of the ongoing strain.
• Original Length: The original length acts as a reference point, allowing us to compare the deformed length to the initial state.

Understanding the Difference Between True Strain and Engineering Strain

Engineering strain (ε_e) is defined as the change in length divided by the original length:

ε_e = (l_t - l₀) / l₀

While simple to calculate, engineering strain fails to account for the changing cross-sectional area. This can lead to inaccuracies, especially when dealing with large deformations.

True strain, on the other hand, provides a more accurate measure by considering the continuous change in cross-sectional area. This makes it crucial for applications involving significant deformation, such as metal forming processes.

Practical Applications of True Strain

• Material Characterization: True strain is used to accurately determine material properties like yield strength, ultimate tensile strength, and ductility.
• Metal Forming Processes: Understanding true strain is essential in metal forming processes, like rolling, extrusion, and forging, where large deformations are involved. It helps engineers predict material behavior and optimize process parameters.
• Finite Element Analysis (FEA): True strain is used in FEA models to accurately simulate the behavior of materials under complex loading conditions.

Example:

Imagine stretching a rubber band. As you stretch it, its length increases, and its cross-sectional area decreases. Engineering strain would only consider the change in length, but true strain considers both length and cross-sectional area changes, giving a more realistic picture of the deformation.

Conclusion

True strain provides a more accurate measure of material deformation compared to engineering strain, especially at large deformations. Understanding the concept of true strain and its equation is crucial for accurate material characterization, optimization of metal forming processes, and reliable FEA simulations.