What is True Stress and True Strain?

In materials science and mechanical engineering, understanding how materials deform under load is critical. While "Engineering Stress" and "Engineering Strain" are based on the original dimensions of a material, "True Stress" and "True Strain" account for the instantaneous changes in the material's cross-sectional area and length during the deformation process.

The Core Formulas

This calculator utilizes standard mechanical engineering formulas to convert engineering values into true values. Note that these conversions are generally valid only up to the point of "necking" in a tensile test:

• True Stress (σₜ): σₜ = σₑ(1 + εₑ)
• True Strain (εₜ): εₜ = ln(1 + εₑ)

Where σₑ represents Engineering Stress and εₑ represents Engineering Strain.

Difference Between Engineering and True Values

Engineering stress is calculated by dividing the load by the original cross-sectional area. However, as a material is stretched, its area decreases. True stress accounts for this instantaneous area reduction, making it a more accurate representation of the material's physical state. Similarly, True Strain provides a more accurate measure of plastic deformation by integrating the instantaneous change in length over the current length.

Frequently Asked Questions

When should I use True Stress/Strain? These values are essential for modeling plastic deformation and performing finite element analysis (FEA) where large deformations occur.

Can strain be negative? Yes, in compression, both engineering and true strain will be negative values.

Is true strain always smaller than engineering strain? For tensile tests (extension), true strain is always smaller than engineering strain. In compression, the magnitude of true strain is larger than engineering strain.