Engineering vs True Stress-Strain: Understanding True Stress and True Strain in Tensile Tests

What you will learn

This video explains the difference between engineering stress-strain curves, which use the initial cross-sectional area, and true stress-strain curves, which account for changes in a specimen’s dimensions during a tensile test. It discusses necking, why engineering curves drop after necking while true curves continue to rise, and how to derive true stress and true strain from engineering data using volume-constancy assumptions. It also notes the conditions under which these derivations are valid and when direct measurements of cross-sectional area are required.

Key takeaways

Engineering stress uses initial area; true stress uses instantaneous area; true strain is the natural logarithm of one plus engineering strain. The video also covers practical applications in manufacturing and finite element analysis.

Introduction and definitions

The video begins by describing the typical ductile stress-strain curve obtained from a tensile test, noting that engineering stress and engineering strain are approximations of the true state in the specimen. Engineering stress is defined as the applied force divided by the test piece's initial cross-sectional area, and engineering strain as the change in length divided by the initial length. These are often denoted with the subscript E as engineering stress and engineering strain. The true stress and true strain, in contrast, consider the changing cross-sectional area and length throughout the test.

Engineering vs true curves and necking

The engineering stress-strain curve typically peaks at the ultimate tensile strength and then drops due to necking, a rapid reduction in cross-sectional area. The true stress-strain curve, however, continues to increase because it accounts for the area reduction. This distinction is crucial when large plastic deformations occur, as the two curves diverge significantly after necking.

Why engineers rely on engineering curves

Two main reasons are highlighted: first, measuring the instantaneous cross-sectional area during a tensile test is difficult in practice; second, many analyses focus on the elastic region where engineering and true curves are very similar, making engineering curves sufficient for many design tasks.

Deriving true stress from engineering data

To relate true stress to engineering measurements, the video explains that the specimen volume is assumed to remain constant in the elastic region and often in the plastic region due to incompressibility during plastic deformation. Under constant volume, the instantaneous cross-sectional area A and the current length L satisfy A L = A0 L0. Substituting this into the true stress definition yields a practical relation: sigma_T = sigma_E (L/L0) = sigma_E (1 + epsilon_E). This provides a way to adjust engineering data to approximate the true curve without instantaneous area measurements, up to necking.

Deriving true strain

True strain is obtained by integrating dL/L over the test, which leads to epsilon_T = ln(L/L0) = ln(1 + epsilon_E). This shows why true strain is also known as logarithmic strain or natural strain. The integration approach formalizes how true strain accounts for the changing length during deformation.

Practical implications and limitations

The constant-volume assumption is valid in the elastic region and generally during plastic deformation when materials are incompressible. Beyond necking, the true stress should be based on actual cross-sectional measurements. The video concludes by noting the relevance of true stress-strain curves for processes with significant deformation, such as manufacturing analyses or finite element modeling, where using engineering data would otherwise misrepresent the material response.

Applications and takeaway

Understanding these relationships enables engineers to approximate true curves from easily measured engineering data, assisting in process design and simulation. The presenter also references related content on Poisson's ratio for material incompressibility and invites viewers to subscribe for more explanations.