What is the use of secant modulus?

Question

Secant modulus is defined as the slope of a line connecting the origin and a specified point (like yield point) in stress-strain diagrams. Instead of elastic modulus, which is the slope of the tangent line at origin, the secant line connects the origin and yield point. But what is the purpose of this method? I know this is used to approximate the behaviour of materials at the nonlinear region, but why do we use secant modulus instead of tangent modulus near the yield point? Tangent near the yield point would probably approximate much better. The secant modulus method seems hugely inaccurate to me.

materials structural engineering

Disrudog · Answer

The modules of elasticity at yield point (or below) is called Young Modulus, while the material still behave in elastic region. In this case the Secant Modulus and Young Modulus is equivalent.
However while entering the elastic-plastic region and plastic region. As the material become incompressible, the study of the material properties requires more complex consideration such as the poison ratio changes in the region.
Methamatically, Secant Modulus is included in the theory during simplification of the stress-strain relationship of material in those regions.

John Pepi · Answer

In the linear region of the stress strain curve the tangent modulus is equal to the secant modulus. Stress= Etangent x strain = Esecant x strain.
However at point A you can see from the curve that stress = Esecant x strain, not E tangent x strain.

What is the use of secant modulus?

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