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Author: dr funda
Time: 03/22/00 12:27 PST
This is a reply to message no. 781 by pganorka
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Current Topic:
Polymer Properties and the test procedure to measure them.
There is a big difference between the Flexural Modulus and the Young's Modulus, even though they are expressed in the same units (MPa, or psi). Don't confuse them, even though it's very easy to do so!

Flexural Modulus is a crutch devised by the plastic industry to simplify the challenge of working with a nonlinear material, i.e. plastics.

Consider this: if the behavior of plastics were linearly elastic instead of plastic, then their stress-strain curves would be linear and only 2 elastic constants would be needed to fully describe their material behavior, just like for steel. These constants are most often the Young's Modulus and Poisson's ratio, and with them we could determine the stress for all loading cases, no matter if it's unaxial tension, or bending, or some combination. There would be no need to talk about a Secant Modulus because it would be identical to the Young's Modulus. There would be no need to define a Flexural Modulus, because the bending behavior would be fully described by elastic beam theory.  All would be hunky-dory.

Unfortunately, plastics aren't elastic, they're plastic (sounds somewhat circular, yes?), which means that if the stress is high enough (i.e. the yield limit, or strength) the material will plastically flow to relieve the stress. This yield limit is often quite low, much lower than the ultimate strength, and as a result plastics are often used in their plastic region in typical engineering applications.

The challenge of modeling a nonlinear material with math, or with FEA, is much greater than that for a linear elastic material. For example, a plastic beam in bending will often experience plastic flow to relieve the maximum stresses, the degree of which depends intimately on the plastic's nonlinear stress-strain curve. To calculate the "stiffness" of a simply-supported plastic beam to a centered load (like this for a linear beam) could be done with math, but why do all this work?

Instead, the plastic industry has designed a specific experiment to measure the "bending stiffness" of a plastic beam under 3-point loading. The result from this test is a measure called the Flexural Modulus, with the units of MPa. It is important to realize that the Flexural Modulus is totally an artifact of the experiment, and cannot be applied to other loading conditions, or even other-sized beams. Most often, the Flexural Modulus is just used as a gauge to compare the relative bending stiffnesses of various plastics.

Likewise, engineers use the Secant Modulus to describe the behavior of nonlinear plastics beyond their yield limit (below this limit, the Secant Modulus and Young's Modulus are identical). There is no strain restriction on the definition of Secant Modulus; it can be applied at any strain level. But again, just like for Flexural Modulus, the actual Secant Modulus value depends on the strain level, the material, and possibly even the shape of the test specimen.

What to use for FEA analysis? If the FEA package can handle plastic flow, then you should be able to enter the complete stress-strain curve for the plastic. This curve contains all the info you need: low-strain elastic behavior, medium strain plastic behavior, and high strain failure. There is no need to worry about Secant Modulus or Flexural Modulus if you can input the entire stress-strain curve, AND the software can truly model plastic behavior. (That's a tall requirement!! Plastic FEA development is a hot research topic at many universities currently.)

If the FEA can only handle linear analysis, then the best you can do is an approximation.  You must guess the strain level your part will be subject to, and then input the Secant Modulus for that particular strain. And don't be too trusting in the FEA results; try to gain some extra confidence by performing experiments on the real parts if at all possible.

eFunda staff
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