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I'm reading the Wikipedia page on flexural modulus. It is said:

Ideally, flexural or bending modulus of elasticity is equivalent to the tensile modulus (Young's modulus) or compressive modulus of elasticity. In reality, these values may be different, especially for polymers.

But how can they be different? Young's/elastic modulus is measured in the tensile test, by pulling a sample of the material and measuring the stress/strain response. In the bending test we bend the sample instead, but the fibers at the bottom (as seen in the picture) are in tension. Thus, if we inspect as small sample at the bottom of the beam, it is subject to tensile forces only and it should therefore behave in the same way as if the sample was being subjected to the tensile test. How does the sample know it is part of a beam being bent instead of being a part of a beam being pulled? How can the two moduli be different? The article mentions polymers specifically, but do the moduli differ for metals as well?

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  • $\begingroup$ If a material has fibres only in one direction then if tested across two different dimensions it can be stiffer in one... $\endgroup$
    – Solar Mike
    Mar 19 '20 at 10:52
  • $\begingroup$ As the wiki link says, they are the same for isotropic linear materials. That includes most metals, but excludes most composite materials for example. Polymers can be considered as a type of composite material at the molecular level. $\endgroup$
    – alephzero
    Mar 19 '20 at 11:35
  • $\begingroup$ @alephzero Why are composites excluded? What difference does it make that a material is a composite? $\endgroup$
    – S. Rotos
    Mar 21 '20 at 9:23
  • $\begingroup$ @Solar Mike Well of course anisotropic materials have an elastic modulus that is different in two directions. But why not just say that? Why define a new number called flexural modulus? $\endgroup$
    – S. Rotos
    Mar 21 '20 at 9:26
  • $\begingroup$ From your question it was not clear if you knew that or understood that... $\endgroup$
    – Solar Mike
    Mar 21 '20 at 11:00
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Unlike many other isotropic materials, the polymers do not demonstrate the same deformation characteristics for tension and compression, evident by the stress-strain curves shown below. Therefore, a flexural modulus (sometimes called “modulus of elasticity in bending” or simply "bending modulus") is required to describe the "stiffness or rigidity of a polymer, as it is a measure of a materials stiffness/ resistance to bend when a force is applied perpendicular to the long edge of a sample - known as the three point bend test.

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Note that the elastic modulus (E) of material is determined from the stress-strain curve obtained from the tension test, and for most materials, it is identical for tension, compression, and bending loads.

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Wiki says that "ideally" (emphasis added), flexural modulus should match Young's modulus, but as related to most polymers, IT DOES NOT. Generally, Young's is used for metals, which deflect (stress) and instantaneously spring-back (strain) when the load is removed, which is elastic. Most polymers are viscoelastic, except PTFE (teflon), which exhibit viscous and elastic properties when undergoing deformation (deflection) and exhibit time-dependent strain (spring-back). The viscous aspect creates the time delay. See Wiki for titles "viscoelasticity" and "rheology", which is the study of the flow of matter, which includes solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force.

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