Flexural modulus

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In mechanics (mechanics is a branch of physics), the flexural modulus or bending modulus[1] is the ratio of stress to strain in flexural deformation, or the tendency for a material to bend. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D 790), and uses units of force per area.[2] It is an intensive property.

Flexural modulus measurement

For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, L is the distance between the two outer supports and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus:[3]

E_{\mathrm{bend}} = \frac {L^3 F}{4 w h^3 d}

From elastic beam theory 
d = \frac {L^3 F}{48 I E } and for rectangular beam  I = \frac{1}{12}wh^3

E_{\mathrm{bend}} = E (Elastic modulus)

Ideally, flexural or bending modulus of elasticity is equivalent to the tensile or compressive modulus of elasticity. In reality, these values may be different, especially for plastic materials.

See also[edit]