# Flexural Modulus

Slope of a stress-strain curve produced by a flexural test, similar to the more familiar Young's modulus from tensile testing. Uses units of stress (force per unit area).

Testing standards include ASTM D790 and ISO 178. Standard tests have a limit on the amount of deflection the specimen can undergo and still produce valid results. Therefore, it is only possible to perform flexural tests on relatively rigid materials.

Flexural modulus should not be confused with "Modulus of Rupture", which is another name for flexural strength.

## Tangent, Secant, and Chord Moduli

When the term tangent modulus of elasticity is used in the context of flexural testing, the word "tangent" refers to the fact that the value is determined by following equation: EB = L3m/4bd3

EB is the modulus. L, b, and d are parameters of testing geometry. And m is the slope of the tangent to the initial straight-line portion of the stress-strain (load-deflection) curve produced by the test.

A secant modulus is produced using the same equation, where m is the slope of straight line drawn between the origin of the stress-strain curve and an arbitrarily chosen point on the curve. When calculating a secant modulus, the stress and strain of the selected point should be reported.

A chord modulus is calculated in a similar fashion, except the straight line is drawn between two arbitrarily chosen points.

The different calculation methods are meant to determine an intrinsic property of the material being tested. Having three different methods for calculating the same value allows the tester to pick the best method to compensate for various artifacts of the testing setup.

## Standards

ASTM testing standards include C580 for mortars, C674 for ceramic whitewares, D790 and D6272 for plastics, C1352 for dimension stone, and D7264 for polymeric-matrix composites.

ISO standards include 178 for plastics, 1209 for rigid polymeric foams, and 14125 for polymeric-reinforced composites.

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