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# Three point flexural test

The three point bending flexural test provides values for the modulus of elasticityin bending $E_B$, flexural stress $sigma_f$, flexural strain$epsilon_f$ and the flexural stress-strain response of thematerial. The main advantage of a three point flexural test is theease of the specimen preparation and testing.However, this method has also some disadvantages: the results of thetesting method are sensitive to specimen and loading geometry andstrain rate.

Testing Method

Calculation of the flexural stress $sigma_f$

$sigma_f = frac\left\{3 P L\right\}\left\{2 b d^2\right\}$ for a rectangular cross section

$sigma_f = frac\left\{P L\right\}\left\{pi R^3\right\}$ for a circular cross section

Calculation of the flexural strain $epsilon_f$

$epsilon_f = frac\left\{6Dd\right\}\left\{L^2\right\}$

Calculation of Young's modulus $E_B$

$E_B = frac\left\{L^3 m\right\}\left\{4 b d^3\right\}$

in these formulas the following parameters are used:
* $sigma_f$ = Stress in outer fibers at midpoint, (MPa)
* $epsilon_f$ = Strain in the outer surface, (%)
* $E_b$ = Modulus of elasticity in bending,(MPa)
* $P$ = load at a given point on the load deflection curve, (N)
* $L$ = Support span, (mm)
* $b$ = Width of test beam, (mm)
* $d$ = Depth of tested beam, (mm)
* $D$ = maximum deflection of the center of the beam, (mm)
* $m$ = Slope of the tangent to the initial straight-line portion of the load deflection curve, (N/mm)

ee also

*Flexural strength
*ASTM materials standards organization

References

* ASTM standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials

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