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# Three point flexural test

The three point bending flexural test provides values for the modulus of elasticity in bending EB, flexural stress σf, flexural strain εf and the flexural stress-strain response of the material. The main advantage of a three point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.

## Testing Method

Calculation of the flexural stress σf $\sigma_f = \frac{3 P L}{2 b d^2}$

Calculation of the flexural strain εf $\epsilon_f = \frac{6Dd}{L^2}$

Calculation of Young's modulus EB $E_B = \frac{L^3 m}{4 b d^3}$

in these formulas the following parameters are used:

• σf = Stress in outer fibers at midpoint, (MPa)
• εf = Strain in the outer surface, (%)
• Eb = 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)