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 strainepsilon_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{3 P L}{2 b d^2} for a rectangular cross section

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

Calculation of the flexural strain epsilon_f

epsilon_f = frac{6Dd}{L^2}

Calculation of Young's modulus E_B

E_B = frac{L^3 m}{4 b d^3}

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


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

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