Three-point flexural test


The three-point bending flexural test provides values for the modulus of elasticity
in bending, flexural stress, flexural strain and the flexural stress–strain response of the material. This test is performed on a universal testing machine with a three-point or four-point bend fixture. 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

The test method for conducting the test usually involves a specified test fixture on a universal testing machine. Details of the test preparation, conditioning, and conduct affect the test results. The sample is placed on two supporting pins a set distance apart.
Calculation of the flexural stress
Calculation of the flexural strain
Calculation of flexural modulus
in these formulas the following parameters are used:
  • = Modulus of Rupture, the stress required to fracture the sample
  • = Strain in the outer surface,
  • = flexural Modulus of elasticity,
  • = load at a given point on the load deflection curve,
  • = Support span,
  • = Width of test beam,
  • = Depth or thickness of tested beam,
  • = maximum deflection of the center of the beam,
  • = The gradient of the initial straight-line portion of the load deflection curve,
  • = The radius of the beam,

Fracture toughness testing

The fracture toughness of a specimen can also be determined using a three-point flexural test. The stress intensity factor at the crack tip of a single edge notch bending specimen is
where is the applied load, is the thickness of the specimen, is the crack length, and
is the width of the specimen. In a three-point bend test, a fatigue crack is created at the tip of the notch by cyclic loading. The length of the crack is measured. The specimen is then loaded monotonically. A plot of the load versus the crack opening displacement is used to determine the load at which the crack starts growing. This load is substituted into the above formula to find the fracture toughness.
The ASTM D5045-14 and E1290-08 Standards suggests the relation
where
The predicted values of are nearly identical for the ASTM and Bower equations for crack lengths less than 0.6.

Standards