Three-point flexural test

The three-point bending flexural test provides values for the modulus of elasticity
in bending formula_1, flexural stress formula_2, flexural strain formula_3 and the flexural stress–strain response of the material. This test is performed on a universal testing machine (tensile testing machine or tensile tester) 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 formula_2
Calculation of the flexural strain formula_3
Calculation of flexural modulus formula_1
in these formulas the following parameters are used:
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 formula_22 is the applied load, formula_23 is the thickness of the specimen, formula_24 is the crack length, and
formula_25 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 formula_26.
The ASTM D5045-14 and E1290-08 Standards suggests the relation
where
The predicted values of formula_29 are nearly identical for the ASTM and Bower equations for crack lengths less than 0.6formula_25.