The three-point bending flexural test provides values for the modulus of elasticity in bending E_f, flexural stress \sigma_f, flexural strain \epsilon_f 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 \sigma_f Calculation of the flexural strain \epsilon_f Calculation of flexural modulus E_f 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 P is the applied load, B is the thickness of the specimen, a is the crack length, and W 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 K_{Ic}. The ASTM D5045-14 and E1290-08 Standards suggests the relation where The predicted values of K_{\rm I} are nearly identical for the ASTM and Bower equations for crack lengths less than 0.6W.

Standards