The three-point bending flexural test provides values for the modulus of elasticity in bending, flexural stress 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.

1. for a rectangular cross section

   for a circular cross section

Calculation of flexural modulus

in these formulas the following parameters are used:

• = Modulus of Rupture, the stress required to fracture the sample (MPa)

• = Strain in the outer surface, (mm/mm)

• = flexural Modulus of elasticity,(MPa)

• = load at a given point on the load deflection curve, (N)

• = Support span, (mm)

• = Width of test beam, (mm)

• = Depth or thickness of tested beam, (mm)

• = maximum deflection of the center of the beam, (mm)

• = The gradient (i.e., slope) of the initial straight-line portion of the load deflection curve, (N/mm)

• = The radius of the beam, (mm)

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

is the width of the specimen. In a three-point bend test, a fatigue crack is created at the tip of the notch.

The ASTM D5045-14 and E1290-08 Standards suggests the relation

where

.

Standards

• ISO 12135: Metallic materials. Unified method for the determination of quasi-static fracture toughness.

• ISO 12737: Metallic materials. Determination of plane-strain fracture toughness.

• ISO 178: Plastics—Determination of flexural properties.

• ASTM C293: Standard Test Method for Flexural Strength of Concrete (Using Simple Beam With Center-Point Loading).

• ASTM D790: Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials.

• ASTM E1290: Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement.

• ASTM D7264: Standard Test Method for Flexural Properties of Polymer Matrix Composite Materials.

• ASTM D5045: Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials.

See also

References