Standard procedure for measuring modulus of elasticity in bending
1940s flexural test machinery working on a sample of concreteTest fixture on universal testing machine for three-point flex 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 (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.
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 [4] and E1290-08 [5] 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
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.
^"Chapter 4 Mechanical Properties of Biomaterials". Biomaterials – The intersection of Biology and Material Science. New Jersey, United States: Pearson Prentice Hall. 2008. p. 152.
^Zweben, C., W. S. Smith, and M. W. Wardle (1979), "Test methods for fiber tensile strength, composite flexural modulus, and properties of fabric-reinforced laminates", Composite Materials: Testing and Design (Fifth Conference), ASTM International, doi:10.1520/STP36912S, ISBN978-0-8031-4495-8{{citation}}: CS1 maint: multiple names: authors list (link)
^Bower, A. F. (2009). Applied mechanics of solids. CRC Press.
^ASTM D5045-14: Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials, West Conshohocken, PA: ASTM International, 2014
^E1290: Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement, West Conshohocken, PA: ASTM International, 2008