Three point flexural test
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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. 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.
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 and a third loading pin is lowered from above at a constant rate until sample failure.
Calculation of the flexural stress
- for a rectangular cross section
- for a circular cross section
Calculation of the flexural strain
in these formulas the following parameters are used:
- = Stress in outer fibers at midpoint, (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 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
- = The radius of the beam, (mm)
Fracture toughness testing
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 E1290-08 Standard suggests the relation
The predicted values of are nearly identical for the ASTM and Bower equations for crack lengths less than 0.6.
- ISO 12135: Metallic materials. Unified method for the determination of quasi-static fracture toughness
- ISO 12737: Metallic materials. Determination of plane-strain fracture toughness
- ASTM D790: Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials
- ISO 178: Plastics—Determination of flexural properties
- ASTM E1290: Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement.
- Euler-Bernoulli beam equation
- Flexural strength
- List of area moments of inertia
- Second moment of area
- "Chapter 4 Mechanical Properties of Biomaterials". Biomaterials - The intersection of Biology and Material Science. New Jersey, United States: Pearson Prentice Hall Bioengineering. 2008. p. 152.
- "Activity 20 - Bendy Wafer". Salters Horners Advanced Physics for Edexcel AS Physics. Essex, United Kingdom: Pearson Education. 2008.
- Bower, A. F. (2009). Applied mechanics of solids. CRC Press.