Four point flexural test

The four point bending flexural test provides values for the modulus of elasticity in bending $E_{f}$, flexural stress $\sigma _{f}$, flexural strain $\varepsilon_f$ and the flexural stress-strain response of the material. This test is very similar to the three point bending flexural test. The major difference being that the addition of a 4th bearing brings a much larger portion of the beam to the maximum stress, as opposed to only the material right under the central bearing.

This difference is of prime importance when studying brittle materials, where the number and severity of flaws exposed to the maximum stress is directly related to the flexural strength and crack initiation.

It is one of the most widely used apparatus to characterize fatigue and flexural stiffness of asphalt mixtures ^[1]

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 and two loading pins placed at an equal distance around the center. These two loadings are lowered from above at a constant rate until sample failure.

Calculation of the flexural stress $\sigma _{f}$

${\displaystyle \sigma _{f}={\frac {3FL}{4bd^{2}}}}$ ^[2] for four point bending test where the loading span is 1/2 of the support span (rectangular cross section)

${\displaystyle \sigma _{f}={\frac {FL}{bd^{2}}}}$ ^[3] for four point bending test where the loading span is 1/3 of the support span (rectangular cross section)

$\sigma _{f}={\frac {3FL}{2bd^{2}}}$ ^[4] for three point bending test (rectangular cross section)

in these formulas the following parameters are used:

• $\sigma _{f}$ = Stress in outer fibers at midpoint, (MPa)
• $F$ = load at a given point on the load deflection curve, (N)
• $L$ = Support span, (mm)
• $b$ = Width of test beam, (mm)
• $d$ = Depth of tested beam, (mm)

Advantages and Drawbacks

Advantages of three-point and four-point bending tests over uniaxial tensile tests include:

• simpler sample geometries
• minimum sample machining is required
• simple test fixture
• possibility to use as-fabricated materials^[5]

Disadvantages include:

• more complex stress distributions through the sample

Application with different materials

Ceramics

Ceramics are usually very brittle, and their flexural strength depends on both their inherent toughness and the size and severity of flaws. Exposing a large volume of material to the maximum stress will reduce the measured flexural strength because it increases the likelihood of having cracks reaching critical length at a given applied load. Values for the flexural strength measured with four-point bending will be significantly lower than with three-point bending.^[6]

Composite materials

Standards

• ASTM C1161: Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
• ASTM D6272: Standard Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending
• ASTM C393: Standard Test Method for Core Shear Properties of Sandwich Constructions by Beam Flexure
• ASTM D7249: Standard Test Method for Facing Properties of Sandwich Constructions by Long Beam Flexure
• ASTM D7250: Standard Practice for Determining Sandwich Beam Flexural and Shear Stiffness

See also

• Bending
• Euler-Bernoulli beam equation
• Flexural strength
• Three point flexural test
• List of area moments of inertia
• Second moment of area

References

1. Pais & Harvey (Eds) (2012). Four Point Bending. Taylor & Francis Group. ISBN 978-0-415-64331-3.
2. ASTM C1161
3. ASTM D6272
4. ASTM C1161
5. Davis, Joseph R. (2004). Tensile testing (2nd ed.). ASM International. ISBN 978-0-87170-806-9.
6. ASTM C1161-13, section 4: http://www.astm.org/Standards/C1161.htm

External links

• ASTM C1161: Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
• ASTM D6272: Standard Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending
• ASTM C393: Standard Test Method for Core Shear Properties of Sandwich Constructions by Beam Flexure
• ASTM D7249: Standard Test Method for Facing Properties of Sandwich Constructions by Long Beam Flexure
• ASTM D7250: Standard Practice for Determining Sandwich Beam Flexural and Shear Stiffness