four-point flexural test

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 $\backslash sigma\_f$

:File:4-point bend simplified.svg$\backslash sigma\_f\; =\; \backslash frac\{3\}\{4\}\backslash frac\{F\; L\}\{b\; d^2\}$ASTM C1161 for four-point bending test where the loading span is 1/2 of the support span (rectangular cross section)

:$\backslash sigma\_f\; =\; \backslash frac\{F\; L\}\{b\; d^2\}$ASTM D6272 for four-point bending test where the loading span is 1/3 of the support span (rectangular cross section)

:$\backslash sigma\_f\; =\; \backslash frac\{3\}\{2\}\backslash frac\{F\; L\}\{b\; d^2\}$ASTM C1161 for three-point bending test (rectangular cross section)

in these formulas the following parameters are used:

• $\backslash sigma\_f$ = 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 or thickness of tested beam, (mm)

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{{cite book|last = Davis|first = Joseph R.|title = Tensile testing|publisher = ASM International|year = 2004|edition = 2nd|url = https://books.google.com/books?id=5uRIb3emLY8C|isbn = 978-0-87170-806-9}}

Disadvantages include:

• more complex integral stress distributions through the sample

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.,ASTM C1161-13, section 4: http://www.astm.org/Standards/C1161.htm Compared with three-point bending test, this method is more suitable for strength evaluation of butt joint specimens. The advantage of four-point bending test is that a larger portion of the specimen between two inner loading pins is subjected to a constant bending moment, and therefore, positioning the joint region is more repeatable.{{Cite journal|last1=Hasanabadi|first1=M. Fakouri|last2=Faghihi-Sani|first2=M.A.|last3=Kokabi|first3=A.H.|last4=Groß-Barsnick|first4=S.M.|last5=Malzbender|first5=J.|date=September 2018|title=Room- and high-temperature flexural strength of a stable solid oxide fuel/electrolysis cell sealing material|journal=Ceramics International|volume=45|pages=733–739|doi=10.1016/j.ceramint.2018.09.236|s2cid=139543143 |issn=0272-8842}}

• 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

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

{{reflist}}

• [http://www.astm.org/Standards/C1161.htm ASTM C1161]: Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature

• [http://www.astm.org/Standards/D6272.htm ASTM D6272]: Standard Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending

• [http://www.astm.org/Standards/C393.htm ASTM C393]: Standard Test Method for Core Shear Properties of Sandwich Constructions by Beam Flexure
• [http://www.astm.org/Standards/D7249.htm ASTM D7249]: Standard Test Method for Facing Properties of Sandwich Constructions by Long Beam Flexure
• [http://www.astm.org/Standards/D7250.htm ASTM D7250]: Standard Practice for Determining Sandwich Beam Flexural and Shear Stiffness
• [http://www.astm.org/Standards/C78.htm ASTM C78]: Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading)

Category:Materials testing

Category:Mechanics