
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
A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a specified procedure that produces a test result. To ensure accurate and relevant results, a test method should b ...
for conducting the test usually involves a specified
test fixture
A test fixture is a device used to consistently test some item, device, or piece of software. Test fixtures are used in the testing of electronics, software and physical devices.
Electronics
In testing electronic equipment such as circuit boa ...
on a
universal testing machine
A universal testing machine (UTM), also known as a universal tester, universal tensile machine, materials testing machine, materials test frame, is used to test the tensile strength (pulling) and compressive strength (pushing), flexural stren ...
. Details of the test preparation, conditioning, and conduct affect the test results. The sample is placed on two supporting pins a set distance apart.
Calculation of the flexural stress
:
for a rectangular cross section
:
for a circular cross section
Calculation of the flexural strain
:
Calculation of
flexural modulus
:
in these formulas the following parameters are used:
*
= Modulus of Rupture, the stress required to fracture the sample (
MPa
MPA or mPa may refer to:
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)
*
= 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
In materials science, fracture toughness is the critical stress intensity factor of a sharp Fracture, crack where propagation of the crack suddenly becomes rapid and unlimited. It is a material property that quantifies its ability to resist crac ...
of a specimen can also be determined using a three-point flexural test. The
stress intensity factor
In fracture mechanics, the stress intensity factor () is used to predict the Stress (mechanics), stress state ("stress intensity") near the tip of a Fracture, crack or Notch (engineering), notch caused by a remote load or residual stresses. It i ...
at the crack tip of a single edge
notch bending specimen is
:
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
[ ] and E1290-08
[ ] 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
The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries.
Me ...
12135: Metallic materials. Unified method for the determination of quasi-static fracture toughness.
*
ISO
The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries.
Me ...
12737: Metallic materials. Determination of plane-strain fracture toughness.
*
ISO
The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries.
Me ...
178: Plastics—Determination of flexural properties.
*
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...
C293: Standard Test Method for Flexural Strength of Concrete (Using Simple Beam With Center-Point Loading).
*
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...
D790: Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials.
*
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...
E1290: Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement.
*
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...
D7264: Standard Test Method for Flexural Properties of Polymer Matrix Composite Materials.
*
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and s ...
D5045: Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials.
See also
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References
{{reflist
Materials testing
Mechanics