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 definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a test m ...
for conducting the test usually involves a specified
test fixture
A test fixture is an environment used to consistently test some item, device, or piece of software. Test fixtures can be found when testing electronics, software and physical devices.
Electronics
In testing electronic equipment such as circuit ...
on a
universal testing machine
A universal testing machine (UTM), also known as a universal tester, materials testing machine or materials test frame, is used to test the tensile strength and compressive strength of materials. An earlier name for a tensile testing machine i ...
. 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 mechanics, the flexural modulus or bending modulus is an intensive property that is computed as the ratio of stress to strain in flexural deformation, or the tendency for a material to resist bending. It is determined from the slope of a stre ...
:
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 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)
m=F/D
*
= 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 crack where propagation of the crack suddenly becomes rapid and unlimited. A component's thickness affects the constraint conditions at the tip of a ...
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 state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses. It is a theoretical construct usually applied to a h ...
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 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
ASTM International, formerly known as American Society for Testing and Materials, is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
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 an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
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 an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
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 an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
D5045: Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials.
See also
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References
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Materials testing
Mechanics