Four-point bending test

The four-point bending test is one of the most important mechanical methods for investigating the behavior of materials under bending loads. It is widely used in various industries, including aerospace, automotive, construction, ceramics, composites, and polymers, to determine the flexural strength and elastic modulus of materials.

The four-point bending test, like the three-point bending test, is one of the most common methods for measuring the mechanical properties of specimens. The main difference between the two tests is the distribution of the load on the specimen and the uniformity of the stress across its cross-section.

Definition of the four-point bending test

In the four-point bending test, the specimen is positioned as a beam simply resting on two supports, and then the load is applied via two pulleys or load handles placed at the same distance from the center of the specimen.

In contrast to the three-point test, in which the load is concentrated on one point, here the load is applied at two points and a relatively large area of the sample is subjected to uniform bending stress.

Purpose of the four-point bending test

Flexural strength : The maximum stress a material can withstand before failure.
Determine the flexural modulus : The initial slope of the load-deflection curve indicates the stiffness of the material with respect to flexural strain.
Investigation of fracture behavior : Determination of the type of fracture (brittle, ductile or ductile) in different materials.
Material comparison : Compare different engineering materials such as metals, ceramics, composites and polymers in terms of their flexural strength.

Advantages of the four-point bending test

Compared to the three-point test, the stress distribution in the middle area of the sample is uniform.
For heterogeneous materials such as composites, the properties of different points are not the same, so the accuracy is higher.
Cracks and damage can be repaired over a larger area.
Suitable for brittle materials (e.g. ceramics) where three-point bending does not provide accurate results.

Disadvantages of the four-point bending test

The equipment and setup are more complex than the three-point test.
A larger and more accurate sample is needed .
The costs are higher because more equipment and time are required.

How to conduct a four-point flexibility test

1. Sample preparation

The shape of the sample is usually rectangular or cylindrical .
The dimensions of the sample are determined according to the test standard (e.g. ASTM or ISO).
The surface of the sample must be smooth and free of cracks.

2. Install the sample into the device.

The samples are placed on two carriers.
The distance between the supports (span) must be measured precisely.
The loading jaws are arranged at equal distances from the center.

3. Download

The load is applied gradually and in a controlled manner .
Load and deflection data are recorded by sensors.

4. Data collection and analysis

Draw a load and deflection diagram.
Flexural strength and flexural modulus were calculated using standard formulas.

ASME BPVC 2023 Section VIII 1

Relationships and formulas for four-point bending tests

Bending force

For rectangular samples:

$σf=3FL4bd2\sigma_f = \frac{3FL}{4bd^2}$

Where:

$F$ : Breaking load (Newton)
$L$ : Distance between two supports (mm)
$b$ : Sample width (mm )
$d$ : sample thickness (mm)

Bending coefficient

$Ef=L3m4bd3E_f = \frac{L^3 m}{4bd^3}$

Where:

$m$ : Initial slope of the load-deflection curve (N/mm)

Standards for the four-point bending test

There are several acceptable criteria for this test:

ASTM D6272 – For polymers and composites.
ASTM C1161 – For advanced ceramics.
ISO 14125 – For fiber composite materials.
ASTM E855 – For metals and alloys.

The selection of the appropriate standard depends on the type of material and the intended application.

Comparison between four-point bending test and three-point bending test

Special feature	Three-point bending	Four-point push-up exercise
How to download	Center	2 charging points
Regular stress zone	A little	Bigger and wider
Accuracy in heterogeneous materials	reduced	higher
Team complexity	Easier	more complex
It’s worth it	fewer	additionally

Industrial application of the four-point bending test

Composites manufacturing : Testing the strength of carbon and glass fibers in aircraft and automotive parts.
Ceramic industry : Determination of the tensile strength of technical ceramics.
Automotive industry : Testing of polymer and metal components under bending load.
Civil engineering : Investigation of the flexural strength of reinforced concrete and building materials.
Aerospace : Assessment of the ability of lightweight materials to withstand dynamic loads.

Simple numerical example

Suppose a four-point bending test is performed on a rectangular specimen with the following properties:

Groove length (L) = 100 mm
Sample width (b) = 10 mm
Sample thickness (d) = 5 mm
Breaking load (F) = 200 N

Calculate:

$sigma_f = 3×200×100 4×10×25 =$

In this example, the flexural strength of the material is 60 MPa.

Problems and limitations

Very sensitive to the condition of the sample surface: the presence of cracks or roughness on the surface can distort the results.
This depends on the precision of the machine settings : the distance between the jaws and the holder must be very precise.
Expensive and time-consuming compared to some simple tests .

Finally

The four-point bending test is an important method for investigating the mechanical properties of materials under bending loads. This method is particularly suitable for heterogeneous, brittle materials such as ceramics and composites, as it provides a more uniform stress distribution in the central region of the specimen, thus enabling more accurate results.

This test determines a material’s flexural strength, flexural modulus, and failure mode . This allows for more accurate material selection decisions for critical industries such as aerospace, automotive, construction, and energy.