# Bend test

## Bending test: Suitable for both brittle and ductile materials

Bending tests are carried out to obtain information on the bending properties of materials intended for industrial use or for research and development. In doing so, different checking fixtures are used.

### What is a bending test?

A bending test (bending tensile test) is a method of testing materials for their bending strength and other important properties. Destructive materials testing is used for plastics, fiber-reinforced plastics (FRP), metals and ceramic materials. Bending tests are similar in their sequence. Depending on the number of pressure points and the support of the test specimen, a distinction is made between the following:

- 1-point bending test
- 3-point bending test
- 4-point bending test

In bending tests, standardized, mostly cylindrical specimens are placed in the center of the checking fixture. The rounded support rollers (bearings) are arranged parallel to each other at a certain distance (support width). The diameter of the cylindrical specimen is proportional to the support width of the bearings. The test punch, which moves down slowly and at a constant speed, loads the sample with increasing force until it breaks or reaches the previously determined deformation. The maximum load exerted during the bending test is called breaking force.

During the test, the values of the bending force and deflection are recorded. The material characteristics are then determined. The entire test sequence is shown in a stress-strain curve and can also be recorded with a video camera. Bending tests are performed to obtain information about the bending behavior of the tested material from the single-axis bending stress. In case of brittle materials, the bending strength is determined this way. Dealing with ductile materials, the limit yield point, the greatest possible bending angle as well as Young’s modulus are determined, in case of an elastic deformation.

During materials testing using a bending test, modern optical measuring systems with high-resolution cameras provide precise images of the test specimen. For the documentation of flat specimen, devices with a single camera are usually sufficient. More complex sample geometries can be accurately measured using two cameras. The material tester first applies a stochastic dot pattern to the sample or uses the existing surface structure. Optical measuring systems use image correlation algorithms: In the high-resolution images, they recognize the deformation caused by the bending test and then calculate the deflection using the pixel coordinates of the dot pattern.

### What is bending stress?

In the bending test, the bending stress is greatest in the center of the specimen (highest deflection). At this point, the greatest bending moment is always present. From the central pressure point, the bending moment decreases linearly in both directions toward the bearings. The material is subjected to pressure on its inner side and tension on its outer side. In the outer fibers of the specimen, the bending stress (tensile and compressive stress) is greatest and decreases inwards toward the neutral fiber. This is also called inhomogeneous stress distribution.

If the partially plastically deformed specimen is relieved during the bending test by raising the test punch, only the internal stresses (residual stresses) present in the material and the resulting torque are still effective. This will partially reshape the sample.

#### Bending behavior of ductile materials

If the bending stress in the sample made of a ductile material is lower than the limit stress of the plastic deformation, the bending stress is exclusively elastic. As the bending stress increases, the yield strength (critical stress) is exceeded first in the peripheral areas of the specimen. These areas then deform plastically (the so-called material flow). The limit yield point is the limit bending stress up to which easily deformable materials can be loaded by bending without permanent deformation in the marginal area.

The moment this kind of deformation occurs can be determined directly from the test punch: The deflection is measured in relation to the force applied. The determined values are shown in a deflection-force diagram. With deflection increasing steadily, more and more internal areas of the specimen are involved in the plastic deformation. This is a result of the stress increase. For steels, for example, the limit yield point is between 10 to 20 percent higher than the yield strength due to the linear stress increase. If the yield strength is exceeded in the edge fibers during the bending test, the inner and exclusively elastically stressed fibers impede the flow movement.

Bending tests with ductile materials are different from those performed with brittle materials: Tough materials can be subjected to extreme plastic deformation, but they cannot be broken, no matter how strong the applied force is. In the worst case, the specimen would be pulled through between the bearings. Therefore, a bending test with a ductile sample is finished when the yield point is exceeded. The bending strength of ductile materials is determined by the point in time at which the plastic deformation occurs.

### Bending behavior of brittle materials

Specimens made of brittle materials show a different bending behavior during materials testing. They break without clearly visible material flow behavior. Therefore, the determination of the limit yield point is more complicated for brittle materials. In order to be able to determine the bending strength nevertheless, the maximum bending stress at which the sample breaks is determined. However, the bending strength is a fictitious value that is not identical to the bending stress actually occurring in the material. Another characteristic of bending tests with brittle materials is the fracture deflection. This technical term describes the greatest possible deflection of a specimen shortly before fracture.The fracture deflection depends on the support width: Larger distances between the bearings allow for greater deflections. In order to check the strength of brittle materials, the bending test is often more suitable than the tensile test, because the materials are subjected to bending stress only. If this sample were to be subjected to a tensile test, it would break prematurely and measurement problems would occur. For certain brittle materials, the tensile test is therefore replaced by the bending test. According to DIN EN ISO 178, these critical materials include thermosetting sheets and molding materials, thermoplastic injection molding compounds and fiber-reinforced plastics.

### Types of bending tests

When testing materials using a bending test, a distinction is made between the 1-, 3- and 4-point bending test, depending on the number of pressure points and the type of specimen support.

#### 1-point bending test

The bending test procedure when using the 1-point bending device is as follows: The specimen is clamped at one end and its exposed side is loaded with the test punch. Following, the flexural modulus is calculated. A flexural modulus or bending-elastic modulus is the ratio of the maximum fiber stress to the maximum strain within the yield point.

#### 3-point bending test

The 3-point bending test bears this name because there are three pressure points in this test setup: Two supports and a centrally loaded test punch. The specimen lies crosswise on the supports and protrudes at the sides. The 3-point bending test is the most frequently performed bending test. However, it has the disadvantage that in addition to the compressive and tensile forces exerted, transverse forces are also effective in the material. Because of this disadvantage, the 4-point bending test was developed at that time.

If the bending moment that occurs is represented graphically, the 3-point bending test forms a triangle whose tip corresponds to the upper, central pressure point. DIN EN ISO 178 imposes the 3- and 4-point checking fixture for determining the bending properties and the elastic modulus (Young’s modulus).

#### 4-point bending test

In the 4-point bending test, the checking fixture differs from the 3-point bending test only in its test punch. Instead of the single punch applying force in the center, a double punch is used. There is a constant bending moment in the area between the two upper pressure points. Transverse forces do not occur in this area. The graphical representation of the bending moment in the 4-point bending test shows a trapezoid.

The bending test achieves more accurate measuring results for fiber-reinforced plastics. However, the checking fixture used is more complicated to handle and more expensive to purchase. According to DIN EN ISO 14125, 3- and 4-point bending test setups can also be used for these materials. They cause the specimen to break. Since further stresses and geometric effects occur, especially at greater deflection due to friction and Hertzian stress, the bending stress and edge fiber strain must also be corrected in these checking fixtures.

### Conclusion

Bending tests are performed with standardized samples and three or four pressure points (3-point, 4-point bending test). They either result in the destruction of the specimen or in its plastic deformation (only with ductile materials). The latest generation of optical metrology delivers far more accurate results than conventional measuring procedures.