Three-point bending flexural test | setup and implementation simply explained

The three-point bending flexural test is used to determine material properties such as the flexural yield point, flexural offset yield point, and ultimate flexural strength. A standardized specimen is placed on two supports and subjected to increasing force from a centrally positioned loading fin until plastic deformation or fracture occurs. This test is particularly relevant for brittle materials such as cemented carbides, tool steels, and grey cast iron.

The maximum stress occurs at the midpoint of the specimen, where the bending moment is greatest. The outer fibers experience tensile stress, while the inner fibers are subjected to compressive stress. The resulting flexural stresses are highest at the surface fibers and decrease towards the neutral axis, which remains unstressed. Unlike the uniform stress distribution seen in tensile or compression tests, the bending test produces a non-uniform stress distribution, with a linear gradient in the elastic range. These stresses can be calculated using the bending equation.

For ductile materials, the specimen remains elastic as long as the applied stress does not exceed the material’s limit. Initially, plastic deformation only occurs in the surface layers, while the inner region remains elastic. Upon unloading, residual stresses remain in the material. The flexural yield point defines the maximum stress that can be applied without permanent deformation. The deflection of the specimen is measured to distinguish between elastic and plastic behavior. Unlike the distinct yield point observed in tensile tests, the flexural test exhibits a gradual transition as the inner regions increasingly participate in plastic deformation.

The obstruction of flowing effect causes the flexural yield point to be 10–20% higher than the tensile yield point because the inner elastic regions constrain the deformation of the surface layers. For materials without a distinct yield point, a 0.2% flexural offset yield point can be defined, similar to the 0.2% offset yield point in tensile testing. The flexural strain is directly proportional to the specimen’s deflection and can be determined mathematically.

Brittle materials, on the other hand, hardly show any plastic deformation and break without a recognizable yield point. The flexural strength indicates the stress at which the fracture occurs. As the stress distribution at break is no longer linear, this is a fictitious value. The fracture deflection describes how much a sample deflects immediately before fracture.

The bending test is often more suitable for brittle materials than the tensile test, as even small misalignments can cause high bending stresses. The classic 3-point bending test involves shear forces, which is why the 4-point bending test was developed for more precise analyses. Here, a double load ensures a shear force-free area with a constant bending moment.

In addition to determining strength values, the bending test can also be used to determine the modulus of elasticity. The elastic deflection depends on the bending moment, the specimen geometry, and the Young's modulus. The greater the flexural rigidity (the product of the Young's modulus and the area moment of inertia), the less the specimen deflects.

If the specimen undergoes plastic deformation, the stress distribution changes. Without strain hardening, the stress in the surface fibers remains constant, while only the inner regions continue to deform. In materials with strain hardening, the stress in the surface fibers continues to increase, while the distribution flattens toward the neutral axis. In a fully plastic state, the stress distribution transitions from a linear shape to a rectangular profile.

After unloading, residual stresses remain in the material, causing partial recovery of the deformation. They result from the difference between the actual stress and the theoretical stress described by Hooke’s law.

In grey cast iron, the stress distribution is unique because the Young’s modulus depends on the applied stress, and the material withstands compressive stress better than tensile stress. This results in an asymmetrical stress distribution, causing the neutral axis to shift toward the compressive stress region.

00:00 Test setup
00:47 Stress distribution
03:32 Flexural stresses
05:37 Testing of ductile materials
06:28 Flexural yield point
08:05 obstruction of flowing / Flexural offset yield point
09:00 Flexural strain
09:53 Testing of brittle materials (ultimate flexural strength)
11:04 Brittle materials in the tensile test
11:34 Four point bending flexural test
12:08 Determination of the Young’s modulus
13:19 Calculating the flexural strain
14:06 Stress distribution without strain hardening
14:58 Stress distribution with strain hardening
16:10 Residual stresses
16:55 Stress distribution for grey cast iron

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