3 and 4 point bending tests: Method comparison and applications in materials evaluation

Introduction

Flexure tests are necessary to evaluate the mechanical properties of the material, allowing to know its resistance and deformability under applied loads. Among these, 3-point and 4-point bending tests are widely used in industry and scientific research. In this article, the fundamentals of these tests, their differences and their practical applications are described.

Fundamentals of bending tests

Bending tests consist of applying a progressive load on a specimen supported at two points until its deformation or fracture is reached. It is used to evaluate the mechanical resistance of a material under bending stresses and allows the determination of several properties such as:

Flexural modulus (Fm): Indicates the stiffness of the material under bending stresses and is defined as the ratio between stress and strain in the elastic phase. It is calculated with the equation:

Where:

• L = Distance between supports (mm or m)
• F = Applied load (N)
• b = Width of the specimen (mm or m)
• d = Height or thickness of the specimen (mm or m)
• δ = Deflection at the center of the specimen (mm or m)
• Flexural strain (εf): It is the relative dimensional change of the specimen under load and is calculated as:

Where δ is the maximum deflection at the center of the specimen.

Bending moment (M): It represents the tendency of an applied force to induce a rotation around a fixed point on the specimen and is calculated with:

In a three-point bending test.

• Elastic and plastic behavior: This refers to the response of the material before and after exceeding its elastic limit. During the elastic phase, deformation is reversible and follows Hooke’s law (σ=Eε). In the plastic phase, the material undergoes permanent deformations until fracture.

• Flexural fracture: This is the way in which the material breaks under bending load. It can occur as a brittle fracture (without significant plastic deformation) or ductile (with deformation prior to fracture).

These properties are determined using principles of classical mechanics and allow the performance of materials in structural and engineering applications to be evaluated.

Comparison between 3-point and 4-point bending tests

Although both techniques follow a similar principle, they differ in stress distribution, accuracy in the measurement of mechanical properties and representativeness of the results. While the 3-point bending test generates a stress concentration at a specific point, the 4-point bending test distributes the load more uniformly, providing more detailed information on the ductility and modulus of elasticity of the material. The selection between both tests depends on the type of material and the objective of the analysis, being fundamental to know their advantages and disadvantages for an adequate application.

• Differences in stress distribution: The main difference between the two tests lies in the way the load and bending moment are distributed:
• 3-point bending test: The load is applied in a single central point of the specimen, generating a maximum bending moment in that area; which generates a high stress concentration, facilitating the identification of the fracture initiation. It is ideal to analyze the mechanical properties of homogeneous and brittle materials such as plastics and ceramics.

The following video presents information on 3-point bending test with ZwickRoell.

• 4-point bending test: The load is distributed at two points equidistant from the center of the specimen, which generates a constant load zone between both force application points. This allows a uniform distribution of the bending moment, reducing stress concentration and providing a more accurate evaluation of the modulus of elasticity and ductility of the material. It is used for composite materials and anisotropic structures, such as wood or reinforced polymers.

• Advantages and disadvantages of test cases: Each type of test has advantages and disadvantages depending on the application context:
• Advantages of the 3-point test: Greater simplicity in execution, less equipment requirement and suitable for homogeneous materials.
• Disadvantages of the 3-point test: High stress concentration in the central point, which can generate localized failures and affect the representativeness of the results in anisotropic materials or with internal microdefects.
• Advantages of the 4-point test Advantages: More realistic representation of the material response under real loads, lower stress concentration, allowing better evaluation of the modulus of elasticity and ductility of the material.
• Disadvantages of the 4-point test: Greater complexity in preparation and execution, requires more advanced equipment and additional measurements with devices such as deflectometers.

Criteria for selecting the type of test

The choice between a 3-point or 4-point bending test depends on factors such as the nature of the material, the type of analysis required and the availability of equipment.

The 3-point bending test is recommended when homogeneous, brittle or low ductility materials are being evaluated, since the concentrated load allows rapid identification of their bending strength and fracture point.

The 4-point bending test is preferred for anisotropic materials, composites, or structures that require a more detailed analysis of the elastic and plastic behavior, due to the uniform distribution of the bending moment.

Applications of flexure tests in materials evaluation

These tests are applied to characterize the mechanical behavior of various materials under loading stresses, among which we have:

Metallic materials: These tests are used to evaluate the mechanical properties of materials such as ductility, mechanical strength and toughness. They are used in the validation of structural alloys and components subjected to cyclic or bending stresses, such as beams, springs, equipment and pipes, among others. The recommended tests are:

• Three-point bending to determine ultimate strength and deformation before fracture.
• Four-point bending to evaluate behavior under distributed loading conditions, such as in supporting structures and metal laminates.

Polymeric materials: In plastics and composite materials, flexural tests allow determination of modulus of elasticity, fracture toughness and long-term mechanical behavior. Recommended test:

• Three-point bending for rigid polymers, providing an efficient method for measuring flexural modulus.
• Four-point bending to evaluate flexible materials and fiber-reinforced composites, where load distribution avoids excessive stress concentrations.

Ceramics and glass: These materials have high compressive strength, but are brittle under tensile stresses. Flexure tests allow determining their mechanical resistance and their capacity to withstand loads without sudden failure. Recommended test:

• Three-point bending, since it concentrates stress at a specific point and allows precise identification of the fracture limit.
• In cases where it is necessary to evaluate the uniform stress distribution over a wider area, four-point bending can be used, although it is less common in ceramics.

Composite materials: Composite materials, such as those used in aerospace and automotive applications, require flexural testing to analyze the interaction between the matrix and the reinforcement. These tests help to optimize their design and ensure their reliability under actual use conditions. Recommended test:

• Four-point bending, as it provides a more accurate evaluation of material behavior without generating excessive stress concentrations. It is crucial for analyzing delamination and fracture in laminates.
• Three-point bending is used in initial studies or when a quick mechanical strength test is required.

Regulatory considerations and standards

Bending tests are regulated by various international standards, including:

• ASTM E290: Standard test methods for metallic materials by bending.
• ISO 7438: Regulates bending tests on metals to evaluate their ductility and strength.
• ASTM D790: Test methods for flexural properties of reinforced and unreinforced plastics.
• ISO 178: Flexure tests for rigid plastics. Defines procedures for the determination of flexural modulus properties in plastics and mechanical strength.
• ASTM C1161: Test methods for flexural strength of advanced ceramic materials.
• ISO 14704: Flexure tests on advanced ceramics.
• ASTM D7264: Test methods for flexural properties of fiber-reinforced composites.
• ISO 14125: Flexure tests for fiber-reinforced plastics.

Step-by-step for performing a 3-point and 4-point bending test

To ensure accurate and reproducible results, it is recommended to follow a standardized procedure from specimen preparation to interpretation of the results. The step-by-step procedure is detailed below.

• Specimen preparation: Before performing the test, it is essential to ensure that the specimen meets the necessary regulatory and structural requirements:
• Material selection: Determine the type of material to be evaluated according to the applicable standards (ISO 178, ASTM D790 or others).
• Verification of dimensions: Ensure that the specimen has the dimensions specified in the applicable standard.
• Visual inspection: Check that the specimen surface is free of visible defects that may affect the results.
• Test equipment configuration: The equipment used to perform flexure tests is a universal testing machine equipped with specific accessories for each type of test. Its correct configuration is key to obtain reliable measurements.

Its main components are:

• Universal testing machine: Applies the load in a controlled manner on the specimen.
• Support device: Formed by two adjustable supports that determine the distance between supports according to the length of the specimen.
• Load application device: In the 3-point bending test, a single load is applied in the center of the specimen. In the 4-point bending test, the load is distributed at two equidistant points.
• Load cell: Accurately measures the applied force.
• Extensometer or strain sensor: Records the deformation of the specimen to calculate its flexural modulus.
• Data acquisition software: Collects load, displacement and strain information to generate stress-strain curves.
• Equipment adjustments before the test: Place the supports in the testing machine with the appropriate spacing. Adjust the distance between supports according to the specimen length. Install the load application device, either single point (3-point bending) or double point (4-point bending).
• Load application: With the specimen correctly positioned on the supports, start the bending test. Apply the load in a controlled manner, ensuring a constant speed as established in the standard.

Record the evolution of load and strain as the specimen flexes.

• Measurement and analysis of results: During the test, key variables are monitored and recorded to evaluate the behavior of the material.
• Maximum applied force: The point at which the specimen reaches its strength limit is determined.
• Bending deformation: The bending of the specimen under load is measured.
• Calculation: The bending modulus and bending moment are calculated, using the applied force and displacement data.
• Identify material behavior: Elastic, plastic or flexural fracture.
• Interpretation and reporting of results: Once the test is completed, the data obtained are analyzed and compared with the standard values of the material evaluated.
• Comparison: Compare the results with the reference values to determine if the material meets the mechanical requirements.
• Generate a technical report: This report should include load vs. deformation graphs and conclusions on the performance of the material.

Conclusions

The 3-point and 4-point bending tests are fundamental tools for evaluating the strength and deformability of materials under applied loads. While the 3-point bending test is simpler and more suitable for homogeneous and brittle materials, the 4-point test offers a more accurate evaluation of ductility and modulus of elasticity, especially in anisotropic and composite materials. The choice between the two methods depends on the nature of the material, the type of analysis required and the availability of equipment.

These tests have applications in a wide range of industries, including metallurgy, polymers, ceramics and composites, with international standards regulating their execution. Their correct selection and application allow the design and reliability of materials in various industrial structures and components to be optimized.

References

1. https://es.scribd.com/document/448498064/ENSAYO-DE-FLEXION
2. https://www.zwickroell.com/es/sectores/papel-carton-y-papel-tisu/carton-corrugado-y-carton-compacto/ensayo-de-flexion-en-3-puntos/