Application Note | Three-Point Bending
3 Point Bend Test Using Microindentation
Flexural Modulus and Fracture Load of Delicate Rods at Micro-Scale Loads
Research & Experimental Testing
Pierre Leroux
Visual Design & Editorial
Andrew Shore
Introduction
The 3 point bend test is a common materials test and involves a wide range of loads. A broad range of samples (metals, composites, rock, concrete and plastics) are tested as flat or rectangular rods with various geometries. Samples are supported at each end while a load is applied to the middle (3 point bend). The data retrieved from the test can provide vital information about flexural strength, performance, durability and service life.
Importance of the Microindentation 3 Point Bend Test
Standard 3 point bend tests are not capable of the low, sensitive loads provided by microindentation and fail to provide adequately precise depth data for delicate samples. The NANOVEA nano or microindentation mode provides the ability to precisely measure the tensile elastic modulus and critical load of a wide range of sensitive materials.
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Measurement Objective
In this application, the NANOVEA Mechanical Tester, in microindentation mode, is used to measure the flexural strength (using 3 point bend) of rod samples (pasta) of different sizes to show a range of data, demonstrating both elastic and brittle characteristics. Using a flat tip indenter to apply a point load, we determine stiffness (Young’s modulus) and identify the critical loads at which the samples fracture.
NANOVEA PB1000 Large Platform
Mechanical Tester
Test Conditions
| Parameter | Value |
|---|---|
| Applied force (N) | 7 |
| Loading rate (N/min) | 1 |
| Unloading rate (N/min) | 1 |
| Indenter type | Flat, 1 mm |
Table 1: Indentation parameters.
Calculating Young’s Modulus
Deflection is the displacement of a structural element under a load. For fixed-ended beams with a point load in the center, deflection is related to Young’s modulus by δ = P·L³/(192·E·I), where P is the applied point load, L is the length of the beam, I is the moment of inertia and E is Young’s modulus. The inertia of a rod is modeled by (π/4)·R⁴. Given a measured load (P) at depth (δ) from the mechanical tester, Young’s modulus is easily obtained.
Results
| Specimen (rod) | Sample 1 | Sample 2 | Sample 3 |
|---|---|---|---|
| Diameter (mm) | 0.90 | 0.95 | 1.67 |
| L (mm) | 25.00 | 25.00 | 25.00 |
| Inertia | 0.71 | 0.75 | 1.31 |
| Load (N) | 1.00 | 1.00 | 1.00 |
| Depth (mm) | 0.46 | 0.38 | 0.07 |
| Young’s modulus (N/mm²) | 252.43 | 288.38 | 893.67 |
Table 2: Young’s modulus of the rod samples.
Critical Load
The mechanical tester identifies the critical depth and load at which the sample fractures.
| Specimen (rod) | Sample 1 | Sample 2 | Sample 3 |
|---|---|---|---|
| Critical depth (mm) | 0.601 | 0.486 | 0.431 |
| Critical load (N) | 1.38 | 1.33 | 5.72 |
Table 3: Critical depth and load at fracture.
Conclusion
In conclusion, we have shown how the NANOVEA Mechanical Tester, in microindentation mode, can determine the tensile elastic modulus using a 3 point bend test. Furthermore, it was illustrated that, thanks to the precise load feedback loop, the system can be used to identify the points, or critical loads and depths, at which brittle samples fail. The system’s fast response provided quick removal of the load when testing the smaller sample before complete fracture failure.
Displacement of up to 50 mm and loads from the mN range to 200 N make the Mechanical Tester an ideal tool for study using the 3 point bend method. The system can also extend into the nano range for applications where fracture loads are in the sub-mN range. It can also remove the load at a specific unloading rate and plot the return depth to indicate the material’s overall elasticity in returning to its original shape, and multiple loading at the same load could be used to study fatigue. This 3 point bending test opens opportunities for studying strengths and materials under different loading conditions and geometries, beyond what is traditionally expected of a nano or micromechanical system.
Frequently Asked Questions About Micro Three-Point Bending
Why use microindentation for a 3-point bend test?
Standard bend testers cannot apply the low, sensitive loads or give the precise depth data that delicate samples need; the micro module measures tensile elastic modulus and critical load on sensitive materials.
How was the test done?
Rods of pasta were supported at both ends over 25 mm and loaded at the middle with a 1 mm flat indenter at 1 N/min, up to 7 N.
How is Young’s modulus calculated?
From the deflection of a fixed-end beam under a central point load, δ = P·L³/(192·E·I), using the measured depth at a given load.
What moduli were measured?
252.43, 288.38 and 893.67 N/mm² for rods of 0.90, 0.95 and 1.67 mm diameter.
At what load did the rods break?
At 1.38 N (0.601 mm depth), 1.33 N (0.486 mm) and 5.72 N (0.431 mm) for Samples 1 to 3.
What else can the method do?
Unload at a set rate to measure elastic recovery, load repeatedly to study fatigue, and extend to the nano range for sub-mN fracture loads.
