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Biological Three-Point Bending & Fracture Toughness Testing

Just as with other mechanical tests, three-point bending (3PB) and fracture toughness tests provide useful information about a material. 3PB and fracture toughness are both compressive tests. Their setups are very similar, but fracture toughness testing is essentially a variation of 3PB with additional steps. Both tests tell us different information about how materials act, such as strength, elasticity, or toughness. This information can be useful for material selection, such as for an effective heart valve or hip replacement.

In biological materials, such as bone, this information can help us understand the consequences of medications, treatments, or lifestyles. I use both of these methods regularly to understand how aging and fatty diets impact bone health on a mechanical level. I will use bone as an example throughout both methods.

An example of the general set-up for three-point bending or fracture toughness testing for mouse and rat long bones. Where the bones span beetween 2 points that hold it up. Then a third point loads the bone from above between the other two points. redit to the author.
An example of the general set-up for three-point bending or fracture toughness testing for mouse and rat long bones. Where the bones span between two points that hold the sample up. Then a third point loads the bone from above between the other two points. Credit to the author.

There are standards for mechanical tests for each material class. Biological materials often use these standards as a starting point. For example, many standards for mechanical tests outline ideal sample dimensions. Sometimes we can machine samples to these dimensions, but sometimes we have to work with what we have.

For example, a procedure for mechanical testing on tissues and biomaterials from Biomomentum states that the ideal ratio of sample width to length should be more than 16. However, if a mouse bone was 16 times as long as it was wide, mice would be terrifying.

Biological materials do not always fit neatly into the categories defined by these standards. Therefore, it is always important to know the material and the assumptions of the tests and calculations you are working with.

A useful resource for various tissue and biomaterials mechanical testing information is Biomomentum.

While using standard-inspired setups can make our lives easier, it can limit the strength of the conclusions we can draw about biological material. Better methods are available for certain measures we get from 3PB or fracture toughness, but they can require more time and money. If you have no idea what a material/tissue might be doing mechanically, it may not be worth starting with the more costly option. 3PB is a relatively fast, cheap, and easy-to-perform compression bending method, and the results can hint if we should do more involved testing.

For both of these tests on biological materials, we need accurate geometric information. This information is often obtained from non-invasive methods, such as computed tomography (CT scans). This helps us calculate more accurate values.

General Assumptions for Both Tests

  • A general rule of thumb is that any biological material being tested by either of these methods will likely not meet all of the assumptions. This includes sample size, cross-sectional shape, and orientation. Meaning that the results are estimates.

  • For a simple stress-strain test the load is applied relatively slowly and uniformly over a cross-section.

  • The geometry of the sample is not changing over time as the load is applied.

  • The geometry of the test fixture matters! We assume this is consistent between all our samples of a study. For example, the span between supports is in the calculations. If comparing between studies, make sure this is consistent or normalize the values.

  • Simple 3PB generally assumes that material is homogenous and fibers are not interacting.

  • All load is normal to the surface so the center of the sample is experiencing max stress and strain.

  • There are sign conventions that tension stresses are positive (+) and compression stresses are negative (-). Thus, for compression tests like three-point bending and fracture toughness, your initial force-displacement and stress-strain curves may appear negative if you do not flip the signs.

Three-Point Bending (3PB)

Notes on 3PB Measurement Definitions and Usage

Drawbacks of 3PB

Fracture Toughness Testing

Notes & Additional Steps of Fracture Toughness Testing

Drawbacks of Fracture Toughness Testing


Silva MJ. Bone Mechanical Testing by Three-Point Bending. [PDF available online] 2016.

Ritchie RO, Koester KJ, Ionova S, Yao W, Lane NE, Ager JW 3rd. Measurement of the toughness of bone: a tutorial with special reference to small animal studies. Bone [Internet]. 2008 Nov;43(5):798–812. Available from:

Turner CH, Burr DB. Basic biomechanical measurements of bone: a tutorial. Bone [Internet]. 1993 Jul;14(4):595–608. Available from:


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