July 13, 2017 at 7:25 PM by Dr. Drang
As I was brushing my teeth before going to bed last night, my toothbrush broke. I set it aside to take a look at today, and you lucky readers will get to see what I found.
This isn’t the first time I’ve blogged about something in my house that broke. There was the flushing arm of the toilet, the garage door spring, and my wife’s glasses. Those all failed in fatigue, the progressive growth of a crack under cyclic loading, and so did the toothbrush.
Here’s a side view of the broken halves. I’ve oriented them to suggest how the break occurred. My teeth push out on the brush,1 and I hold the handle just about where the break is. The toothbrush, therefore, acts like a cantilever beam with high tensile stresses on the brush side of the handle near my hand. It’s not a coincidence that it broke where the tensile stresses are high.
How do I know it failed in fatigue? For that, we have to look at the fracture surfaces. Here’s the fracture surface on the bottom half of the handle,
and here’s the mating fracture surface on the top (brush) half,
The markings on the surfaces, which are made easier to see by strong side lighting, tell us that the fracture started in the lower left corner of the bottom fracture surface (the lower right corner of the top fracture surface) and grew via fatigue through that zone that looks like a set of parallel circular arcs. Let’s zoom in on those areas.
Now you can see those parallel arcs better. They represent the extent of the crack at different points in its growth history. This area is called the fatigue zone.
Last night, before I started brushing, the edge of the crack had grown to the outermost arc. When I started to brush, I put enough load on it to break the handle the rest of the way through. All of the fracture except the small fatigue zone near the corner broke at once. This larger fracture area is called the overload zone.
You may have noticed that all four examples I’ve blogged about have been fatigue failures. That’s partly because fatigue fracture surfaces are cool looking, but it’s also because fatigue is a common mode of failure in household objects. Environmental stress cracking is another interesting mode of failure and I’ve seen a lot of it, but unfortunately most of those failures are from my work and I can’t show you pictures of them. Maybe after I retire.
Do my teeth push on the brush or does the brush push on my teeth? Both. That’s what Newton’s Third Law is all about. ↩