My “Indian sister” who attended the seminar also wanted to know WHY the curvature reverses. So now that we’ve made clear that this does not always happen, I’d like to venture several factors that might give an idea about the answer. Note in Figure 8 (refer to previous blogs for referenced photos) that there is a visible “bowl” shape on the larger-diameter fragment, at least near the final separation area, and a small protrusion on the threaded fragment. I’m not sure WHY the crack reliably grows INTO the LARGER-diameter portion of the crack, but this (I have noticed with my own eyes) tends to be consistent. So, it’s possible that the center of the length of the crack front has its stress reduced as it penetrates into the larger diameter, maybe just a bit, compared to the ends of the crack that are closer to the surface of the part. The more highly loaded portion of the material just ahead of the crack now starts to separate at a faster rate.
Another question I have is why this crack front obviously started to reverse itself so rapidly. But it looks like there were initiations along maybe 80% of the circumference, so what we are seeing as a single reversed crack front is really a result of probably at least 10 smaller – and adjacent – crack fronts that have merged. It’s possible that the increased stress caused by the first cracks opened additional cracks adjacent to the original ones. So, the central cracks had the longest time to grow and the crack front didn’t so much reverse itself, as other cracks add their features to the initial ones.
Maybe I missed something, though. Are the teeth on the long piece a gear or a spline? I think it’s a spline, so I think my original diagnosis that this is a legitimate representation of a reversed crack front axially loaded part may stand. But I really don’t think this is what the original author was talking about. Furthermore, it’s possible that the crack reversal is due to vibratory influences that randomize the bending loading while the remaining load-supporting area diminishes in size.
As I thought further about this, it also occurred to me that once the crack front passes the diameter, even in the case of a single-initiation crack, there’s a “knife-edge” effect. The ends of the crack have less “meat” (or material) behind them to stiffen those end locations. Now that I understand that, I wonder why the parts shown in Figures 5 and 7 don’t have this feature, even though the fatigue area is clearly past the diameter.
One of my colleagues reminds me that the crack growth is always a result of the extremely localized conditions all along its length. He also reminds me that the farther the position from the neutral axis, when there is bending present, the higher the crack opening (normal) stresses. I am still trying to visualize in my mind how these facts would lead to crack-front curvature reversal. If you have any ideas, please speak up!
I think I will close by saying that I acknowledge I have not clearly answered the questions posed. However, I’m glad the questions were posed. And maybe someday I’ll figure it out. Thanks to Valar for asking this hard question. It is by demonstrating my thought processes that I hope to encourage others to try to truly understand, rather than taking what we find in published references to be “unquestionable truth.” We are doing science and engineering here, not religion. There’s a place for belief, so we can get things done. But when we struggle to understand at a deeper level, we understand more than the simple thing we set out to understand. Sometimes it might just be an understanding that we should not be so overly confident.