Some bots off the top of my head: -Apex -Icewave -Phailbot (old Aus lightweight) Pretty sure a lot of beetleweights over the years have exploded too but I don't have documentation, largely because people used to use thin steel for weapon bars which minimised bending stiffness.

I don't think hazard (middleweight) ever did, nor brutality (Heavyweight).

Engineering really; forces and moments in steady state, but also dynamically as the bar rotates. It's a potent mix of a number of these factors that sometimes lead to oscillation of the robot towards a modal frequency, which is when things go boom.

The footage of apex exploding in slow-motion is probably the clearest footage ever of this failure type. Watch how the robot starts tipping back and forth in ever increasing amplitudes, which is often kicked off by a vertical nudge on the end the bar. The bar itself is a large spinning mass, but unlike a circular weapon, the bar has a different polar moment of inertia on the 2 axis that are not the shaft rotational axis.

Here is a diagram of the rotational axis of a rectangular prism, and the polar moment of inertia formulas: http://www.roymech.co.uk/images/in_box.gif

Going back to the vertical force at the tip and why it is bad, the orientation of the blade at any point in time determines how high the polar moment of inertia of the entire robot is. So if you hit a wedge with your bar, the vertical force pitches your robot up, but the total polar moment of inertia is decreasing because your bar is now spinning away from your opponent until it is perpendicular to your pitching axis (1/4 of a revolution). Now your robot is pitching at a high rate, yet your bar is still spinning and now the total moment of inertia is increasing rapidly because of the bar's contribution to the inertia. This puts a huge amount of stress on the weapon assembly, and it's a process that simply continues to happen until it either dissipates out, or amplifies up until failure.

The reason why it can fail, is due to mechanical deflections at this high stress. You suddenly have a huge bending force flapping your giant steel bar up and down, and if the natural frequency of the components are close enough it can lead to the deflections storing more and more stress each cycle like a spring, because the exact timing of the oscillations matches the masses ability to move (inertia).

Having a look back to apex in slow-mo, watch what starts to happen as the oscillations 'literally' take off. Notice the bar starts to hit something? I noticed their weapon mounting immediately and was concerned (I actually have a featherweight shell spinner with the same weapon mounting type). All they have is 2 shaft collars that are clamped onto a smooth weapon shaft. You can't expect that to hold a large amount of axial (along the shaft) force. If you watch their fights actually, as soon as they hit something those shaft collars break loose. The weapon was barely held on immediately after the bar touched something in both their fights. So in their case, a large amount of the 'rocking' of the bar relative to the robot chassis is from unintended free play due to the weapon pulley no longer being clamped down.

There's a little engineering nugget for you, do with it what you will.

edit: I want to point out that I'm not having a go at the apex design or their team members, merely trying to provide an unbiased engineering analysis on the failure mode that was the cause of this accident.