Do I have too much chafer strip showing after fixing a puncture? I have had two innertubes explode on me on my bicycle, on the same wheel and tire. The first time I was inflating my inner tube after aquiring a puncture. On this occassion I was pumping my tires (rated at 50-90psi) beyond 70psi.

After the first explosion I replaced the innertube, being careful to avoid pinching. I pumped up to 60psi. A few days later the inner tube exploded while the bike was hanging on it's rack.

After becoming the recipient of yet another puncture on the same tire (city streets...), I am wary of my inner tube installation. This time I inserted the inner tube under the tire, moved the tire beed back to the inner rim, and carefully checked to ensure that no pinching occurred. I have now inflated the tire to 60psi.

My concern is that, despite being very careful, I have sections where beed appears to be showing. My question is, given the amount of bead showing (about 2mm in one section), could the inflation cause another inner tube burst?
The visible strip sticking out from the top of the rim and inside the line is in fact the Chafer strip. This is on the tire to prevent the bead hook on the rim from cutting into the tire. 

The bead is the wire or in the case of folding tire such as the x'plor ush Kevlar ring on the edge of each tire. When seating the tire the bead is place inside the bead hook on the rim with a tube inside.

Rims have a few different standards and many proprietary designs so do not have a consistent inner sidewall height. The tire bead when seated actually sits at the bottom of the rim rather than on the hook, so the amount of Chafer strip shown is dependent on the depth of the rim.

The amount of Chafer strip showing would not be a cause of your tube exploding and there are many answers that address punctures  but my thought would be something loose in the tire.