I would agree with Liz that it looks very much like the right umbo of an Ostrea sp. - possibly Ostrea edulis.
If you want to get into studying and recording marine shell fragmentation, a good starting point is Zuschin, M., Stachowitsch, M., and Stanton, R.J., Jr., 2003. Patterns and processes of shell fragmentation in modern and ancient marine environments. Earth-Science Reviews, 63, pp. 33–82. doi: 10.1016/S0012-8252(03)00014-X. although this doesn't deal with deliberate breakage by humans. Jessica Winder and I published a very brief note on the different rates of survival of left and right valves of Ostrea edulis in Britain a couple of years ago, which you can find here http://bit.ly/pWBWl2
Matt
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