If the volume of the specimen is halved, which is the case when halving the thickness, we expect the absorbed energy would be halved as well. But be careful about the slenderness effects which come into account when the with/thk. ratio inceases. In this case a tendency to lateral buckling increases, which tends to decrease the absorbed energy of failure. If this would be the case, you can readily see it in the specimen as some kind of torsion happens in it, instead of a plain failure surface in the notch position. I haven't practice it in an standard charpy test, but I have seen it in a notched plug whcih was supposed to fail under shear after the load increased a certain amount. The plug failed by a torsional buckling instead of shear in a lower load as the thk. was so small.