arunmrao's post above is on target. For a fairly straightforward set of assumptions, a fracture mechanics approach may be able to elicit the same answer.
Another thought--somebody please help me on this term if I am wrong. I recall that this is known as the "Theory of Verisimilitude" (but I could be wrong on the term). This is commonly used in fluids and structures testing. Essentially, if one can qualify the dependency of terms for specific function, then one can appropriately scale terms as the model scales. This is commonly taught in an undergrad fluids course.
If you could describe the behavior using a basic functional relationship, you could apply this and arrive at the equivalent energy. However, this may not work for your specific problem.
What are the dimensions of the specimen, and are there notches, etc? Also, is the material brittle or ductile? If it is ductile, it would definitely be hard to characterize the effect on the energy due to this change.
Brad