Energetic Size Effect for Tensile Loading

[person123]

TL;DR Summary

Is there no energetic size effect for tensile loading because there is no stress gradient?

For quasi-brittle materials, there is an energetic size effect as well as a statistical size effect, as described here. However, it seems to require a stress gradient for it to play a role, as in the example given with a 3-point bending test. The stress at the middle of the fracture process zone, which is less than the stress at crack initiation due to the stress gradient, is equal to the material strength at failure (it is at this location where the material is being damaged). This causes the maximum load to be greater than expected as the size of beam decreases. (It's very possible this is wrong, so please correct me if it is!)

In the case of tensile loading, the stress is (at least ideally) uniform, so there is no stress gradient. Would this then mean that there is no energetic size effect?

Thank you!