I Size Effect on Structural Strength

[person123]

TL;DR Summary

I want to check if my intuition behind the size effect is generally correct, even if I don't fully understand the derivation.

I'm using the wikipedia page on Size Effect to get an understanding of it. It identifies Statistical and Energetic size effects and two types within energetic.

I believe I understand statistical, as it seems to essentially say that assuming there's some variation in the material strength, the larger the object, the weaker the weakest points, decreasing the overall strength.

I'm a bit less sure on the first type for energetic size effect. It takes a beam undergoing bending, with a weaker region on the side undergoing tension due to microcracks. I think it argues that because that region can take on less stress, in order to provide the same internal moment, there must be a greater max stress. However, the derivation doesn't seem to make sense to me (I could go into more detail on that), and I was also wondering if it only applies for the specific situation of a bending beam with microcracks at the tensile region.

The second type seems to apply when a significant crack has already formed. I think it's arguing that as the beam is scaled up, the cracks scales as well. By understanding the relation between the change in surface energy and elastic energy you can show that a larger crack will fail at a lower stress. This seems essentially equivalent to the derivation of Griffith's Criterion. Are there significant differences, and would this also apply to a beam just undergoing uniaxial tension for example?

 

[trurle]

I'm a bit less sure on the first type for energetic size effect. It takes a beam undergoing bending, with a weaker region on the side undergoing tension due to microcracks. I think it argues that because that region can take on less stress, in order to provide the same internal moment, there must be a greater max stress. However, the derivation doesn't seem to make sense to me (I could go into more detail on that), and I was also wondering if it only applies for the specific situation of a bending beam with microcracks at the tensile region.

Same consideration (of finite thickness of damage zone) is applicable for compression too. For example, cracks initiate in ring-shaped zone around entry point of rod forced into concrete, not only on rod surface.

The second type seems to apply when a significant crack has already formed. I think it's arguing that as the beam is scaled up, the cracks scales as well. By understanding the relation between the change in surface energy and elastic energy you can show that a larger crack will fail at a lower stress. This seems essentially equivalent to the derivation of Griffith's Criterion. Are there significant differences, and would this also apply to a beam just undergoing uniaxial tension for example?

That chapter of wikipedia article "size effect" is based on Bazant's law, which is extension of Irwin`'s equation for ductile materials which is derived from Griffith`s equation. The Griffith's equation itself is applicable only for brittle materials.