The size effect in concrete is well studied since Bazant's famous paper (1983). The main source of size effect is found to be energy available from fracture process zone ahead of a crack tip. As we know concrete is a pressure sensitive material, under confinement yield surface of concrete will expand, meaning size of fracture process zone will also increase. In such situation, shall we observe any size effect in concrete?
"The main source of size effect is found to be energy available from fracture process zone ahead of a crack tip. " I feel a little uncomfortable with this statement.
This is my understanding as a layman with some graduate coursework background. The elastic energy stored in the structure is dissipated by formation of crack( or micro-cracks). For larger size structure, more elastic energy (per unit crack length) is available for formation of a crack. This brings size dependent non-linearity in the failure load of the structure. As a result, the critical load P which is required for failure does not increase linearly with size of the structure. When translated into stress terms, the critical failure stress is not constant and decreases with size.
I am not convinced that the size of FPZ has a role to play in explaining the non-linearity. This non-linearity is also observed in metals which have negligible FPZ(?).
This is my view and I am open to different viewpoint!
Dear Mahendra Gattu,
Thanks for the suggestion. However in Bazant's 1984 paper on 'SIZE EFFECT IN BLUNT FRACTURE:CONCRETE, ROCK, METAL', while discussing the energetic size effect with some example (Page 521), the energy release for fracture is mainly coming from crack band and stress relief zone(eqn.2), not from the absolute size of the structure, later in energy balance eqn. he introduce size(d) to account for self similar size effect(a/d = constant). In his derivation, in absence of self similar sizes(a/d = constant), size effect of strength will become dependent only on 'a'.
This is what I understood and I am open to other viewpoints.
Thank you for pointing out this paper. I read the portions you indicate.
I had the following scenario in my mind when I wrote that comment:
A double cantilevered specimen of length 'a' pulled apart on either side. The applied load is P and displacement is u. The elastic energy stored in 1/2 Pu when there is no crack initiation. u = Pa^3/3EI and the energy is 2* P^2a^3/6EI.
When does the crack form?
On one hand the displacement can increase and on other hand crack can propagate. For an incremental , Gf be the energy released.
When partial U/ partial P > partial U/ partial a, the body can go to lower energy state when the crack advances by .
When the load applied P_appl = 3EI Gf/a^3, the crack advances. My idea was for larger a, the P_appl is small. However, after some thought this is layman's way to look at this problem. Anyway, I think I am on same side as you regarding this part of the discussion.
When you said self-similar, I understand that what happens at the crack tip is independent of the size of the structure. The paper has the derivation for FPZ of concrete and plastic yielding( point size FPZ) which demonstrate size dependency of \sigma_N. Also there are the last two paragraphs of page 525.
At this point, I have the following unknowns:
does the crack propagate in a stable manner when the control variable is displacement.
In the derivation for non-negligible FPZ and plastic yielding in the paper you mentioned, the \sigma_N deals with the crack formation only (correct me ..). Does the structure fail once this \sigma_N is reached? What exactly is this is \sigma_N?
There are some resistance curves for materials which are developed by material science ppl. The are used for deterimining the stability of crack growth
partial G/ partial a < partial Gr/ partial \Delta a. They are not used anywhere. At this point, I stop train of thought.
Me
A slight addition: In the latest papers, there is g(alpha) and g'(alpha) term... which takes care of crack propagation.
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