Discussion of fracture paper #28 - Rate effects and dynamic toughness of concrete

The paper "Estimating static/dynamic strength of notched unreinforced concrete under mixed-mode I/II loading" by N. Alanazi and L. Susmel in Engineering Fracture Mechanics 240 (2020) 107329, pp. 1-18, is a readworthy and very interesting paper. Extensive fracture mechanical testing of concrete is throughly described in the paper. The tests are performed for different fracture mode mixities applied to test specimens with different notch root radii at various elevated loading rates. 

According to the experimental results the strength of concrete increases as the loading rate increases. The mixed-mode loading conditions refers to the stress distribution around the original notch. Fracture starts in all cases at a half circular notch bottom. Initiation of a mode I cracks are anticipated and were clearly observed in all cases. The position of maximum tensile stress along the notch root as predicted by assuming, isotropic and linear elastic material properties correlates very nicely with where the cracks initiate. The selected crack initiation criterion is based on stresses at, or alternatively geometrically weighted inside, a region ahead of the crack tip. The linear extent of the region is material dependent. The criterion, used with a loading rate motivated modification, is strongly supported by the result.

The result regarding the rate dependence is different from what is observed for ductile metals, where at high strain rate dislocation motion is limited. This reduces the plastic deformation and increases the near tip stress level. It therefore decreases the observed toughness as opposed to what happens in concrete. Should the stress level or energy release rate exceed a critical value, the crack accelerates until the overshooting energy is balanced by inertia as described by Freund and Hutchinson (1985). Usually this means a substantial part of the elastic wave speed. For concrete I guess this must mean a couple of km/s. This is outside the scope of the present paper but a related question arises: What could be the source of the strain rate effects that are observed? Plasticity/nonlinearities are mentioned. I would possibly suggest for damage as well. We know that reinforced ceramics are affected by crack bridging and micro-crack clusters appearing along the crack path or offside it. If such elements are present then both decreased and increased toughnesses may be anticipated according to studies by Budiansky, Amazigo and Evans (1988) and Gudmundson (1990). Could concrete be influenced by the presence of crack bridging elements or micro-cracks or anything related? If not, what could be a plausible guess?  

Does anyone know or have suggestions that could lead forward? Perhaps the authors of the paper or anyone wishes to comment. Please, don't hesitate to ask a question or provide other thoughts regarding the paper, the method, or anything related.

Per Ståhle