Rebuttal: Shallow and deep scratch tests as powerful alternatives to assess the fracture properties of quasi-brittle materials

• We elucidate the mechanisms of crack initiation and propagation in quasi-static scratch tests.
• Knowing the energy release rate function, we apply the Size Effect Law to dissimilar specimens.
• The SEL is written for both 2-D and 3-D similitude cases in scratch testing.
• Scratch tests provide a means to assess the fracture toughness even with shallow depths.

We recall the principles of Dimensional Analysis. We do not violate the principle of geometrical similarity: the Size Effect Law can be applied to dissimilar specimens when the energy release function is known. By considering a two-dimensional and a three-dimensional similitude case, we can predict the fracture toughness using scratch tests. Finally, we recall our Scratch Fracture Mechanics model that was validated via an exhaustive campaign of numerical simulations. In sum, whether deep or shallow, the ductile-to-brittle transition in scratch tests is governed by the out-of-plane width and the width-to-depth ratio.