“…The metallographic methods are also described in the references [ 5 , 11 , 12 , 13 ]. In these experiments, cracks have been described by different measures, i.e., crack density determined on cross sections by light microscopy [ 5 , 12 ], crack volume determined by X-ray microtomography [ 13 ] and total crack length per area determined on cross sections by light microscopy [ 11 ]. To compare these different crack measures, we suggest a crack characteristic value C, which is defined by the ratio of the crack measure with nanoparticles to the maximum crack measure without nanoparticles, equations (1–3).…”