On the probabilistic–deterministic transition involved in a fragmentation process of brittle materials

Dynamic fragmentation of ceramics, signature of defects and scaling of fragment sizes

“…Ultimately, this suggests that the energetic criterion governs the dynamic regime. Indeed, statistical predictions would have inferred a dependence of the power exponent to the initial distribution of defects (Hild et al, 2003), and an impulse criterion would have lead to an inverse one-third exponent (Grady, 2006;Tuler and Butcher, 1968). Our results confirm that, even though dynamic brittle fragmentation is not energy-equilibrated, its asymptotic behavior is energy controlled.…”

“…If they propagate fast, the waves encompass a large region which may prevent numerous defects from getting damaged. Hild et al (2003) went further by considering that once a defect is encompassed by a wave, it is definitively protected and cannot get damaged anymore. In this case, the communication between defects is then prevailing.…”

Tensile strength of the brittle materials, probabilistic or deterministic approach?

“…Recently, the study concerning the strength o f the brittle materials under high loading rate has become an important subject regarding to several industrial applications as foreign object impact and thermal shock problem. It is well known that the brittle materials exhibit the strength increase under high loading applications [4][5][6][7]. The advanced study was carried out to demonstrate more strength variation sensitivity reason under the high loading application for the brittle materials than the ductile materials via Weibull's modulus [8].…”

“…These fracture mechanisms have been interpreted as a damage phenomenon in the literature [5]. Some works show that the mentioned dynamic brittle fracture mechanism provides less scatter value than the static's one and so, the deterministic approach was proposed in [4]. According to their works, the brittle material exhibits one strength value if it is subjected to the high loading rate.…”

“…In another work [4], a deterministic approach for the mentioned condition loading was proposed to supersede the probabilistic one based on the obtained deterministic strength value under high loading rate. Accordingly, we conclude that the brittle materials, especially the glass material, subjected to impact condition should not be considered as a "simple" dynamic problem due to the very high sensitivity contact zone and corresponding defect activations regarding to impact and CSHPB.…”