“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.

Smaller Deborah number inducing more serrated plastic flow of metallic glass

Spherical nano-indentations of Cu46Zr54 bulk metallic glass (BMG) model systems were performed using molecular dynamics (MD) computer simulations, focusing specifically on the physical origin of serrated plastic flow. The results demonstrate that there is a direct correlation between macroscopic flow serration and underlying irreversible rearrangement of atoms, which is strongly dependent on the loading (strain) rate and the temperature. The serrated plastic flow is, therefore, determined by the magnitude of such irreversible rearrangement that is inhomogeneous temporally. A dimensionless Deborah number is introduced to characterize the effects of strain rate and temperature on serrations. Our simulations are shown to compare favorably with the available experimental observations.

Scanning electron microscopy of Aspidogaster ijimai Kawamura, 1913 and A-conchicola Baer, 1827 (Aspidogastrea, Aspidogastridae) with reference to their fish definitive-host specificity

Two species of aspidogastreans, namely Aspidogaster ijimai and A. conchicola, were studied by scanning electron microscopy. In nine lakes and an old river course, the Tian'ezhou oxbow, investigated in the flood plain of the Yangtze River, A. ijimai was obtained from the common carp (Cyprinus carpio) in three lakes, and A. conchicola from the black carp Mylopharyngodon piceus in three lakes and the oxbow. In none of the localities, however, were the two species found together. It is suggested that A. ijimai may be considered as a specialist parasite for the common carp, at least in the flood-plain lakes of the Yangtze River. The two parasites were similar in many aspects of their morphology. Their bodies can both be separated into a dorsal part and a ventral disc, with the body surface of the dorsal part elevated by transverse folds, and the disc subdivided into alveoli by transverse and longitudinal septa, although the number of alveoli was different in the two species. The depression on the ventral surface of the neck region was prominent for both species, and their ventral disc was covered densely with non-ciliated bulbous papillae. The position of mouth, osmo-regulatory pore and marginal organ was also similar for A. ijimai and A. conchicola. However, microridges in the trough of the folds in the neck region and numerous small pits on the upper part of the septa were found exclusively in A. ijimai, but uniciliated sensory papillae in A. conchicola.