Spallation analysis with a closed trans-scale formulation damage evolution

A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbers De* and De, Mach number M and damage number S. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is deter-mined by Deborah number De+. Deborah number De* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbers De* and De, Mach number M and damage number S is discussed.

The interaction between poly(vinylpyrrolidone) and reversed micelles of water/AOT/n-heptane

The interactions between poly(vinylpyrrolidone) (PVP) and the reversed micelles composed of water, AOT, and n-heptane are investigated with the aid of phase diagram, measurements of conductivity and viscosity, Fourier transform infrared (FTIR) spectrum, and dynamic light scattering (DLS). The phase diagrams of water/AOT/heptane in the presence of and absence of PVP are given. The conductivity of the water/AOT/heptane reversed micelle without PVP initially increases and then decreases with the increase of water content, ω0 (the molar ratio of water to AOT), while the plots of conductivity (K) versus ω0 of the reversed micelle in the presence of PVP depend on the PVP concentrations. The plot of K versus ω0 with 2.0%wt PVP is similar to that without PVP. Only the ω0,max (the water content that the maximum conductivity corresponds to) is larger than that without PVP. Nevertheless, the conductivity of the reversed micelle containing more than 4%wt PVP always rises with the increase of the water content in the measured range. The DLS results indicate that the hydrodynamic radius (Rh) in the presence and absence of PVP rises with the increase of ω0. The plots with PVP and without PVP have almost the same value when ω0<17; and after that, it quickly increases with the increase of ω0. It is interesting to find that there is almost no effect of the PVP concentration on the viscosity and Rh of the reversed micelle at ω0 = 15. The FTIR results suggest that the contents of SO3--bound water and Na+-bound water both decrease with PVP added, while the content of the bulky-like water increases. However, the trapped water in the hydrophobic chain of the surfactant is nearly unaffected by PVP. It is also found from the FTIR that the carbonyl group stretching vibration of AOT is fitted into two sub-peaks, which center at 1740 and 1729 cm-1, corresponding to the trans and cis conformations of AOT, respectively.

Microdamage Evolution, Energy Dissipation and Their Trans-Scale Effects on Macroscopic Failure

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number P, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of P and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Trans-Scale Mechanics: Looking For The Missing Links Between Continuum And Micro/Nanoscopic Reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frameworks of either particle or continuum mechanics. In this paper, four cases studies (shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics) are provided to illustrate the three levels of trans-scale problems (problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/molecules and a finite size body at micro/nano-level) and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Mechanisms and concentrations dependence of up-conversion luminescence in Tm3+/Yb3+ codoped oxyfluoride glass-ceramics

The up-conversion properties of Tm3+/Yb3+ codoped oxyfluoride glass-ceramics under 980 nm excitation were investigated. Intense blue up-conversion luminescence due to the Tm3+: (1)G(4) -> H-3(6) transition was observed in the glass-ceramics. The intensity of the blue up-conversion luminescence in a 1 mol% YbF3-containing glass-ceramic was found to be about 40 times stronger than that in the precursor oxyfluoride glass. The up-conversion mechanism is proposed. The reason for the intense Tm3+ up-conversion luminescence in the oxyfluoride glass-ceramics and the concentrations dependence of upconversion luminescence are also discussed. (c) 2005 Elsevier B.V. All rights reserved.