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*.

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, "mesofracture mechanics" could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.

Statistical Simulation of Rarefied Gas Flows in Micro-Channels

Rarefied gas flows through micro-channels are simulated using particle approaches, named as the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method. In simulating the low speed flows in long micro-channels the DSMC method encounters the problem of large sample size demand and the difficulty of regulating boundary conditions at the inlet and outlet. Some important computational issues in the calculation of long micro-channel flows by using the IP method, such as the use the conservative form of the mass conservation equation to guarantee the adjustment of the inlet and outlet boundary conditions and the super-relaxation scheme to accelerate the convergence process, are addressed. Stream-wise pressure distributions and mass fluxes through micro-channels given by the IP method agree well with experimental data measured in long micro-channels by Pong et al. (with a height to length ratio of 1.2:3000), Shih et al. (l.2:4800), Arkilic et al. and Arkilic (l.3:7500), respectively. The famous Knudsen minimum of normalized mass flux is observed in IP and DSMC calculations of a short micro-channel over the entire flow regime from continuum to free molecular, whereas the slip Navier-Stokes solution fails to predict it.

Robust approach to dynamic statistical process control

Statistical Process Control (SPC) technique are well established across a wide range of industries. In particular, the plotting of key steady state variables with their statistical limit against time (Shewart charting) is a common approach for monitoring the normality of production. This paper aims with extending Shewart charting techniques to the quality monitoring of variables driven by uncertain dynamic processes, which has particular application in the process industries where it is desirable to monitor process variables on-line as well as final product. The robust approach to dynamic SPC is based on previous work on guaranteed cost filtering for linear systems and is intended to provide a basis for both a wide application of SPC monitoring and also motivate unstructured fault detection.

Micro-scale Mechanics of the Surface-Nanocrystalline Al-Alloy Material

Based on the microscopic observations and measurements, the mechanical behavior of the surface-nanocrystallized Al-alloy material at microscale is investigated experimentally and theoretically. In the experimental research, the compressive stress-strain curves and the hardness depth curves are measured. In the theoretical simulation, based on the material microstructure characteristics and the experimental features of the compression and indentation, the microstructure cell models are developed and the strain gradient plasticity theory is adopted. The material compressive stress-strain curves and the hardness depth curves-are predicted and simulated. Through comparison of the experimental results with the simulation results, the material and model parameters are determined.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Basic Mechanical Behaviors And Mechanics Of Shear Banding In Bmgs

In this paper, some basic mechanical behaviors of bulk metallic glasses (BMGs) were discussed. It can be found from the discussions that the mechanical behaviors of BMGs are mainly due to the formation and operation of shear bands in BMGs. Furthermore, the relevant mechanics of shear banding were investigated in the paper. The theoretical analysis of deformation coupling thermal softening and free volume creation softening demonstrates that the free volume creation and thermal softening can jointly promote the formation of shear bands in BMGs, and the observed post mortem. shear band width looks more like that governed by free volume creation. (C) 2007 Elsevier Ltd. All rights reserved.