Multiscale modeling metals

Fig. 4.3 Multiscale modeling example of a metal alloy used for design in an automotive component...

Concurrent multiscale methods have also been employed to address fatigue. Oskay and Fish [82] and Fish and Oskay [83] introduced a nonlocal temporal multiscale model for fatigue based upon homogenization theory. Although these formulations were focused on metals, Fish and Yu [84] and Gal et al. [85] used a similar concurrent multiscale method for analyzing fatigue of composite materials. 

The recent growth of multiscale modeling has permeated every material type known to mankind regarding structural members. Although most of the work has been focused on metal alloys as they have been used the most over time as reliable structural materials, multiscale modeling has also been employed for ceramics and polymer systems (both synthetic and biological). 

Since most of the methods and examples in this review are focused on metals, this section will be shortened. Albeit, it is important to note that multiscale modeling has been applied to basic metal alloy structures such as face center cubic aluminum alloys, hexagonal close pack magnesium alloys, and body center cubic iron and... 

Kinetic Monte Carlo and hyperdynamics methods have yet to be applied to processes involved in thermal barrier coating failure or even simpler model metal-ceramic or ceramic-ceramic interface degradation as a function of time. A hindrance to their application is lack of a clear consensus on how to describe the interatomic interactions by an analytic potential function. If instead, for lack of an analytic potential, one must resort to full-blown density functional theory to calculate the interatomic forces, this will become the bottleneck that will limit the size and complexity of systems one may examine, even with multiscale methods. 

I.S. Cole, T.H. Muster, N. Azmat, M. Venkatraman, A. Cook, Multiscale modelling of the conrosion of metals under atmospheric corrosion, Electrochim. Acta 56 (2011) 1856-1865. 

In the past decade, we have used multiscale modeling to study some key problems in H embrittlement of metals by focusing on H-defect interactions, which are summarized in the following. 

Saldccioli, M., M. Stamatakis, S. Caratzoulas D. G. Vlachos (2011) A review of multiscale modeling of metal-catalyzed reactions Mechanism development for complexity and emergent behavior. Chemical Engineering Science, 66, 4319-4355,1SSN 00092509. 

Multiscale models are making possible both the integration of insight between scales to improve overall understanding and the integration of simulations with experimental data. For example, in the case of plastic deformation of metals, one can incorporate constitutive theory for plastic displacements into macroscopic evolution equations, where parameterization of the constitutive equations is derived from analysis of MD simulations. 

We begin by introducing and briefiy discussing the specific computational methods we have used in the present work to implement our multiscale modeling strategy for bcc transition metals. 

Next to metals, probably the synthetic polymer-based composites have been modeled most by hierarchical multiscale methods. Different multiscale formulations have been approached top-down internal state variable approaches, self-consistent (or homogenization) theories, and nanoscale quantum-molecular scale methods. 

Several length-scales have to be considered in a number of applications. For example, in a typical monolith reactor used as automobile exhaust catalytic converter the reactor length and diameter are on the order of decimeters, the monolith channel dimension is on the order of 1 mm, the thickness of the catalytic washcoat layer is on the order of tens of micrometers, the dimension of the pores in the washcoat is on the order of 1 pm, the diameter of active noble metal catalyst particles can be on the order of nanometers, and the reacting molecules are on the order of angstroms cf. Fig. 1. The modeling of such reactors is a typical multiscale problem (Hoebink and Marin, 1998). Electron microscopy accompanied by other techniques can provide information on particle size, shape, and chemical composition. Local composition and particle size of dispersed nanoparticles in the porous structure of the catalyst affect catalytic activity and selectivity (Bell, 2003). 

The multiphysics and multiscale character of the important features of Hall-Heroult cell operation makes difficult laboratory scale experimentation that is relevant to industrial pot operations. For example, cell C E is influenced by the cell-scale flow of the metal and electrolyte, which is determined in turn by the magnetic field which depends on the entire cell current. CE also depends on the finer scale flow due to release of the carbon dioxide bubbles from the anodes. It is generally not possible to examine these two effects simultaneously in the laboratory. Also, the generally hostile environment inside Hall-Heroult cells makes experimentation difficult, and the high cost of modification of full-scale pots further complicates industrial trials. In this environment, numerical or mathematical modeling of pots would be expected to be a useful tool. 

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