Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly theoretical, but when appropriate the relation with experimental results is mentioned. While simple band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio treatments will be introduced to discuss more subtle physical effects, such as those induced by curvature, tube-tube interactions, or topological defects. The same approach will be followed for transport properties. The fundamental aspects of conduction regimes and transport length scales will be presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of shortand long-range static perturbations. Further, the latest developments in semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers chemical impurities, adsorbed molecules, etc. or inelastic electron-phonon interactions will be emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the Luttinger liquid, charge density waves, or superconducting transition.

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Electronic and transport properties of nanotubes

This chapter is aimed at describing the Monte Carlo method for the simulation of grain growth and recrystallization. It has also been extended to phase transformations and hybrid versions (Monte Carlo coupled with Cellular Automaton) of the model can also accommodate diffusion. If reading this chapter inspires you to program your own version of the algorithm and try to solve some problems, then we will have succeeded! The method is simple to implement and it is fairly straightforward to apply variable material properties such as anisotropic grain boundary energy and mobility. There are, however, some important limitations of the method that must be kept in mind. These limitations include an inherent lattice anisotropy that manifests itself in various ways. For many purposes, however, if you pay attention to what has been found to previous work, the model is robust and highly efficient from a computational perspective. In many circumstances, it is best to use the model to gain insight into a physical system and then obtain a new theoretical understanding, in preference to interpreting the results as being directly representative of a particular material. Please also keep in mind that the “Monte Carlo Method” described herein is a small subset of the broader use of Monte Carlo methods for which an excellent overview can be found in the book by Landau and Binder (2000).

The Monte Carlo Method

The study of preferred orientation of minerals in rocks dates back to Omalius d’Halloy (1833) who attributes a special significance to the alignment of crystals as an indicator of the formation process. Much later the influence of crystal alignment on physical properties was quantified (e.g., Weissenberg 1922, Voigt 1928, Reuss 1929). Only recently has this field emerged as a coherent part of earth science research linking such branches as mineralogy, petrology, structural geology, geodynamics and seismology. The reason for this was the emergence of quantitative methods to analyze preferred orientation, or “texture” as it was first called by Naumann (1850). These methods were largely developed in collaboration with materials science and mechanics. Quantitative measurements, detailed field studies, rigorous data analysis, theories to predict textures, and improvements in characterizing seismic anisotropy in the Earth are leading to a coherent picture that is now being refined.

Though seismologists have long accepted that there is a causal relationship between anisotropic propagation of seismic waves, the deformation field and crystal orientation, the prevailing view is still largely the mythological concept that seismic fast directions align with the flow direction. While this may be approximately the case for olivine deformed under certain conditions, it is certainly no universal law, as we will try to illustrate in this review. The “fast” direction of a crystal depends on the mineral species and its crystal structure. The alignment of crystals depends on microscopic, intra-crystalline deformation systems and the deformation history. Both relationships are complex and not intuitive, but there are well-established theories to compute single crystal physical properties as well as orientation patterns. Simulations can be compared with experimental data and then applied with some caution to the macroscopic Earth.

This review is intended to provide a brief introduction, highlighting some of the issues with …

Texture and Anisotropy

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Scaling, dimensional analysis, and indentation measurements

New analytical procedure to determine stress-strain curve from spherical indentation data

The objective of this work was to analyze the residual stress state in spot welds made in an HY-100 steel disk by an autogenous gas tungsten arc (GTA) welding process An uncoupled thermal-mechanical finite element (FE) model was developed that took into account the effects of liquid-to-solid and solid-state phase transformations Effects of variations in mechanical properties due to solid-state phase transformations on residual stresses in the weld were studied Extensive experimental testing was carried out to determine the mechanical properties of HY-100 steel The residual stresses in the disk with the spot weld were measured by a neutron diffraction (ND) technique The FE results are in good agreement with the ND measurements The results show that the volumetric changes associated with the austenite to martensite phase transformation in HY-100 steel significantly affect residual stresses in the weld fusion zone and the heat affected zone

Numerical analysis of GTA welding process with emphasis on post-solidification phase transformation effects on residual stresses

Modeling the kinetics and microstructural evolution during static recrystallization—Monte Carlo simulation of recrystallization

Field emission properties of B-doped carbon nanotubes are investigated from both theoretical and experimental standpoints. Using tight-binding and ab initio calculations, it is observed that B-saturating tip edges of carbon nanotubes induce the presence of large peaks within the local density of states (LDOS) located in an energy region close to the Fermi level (Ef). These localized states suggest a field emission enhancement for the B-doped tubes. In addition, ab initio theoretical results indicate that the work function for B-doped tubes is 1.7 eV lower when compared to pure carbon-terminated nanotubes. Experimentally, it is found that B-doped tubes, which are produced by arc discharge techniques and contain B mainly at the tips, exhibit stable electron field emission at lower turn-on voltages (1.4 V/mum) when compared to pure single- and multiwalled carbon nanotubes (2.8 and 3.0 V/mum, respectively) measured under the same conditions. We strongly believe our results will bring new insights in the fabrication of stable field emission sources.

Enhanced electron field emission in B-doped carbon nanotubes

Theoretical and experimental investigations were carried out to determine the effect of process parameters on weld metal microstructures of austenitic stainless steels during pulsed laser welding. Laser welds made on four austenitic stainless steels at different power levels and scanning speeds were considered. A transient heat transfer model that takes into account fluid flow in the weld pool was employed to simulate thermal cycles and cooling rates experienced by the material under various welding conditions. The weld metal thermal cycles and cooling rates are related to features of the solidification structure. For the conditions investigated, the observed fusion zone structure ranged from duplex austenite (γ)+ferrite (δ) to fully austenitic or fully ferritic. Unlike welding with a continuous wave laser, pulsed laser welding results in thermal cycling from multiple melting and solidification cycles in the fusion zone, causing significant post-solidification solid-state transformation to occur. There was microstructural evidence of significant recrystallization in the fusion zone structure that can be explained on the basis of the thermal cycles. The present investigation clearly demonstrated the potential of the computational model to provide detailed information regarding the heat transfer conditions experienced during welding.

Thomas Zacharia

Papers

New analytical procedure to determine stress-strain curve from spherical indentation data

Numerical analysis of GTA welding process with emphasis on post-solidification phase transformation effects on residual stresses

Modeling the kinetics and microstructural evolution during static recrystallization—Monte Carlo simulation of recrystallization

Enhanced electron field emission in B-doped carbon nanotubes

Heat transfer during Nd: Yag pulsed laser welding and its effect on solidification structure of austenitic stainless steels