ICME analysis of modeling copper during penetration

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In order to investigate changes of copper structure and property during penetration, the ICME approach, which includes downscaling and upscaling, has been utilized. With the development of material science, Multiscale Modeling has become a hotspot and has received increasing attention. It could be treated as a potential linkage between material structure and material property from macroscale to nanoscale.Literature Reviews about key points in my research are listed below.

Downscaling and Upscaling Methodology

To better understand the internal structure of copper and various changes during penetration modeling, it seems very important to determine cause and effect during the process and understand the way messages are passed between different size scales. The multiscale concept could be divided into several parts which are electronic scale, atomistics, nanoscale, microscale, mesoscale and macroscale.

DFT is a short name of Density functional theory, which is a basic theory in electronic scale. It is a mechanical modelling method which is found in physics, chemistry and material science in order to investigate the electronic structure of many-body systems, especially for atoms, molecules and the condensed phase. In order to get interfacial energy and elastic module of copper, DFT could be used for calculation in electronic scale.

Two parameters could be passed up to atomistic scale, by using molecular dynamic codes such as MEAM or LAMMPS, the high rate mechanism and mobility could be acquired. In order to fully understand hardening effects for crystal plasticity, dislocation mobility from lower scale could be utilized by Micro-3D calculations on microscale.

Grain Boundary in Nanoscale

Grain boundaries (GBs) could be taken as significant factors not only in material properties of metal, but also in the mechanical and physical properties of the nanoscale. Grain Boundaries contribute a lot to material properties. The GB behavior has a major effect on the macroscopic response of metallic materials with large GB-to-volume ratios[1] In past research, the original static GB structure and the evolution of this structure would play a vital role in the deformation behavior due to the interaction of grain boundaries with other lattice defects[2] In order to simulate polycrystalline metal at the nanoscale, the more attention that is paid to Grain Boundary, the more accurate the model will be. Moreover, grain boundary interface mechanics are also an inevitable aspect which needs to be taken into consideration. However there are only a couple of approaches that are able to emphasize initial and evolving GB structure[3]

Mechanical Behavior in Microscale/Mesoscale

Material behavior at all scales varying from atomistic to continuum includes many processes such as elastic deformation, dislocation generation and multiplication, cleavage, void/microcrack formation and its growth into macrocracks, and final failure[4] Constitutive laws play a major role in the investigation of mechanical behavior of single crystal or polycrystalline materials in applications spanning from microscale to macroscale.[5]. Mesoplasticity serves as an appropriate formalism that bridges the atomistic mechanisms of deformation and fracture to the macroscopic behavior [6]. Y. Liu proposed a combined FEM simulation and experimental nanoindentation approach which implements the mesoplastic constitutive model in order to determine the mechanical behavior of single crystal copper. Based on FEM analysis, the mechanical behavior of the crystalline structure in mesoscale and the effect of the mesoplastic parameters on the nanoindentation load–displacement relationships are investigated[7]

Simulation in Multiscale

There are various and plenty of computer simulation methods which are used in the development of scaling laws. Multiscales are defined by length scales or time scales. With increase in length (or time) scale, material behavior is modeled using molecular dynamics (MD) and/or Monte Carlo (MC) simulations, then to micro or mesoplastic, and finally to continuum mechanics(e.g. finite element method (FEM)).With increasing computational power at decreasing costs, mesoplastic constitutive relation can be implemented in some FEM codes to solve complex 3D problems. For example, Fivel developed a 3D model to combine discrete dislocations with FEM for nanoindentation simulation on single crystal copper.




  1. "P. R. M. van Beers, V. G. Kouznetsova, M. G. D. Geers, M. A. Tschopp, and D. L. McDowell, “A multiscale model of grain boundary structure and energy: From atomistics to a continuum description,” Acta Mater., vol. 82, pp. 513–529, 2015".
  2. "R. Z. Valiev, V. Y. Gertsman, and O. A. Kaibyshev, “Grain boundary structure and properties under external influences,” Phys. status solidi, vol. 97, no. 1, pp. 11–56, 1986.".
  3. "V. Taupin, L. Capolungo, C. Fressengeas, A. Das, and M. Upadhyay, “Grain boundary modeling using an elasto-plastic theory of dislocation and disclination fields,” Journal of the Mechanics and Physics of Solids, 2012.".
  4. "W. E. King, G. Campbell, T. Gonis, G. Henshall, D. Lesuer, E. Zywicz, and S. Foiles, “Theory, simulation, and modeling of interfaces in materials—bridging the length-scale gap: a workshop report,” Materials Science and Engineering: A, vol. 191. pp. 1–16, 1995".
  5. "M. C. Fivel, C. F. Robertson, G. R. Canova, and L. Boulanger, “Three-dimensional modeling of indent-induced plastic zone at a mesoscale,” Acta Mater., vol. 46, pp. 6183–6194, 1998."
  6. "C. S. Hartley†, “A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory,” Philosophical Magazine, vol. 83. pp. 3783–3808, 2003."
  7. "L. Yang, A. Radisic, M. Nagar, J. Deconinck, P. M. Vereecken, and A. C. West, “Multi-scale modeling of direct copper plating on resistive non-copper substrates,” Electrochim. Acta, vol. 78, pp. 524–531, 2012. "
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