Progress has been made in research on several fronts in an effort to develop computational simulation capabilities for use in virtual design and testing of advanced structural materials. It is envisioned that the capabilities will be embodied in a coherent set of methods, software to implement the methods, and advances in the fundamental understanding of many issues in the thermo-mechanical performance of materials. It is further envisioned that the methods and software will be organized into a hierarchy (see figure) corresponding to a hierarchy of spatial scales from electronic through atomic, mesoscale, micro-structural, and continuum to macrostructural, and that there will be seamless coupling of information from each scale to the next larger scale. A secondary objective of this research and development effort is to provide direct simulation output at each level of the hierarchy for investigating specific phenomena at the corresponding spatial scale. For the purposes of demonstrating the capabilities and providing specific focus for the overall research, it is intended to predict nano-, micro-, and macroscopic degradation of aluminum and titanium alloys under fatigue loading and in a corrosive (oxidative) environment and as a function of temperature.

Computational Simulations are performed by different methods at different spatial scales. Results obtained at each scale are, variously, fed the next larger scale or taken as direct output.

The innovations produced in this effort include the following:

  • The first discrete-dislocation model for predicting fatigue-crack-growth behavior with no a priori assumptions about fatigue. The approach taken in developing this model was to directly address the mechanics and other aspects of the applicable physics of plastic deformation at the individual-dislocation level.
  • The first method for combining continuum and atomistic descriptions of defects within one conceptual framework. The framework is a model that combines power of the aforementioned discrete-dislocation model with the atomistic resolution of molecular dynamics.
  • The first model to couple quantum-mechanical and atomistic submodels for metals. In this model, either standard density-functional theory (DFT) or orbital-free density-functional theory (OF-DFT) is used to embed quantum- mechanical calculations within an atomistic computational submodel that employs semi-empirical atomistic potentials.
  • Extension of a static, zero-temperature quasi-continuum model to nonzero finite temperature. The extension was made by considering a formal "coarse graining" of the microscopic partition function of a classical material at finite temperature, then generating an approximate effective coarse-grained potential by making a self-consistent quasi- harmonic approximation for the atoms that were eliminated through the coarse graining process.
  • The first quantum/continuum coupling method. This method provides for utilization of first-principles OFDFT calculations in a "local" quasi-continuum model. The energy of strained unit cells of a material is used to compute the deformation of the material in continuum domains that are treated by use of finite elements.
  • The first quantum-mechanical determination of decohesion with and without embrittlement by impurities. DFT was used to predict the fundamental cohesive behaviors of metals with and without hydrogen and oxygen atoms as impurities along separating surfaces. The appropriate thermodynamic potential (the so-called grand force potential) was developed for converting the results of computations of decohesion at fixed impurity concentration to those of decohesion at fixed chemical potential. It was shown that the cohesive strength of aluminum drops precipitously, from about 12 GPa to 4 GPa in hydrogen and to between 1 and 2 GPa in oxygen when the chemical potential exceeds a critical value.
  • A continuum model of cracking by chemical embrittlement. The results of the above mentioned research on decohesion were used to develop a continuum model for simulation of stress corrosion cracking in steels. An integral part of this development was the renormalization of the decohesion as modelled by first principles, occurring at a length scales of the order of an Angstrom, into an effective cohesion law at a length scale suitable for efficient continuum modeling. The model also includes the stress-dependent diffusion of chemical species (e.g. hydrogen) through the material in the presence of the non-uniform crack-tip field. The model predicts a number of features of crack growth that are observed in experiments.
  • The first basic discrete/continuum model for non-steady flow of diffusing chemical species. This is a multiscale diffusion model in which one region of material is treated by use of the full discreteness of the diffusing entities while another, much larger region is treated by use of the continuum diffusion equation. By making the discrete-submodel region small, considerable time is saved in computations, making it possible to perform much longer simulations with no loss in accuracy.

This work was done by W.A. Curtin and A. Needleman of Brown University; M. Ortiz and R. Phillips of California Institute of Technology; E. Kaxiras of Harvard University; G. Cedar of Massachusetts Institute of Technology; E. Carter of the University of California, Los Angeles; R. Miller of Carleton University; C. Woodward of Northwestern University; and D. Farkas of Virginia Polytechnic Institute and State University for the Air Force Research Laboratory. For more information, download the Technical Support Package (free white paper) at under the Information Sciences category. AFRL-0037

This Brief includes a Technical Support Package (TSP).
Multiscale Virtual Design and Testing of Materials

(reference AFRL-0037) is currently available for download from the TSP library.

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This article first appeared in the August, 2007 issue of Defense Tech Briefs Magazine.

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