Multiscale Simulation of Precipitation in Copper-Alloyed Pipeline Steels and in Cu-Ni-Si Alloys

  • Dennis RappEmail author
  • Seyedsaeid Sajadi
  • David Molnar
  • Peter Binkele
  • Ulrich Weber
  • Stephen Hocker
  • Alejandro Mora
  • Joerg Seeger
  • Siegfried Schmauder
Living reference work entry


In crystalline solids, the formation of precipitates is caused by the clustering of individual solute atoms dissolved in the matrix. This can happen, if the formation of clusters is energetically favorable relative to the dissolved state of atoms randomly distributed within the matrix. The clustering is driven by the stochastic process of diffusion and depending on diffusion speed, solute concentration, and mixing energies, atom clusters will form and grow, shrink or reach an equilibrium state after a long time of diffusion. As the presence of precipitates can greatly alter the mechanical properties of materials, the simulation of this nanoscopic process starting from the alloy composition up to the final distribution of precipitate numbers and sizes is key for computational design of alloys with desired mechanical properties. For achieving this, the atomistic kinetic Monte Carlo (AKMC) simulation method is used to mimic the stochastical diffusion process. For later stages of precipitation involving bigger clusters, the continuum phase-field method (PFM) can be used to accelerate the simulation. In this chapter, we will present two successful examples for the simulation of precipitation: One coupled approach of AKMC and PFM that was used for predicting the precipitation in copper-alloyed iron and another example of AKMC in the multicomponent Cu-Ni-Si system.



Support from the DFG through Collaborative Research Centre SFB 716, Project B.2 is gratefully acknowledged. The detailed description of each example in the chapter is reproduced from recently published works of the authors with kind support of the involved publishing company John Wiley & Sons, Inc. The original sources are Molnar et al. [1] and Sajadi et al. [2].


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Dennis Rapp
    • 1
    Email author
  • Seyedsaeid Sajadi
    • 1
  • David Molnar
    • 1
  • Peter Binkele
    • 1
  • Ulrich Weber
    • 2
  • Stephen Hocker
    • 1
  • Alejandro Mora
    • 1
  • Joerg Seeger
    • 3
  • Siegfried Schmauder
    • 1
  1. 1.Institut für Materialprüfung, Werkstoffkunde und Festigkeitslehre (IMWF)University of StuttgartStuttgartGermany
  2. 2.Materials Testing Institute, University of StuttgartStuttgartGermany
  3. 3.Wieland-Werke AGUlmGermany

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