Calibration of a multi-phase field model with quantitative angle measurement
Source abstract
Abstract
Over the last years, the phase-field method has been established to model capillarity-induced microstructural evolution in various material systems. Several phase-field models were introduced and different studies proved that the microstructure evolution is crucially affected by the triple junction (TJ’s) mobilities as well as the evolution of the dihedral angles. In order to understand basic mechanisms in multi-phase systems, we are interested in the time evolution of TJ’s, especially in the contact angles in these regions. Since the considered multi-phase systems consist of a high number of grains, it is not feasible to measure the angles at all TJ’s by hand. In this work, we present a method enabling the localization of TJ’s and the measurement of dihedral contact angles in the diffuse interface inherent in the phase-field model. Based on this contact angle measurement method, we show how to calibrate the phase-field model in order to satisfy Young’s law for different contact angles.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Solidification and crystal growth phenomena · Aluminum Alloy Microstructure Properties · Metallic Glasses and Amorphous Alloys
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (35)
Show source-provided references
1. Boettinger W, Warren J, Beckermann C, Karma A (2002) Phase-field simulation of solidification 1. Ann Rev Mater Res 32(1):163–19410.1146/annurev.matsci.32.101901.155803 ↗
2. Cogswell DA, Carter WC (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases. Phys Rev E 83(6):061602–061615. doi: 10.1088/0965-0393/17/7/07300110.1103/PhysRevE.83.061602 ↗
3. Nestler B, Choudhury A (2011) Phase-field modeling of multi-component systems. Curr Opin Solid State Mater Sci 15(3):93–10510.1016/j.cossms.2011.01.003 ↗
4. Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28(2):258–26710.1063/1.1744102 ↗
5. Kobayashi R (1993) Modeling and numerical simulations of dendritic crystal growth. Phys D 63:410–42310.1016/0167-2789(93)90120-P ↗
6. Langer JS (1986) Models of pattern formation in first-order phase transitions. Directions in condensed matter. World Scientific, Singapore, pp 165–18610.1142/9789814415309_0005 ↗
7. Kim SG, Kim WT, Suzuki T (1999) Phase-field model for binary alloys. Phys Rev E 60:7186–719810.1103/PhysRevE.60.7186 ↗
8. Plapp M (2011) Unified derivation of phase-field models for alloy solidification from a grand-potential functional. Phys Rev E 84:031601–03161610.1103/PhysRevE.84.031601 ↗
9. Garcke H, Nestler B, Stoth B (1999) A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions. SIAM J Appl Math 60(1):295–315. doi: 10.1137/S003613999833489510.1137/S0036139998334895 ↗
10. Nestler B, Garcke H, Stinner B (2005) Multicomponent alloy solidification: phase-field modeling and simulations. Phys Rev E 71:041609–04161510.1103/PhysRevE.71.041609 ↗
11. Chen LQ, Yang W (1994) Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: the grain-growth kinetics. Phys Rev B 50(21):15752–1575910.1103/PhysRevB.50.15752 ↗
12. Fan D, Chen LQ (1997) Computer simulation of grain growth using a continuum field model. Acta Mater 45(2):611–62210.1016/S1359-6454(96)00200-5 ↗
13. Garcke H, Nestler B, Stoth B (1998) On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Phys D 115(1):87–10810.1016/S0167-2789(97)00227-3 ↗
14. Steinbach I, Pezzolla F (1999) A generalized field method for multiphase transformations using interface fields. Phys D 134(4):385–39310.1016/S0167-2789(99)00129-3 ↗
15. Steinbach I, Pezzolla F, Nestler B, Seeßelberg M, Prieler R, Schmitz G, Rezende J (1996) A phase field concept for multiphase systems. Phys D 94(3):135–14710.1016/0167-2789(95)00298-7 ↗
16. Warren JA, Kobayashi R, Lobkovsky AE, Carter WC (2003) Extending phase field models of solidification to polycrystalline materials. Acta Mater 51(20):6035–605810.1016/S1359-6454(03)00388-4 ↗
17. Lu Y, Zhang L, Zhou Y, Chen Z, Zhang J (2013) Phase-field study for texture evolution in polycrystalline materials under applied stress. J Mater Sci Technol 29(10):999–100410.1016/j.jmst.2013.08.011 ↗
18. Ravash H, Vleugels J, Moelans N (2014) Three-dimensional phase-field simulation of microstructural evolution in three-phase materials with different diffusivities. J Mater Sci 49(20):7066–7072. doi: 10.1007/s10853-014-8411-010.1007/s10853-014-8411-0 ↗
19. Ahmed K, Allen T, El-Azab A (2015) Phase field modeling for grain growth in porous solids. J Mater Sci. doi: 10.1007/s10853-015-9107-9
20. McKenna I, Gururajan M, Voorhees P (2009) Phase field modeling of grain growth: effect of boundary thickness, triple junctions, misorientation, and anisotropy. J Mater Sci 44(9):2206–2217. doi: 10.1007/s10853-008-3196-710.1007/s10853-008-3196-7 ↗
21. Moelans N, Wendler F, Nestler B (2009) Comparative study of two phase-field models for grain growth. Comput Mater Sci 46(2):479–49010.1016/j.commatsci.2009.03.037 ↗
22. Johnson A, Voorhees P (2014) A phase-field model for grain growth with trijunction drag. Acta Mater 67:134–14410.1016/j.actamat.2013.12.012 ↗
23. Gottstein G, King A, Shvindlerman L (2000) The effect of triple-junction drag on grain growth. Acta Mater 48(2):397–40310.1016/S1359-6454(99)00373-0 ↗
24. Caroli C, Misbah C (1997) On static and dynamical Young’s condition at a trijunction. J Phys I 7(10):1259–1265
25. Guo W, Steinbach I (2010) Multi-phase field study of the equilibrium state of multi-junctions. Int J Mater Res 101(4):382–388. doi: 10.3139/146.110298
26. Holm E, Srolovitz DJ, Cahn J (1993) Microstructural evolution in two-dimensional two-phase polycrystals. Acta Metall Mater 41(4):1119–113610.1016/0956-7151(93)90160-T ↗
27. Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys Rev E 45:7424–745110.1103/PhysRevA.45.7424 ↗
28. Choudhury A, Nestler B (2012) Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential. Phys Rev E 85:021602–02161810.1103/PhysRevE.85.021602 ↗
29. Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–29410.1016/j.calphad.2007.11.003 ↗
30. Vondrous A, Selzer M, Hötzer J, Nestler B (2014) Parallel computing for phase-field models. Int J High Perform C 28(1):1–12. doi: 10.1177/109434201349097210.1177/1094342013490972 ↗
31. Stinner B, Nestler B, Garcke H (2004) A diffuse interface model for alloys with multiple components and phases. SIAM J Appl Math 64(3):775–79910.1137/S0036139902413143 ↗
32. Chen Y, Ye X (2011) Projection onto a simplex, arXiv preprint arXiv:1101.6081 , pp 1–7
33. Wendler F, Becker JK, Nestler B, Bons PD, Walte NP (2009) Phase-field simulations of partial melts in geological materials. Comput Geosci 35(9):1907–191610.1016/j.cageo.2009.01.011 ↗
34. Adams BL, Ta’Asan S, Kinderlehrer D, Livshits I, Mason D, Wu CT, Mullins W, Rohrer G, Rollett A, Saylor D (1999) Extracting grain boundary and surface energy from measurement of triple junction geometry. Interface Sci 7(3–4):321–33710.1023/A:1008733728830 ↗
35. Stinner B (2006) Derivation and analysis of a phase field model for alloy solidification, Dissertation, University of Regensburg