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Multi phase field simulation for phase transformation and fracture

By Vigneswaran Govindarajan (IMT School for Advanced Studies)
Co-authors: Marco Paggi (IMT School for Advanced Studies)

A phase field model is developed to investigate the integrated phenomena for studying fracture and phase transformation in steels. The researchers from the physics and mechanics communities have explored the potentialities of phase field modeling of fracture, see [1] and [2], the model had proven its efficiency to study wide range of problems. Also, phase field model widely used for modeling martensitic phase transformation, capable of predicting microstructure evolution at various length scales. Mamivand [3] provided a literature review of phase field model that used to capture the formation and growth of martensite. In a coupled context, this model can capture both the short-scale physics of phase transformation and fracture within a self-consistent set of equations that can simulate at experimental relevant length and time scales. The face-centred cubic crystal of austenite crystal with crack, which is made of an isotropic material under static loading investigates the interaction between phase transformation and fracture. The evolution of phase transformation and fracture at the crack tip will be elucidated. The singularities at crack tip are the un-stable nucleation points for phase transformation and fracture. The propagation cracks can exhibit an interplay during phase transformation process. As follows, we recall the phase field model for martensitic transformation and damage by Schmitt et al. [4], the process of phase transformation and crack propagation is governed by a minimization problem of the total free energy of the system. The phase field modelling for fracture and phase transformation is derived using dynamical equations from Ginzburg and Landau theory results to constitutive form in finite element implementation. The solution from Schmit et al. [4] is an admissible for crack evolution in single variant martensitic phase, whereas this paper contributes an efficient numerical treatment for crack evolution in multi variant martensitic phase. The outcome of the developed model address the interesting crack propogation phenomena in phase transformed localization zone. REFERENCES [1] C. Miehe, M. Hofacker, F. Welschinger(2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199, 27652778. [2] M. Ambati, T. Gerasimov, L. De Lorenzis (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation, Computational Mechanics, 55: 383405. [3] M. Mamivand, M.A. Zaeem, H.E. Kadiri (2013) A review on phase field modeling of martensitic phase transformation, Computational Materials Science, Volume 77, Pages 304-311, ISSN 0927-0256. [4] R. Schmitt, C. Kuhn, R. Skorupski, M. Smaga, D. Eifler, R. Mueller (2014) A combined phase field approach for martensitic transformations and damage, Archive of Applied Mechanics Volume 85, Issue 9, pp 1459-1468.

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