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On the phase field modeling of crack growth and analytical treatment on the parameters

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Abstract

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is utilized to solve the complete system of crack phase field and mechanics equations. The analytical expressions for the crack surface profile and the crack tip velocity are verified with the numerical solutions. It is shown that under mode I cracking and proper calibration of parameters, phase field models always agree with Griffith’s theory.

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Authors and Affiliations

  1. School of Mechanical Engineering, Sharif University of Technology, Tehran, 11365-11155, Iran

    Gholam Hossein Farrahi & Hossein Jafarzadeh

  2. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Mahdi Javanbakht

Authors
  1. Gholam Hossein Farrahi
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  2. Mahdi Javanbakht
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  3. Hossein Jafarzadeh
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Correspondence to Gholam Hossein Farrahi.

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Communicated by Francesco dell’Isola.

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Farrahi, G.H., Javanbakht, M. & Jafarzadeh, H. On the phase field modeling of crack growth and analytical treatment on the parameters. Continuum Mech. Thermodyn. 32, 589–606 (2020). https://doi.org/10.1007/s00161-018-0685-z

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