text: from pybamm import Parameter, constants, exp
  
  
  def graphite_cracking_rate_Ai2020(T_dim):
      """
      graphite particle cracking rate as a function of temperature [1, 2].
  
      References
      ----------
       .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
       Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
       Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
        DOI: 10.1149/2.0122001JES.
       .. [2] Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
       Battery cycle life prediction with coupled chemical degradation and fatigue
       mechanics. Journal of the Electrochemical Society, 159(10), A1730.
  
      Parameters
      ----------
      T_dim: :class:`pybamm.Symbol`
          temperature, [K]
  
      Returns
      -------
      k_cr: :class:`pybamm.Symbol`
          cracking rate, [m/(Pa.m0.5)^m_cr]
          where m_cr is another Paris' law constant
      """
      k_cr = 3.9e-20
      T_ref = Parameter("Reference temperature [K]")
      Eac_cr = Parameter(
          "Negative electrode activation energy for cracking rate [J.mol-1]"
      )
      arrhenius = exp(Eac_cr / constants.R * (1 / T_dim - 1 / T_ref))
      return k_cr * arrhenius
  