Meshless Method Modeling for Crack Initiation and Propagation of Continuous Casting Billets

In the numerical calculation of crack propagation for continuous casting billets, mesh-based methods require continuous reconstruction of the mesh to ensure the consistency between the mesh boundaries and the discontinuous crack paths, making computational accuracy and efficiency more difficult to achieve. The present paper develops a calculation model for crack initiation and propagation of continuous casting round billets based on the Element-Free Galerkin method. Specifically, the diffraction criterion is used to modify the weight function in the field function approximation around the discontinuous crack. The direct displacement method is adopted to calculate the stress intensity factors at the crack tips, and the deflection angle of crack propagation is determined by the maximum circumferential stress criterion. The calculation results show that subcutaneous cracks form in the brittle temperature range near the inner arc and outer arc of the round billets. The cracks are located within 2.35 mm from the shell surface and have a length of less than 3 mm. The crack propagation is mainly concentrated at 110 to 300 mm below the meniscus, and the crack propagation velocities approximately 0.33 to 0.35 mm/s. The arbitrary node discretization model developed in this paper has immense potential in crack propagation calculations and provides a powerful tool for the prediction of cracks in continuous casting billets.