Non-uniform shrinkage analysis of round billet using element-free Galerkin method

An element-free Galerkin thermal–mechanical calculation model for the solidification and shrinkage of round billet was established. The non-uniform heat flux measured in the plant trial was used as the boundary condition to simulate and analyze the deformation of solidified shell. The results indicate that the maximum and minimum shrinkages of the round billet at mold outlet are 0.78 and 0.21 mm, respectively, with apparent non-uniform characteristic. The local high-heat-flux region substantially dominates the non-uniformity of shell shrinkage, and the larger shrinkage usually derives from the high heat flux between the solidified shell and the mold in the circumferential direction. Also, the shrinkage on the shell surface has an immediate connection with the equivalent stress. Specifically, the shrinkage is more closely related to the radial stress component than the circumferential stress component.