An experimental and numerical study were made on the time-varying heat transfer coefficient h(t) between a tube-shaped casting and metal molds. One-dimensional treatment was adopted in analyzing the heat flows between the casting and the inner and the outer mold. The sequential function specification method was employed to solve the nonlinear inverse heat conduction problem. In order to investigate the different behavior of h(t) for different alloys, casting experiments were carried out with three Al-base alloys and pure Al having different types of solidification behavior. It was found that the temperature change of the outer mold showed a normal heating and cooling curve. However, that of the inner mold was unusual especially for the alloys with a wide solidification range, i.e the temperature increases first rapidly, then halts for a while and then increases again showing finally a regular heating and cooling curve. The resulting heat transfer coefficient at the interface to the inner mold $h_i$(t) decreases temporarily and then increases, while the one at the interface to the outer mold $h_o$(t) decreases monotonously to a quasi-steady state. The abnormal heat transfer phenomenon at the inner interface for the alloys with a wide solidification range was concluded to be caused by a slight movement of the semi-solid inner wall at the inside of the tube-shaped casting due to the solidification contraction of the casting freezing in a mushy type.
To make clear an air gap formation process at the inner interface, displacements of inner surface of casting and inner mold were measured during solidification of tube-shaped casting of AC8A alloy. The thickness of the air gap was measured as the difference between the location of the casting surface and that of the inner mold surface. The inner mold began to move toward casting pushing the casting immediately after pouring, while the casting moved greatly inward during solidification due to the low pressure in the casting caused by the solidification shrinkage. It was expected that the convex outer wall is stressed compressively and the concave inner wall is exposed to tensional stress. The bridged dendrite network (coherent dendrite network) can be pulled apart much easier than being compressed together. Therefore only the inner wall of the casting is considered to be pulled outward, i.e to the inside of the casting and this should create a gap between the casting and the inner mold. By measuring the displacements of casting and inner mold, the maximum air gap thickness at the casting/inner mold interface was about 60㎛ during solidification. The deduced $h_i$(t) depending on the measured air gap width showed a similar tendency to the predicted one by solving the inverse heat conduction problem. When the contraction of the casting began, the air gap became small quickly, and then disappeared.
A coupled thermal and mechanical axisymmetric finite element analysis of tube-shaped AC8A alloy casting has been performed by ABAQUS code. A thermoelastic-visco-plastic rheological model was used to compute a deformation of casting, resulting in an air gap width calculation and a prediction of stress distribution. Comparisons of measured temperatures and model predictions were given, showing a similar trend of temperature-time curves. The air gap formation between casting and outer mold was well predicted, while the inner gap at the casting/inner mold interface was not shown, because the solidification type was not introduced into casting solidification.
