Theory of Maximum Tensile Stresses in the Solidifying Shell of a Constrained Rectangular Casting

A theoretical model is derived for determining the stresses that develop during the early stages of solidification in flat-sided ingot molds. The model requires flatness of the solidifying skin and is strictly valid only up to the time when an air gap begins to form at the corners. Here it is argued that the model continues to provide a valid estimate of the maximum stresses in the central portion of the flat sides, where mold contact is maintained long after the first appearance of an air gap at the corners. This argument is supported by the fact that the lateral contraction of this portion is inhibited both by mold friciton and by tensile forces transmitted through the contracted corners from adjacent faces of the skin. Specific calculations are made for low-carbon steel by using physical property data from the literature. The maximum tensile stresses occur at the outer face and have values between 500-1500 psi, depending on the cooling rate. The theory is believed to be relevant to the interpretation of “center-line” cracking.