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Susceptibility to weld solidification cracking in transformation-induced plasticity steel sheets was studied using a modified standard hot cracking test used in the automotive industry. To vary the amount of self-restraint, bead-on-plate laser welding was carried out on a single-sided clamped specimen at increasing distances from the free edge. Solidification cracking was observed when welding was carried out close to the free edge. With increasing amount of restraint, the crack length showed a decreasing trend, and at a certain distance, no cracking was observed. With the aid of a finite element-based model, dynamic thermal and mechanical conditions that prevail along the transverse direction of the mushy zone are used to explain the cracking susceptibility obtained experimentally. The results indicate that the transverse strain close to the fusion boundary can be used as a criterion to predict the cracking behavior. The outcome of the study shows that optimum processing parameters can be used to weld steels closer to the free edge without solidification cracking.