Dendrite fragmentation by catastrophic elastic remelting

A new fragmentation mechanism of dendrite arms is proposed. The theoretical basis of this mechanism is a shift in the thermodynamical equilibrium at the solid–liquid interface due to the presence of elastic energy. This effect is modelled by the generalized Gibbs–Thomson condition [Larché FC, Cahn JW. Acta Metallurgica. 1973;21:1051], where each term is calculated analytically using a simple Bernoulli–Euler beam model. The resulting non-linear system of ordinary differential equations is integrated in time using a fully implicit scheme. It is demonstrated that there is a critical level of loading, exceeding which causes a catastrophic reduction in the neck cross section, leading to dendrite detachment.