Dendrite fragmentation by catastrophic elastic remelting

TL;DR

This paper introduces a novel dendrite fragmentation mechanism driven by elastic energy effects, modeled through a generalized Gibbs-Thomson condition, revealing a critical load threshold for dendrite detachment.

Contribution

It presents a new theoretical model linking elastic energy to dendrite fragmentation, with analytical calculations and numerical simulations demonstrating catastrophic detachment.

Findings

Identification of a critical load level causing dendrite detachment

Development of a nonlinear differential equation model

Analytical calculation of interface thermodynamics

Abstract

The paper proposes a new fragmentation mechanism of dendrite arms. 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 [1], where each term is calculated analytically using a simple Bernoulli-Euler beam model. The resulting nonlinear 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 of the neck cross section leading to dendrite detachment.