A coupled temperature-displacement phase field model for grain growth during laser-aided metal deposition

Laser metal deposition (LMD) by powder injection is an attractive and innovative additive manufacturing of metals. The key to predict material properties is the state of microstructure. In this paper, we develop a thermodynamically consistent temperature-displacement phase field model for grain growth during the LMD process. The governing equations that follow from the balance laws involve the phase variable, the displacement field, and the temperature field, with significant couplings between all equations. The model includes thermal expansion, transformation dilatation, strain dependency on phase transformation and local mechanical equilibrium conditions. Extensions to plastic models are discussed. Temperature dependencies of material properties (Young's modulus, Poisson's ratio, thermal expansion coefficient) are also included in the model formulation.