Page 31 - MSAM-4-3

Materials Science in Additive Manufacturing Numerical simulation of plasma WAAM for Ti-6Al-4V

The heat flux per unit of surface q (W/[m²⋅K]) is In addition to radiation and convection, heat transfer
s
computed using Fourier’s law. According to Fourier’s law, between bodies in contact affects thermal behavior. Heat
the rate of heat transfer through a material is proportional transfer at an interface depends on the temperature of the
to the negative temperature gradient and the area through contacting bodies and the contact heat transfer coefficient
which the heat flows. Heat transfer continues as long as a (W/[m²⋅K]) in Equation VIII.
a temperature gradient is present. The proportionality q = a (T − T ) (VIII)
constant λ depends on factors, such as chemical a 1 2
composition, microstructure, and temperature. Due to manufacturing limitations, technically, processed
surfaces are not perfectly smooth, and microscopic surface
Thermal boundary conditions applied on the surface roughness leads to small media-filled gaps at the interface.
of the computational domain can be described as a Consequently, heat transfer across the contact interface
Dirichlet (temperature history), Neumann (heat flux occurs through two mechanisms. First, solid-to-solid
history), or Robin boundary condition, which represents a conduction at points where contact is established, and
combination of both. In WAAM, the primary heat transfer second, media conduction through the air- or gas-filled
mechanisms include conduction and surface heat losses, gaps. The contact heat transfer coefficient a depends on
both of which vary depending on the location within the the materials in contact, the surface conditions of the
component. In the first layers, the cold baseplate acts as a contacting bodies, contact pressure, and the fluid inside
heat sink, making conduction the dominant heat transfer the cavities.
mechanism. However, as the deposition progresses, the Thermal boundary conditions are modeled by
increasing substrate temperature and wall height lead to a integrating Equations VI to VIII into Equation V, as
greater influence of convective and radiative heat transfer. Equation IX

Heat radiation is the transfer of internal energy in the 
S (
hT − ) + (
T
4
T
4
form of electromagnetic waves, governed by the Stefan– σ T − ) + ( S T ∞ a T − ) =− λ T∇ (IX)
∞
c
1
2
Boltzmann law, which describes the heat flow rate emitted
or absorbed by an object as a function of its temperature. Since the cooling behavior of the model is governed by
This law applies to all free surfaces, including those of the heat transfer at the boundaries, inaccuracies in defining
newly deposited material, and represents the Neumann these mechanisms can significantly impact the simulation
component of Equation V, as in Equation VI, results. 25
q = ( T − ) (VI) 2.1.2. Thermal material properties
σ
4
T
4
∞
S
R
Structural welding simulations require the specification
where ε is the emissivity (-), σ is the Stefan–Boltzmann of temperature-dependent Thermo-physical and thermo-
constant (W/[m²⋅K ]), T is the surface temperature, and T mechanical material parameters. Thermo-physical
4
∝
s
is the far field temperature. The emissivity can be determined parameters include thermodynamic quantities, such as
experimentally and numerically as an inverse problem. If the thermal conductivity, density, and heat capacity, as well as
emissivity is known, the temperature of a body can be determined thermo-metallurgical parameters that characterize solid
from the heat radiation emitted by the body. However, the phase transformations. Thermo-mechanical properties
emissivity is not only material-dependent but is also influenced encompass material characteristics, such as thermal
expansion, modulus of elasticity, transverse contraction,
by surface conditions of the body, such as oxidation.
stress-strain behavior, and transformation plasticity. These
Heat convection is a mode of heat transfer driven by parameters are determined experimentally or sourced
the mass motion of a fluid. The movement of a fluid can from literature and material databases, such as JMatPro.
be forced (forced convection) or free (natural convection). Simufact Welding includes an integrated material database
The governing equation of heat convection is Newton’s law, that provides relevant parameters for conducting structural
expressed as in Equation VII, welding simulations.
q = h (T−T ) (VII) 2.2. Experimental setup
c
c
∝
s
where h is the convective heat transfer coefficient in W/ Deposition experiments were performed using a custombuilt
c
(m²⋅K). The coefficient depends on the type of media (gas WAAM system at RHPTechnology GmbH, Austria. The
or fluid), flow conditions on the surface, surface properties, system utilizes plasma metal deposition, a process that uses a
and temperature, and is typically determined using plasmatransferred arc energy source in combination with wire
empirical formulas based on dimensionless parameters. feeding to produce three-dimensional parts (Figure 2A). The
Volume 4 Issue 3 (2025) 4 doi: 10.36922/MSAM025140021