SAMPE Journal - July/August 2024 - 27

1. INTRODUCTION
There are two main approaches to simulating this progressive
The adoption of AM parts in the aerospace industry has grown
increasingly from prototype technology to flight hardware. Two
primary processes exist for metal part production: laser powder
bed fusion (LPBF) and directed energy deposition (DED). In
LPBF, an initial layer of metal powder is deposited on a build plate
or substrate, and a highly focused laser beam of energy is moved
over its surface to melt the metal powder and fuse it to the build
plate. Successive thin layers of metal powder are deposited and
melted to fuse it to the preceding layer. DED also uses a focused
energy source but blow powder or feed wire is introduced to
add material. Both processes produce high temperatures and
severe thermal gradients, leading to significant part distortion
and buildup of residual stresses as layers are deposited[1,2]
. It is
desired to simulate this process to predict final part distortion
and build completion. Simulating LPBF is the focus of this paper
using direct and indirect physics-based methods.
Additive manufacturing has its limitations and must be
accounted for in the design process. These limitations include
internal porosity, support structure complications, part size,
and thermal distortion[3]
. Bridging and stepping behaviors are
two phenomena resulting from thermal distortion. Bridging
behavior is the connection of printed features over a gap and
can lead to blade crash if the " bridge " lifts sufficiently due to
thermal distortion[3]
deformation with CAD geometry that can lead to stairs[1,3]
. Stepping behavior is the mismatch of part
or
detachment in the printed part.
Additive manufacturing process simulation (AMPS) aims
to predict the influence of process parameters on final part
distortion,
residual stresses, and build completion. Factors
such as part orientation, support placement, and build plate
layout may be investigated by AMPS to determine trends and
inform a successful print without the user experiencing build
interruptions or part failure on the build plate.
2. NUMERICAL APPROACH
2.1 General Approach
The part and support structure geometries were first sliced
into layers, and each layer was meshed in groups of elements[4]
.
Each layer of elements represented an aggregation of physical
build layers, which can be on the order of tens of microns thick,
into a " superlayer. " Typically, each superlayer represents 1050
deposition layers[1]
simulation run times. Each superlayer or part of superlayer is
activated sequentially to simulate the build progress[1,5]
. The
thermal stress buildup was observed by the sequential layer
activation. The approximation for LPBF with a single laser source
is a reasonable approximation but may not be for DED and LPBF
with multiple heat sources.
To avoid shortcomings with homogenization techniques, a
conformal mesh was used to discretize the geometry over voxel
elements. Voxel elements use a homogenization approach to
capture stiffness for partially filled elements where the element
is outside the geometry of the part[1]
. This allows for a coarser
mesh to shorten simulation time. In certain applications,
homogenization techniques can erroneously represent the
stiffness of the part[6]
. It is well known that mesh density affects
the speed and accuracy of the simulation. The layer height, and
thus mesh size, was chosen to adequately capture the bridging
phenomenon with a layered mesh.
build-up process at the macro scale: a weakly coupled sequential
thermal-mechanical simulation and an inherent strain
simulation[1]
. Each method has its advantages and disadvantages,
which are detailed below. The best approach to solve a particular
problem depends on the application, geometry of the part, and
the goal of the analysis[7]
.
2.2 Sequential Thermal-Mechanical Approach
The sequential thermal-mechanical analysis assumed a weak
coupling between the thermal and structural physics[1]
. First,
a transient heat transfer analysis is performed to solve for the
thermal history of the part as shown by the balance of thermal
energy equation below:
[1]
where r is the mass density, Cp
is the specific heat capacity, T is
the temperature, q is the heat flux, and r is the heat source such
as laser heating. Conduction, convection, and radiation effects
are captured during this step. Based on the temperature history,
a series of nonlinear static analyses are performed to solve for the
residual stresses and part distortion, as shown by the balance of
force below:
[2]
where U is deformation, T is the Cauchy stress tensor, and b is
the body force. This approach is more time consuming but more
accurate than the inherent strain approach. Several commercial
AM process simulation software packages are available, including
Ansys[2]
and Dassault Systèmes 3DExperience[10]
. This paper
. This is necessary to achieve reasonable
employs Ansys Workbench™ Additive to perform the study.
Ansys software first simulates the thermal phenomena by
heating up each element layer all at once with layer-by-layer
addition. As a simplifying assumption, the entire superlayer
was initially set to the melt temperature of the print material
regardless of scan pattern and did not explicitly model a heat
source from the laser. The underlying assumption for this
simplification is it assumed that process parameters, such as
laser power and scan speed, are appropriately set such that
lack-of-fusion porosity or keyhole defects do not develop. The
thermal history from a transient thermal analysis was used as an
input for a static structural analysis to calculate part distortion.
A simplified ideal elastic-plastic bilinear isotropic hardening
was used in the static structural analysis. The total strain
model[2]
vector is given by:
[3]
where {ee
}, {ep}, and {et
and thermal strain vectors, respectively[2]
obtained by:
[4]
where Tref
is the material reference temperature and a is the
coefficient of thermal expansion.
2.3 Inherent Strain Approach
The inherent strain approach is a simplified approach that
assumes an initial strain, which is calibrated for a given thermal
history based on the scan pattern used[4,11,12]
, for a mechanical
analysis. The Ansys approach uses a strain scale factor (SSF) to
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} are the elastic strain, plastic strain,
. Thermal strain, et
, is
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