Sequential thermomechanical analysis of a directed energy deposition
build
This example illustrates sequential thermomechanical analyses of
directed energy deposition builds of a thin-wall structure on a cantilevered
substrate.
The model in this problem is created based on published
experiments (Denlinger et al., 2015). The predicted results of temperature and
distortions histories during printing are in good agreement with experimental
measurements.
This example demonstrates the following
Abaqus
features and techniques:
using temperature-dependent thermal and mechanical properties;
performing thermomechanical simulation of additive manufacturing
processes, including techniques of progressive element activation, progressive
heating by a moving nonuniform heat flux, and progressive cooling on evolving
free surfaces; and
using special-purpose techniques for additive manufacturing.
Additive manufacturing (AM) technology has revolutionized design and
manufacturing. Directed energy deposition (DED) is one of the common additive
manufacturing technologies. During directed energy deposition, the material is
deposited by a nozzle mounted on a multi-axis arm and simultaneously melted by
a heat source (such as a laser or an electron beam). New material is added and
solidifies in a layer-by-layer fashion until the desired three-dimensional part
is built.
This example problem simulates the fabrication of a thin-wall structure on a
cantilevered substrate using the directed energy deposition process (Denlinger
et al., 2015). The test setup consists of an aluminum clamp, a substrate, and a
wall to be built on the center of the substrate. The substrate and the wall are
made of Inconel nickel-chromium alloy 625.
Geometry
As shown in
Figure 1,
the dimensions of the thin-wall structure are 101.6 mm (L) × 6.7 mm (W) × 38.1
mm (H). The dimensions of the substrate are 152.4 mm (L) × 38.1 mm (W) × 12.7
mm (H). The clamped region of the substrate is 8.46 mm long. The dimensions of
the clamp are 38.1 mm (L) × 38.1 mm (W) × 28.6 mm (H).
Material deposition
The wall is built using a three-bead deposition sequence per layer and a
total of 42 layers. The in-plane material deposition motion is shown in
Figure 2.
For each layer, the center bead is deposited first, followed by the two side
beads. All beads in a layer are deposited in the same direction. The deposition
direction alternates between layers.
The travel speed of the nozzle is 10.6 mm/second. Thus, it takes 9.58
seconds to deposit one bead. After the deposition of each bead, there is a
cooling period of 4.66 seconds. Three dwell times are considered for additional
cooling after the deposition of each layer: 0 seconds, 20 seconds, and 40
seconds.
The raw material (powder) is melted upon deposition by a laser with a power
of 2 kW. The laser beam spot size at the part surface is 4 mm in diameter. The
penetration depth of the laser is 1.1 mm.
Experimental measurements
Temperature histories were measured during the printing process using three
thermocouples placed on the bottom of the substrate, away from the action zone.
A laser displacement sensor was used to measure the end deflection history of
the substrate.
Figure 3
shows the location of the thermocouples and the measurement location of the
displacement sensor.
Abaqus modeling approaches and simulation techniques
Three pairs of sequentially coupled thermomechanical analyses are performed
in
Abaqus/Standard
to simulate three test cases of the Inconel builds of the thin-wall structure
with different interlayer dwell times.
Summary of analysis cases
Case 1
Sequential thermomechanical analysis of
the build with a 0 second interlayer dwell time
Case 2
Sequential thermomechanical analysis of
the build with a 20 second interlayer dwell time
Case 3
Sequential thermomechanical analysis of
the build with a 40 second interlayer dwell time
The following sections discuss analysis considerations that are applicable
to all cases.
Analysis types
A transient heat transfer analysis is performed first, considering thermal
loads introduced by the deposition process on the thin-wall structure. This
analysis is followed by a static structural analysis that is driven by the
temperature field obtained by the thermal analysis.
The wall mesh is progressively activated using full element activation (see
Progressive Element Activation).
The cross-section of a bead of material being deposited is assumed to be
rectangular with dimensions 3.35 mm (W) × 0.9071 (H), which is four elements
wide and one element high. The material deposition sequence is defined through
an event series.
Mesh design
Figure 4
shows the finite element mesh of the model. The thin-wall structure is modeled
with a uniform mesh of 8-node linear brick elements. The element size is 1.016
mm (L) × 0.838 mm (W) × 0.907 mm (H). A coarser mesh is used for the substrate
and the clamp. The heat transfer analysis and the structural analysis share the
same mesh strategy. DC3D8 elements are used in the heat transfer analysis, and C3D8 elements are used in the structural analysis.
Materials
The substrate and the wall are made of Inconel 625. The
temperature-dependent thermal conductivity, specific heat, the coefficient of
thermal expansion, elastic modulus, and yield stress are shown in
Table 1
(Denlinger and Michaleris, 2016). The density is 8.44 × 10-9
tonne/mm3. The solidus temperature is 1290°C, the liquidus
temperature is 1350°C, and the latent heat of fusion is 2.72 × 1011
mJ/tonne. The Poisson's ratio is 0.366.
The clamp is made of aluminum. Constant material properties are used:
Density
2.70 × 10-9 tonne/mm3
Conductivity
237 mW/(mm·°C)
Specific heat
9.1 × 108 mJ/(tonne·°C)
Elastic modulus
70 × 103 MPa
Poisson's ratio
0.366
Coefficient of thermal expansion
2.31 × 10-5 /°C
Analysis steps
Each simulation is performed using three analysis steps. The deposition
process is modeled in the first step with a small time increment of 0.5
seconds. The second and the third steps simulate additional cooling periods
after the built with larger time increments, 10 seconds and 100 seconds,
respectively. The total time for cooling is 10,500 seconds.
Heat transfer analysis
Initial conditions
Newly deposited material comes in at room temperature, 26°C. The initial
temperature of the clamp and the substrate are also at room temperature.
Loads
A moving heat flux with a Goldak distribution is used to model the heating
by the laser upon deposition (see
Specifying a Moving Heat Source with a Goldak Distribution).
The laser beam spot at the intersection with the part surface is assumed to be
circular. The laser scanning path is defined through the same event series that
defines the material deposition sequence. The energy absorption efficiency is
calibrated to be 40% for all cases.
Nodal temperature (NT) field output is requested for the whole model at every
increment of the analysis for use in the subsequent structural analysis. In
addition, nodal temperature (NT11) history output is requested for the three nodes at the
locations where the three thermocouples were placed in the experiments.
Static structural analysis
Initial conditions
Based on the mesh size and the time incrementation used, the analyses
presented in this example can be categorized as part-level simulations of
additive manufacturing processes. To capture the melting effect in the
structural analysis accurately, it is often necessary to assign an initial
temperature representing a relaxation temperature above which thermal straining
induces negligible thermal stress (see
Controlling the Scale of the Simulation and the Solution Fidelity).
In the structural analysis, the initial temperature of the wall is set to the
melting temperature of the material, 1290°C. The substrate and the clamp are
initially at the room temperature, 26°C.
Boundary conditions
All degrees of freedom of the nodes on the bottom and top surfaces of the
clamp are fixed.
Predefined fields
Nodal temperatures stored in the output database
(.odb) file of the previous transient heat transfer
analysis are read as a predefined field.
Abaqus
automatically maps the nodal values of temperature by interpolation (both in
space and time) of the previous results.
Output requests
Nodal displacement (U), stress (S), strain(E), and equivalent plastic strain (PEEQ) field output are requested for the whole model. In addition,
nodal displacement (U3) history output is requested for the node at the location where
the deflection of the substrate was measured in the experiments.
Discussion of results and comparison of cases
As shown in
Figure 5,
the simulations of the temperature histories of the three locations on the
bottom of the substrate agree well with the in-situ experimental measurements
for all cases. The agreement in temperature histories at locations that are
away from the action zone indicates that the heat energy balance of the system,
including heat energy input by the laser, thermal conduction, and cooling by
convection and radiation, is well captured.
Figure 6
compares the simulated and measured deflections of the free end of the
substrate for all cases. The oscillation due to the alternating deposition and
cooling periods and the accumulated deflection of the substrate are well
captured. The substrate bends downward during deposition due to a larger
thermal expansion of the top surface relative to the bottom surface, while it
bends upward during the cooling period because the substrate cools down and the
deposited material also starts to contract (Denlinger et al., 2015). The final
distortion and residual stresses of the substrate are caused primarily by the
thermal contraction of the thin-wall structure.
Types of property tables, parameter tables, and event series used by the
special-purpose techniques for the simulation of common additive manufacturing
processes in
Abaqus.
Event series data of the material deposition (and laser
scanning) motion, used by the analyses of the builds with a 40 second
interlayer dwell
time.
References
Denlinger, E.R., J. C. Heigel, P. Michaleris, and T. A. Palmer, "Effect
of Inter-layer Dwell Time on Distortion and Residual Stress in Additive
Manufacturing of Titanium and Nickel Alloys,"
Journal of Materials Processing
Technology, vol. 215, pp. 123–131, 2015.
Denlinger, E.R., and P. Michaleris, "Effect
of Stress Relaxation on Distortion in Additive Manufacturing Process Modeling,"
Additive
Manufacturing, vol. 12, pp. 51–59, 2016.
Tables
Table 1. Temperature-dependent material properties of Inconel 625 (Denlinger and
Michaleris, 2016).
Temperature (°C)
Conductivity (mW/(mm·°C))
Specific Heat (mJ/(tonne·°C))
Coefficient of Thermal Expansion
(1/°C)
Elastic Modulus (MPa)
Yield Stress (MPa)
20
9.9
4.10 × 108
1.28 × 10–5
2.08 × 105
493
93
10.8
4.27 × 108
1.28 × 10–5
2.04 × 105
479
205
12.5
4.56 × 108
1.31 × 10–5
1.98 × 105
443
315
14.1
4.81 × 108
1.33 × 10–5
1.92 × 105
430
425
15.7
5.11 × 108
1.37 × 10–5
1.86 × 105
424
540
17.5
5.36 × 108
1.40 × 10–5
1.79 × 105
423
650
19.0
5.65 × 108
1.48 × 10–5
1.70 × 105
422
760
20.8
5.90 × 108
1.53 × 10–5
1.61 × 105
415
870
22.8
6.20 × 108
1.58 × 10–5
1.48 × 105
386
Figures
Figure 1. Dimensions (Denlinger et al., 2015).
Figure 2. The material deposition (and laser scanning) path (Denlinger et al.,
2015). Figure 3. Locations of the thermocouples (TC) and the measurement location of
the laser displacement sensor (LDS) on the bottom of the substrate (Denlinger
et al., 2015). Figure 4. Finite element mesh. Figure 5. Temperature histories of thermocouples.
Figure 6. End deflection histories of the substrate.
