ORIGINAL RESEARCH

published: 10 May 2022

doi: 10.3389/fmats.2022.797226

Linkage of Macro- and Microscale

Modeling Tools for Additive
Manufacturing of Steels
Julia Sjöström 1,2, A. Durga 1 and Greta Lindwall 1*
1
Department of Materials Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden, 2VBN Components
AB, Uppsala, Sweden

Additive manufacturing (AM) offers several benefits including the capability to produce
unique microstructures, geometrical freedom allowing for material and energy savings, and
easy production lines with fewer post-processing steps. However, AM processes are
complex and phenomena occurring at different length and time scales need to be
understood and controlled to avoid challenges with, for example, defects, residual
stresses, distortions, and alloy restrictions. To overcome some of these challenges and
to have more control over the final product, computational tools for different length scales
Edited by:
Wentao Yan, need to be combined. In this work, an 18Ni300 maraging steel part is studied to
National University of Singapore, understand the link between the process parameters and the as-built microstructure.
Singapore
The temperature evolution during laser powder bed fusion is simulated using the MSC
Reviewed by:
Xin Wang,
simulation software Simufact Additive. This result is then linked to microscale models within
University of Pittsburgh, United States the Thermo-Calc software package to predict the elemental micro-segregation, martensite
Yefeng Yu,
start (Ms) temperature, and martensite fraction. The different values of the key process
Tsinghua University, China
parameters such as laser speed, laser power, heating efficiency, and baseplate
*Correspondence:
Greta Lindwall temperature are considered, leading to different thermal histories. The thermal histories
gretal@kth.se affect the elemental segregation across the solidification structure, which in turn results in
different Ms temperatures at different locations of the built part. It is found that higher laser
Specialty section:
This article was submitted to energy generally causes higher temperatures and higher cooling rates, which results in a
Computational Materials Science, larger degree of elemental segregation and lower Ms temperatures in segregated regions.
a section of the journal
Furthermore, the segregated regions are predicted to have Ms temperatures below 200°C,
Frontiers in Materials
which would result in retained austenite when using a baseplate temperature of 200°C. On
Received: 18 October 2021
Accepted: 28 March 2022 the other hand, by using a baseplate temperature of 100°C, all regions would reach
Published: 10 May 2022 temperatures below the Ms temperature, and an almost fully martensitic structure would
Citation: be possible. In summary, it is demonstrated how the linkage of macro- and microscale
Sjöström J, Durga A and Lindwall G
(2022) Linkage of Macro- and modeling tools for AM can be used to optimize the process and produce the desired
Microscale Modeling Tools for Additive microstructure, thereby achieving the desired mechanical properties.
Manufacturing of Steels.
Front. Mater. 9:797226. Keywords: maraging steel, laser powder bed fusion, temperature evolution, macro-scale modeling, micro-
doi: 10.3389/fmats.2022.797226 segregation, multi-scale modeling

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Sjöström et al. Modeling Tools for Additive Manufacturing

INTRODUCTION Material development is needed to accompany the new

additive way of manufacturing, and much focus is put on
Metal additive manufacturing (AM) is expanding in use and powder bed fusion (PBF)-based technologies in which the
research. More companies and institutions discover and explore powder is melted in a layer-by-layer pattern by a specific
the benefits of this growing and relatively novel technology. The energy source. Different steel grades are of major interest due
novelty, however, brings several challenges and areas to improve. to many possible benefits of steels in combination with the
For example, challenges arise regarding microstructure, residual geometrical freedom that the PBF technologies offer. In the
stresses, and distortions. The use of computational tools helps to tooling industry, for example, which has large requirements on
predict different aspects of the AM process in order to overcome material performance, high-strength martensitic steels are of
these challenges and control the final material properties. interest for AM. Chou et al. (2021) investigated a martensitic,
Process parameters such as laser scanning speed, laser power, medium carbon steel for hot-work tooling applications and
efficiency or absorptivity, hatch spacing, and baseplate correlated the Ms temperature and its dependence on the
temperature impact the final quality of the finished degree of micro-segregation with the retained austenite
component, such as surface roughness, microstructure, fatigue fraction using computational thermodynamics and kinetics
strength, density, and hardness (Sinaei and Fatemi, 2021). The tools. New alloy families for PBF are continuously being
laser scanning speed affects the amount of energy available to
melt the powder. If the speed is too high, it will leave unmelted
®
developed and the Vibenite group of alloys is one example in
which high carbon contents do not cause cracking but rather
powder resulting in porosity and poor surface quality. If the speed enhance performance further through the electron beam powder
is too low, the energy consumption is unnecessarily large, and the bed fusion (E-PBF) manufacturing method (VBN Components
risk for evaporation is larger. Similar consequences will rise if the AB, 2019). Up to 65% carbides are achieved which previously was
selected laser power is inappropriate. The efficiency of the process considered impossible to print and give rise to hardness levels up
is set by the amount of laser energy that is transferred to the
powder bed, after accounting for radiation, reflection, and
®
to 72 HRC in the case of Vibenite 290, which makes it one of the
hardest alloys in the world. These are examples in which AM
convection losses. In addition, a suitable build baseplate clearly provides improved performance, in addition to the
temperature can lower the risk of solidification cracking and geometry freedom (Beste, 2021).
distortions (Kempen, 2014). These factors, together with the Maraging steels have also been researched extensively for AM.
hatch distance, powder layer thickness, and scan orientation, Their low carbon content leads to a relatively soft martensitic
should be chosen optimally in relation to each other to reduce this matrix, which makes them less challenging to manufacture by
risk of porosity and to achieve dense parts. The thermal history AM than the higher carbon grades mentioned above. A common
and level of cleanliness also have a large impact on the final maraging steel used for laser powder-bed fusion (L-PBF) is of the
microstructure. During AM, high cooling rates cause phase grade 18Ni300 (Shamsdini et al., 2020). During L-PBF, the high
transformations far from equilibrium and large temperature cooling rates result in an as-built microstructure of highly
gradients may induce residual stresses and distortions (Kruth, dislocated martensite (Conde et al., 2021). The presence of the
2004; Belle, 2013; Papadakis et al., 2014). alloying elements Ni, Mo, and Ti results in nano-sized
Modeling may be used to predict the resulting characteristics of a intermetallic precipitates during post-heat treatments
printed component and can be helpful to minimize time-consuming performed for the material to reach desired toughness,
and expensive trial-and-error experimental methods. There are hardness, and Young’s modulus, etc. Aging also increases the
various approaches to simulate AM processes, ranging from austenite fraction (Kapoor et al., 2003; Jägle, 2014), and this
computational fluid dynamic tools such as ANSYS Fluent, austenite reversion typically occurs in Ni-rich regions of retained
ABAQUS, Sierra Multiphysics, Flow 3D, and ALE3D that austenite during over-aging and is desired when higher ductility is
simulate the temperature and strain evolution at the melt pool needed. In the case of L-PBF of 18Ni300, there is a possibility that
scale in great detail to those such as Simufact Additive, 3DSIM, the fraction of austenite increases during the process due to
Additive Works, and GEONX that use a simplified approach by intrinsic heat treatment. The upper part of the component
using an element layer technique instead of a moving heat source. experiences shorter intrinsic heating times, and there is less
The key to an efficient modeling approach is to enable interlinkage of time for austenite to grow and also for precipitation of the
phenomena occurring at different length scales. For this, simulated hardening precipitates. These aspects show why it is important
microscale information on a small computational domain should be to understand, and be able to predict, the influence of the process
connected to a macroscale calculation on a full component (Fan, parameters in order to optimize or control the resulting
2017). Due to the complexity of influencing factors, a combination of microstructure and material performance. Typically, a fine
modeling tools is needed. By combining CALPHAD-based tools cellular solidification sub-structure is seen in the as-built
with finite element method (FEM) modeling, meso- and macroscale microstructure after L-PBF of 18Ni300 in which the cell
aspects such as thermal evolution can be linked with microstructure diameter is ≤ 1 μm (Tan, 2017; Mutua et al., 2018). This very
models. This approach is necessary to understand the fine segregated cellular structure is achieved due to the high
connection between process parameters and material solidification velocities affected by the laser scanning speed.
characteristics and has for example been applied by Smith Higher speeds usually increase the cooling rate and leave no
et al. (2016) to predict the microstructure evolution during time for secondary dendrite arm formation (Freeman et al.,
solidification of an AM processed SS316L material. 2019).

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Sjöström et al. Modeling Tools for Additive Manufacturing

In the context of maraging steels, one particularly interesting all affect the energy density and, in turn, the temperature
area to investigate is martensite transformation. As-built evolution and the elemental segregation. The combination of
maraging steels consist of approximately 94% martensite printing parameters determines the process result, and it is
(Kempen et al., 2011; Mutua et al., 2018). The amount of therefore of interest to investigate different sets of parameter
retained and reversed austenite is correlated to the segregation combinations.
during solidification, which in turn depends on the cooling rates. One way to define the printing parameters more easily is to
Interdendritic/cellular regions tend to contain increased amounts introduce the volumetric energy density Ev. The parameters
of austenite-stabilizing elements, which decrease the Ms influencing Ev for L-PBF are defined in Equation 1 where P is
temperature in those regions. Chou et al. (2021) have shown the absorbed laser power [energy efficiency · laser power], v is the
that the segregation during L-PBF affects the martensite scanning speed according to Equation 2, D is the point distance, θ
transformation in hot-work tool steels. The is the exposure time, h is the hatch spacing, and w is the layer
martensite–austenite balance determines the material thickness.
properties and is therefore an important factor to predict. The
P
link between process parameters and phase fractions is thus Ev  , (1)
v×h×w
studied in this work with the aim to link macro- and
D
microscale modeling tools for 18Ni300 produced using L-PBF. v . (2)
The results can be used to find relations between different process θ
parameter sets and material characteristics so that desired The energy density needed to melt the powder, Em, depends on
microstructure and thereby mechanical properties may be the specific heat capacity, c, material density, ρ, melting
achieved. temperature, Tm, and the ambient temperature, Ta, according
to the following equation:

MATERIALS AND METHODS Em  c × ρ (Tm − Ta ). (3)

To study the microstructure evolution in an 18Ni300 component Furthermore, the latent heat of fusion is also considered in the
during L-PBF, the macroscale temperature evolution was first simulations. These equations include the most important process
simulated using MSC simulation software Simufact Additive parameters and are hence helpful when optimizing the L-PBF
(Simufact Additive, 2020). The results from these simulations process (Yakout, 2017; Yin et al., 2018; Shamsdini et al., 2020).
were then linked to microstructure models within the Thermo-
Calc software package (Andersson et al., 2002) to study how Simulation Setup
printing parameters affect the micro-segregation and The simulations were run on a Windows 10 Version 1903 for
subsequently, the Ms temperature. x64-based systems and Intel Core i5, seventh generation
Simufact Additive is an MSC software tool developed for fast computer. When deciding the different build parameters, the
prediction of macroscale properties for powder bed-based highest as-built density was aimed for according to the previous
additive manufactured components. Simufact Additive uses the L-PBF studies of 18Ni300. The range of energy density giving
Lagrangian computational framework by MSC Marc which optimal part densities is usually 67–123 J/mm3, and reported
allows for the easy activation/deactivation of element parameters (Yakout, 2017; Yin et al., 2018; Shamsdini et al.,
technique saving computational cost (Megahed et al., 2016). 2020) were used for this study, as shown in Table 1. The laser
Heat conduction and radiation are solved at every time step. energy efficiency was set to 99.2% to reach the recommended
Phase transformation is considered using the Leblond model energy density of 67.47 J/mm3 (Tan et al., 2017; Bhardwaj and
involving CCT and TTT diagrams (Leblond and Devaux, 1984). Shukla, 2018). It is assumed that the energy density given in the
Furthermore, it assumes a flat powder and layer surface and does literature is the one reaching the powder, after considering
not consider element vaporization during the build. The powder energy losses from radiation, reflection, and convection. It is
characteristics are also not considered in the simulations, and the also assumed that this energy density is large enough to remelt
powder does not possess any material differences from bulk the underlying layer, ensuring a high densification. A “stripe-
material such as density and conduction. Densities for bulk wise” scanning strategy was set in accordance with Shakerin
material are, however, considered temperature-dependent for et al. (2019), and the initial baseplate temperature was 200°C.
martensite and austenite as well as Young’s modulus (Wang, The scan width is defined as the distance between two parallel
2018). Finally, the thermal model does not consider the beam centers. The simulated part geometry is shown in Figure 1
microscale properties such as surface tension, evaporation, and the selected measuring points are shown in Figure 2. The
recoil pressure, and Marangoni effect of the melt pool part geometry was chosen to include different shape types, in
(Megahed et al., 2016). order to compare and see if there were any local differences
between the points at varying locations. The points were chosen
Thermal Evolution accordingly and kept the same for all simulations to observe any
The printing parameters that were varied and examined in the geometrical related differences. The part was imported as a
Simufact Additive simulations are laser speed, laser power, laser CAD-file (Guillaume, 2019) and placed 3 mm above the
energy efficiency, and baseplate temperature. These parameters baseplate. An orientation assistant, included in the Simufact

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Sjöström et al. Modeling Tools for Additive Manufacturing

TABLE 1 | Recommended printing parameters for 18Ni300 (Yakout, 2017; Yin et al., 2018; Shamsdini et al., 2020).

Laser Speed Beam Scan Scan Hatch Layer Energy density

power [W] [mm/s] width [mm] width [mm] overlap [mm] distance [mm] thickness [mm] [J/mm3]

285 960 0.15 10 0.08 0.11 0.04 67.47

TABLE 2 | Composition of 18Ni300 in weight % (wt%).

Ni Co Mo Ti Al Mn C Fe

18.5 9 4.8 0.6 0.1 0.1 0.03 Balance

Simufact Additive simulations. Since this efficiency depends

on the powder and the laser source and thus is not readily
available, it was also varied in the simulations. The efficiency
values were selected either to match a reported energy density
or set to a more expected value. For the other parameters in the
Simufact Additive simulations, the recommended actual build
parameters (Yakout, 2017; Yin et al., 2018; Shamsdini et al.,
FIGURE 1 | Part geometry used in the Simufact Additive simulations. 2020) were used as a starting point (Case 1-reference). The
values were then varied (Cases 2–7) to values large enough to
see changes in the simulation results.
Additive software, calculated the optimal geometry orientation
considering the support area and volume, projected area,
Micro-Segregation During Printing
The diffusion module (DICTRA) in the Thermo-Calc software
component height, cost, and local minima. A support
package was used as a linkage tool to connect the process
structure of 0.12 mm thickness was generated.
simulation to the microstructure evolution. DICTRA
The composition of 18Ni300 applied in this work is listed in
simulates diffusion-controlled phase transformations in one
Table 2. For the thermal evaluation, a copy of the “MS1-MPM,”
dimension for multi-component systems assuming a sharp
a similar maraging steel powder from the Simufact Materials
phase interface and that local equilibrium holds at that
database was first set as the material. The thermal conductivity
interface. The temperature evolution is required as an input,
and specific heat capacity of 18Ni300 are temperature-
as well as the CALPHAD atomic mobility data for diffusion in
dependent properties which may highly influence the
the liquid and the solid phases in addition to the CALPHAD
simulation results. In order to obtain reliable results, the
thermodynamic data.
predefined values in Simufact Material were compared to
values calculated using Thermo-Calc (Andersson et al., 2002)
Simulation Setup
and to literature data. The thermal conductivity, latent heat of
The elemental segregation in the current work was simulated
fusion, Young’s modulus, and density were kept as the
in the diffusion module DICTRA in Thermo-Calc 2020a, using
predefined MS1-MPM values whereas the specific material
the Thermo-Calc Software TCFE10 and MOBFE5 Steels/Fe-
properties such as solidus and liquidus temperatures, specific
alloys databases2. The thermal histories of Cases 1, 4, and 5
heat capacity, and thermal expansion factor were calculated for
were imported from Simufact Additive to consider the non-
the 18Ni300 composition using the thermodynamic database
isothermal and time-dependent nature of AM. The small time
TCFE101, see Table 3. Lastly, the numerical setting of calculated
steps in the FEM data caused numerical problems in the
time steps considered for each voxel layer was increased from
DICTRA calculations. Therefore, the temperature evolutions
the default value of 14 to 20.
were approximated as stepwise functions ensuring that the
To investigate the thermal evolution at the chosen points of
cooling rates remained within around 30% of the cooling rates
the geometry, the mesh setting was fixed to 0.7 mm and power,
obtained from the Simufact simulations between each time
efficiency, speed, and baseplate temperature were varied. The
step. A computational 1D region of 250 nm representing half
different combinations of varied parameters are listed in
of the cellular spacing was entered as the computational
Table 4, and each case has been addressed with a number
domain size with a double geometric grid with 180 points
for convenience. In addition to the process parameters (laser
with 10% increased grid point density at each edge. Liquid was
power, scanning speed, and baseplate temperature), the laser
entered as the active phase present at the start of the
power absorption efficiency is needed as an input for the

1 2
Thermo-Calc Software TCFE10 Steels/Fe-alloys database. Thermo-Calc Software MOBFE5 Steels/Fe-alloys mobility database.

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 2 | Measuring points for temperature evolution in the geometry.

TABLE 3 | Thermodynamic material properties for 18Ni300 calculated using the TCFE10 database1.

Solidus temperature [°C] Liquidus temperature [°C] Evaporation temperature [°C] Latent heat for Latent heat for
melting [J/kg] evaporation [J/kg]

1387 1441 2862 256,400 6.09, 106

TABLE 4 | Seven cases of different combination of process parameters studied by the Simufact Additive simulations.

Case 1-Reference 2-Speed 3-Efficiency 4-Baseplate 5-Power 6-Same Ev as Case 1 7-Only power change

Mesh [mm] 0.7 0.7 0.7 0.7 0.7 0.7 0.7

Power [W] 285 285 285 285 400 400 400
Speed [mm/s] 960 1000 1000 960 960 960 960
Efficiency [%] 99.2 99.2 80 99.2 80 70.7 99.2
Baseplate T [˚C] 200 200 200 100 200 200 200
Energy density [J/mm3] 67.5 64.8 52.2 67.5 76.4 67.5 94.7

simulation, and FCC (austenite) was set as the inactive phase, but excluding the liquid phase which allowed them to run till
allowed to form at the right interface boundary. In order to the end.
improve the speed of the simulations, but without affecting the
results significantly, only the major alloying elements were Ms Temperature
considered in the simulations, namely, Ni, Co, Mo, Ti, and Fe. Based on the segregated compositions calculated using DICTRA
Points A and D in the geometry were compared for the for Cases 1 and 5, the Ms temperatures at point A and D were
reference case (Case 1), Case 5 with higher power, and Case 4 calculated using the Ms temperature property model in Thermo-
with lower baseplate temperature. During the solidification Calc.
calculation, the elemental segregations led to interface The Ms temperature model is a semi-empirical,
compositions at which liquid and austenite could not coexist thermodynamic-based model based on the work by
at equilibrium. Therefore, the calculations for both points for Borgenstam and Hillert (1997) and Stormvinter et al. (2012).
Case 5 and point A for Case 1 could not be completed and It uses the information of experimentally determined Ms
stopped when around 0.0005–0.05% liquid remained. In these temperatures for binary systems and thermodynamic
cases, the calculations were re-started from the same point in time calculations of the driving force for the austenite-to-martensite

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 3 | Temperature–time profiles at the bottom of the part (point D) using different sets of build parameters for (A) the first 1300 s/six temperature peaks for
Case 1, (B) the two first scans leading to melting and solidification, and (C) the second scan leading to melting and solidification for all cases.

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 4 | Cooling rates at the bottom of point D using different sets of build parameters.

transition. The model is capable of predicting Ms temperatures of same thermal history with near-identical cooling rates, see
multi-component systems such as commercial steels with good Figure 3C where the second temperature peak is shown.
accuracy (Stormvinter et al., 2012). These two cases use different build parameters but the same
energy density. Case 7 shows that a power increase has a
Simulation Setup significantly larger impact on the temperature evolution
The input composition for the Ms model was the composition compared to a change in the scanning speed. Case 5, in
profile across the cell calculated with DICTRA, grain size (set to which a higher laser power is used, leads to higher
100 µm) and the end of the martensite transition was taken as the temperatures than the other cases, even though the efficiency
baseplate temperature, which is assumed to be the temperature to is lowered. Case 4 uses a lower baseplate temperature, 100°C,
which the material is cooled to during printing. The which does not lead to a remarkable change in the cooling rate
thermodynamic Thermo-Calc Software TCFE10 Steels/Fe- compared to the baseplate temperature of 200°C. However, a
alloys database3 was used, and the calculations were run using lower minimum peak temperature is reached. As the cooling
TC-Python API of Thermo-Calc to enable efficient calculations proceeds, Case 4 exhibits higher cooling rates than Case 1.
for multiple compositions. Figure 4 shows the cooling rates for point D. Higher peak
temperature also correlates with a higher cooling rate.
The same pattern is shown when evaluating point A at the top
RESULTS of the component, see Figure 5. The first temperature peaks reach
a lower value than for point D, while the second reaches slightly
Thermal Evolution higher temperatures. Furthermore, point A exhibits much higher
The thermal history at point D at the bottom of the part is cooling rates as seen in Figure 6.
shown in Figure 3A for Case 1. It shows the first 1300 s during When comparing the first temperature peaks for point D
which the location experiences six temperature peaks and is with those for point A from time 0 (corresponding to the start
representative of all cases. The thermal histories for all sets of of complete melting of the region), it is shown that at point A,
process parameters are shown in Figure 3B. Here, only the first the time between each layer is shorter, see Figure 7. The
two temperature peaks are shown to make the comparison results for point C resemble the results for point D. However,
between the different cases easier. They indicate the peaks at the first temperature peak, the cooling rate and
during which melting and solidification occur. The time temperature are initially higher for point D but reaches
interval between each peak is a result of the time needed to lower temperatures faster than for point C. For the
finish melting that particular layer. The slight change in time subsequent peaks, the maximum cooling rates are instead
interval between each case is due to the variation in the higher for point C.
parameter settings, for instance, a higher speed results in a A summary of the results and how different parameter inputs
shorter time interval. Cases 1 and 6 show approximately the affect the resulting cooling rates and segregations are shown in
Table 5.
The results of the first three temperature peaks for all cases are
3
Thermo-Calc Software TCFE10 Steels/Fe-alloys database. shown in Table 6. The results for point B are in line with the

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 5 | Temperature–time profiles at the top of point A using different sets of build parameters.

FIGURE 6 | Cooling rates for the top of point A using different sets of build parameters.

expected trends, moving further from the baseplate from point D, The temperature–time profiles from the Simufact Additive
to point B and to point A. simulations used as an input to the DICTRA calculations for the
reference case (Case 1), and the increased energy density printing
Micro-Segregation During Printing condition case (Case 5) are shown in Figures 9 and 10,
To study the effect of the thermal histories on the micro- respectively. Only one temperature peak is shown to enable
segregation and the Ms temperature when using a lower the comparison of the different temperature profiles.
baseplate temperature and higher energy density compared to For each case, the DICTRA calculations resulted in the same
the results of the reference Case, Cases 1, 4 and 5 were used as an compositional segregation profiles irrespective of whether one,
input to the DICTRA simulations. two, or three temperature peaks from the last temperature peak
The equilibrium phases for 18Ni300 expected to be present at reaching above the liquidus temperature were used as an input.
different temperatures are shown in Figure 8 and the first solid Supplementary Material shows an example simulation using one
phase to form, FCC (austenite), was used in the diffusion and two scans from the last temperature peak above the liquidus.
simulations together with the liquid. Hence, only one peak for each case was used.

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 7 | First temperature peaks of points A and D for reference Case 1.

TABLE 5 | Summary of parameter effects on cooling rate and segregations.

Case ↑ Speed ↑ Efficiency/absorbed ↓ Baseplate temperature ↓ Efficiency/absorbed

power power

Cooling rate Slightly Increased Slightly decreased for the second peak but increased for following Decreased
decreased peaks
Segregation Slightly Increased Increased Decreased
decreased

TABLE 6 | Summary of the thermal simulation results for all cases and locations.

Case 1A 1B 1C 1D 4A 4B 4C 4D 5A 5B 5C 5D

First peak, T [°C] 4280 4434 4433 4434 4279 4432 4432 4432 4696 4901 4901 4901
Cooling rate [°C/s] -77876 -40359 -21821 -22519 -77852 -40348 -21785 -22506 -94313 -47767 -25122 -26059
Time [s] 0 0 0 0 0 0 0 0 0 0 0 0
Second peak, T [°C] 2755 2701 2691 2695 2715 651 2637 2638 3016 2953 2944 2948
Cooling rate [°C/s] -33635 -18482 -10745 -10443 -33461 -18285 -10610 -10302 -41434 -22316 -12571 -12275
Time from the first peak [s] 180 191 222 218 180 191 222 218 180 191 222 218
Third peak, T [°C] 1150 121 1053 1095 1107 072 1003 1042 1220 1192 1120 1167
Cooling rate [°C/s] -735 -701 -629 -569 -704 -683 -608 -543 -826 -774 -710 -645
Time from the first peak [s] 361 383 444 439 361 383 444 439 361 383 444 439

The composition profiles obtained from the DICTRA 2755 °C for Case 1 and 3016 °C for Case 5 and the cooling rates
simulations for Cases 1, 4, and 5 after around 200 s after were approximately −34,000 °C/s and −41,000 °C/s,
cooling from approximately 3000°C to 200°C are shown in respectively. The composition profile for Case 4 is shown
Figure 11 for point D and in Figure 12 for point A. in Figure 13 comparing points A and D, illustrating the
Slightly more segregation was obtained for the increased increased segregation for point A due to higher cooling rates.
energy density (Case 5) except for point A where Case 1
instead resulted in the largest segregation. The higher energy Ms Temperature
density created higher peak temperature and a higher cooling The Ms temperature calculations indicate that higher Ni and
rate. The maximum temperature for point D was 2695 °C for Mo contents decrease the Ms temperature. Figures 14 and 15
Case 1 and 2948°C for Case 5 and the cooling rates were show how the Ms temperature changes over distance. The
approximately −10,000 °C/s and −12,000 °C/s, respectively, for closer the last solidified material (distance = 0, intercellular
the last temperature peak reaching the liquid state for each region), the lower the Ms temperature. The center of the cell is,
printing condition. The peak temperatures for point A were thus, experiencing a higher Ms temperature than the

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Sjöström et al. Modeling Tools for Additive Manufacturing

point D and a slightly larger variation of the Ms temperature as

a consequence.

DISCUSSION
Thermal Evolution
The thermal history varies depending on where in the
component the results from the Simufact Additive
simulations are collected. It also depends on the baseplate
temperature and process parameters. The process parameters,
represented by the energy density, affect the cooling rate and
resulting microstructure. The second temperature peak was in
all cases the last scan reaching to a temperature above the
liquidus temperature where the material was completely
melted and the corresponding cooling rate from that peak is
thus the one affecting the as-solidified microstructure and the
cooling rate that is referred to in coming sections.
The calculated cooling rates (Table 6) are lower than
normally expected for the L-PBF process, for which cooling
rates up and above 106 K/s are possible (DebRoy et al., 2018).
In the cases where the cooling starts from around 3000°C for
top point A, the simulated cooling rates reach the largest values
but are still not close to reported values for L-PBF of 18Ni300
FIGURE 8 | Calculated equilibrium phase fractions for the 18Ni300 (Bai et al., 2017). The literature values are not specified to be
composition at 1 atmospheric pressure. the maximum rates or the rates during solidification, which is
necessary to know to make a valid comparison since the
cooling rates are not constant during the process. However,
the current results show that Simufact Additive
intercellular region. For point A in Case 1, Ni and Mo have underestimates the cooling rates at higher temperatures
segregated more than those in the other cases, and lead to a where melting and solidification occur.
larger variation in the Ms temperature which reaches lower In an attempt to evaluate the FEM simulations, the calculated
values in the intercellular region. Case 4, in the case of lower cooling rate is used to predict the primary dendrite arm spacing
baseplate temperature, shows more segregation than Case 1 at (PDAS), λ1 (μm), and compared to experimental information on the

FIGURE 9 | Temperature–time profile retrieved from Simufact Additive and used as an input to DICTRA for reference Case 1.

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 10 | Temperature–time profile retrieved from Simufact Additive and used as an input to DICTRA for power Case 5.

FIGURE 11 | Calculated composition profile for point D for Cases 1, 4, and 5. Dendrite/cell center at the right side and interdendritic/intercellular region to the left.

microstructure available in the literature. An equation for the PDAS suggests that the calculated cooling rates are
is given as follows: underestimated. Nevertheless, in this way, Equation 5 could
be used to connect the temperature profiles from Simufact
−n Additive to the DICTRA calculations and thus, provide
λ1  αT_ , (5)
guidance when selecting the computational domain size for
where α and n are material specific constants, respectively, and DICTRA simulations.
T_ is the cooling rate. The n coefficient should be between 0.2
and 0.5 and α should be in the range 60–100 ms/K for steels Location
(Freeman et al., 2019). The exact values need to be calibrated Both the local geometry and distance to the baseplate influence
through experiments, but if α and n are set to 0.35 and 80 ms/ the thermal history. The top of the geometry reaches higher
K, respectively, PDAS in the range of 1.5–3 µm are obtained for temperatures which can be explained by less surrounding
the simulated cooling rates. This is somewhat larger size than material to act as conducting media and shorter time between
reported for as-built microstructures of L-PBF processed each scan, which accumulates heat. The higher cooling rates for
18Ni300 (Tan, 2017; Mutua et al., 2018), which further point A can be explained by the longer distance to the baseplate.

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 12 | Calculated composition profile for point A for Cases 1, 4, and 5. Cell center is at the right side and interdendritic/intercellular region to the left.

FIGURE 13 | Calculated composition profile for Case 4 for points A and D. Dendrite/cell center at the right side and interdendritic/intercellular region to the left.

Even though the amount of surrounding material to act as baseplate temperature. Since the temperature difference
conductive media is less, the fewer added layers on top of between the melted spot and baseplate is large in the
point A than those on points B and C, may have a larger beginning, an explanation of this can be that the relatively
influence. This decreases the accumulation of heat at the top small change in baseplate temperature will not influence the
of the geometry. cooling for the first peaks, but rather the laser scanning
strategy.
Baseplate Temperature
The cooling rate is not significantly affected by lowering the Energy Density
baseplate temperature from 200 °C (Cases 1–3 and 5–7) to The simulations indicate that similar temperature history and
100 °C (Case 4). In fact, the cooling rate is slightly lower for the segregation results are obtained when using the same energy
first peaks, but higher for the other peaks as the process density. Similarly, Yakout (2017) found that the same energy
proceeded for Case 4 compared to the cases with a higher density value gave similar material density and microstructural

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Sjöström et al. Modeling Tools for Additive Manufacturing

FIGURE 14 | Calculated Ms temperature variation for point D as a function of distance from the intercellular region for cases 1, 4, and 5.

FIGURE 15 | Calculated Ms temperature variation for point A as a function of distance from the intercellular region for cases 1, 4, and 5.

results after processing. The energy density, according to et al. (Reis et al., 2015), the Ms temperature is 194 °C and the
Equation 1, increases proportionally with increasing power. If Mf temperature is 62°C for this maraging steel, implying that a
the energy density is kept constant by increasing the laser power fully martensitic structure at room temperature is possible.
and by equivalently decreasing the scanning speed, similar These values are based on the nominal composition of the
thermal results will, thus, be obtained, although the simulation alloy. Due to segregation, however, the local composition
time will increase. It is, however, important to remember that changes, and thereby, the Ms temperature. Generally, the
changes of the scanning speed will affect the melt pool. Higher current simulations show that the higher energy density
scanning speed cannot always be compensated by an increase in creates more segregations due to the higher cooling rate,
power and will result in unmelted powder and rough surfaces. A which is expected when solute trapping is not considered.
change in the laser power alone does, however, influence the At higher cooling rates, there is less time for elemental
temperature evolution remarkably according to both Simufact diffusion and homogenization of the elements in the solid
Additive simulations and literature. In the current simulations phase. This causes alloying elements such as Ni, Mo, and Ti to
with Simufact Additive, the energy density is the major input segregate to the liquid during the solidification, which
parameter influencing the thermal results. stabilizes austenite and lowers the M s temperature for the
current material system. The DICTRA results for the
Segregation and Ms Temperature composition profiles as a function of distance from the
The calculations show a clear correlation between the cooling intercellular regions correspond to the reported Ms
rate, segregation, and Ms temperatures. According to dos Reis temperatures. The intercellular region, with a higher Ni

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Sjöström et al. Modeling Tools for Additive Manufacturing

content which stabilizes the austenite, has lower Ms Furthermore, the thermal histories reach higher
temperature. On the contrary, the regions with a lower Ni temperatures and larger cooling rates when using higher
content have higher Ms temperature. energy density. This may affect pore formation, spatter, and
The thermal simulations show that the build never reaches unmelted powder which is currently neglected in the
temperatures far below the baseplate temperature. Relating simulations. The results based on the specific printing
this to the Ms temperature, it is found that some parts of the parameters are hard to evaluate quantitatively and validate
build do not reach the Ms temperature when using the 200°C due to lack of similar experimental setups and thermal results
baseplate. Figures 14 and 15 show that the intercellular region to compare with. In order to reach the recommended energy
has an Ms temperature below 200°C, explaining why retained density with the suggested printing parameters, the efficiency
austenite is found in those areas (Jägle, 2017; Conde et al., is needed to be set to 99.2% which is unlikely due to thermal
2021). When instead of simulating with a baseplate losses.
temperature of 100°C, the segregated regions of the build The applied Ms temperature model does not consider the
reach temperatures below the Ms temperature, allowing for effect of thermal stress on the transformation temperature
a full or almost full martensitic structure. Figures 14 and 15 which introduces uncertainties in the calculations. In addition,
show that a lower baseplate temperature, and hence a slightly sample preparation can lead to phase transformations and
higher cooling rate as in Case 4, affect the Ms temperature affect the fraction of austenite and martensite observed during
compared to reference Case 1. experimental microstructure evaluation (LeBrun et al., 2015;
Comparing points A and D for all cases shows a larger Conde et al., 2019). Another factor to consider is the slightly
degree of segregation at point A than at point D. This can be lower cooling rate used in the DICTRA calculations compared
explained by the higher cooling rates at point A. While with the one obtained from the Simufact Additive calculations
comparing similar locations across different cases, however, due to the approximation of stepwise temperature functions.
there is an exception when comparing point A in Case 1 and In addition, the temperature history is in reality cyclic, with
point A in Case 5. Although the cooling rates are higher for higher cooling rates, which also has an effect on the martensitic
Case 5, the segregation is lower than Case 1. The reason for this transformation. In the current simulation, the sixth peak is still
can be that the temperature where the cooling starts to slow within the austenite phase region but for a very short period of
down after solidification, see Figure 5, is higher in Case 5 time, leaving little time for homogenization of the elemental
compared to Case 1. Hence, point A for Case 5 experiences segregation. Experimentally, the material is less homogenized,
longer times at slightly higher temperatures than point A for leaving only the very last segregated liquid that solidified to
Case 1. This allows for more elemental diffusion and hence, form austenite. The thermal distribution within the melt pool
less segregation. is also not considered in the layer-based simulations in this
By using a baseplate temperature of 200°C, the maximum work. The higher cooling rates at the melt pool boundaries
predicted martensite fraction is approximately 73%, which is compared to those at the middle create segregation differences
lower than the experimental values of 94.2% (Kempen et al., within a layer, and the interaction of neighboring tracks can
2011) and 99.9–99.98% (Conde et al., 2021). However, it is cause local differences in the cooling rate, thus altering the
difficult to compare the simulated results with the austenite/martensite phase fractions.
experimental data quantitatively since the predicted cooling Although the DICTRA results lead to the expected influence
rates are lower than expected, which in turn affects the degree on the Ms temperatures, the model also comes with
of segregation. simplifications to consider. For example, at high solidification
Furthermore, inhomogeneous distribution of elements has velocities, finite interface kinetics and solute trapping may
also shown to promote austenite reversion. Studies have influence the segregation which is not accounted in these
observed enrichments of Ti, Ni, Mo, and Co in intercellular simulations.
areas which obstruct the martensitic transformation on cooling Finally, since the calculations are dependent on each other,
(Jägle, 2017). The locally increased alloying in the last solidified uncertainties in the models may lead to the propagation of errors
material, in the intercellular areas, accelerates the austenite in the proceeding steps, and the accumulated uncertainty is
reversion during post-heat treatments. Since the reversion is difficult to quantify.
diffusion controlled, homogenization and quenching of the
material post L-PBF will facilitate a fully martensitic Benefits
microstructure. The linkage of the different modeling tools made this
investigation possible. In order to run a reliable thermal
Limitations and Challenges simulation, accurate material input parameters are required
A limitation with this approach is that Simufact Additive does which were first obtained from the thermodynamic
not aim to describe the AM process on the melt pool scale in calculations and inserted in the material database in Simufact
detail, which is needed in order to accurately predict the Additive. To relate the thermal histories to segregation, Ms
cooling rates during solidification. Consequently, the temperatures, and martensite fractions, the macroscale
current simulations underestimate the cooling rate which in temperature profiles were used as an input in the microscale
turn affect the predicted micro-segregation and Ms DICTRA calculation. These results could also be used to further
temperatures. analyze the Ms temperature and martensite fractions and

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Sjöström et al. Modeling Tools for Additive Manufacturing

compare them with experimental results reported in the • The choice of input build parameters, including baseplate
literature. There are numerous advantages of this approach. temperature, can be used to obtain microstructure with less
There are no material and equipment needed, apart from a micro-segregation with effects on the amount of martensite
computer, which makes the procedure cheap and relatively and austenite in the as-built microstructure. By lowering the
simple. This facilitates the investigation of many iterations and baseplate temperature, for instance, the martensite fraction
cases. The approach is also quick, giving fast indications and help can be increased.
before the actual manufacturing.
The majority of the FEM studies in the literature have
concerned fully thermomechanical approaches, focusing on DATA AVAILABILITY STATEMENT
distortions and/or residual stresses as a result of the thermal
history at the melt pool level. The connection of different The raw data supporting the conclusion of this article will be
length scales, including material characteristics, process made available by the authors, without undue reservation.
temperature, and microstructural impact, is not as
extensively explored. This study thus contributes to the
pathway of linking simulation tools for direct AUTHOR CONTRIBUTIONS
microstructure control by optimizing the process.
JS performed the simulations, wrote the first draft of the manuscript,
and edited it further. GL and AD supervised the work and reviewed
CONCLUSION and edited the manuscript. GL conceptualized the work.

Modeling tools were used to link macroscale results with

microstructure predictions to find relations between printing FUNDING
parameters and microstructural aspects such as segregation
and martensitic start temperature. The conclusions are as The strategic innovation program Metalliska Material
follows: through the project Design of Novel Materials and
Processes for Next Generation Additive Manufacturing
• The macro- and microscale results of L-PBF 18Ni300 (DEMA, 2018-00803), financed by the Swedish
maraging steel were successfully linked, and the results Governmental Agency for Innovation Systems
are qualitatively representative despite simulation (VINNOVA), Formas, and Energimyndigheten, is
simplifications. acknowledged for financial support.
• A higher energy density causes increased cooling rates
which lead to a larger degree of micro-segregation within
the cellular solidification structure. This, in turn, leads to ACKNOWLEDGMENTS
lower Ms temperature and more retained austenite at the
intercellular regions. The locations at the top of the JS also acknowledges VBN Components for the support, and GL
simulated component geometry show a larger degree of acknowledges support from VINNOVA, Energimyndigheten,
segregation when using recommended printing parameters and Formas via LIGHTer Academy.
compared to when an increased laser power is used. This is
explained by the higher temperatures reached due to the
increased power. SUPPLEMENTARY MATERIAL
• The locations closer to the top of the simulated component
generally experience higher cooling rates than a point closer The Supplementary Material for this article can be found online at:
to the baseplate. This causes segregation variation within https://www.frontiersin.org/articles/10.3389/fmats.2022.797226/
the part. full#supplementary-material

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Mutua, J., Nakata, S., Onda, T., and Chen, Z.-C. (2018). Optimization of Selective Publisher’s Note: All claims expressed in this article are solely those of the authors
Laser Melting Parameters and Influence of post Heat Treatment on and do not necessarily represent those of their affiliated organizations, or those of
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Papadakis, L., Loizou, A., Risse, J., and Schrage, J. (2014). Numerical Computation endorsed by the publisher.
of Component Shape Distortion Manufactured by Selective Laser Melting.
Proced. CIRP. 18, 90–95. doi:10.1016/j.procir.2014.06.113 Copyright © 2022 Sjöström, Durga and Lindwall. This is an open-access article
Reis, A. G. d., Reis, D. A. P., Abdalla, A. J., and Otubo, J. (2015). High-temperature distributed under the terms of the Creative Commons Attribution License (CC BY).
Creep Resistance and Effects on the Austenite Reversion and Precipitation of 18 The use, distribution or reproduction in other forums is permitted, provided the
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Shakerin, S., Hadadzadeh, A., Amirkhiz, B. S., Shamsdini, S., Li, J., and No use, distribution or reproduction is permitted which does not comply with
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