Modeling the Microstructure Evolution During Additive Manufacturing of Ti6Al4V: A Comparison Between Electron Beam Melting and Selective Laser Melting
Modeling the Microstructure Evolution During Additive Manufacturing of Ti6Al4V: A Comparison Between Electron Beam Melting and Selective Laser Melting
Q.X. PEI peiqx@ihpc
Beam-based additive manufacturing (AM) is an innovative technique in which parts are built layerwise, starting from the material in powder form. As a developing manufacturing technique, achievement of excellent mechanical properties in the final part is of paramount importance for the mainstream adoption of this technique in industrial manufacturing lines. At the same time, AM offers an unprecedented opportunity to precisely control the manufacturing conditions locally within the part during build, enabling local influence on the formation of the texture and microstructure. In order to achieve the control of microstructure by tailoring the AM machine parameters, a full understanding and modeling of the heat transfer and microstructure evolution processes is needed. Here, we show the implementation of the non-equilibrium equations for phase formation and dissolution in an AM modeling framework. The model is developed for the Ti6Al4V alloy and allows us to show microstructure evolution as given by the AM process. The developed capability is applied to the cases of electron beam melting and selective laser melting AM techniques to explain the significantly different microstructures observed in the two processes.
Rapid prototyping differs from additive
manufacturing (AM) in that the former is concerned with
geometrical accuracy, while the latter adds a
stringent requirement for the part’s mechanical
properties.1 This requirement arises from the fact that AM
parts not only need to be built but also to be put into
service with an expected performance similar to, if
not better than, corresponding cast parts (if
available).2 In AM, several factors contribute to the
ultimate mechanical properties of the part,
including the manufacturing technique,3 the presence of
porosity, including incomplete melting,4 proper
thermal control to avoid balling/overmelting,5 and
the quality of the powder feedstock.6 Moreover, even
at optimal build conditions, in which the former
issues are minimized, a large role is played by the
actual metal microstructure, which represents the
ultimate factor that dictates the mechanical
properties of the part.
Ti6Al4V is a pseudo-binary alloy with rich
equilibrium7 and non-equilibrium8 phase diagrams. The
main phases are represented by b, which is
stable above 1000 C (beta transus),7 a, which is a
diffusion-controlled phase stable below the beta
transus, and martensite a0, which is a-competing
and originates from diffusionless transformation of b
under specific circumstances. From a traditional
metallurgy point of view, Ti6Al4V has been
extensively studied and significant works on it have been
published.9–11 For example, Lu¨ tjering et al. have
shown that the thickness of the a lath is the primary
factor influencing strength and ductility.12 In turn,
the a lath thickness is controlled by the cooling rate
after solidification, where faster cooling rates
correspond to thinner a laths.13 Moreover, rapid
quenching below the so-called martensite start temperature
(Tms) originates the a0 phase, which is hard but
brittle.14 Overall, metallurgy of Ti6Al4V has been
very successful in showing the relationship between
the microstructure and its mechanical properties.
Introduction of Ti6Al4V in AM opens tremendous
opportunities for manufacturing complex shapes
with industrial relevance, for example, cellular
structures for lightweight aircraft components.15
Therefore, understanding how the AM process
influences the part microstructure is of paramount
importance. In this regard, the focus of this work
will be on electron beam melting (EBM) and
selective laser melting (SLM), which are among the main
AM processes for Ti6Al4V. The primary footprint of
these two techniques is that SLM produces samples
with close to 100% martensite, while EBM (both
powder bed and wire feed) produces milder alloys
with fine a laths and retained b.3 At the same time,
a more sophisticated control of microstructure
would be highly desirable. For example, such
control could allow the production of parts with locally
tailored mechanical properties. In order to control
the microstructure during AM builds, it is first
necessary to understand how microstructure
evolves during the AM process. In this regard,
modeling is useful because it allows the study of the
process under well-defined and constant process
parameters, which is not necessarily the case in
actual machine builds in which process parameters
In this paper, we show the implementation of the
non-equilibrium equations of microstructure
evolution for Ti6Al4V in the framework of the additive
manufacturing process simulation, where particular
attention is paid to the modeling of martensite
formation and decomposition. Using the finite
element method (FEM) and starting from the solution
of the thermal problem, we use the thermal field as
input for the local microstructure calculation in
terms of the volume fraction of each Ti6Al4V phase.
The modeling allows us to show the evolution of the
phases as the laser or electron beam travels across
the domain. We apply the capability to both
scenarios of SLM and EBM additive manufacturing. Our
integrated thermal and microstructure model can
be a useful tool for modelers and designers to
understand and control microstructure evolution
during additive manufacturing of Ti6Al4V.
Modeling was based on the finite element method
(FEM) in which the commercial software ABAQUS
was used for meshing, solution, and post-processing.
Customization for additive manufacturing, as well as
for microstructure evolution, was implemented
through user subroutines. Additive manufacturing
was modeled by considering a two-dimensional (2D)
mesh of length 9 height of 5 9 1.2 mm. While such a
size is small compared to common AM parts, our
intention was to focus on a small mesh with fast
convergence, which could show us the details of the
thermal field as well as the microstructure evolution,
which would be hindered at a larger scale. Addition of
four layers of powder was considered, namely, the
simulation consisted in the sequential addition of
elements, using the ‘‘element birth’’ technique.
Between two subsequent layers, a representative
inter-layer time of 0.5 s was used to model the time
needed by the recoater to spread the new powder
layer. The simulation domain is shown in Fig. 1.
Element size was 50 lm, which was one powder layer
since the typical layer thickness for Ti6Al4V powder
is 50 lm.16 Quadrilateral, linear elements with four
integration points were employed.
The first step of the simulation consisted in the
solution of the thermal problem. Here, the beam
was modeled as a traveling body heat source, with
intensity in the SLM and EBM cases given by,
Iðx; zÞ ¼ px2 e
Iðx; zÞ ¼ px2 e
2 d0 þ 5
where P is the laser power, A is the absorptivity
(A = 0.4), i is the beam current (i = 10 mA), and V is
the electron gun voltage (V = 60 kV). Consistent
with experimental measures, the penetration depth
was set to 40 lm for SLM17 and 28 lm for EBM.18
Scan speed was set to v = 4.5 m/s and beam size was
x = 250 lm. Moreover, powder–liquid–solid phase
transformations were implemented such that the
material was explicitly described by a different set
of material properties depending on the local phase.
In particular, material properties were taken as in
Ref. 19. A phase-change rule was implemented to
allow phase change depending on local temperature.
For example, if the local phase was ‘‘powder’’ and
the temperature was rising above the liquidus, the
local phase was changed to ‘‘liquid’’ and the
corresponding material properties were used. Liquidus
and solidus temperatures were taken as 1650 C and
1605 C, respectively, and latent heat was 286,000 J/
Kg.7 More details on the thermal modeling,
including the implementation of the powder–liquid–solid
phase changes, can be found in Ref. 20.
As the thermal problem was solved, the
temperature evolution became available at each integration
point of the mesh. In turn, temperature was used as
input to a set of equations to describe the concurrent
microstructure evolution. In particular, our
modeling started from the work by Kelly and Babu21 to
describe evolution of the a and b phases, where
consideration for martensite a0 formation and
decompostion was added. At each integration point f, the
volume fraction of a at thermodynamic equilibrium,
fa;eq was first computed. Following
Charles-Murgau et al.,22 this quantity was calculated as
fa;eqðTÞ ¼ a8ðT=1000Þ8þa7ðT=1000Þ7þa6ðT=1000Þ6
þ a5ðT=1000Þ5þ þ a4ðT=1000Þ4
þ a1ðT=1000Þ þ a0
where T is the temperature in C and the numerical
constants read a8 ¼ 31188:514, a7 ¼ 170526:26,
a6 ¼ 388991:69, a5 ¼ 471927:45, a4 ¼ 315178:49,
a3 ¼ 99079:891, a2 ¼ 1667:1991, a1 ¼ 9726:8403,
and a0 ¼ 1884:7280. Moreover, the lower bound for
b was ensured by imposing aeq ¼ 0:917 for T < 650 C.
Then, the actual volume fraction of a was compared to
aeq and two scenarios arise, namely, b ! a if fa < fa;eq
and a ! b if fa > fa;eq. Both formation and dissolution
of a were governed by Johnson–Mehl–Avrami
equations of the form
Faðt; TÞ ¼ 1 e ktn fa;eqðTÞ
where t is time, k is the kinetic rate of the phase
transformation, and n is the Avrami coefficient. Both k
and n are dependent on temperature, and details of
their exact formulation have been reported in Ref. 21.
The exact implementation of the equations, as well as
the explicit value for the numerical coefficients, are
reported in the Supplementary Material.
The diffusionless transformation b ! a0 was
modeled as a competitive mechanism to the formation of
a. In particular, the following criteria was
implemented: if the local temperature was below 800 C
(martensite start temperature Tms16) and the local
cooling rate was faster than 410 C=s,23 the available
amount of b would transform into a0. Finally,
decomposition of martensite was implemented from
Gil Mur et al.,24 namely, the volume fraction of
recovered martensite upon heating was given by
vrðtÞ ¼ 1 e btk ð5Þ
where both b and k were temperature-dependent
and their numerical values were set as in Ref. 24.
Upon decomposition, the assumption was made that
a0 was forming equilibrium a and b. In other words,
naming da and db the volume fraction changes of the
respective phases during martensite decomposition,
the following relationships were implemented:
( dfa þ dfb ¼ dfa0
dfb ¼ 1 faeq
where fa0 is the change in martensite volume
fraction at time t. Machine specifications of EBM
and SLM were modeled as follows. The sample free
surface (i.e., the free surface of the topmost layer of
elements, independently of the number of layers
built) was allowed to exchange heat through
convection and radiation in the case of SLM, while only
through radiation for the case of EBM. The heat
convection coefficient was taken from Ref. 25 and
Ti6Al4V emissivity was set to 0.7.7 The difference in
preheating strategy between SLM and EBM was
considered by setting the initial domain
temperature, as well as the fixed temperature of the
boundary nodes to 700 C for the case of EBM, and
to 30 C for the case of SLM.
RESULTS AND DISCUSSION
We begin by validating our microstructure
implementation by directly comparing our computed
phases volume fraction with that of Kelly.21 At
this preliminary stage, the specifications of the AM
build are not yet activated, and the FEM domain is
used as a block of Ti6Al4V in which the
temperature of the entire domain is prescribed to the path
shown in Fig. 2a. Under these circumstances, the
predicted volume fraction of a, and the comparison
with the original implementation by Kelly, is
shown in Fig. 2b. Further checks showed that the
slight discrepancy in the predicted fa during the
second cooling stage was to be ascribed purely to
our choice of reference for aeq (Eq. 3). Therefore,
the level of agreement was considered satisfactory
and modeling was continued by activating the
beam heat source and heat boundary conditions
specific to AM. Moreover, the domain was set with
initial material of ‘‘powder’’ with enabled powder–
liquid–solid phase changes. The initial condition
for the microstructure was set to 91%a,
corresponding to 9% of retained b, as measured by
Malinov et al.26
Representative snapshots of the temperature and
of the microstructure evolution are shown in Figs. 3
and 4, respectively, where the blue and red colors
represents the volume fraction of b and a phase,
respectively. In particular, as the beam travels
across the powder and melts it, the temperature
increases above the beta transus, and in fact the
local phase is 100% b. Later, as the material cools, b
progressively transforms into a. At this point, a
distinction between a and a0 is not made yet, in the
sense that the volume fraction of a0 is incorporated
into that of a. A focus on the martensite component
will be the subject of the next paragraph. As a tries
to reach its thermodynamic equilibrium, its volume
fraction increases. This increase is shown in Fig. 4
by the progressive increase of a behind the melt
pool, and also during the interlayer cooling time
before deposition of two subsequent layers.
Moreover, it is shown that the scan of the following layer
has indeed a clear effect on the microstructure of the
layers below. In particular, heat is sufficient to
transform a into b through a thickness of about 10
equivalent powder layers. This result shows that,
indeed, materials processing in additive
manufacturing is characterized by multiple cycles of heating
and cooling above and below the beta transus.
Next, our focus was on the formation and
dissolution of martensite. To this end, two simulations
were designed to represent the typical conditions of
an EBM and a SLM machine, respectively. Here,
because of the importance of resolving as many
microstructure details as possible, a choice was
made to halve the mesh size to 25 lm 9 25 lm.
Specifically, the two simulations differ in the heat
source profile, the heat exchange at the free surface,
and the preheating temperature, as described in the
‘‘Model’’ section. Under these conditions, the volume
fraction of martensite at the end of the scanning of
the four layers is shown in Figs. 5 and 6 for SLM
and EBM, respectively. Comparison between the
two panels show the formation of martensite in both
cases, with slight variations in terms of qualitative
distribution. In particular, the distribution a0 is
shown to be more abrupt in the case of SLM than in
EBM. This feature can be understood by recalling
the lower build temperature, and therefore the
sharper thermal gradients, that characterize SLM
and therefore that limit the region of the sample
where the conditions for martensite formation are
After scanning was complete, the material was
allowed to anneal by keeping the boundary
temperature constant. Figures 5 and 6 show the evolution
of as-built martensite and, in particular, suggest
that martensite decomposition is complete in EBM,
while martensite is still mostly retained in SLM.
This result is in agreement with actual
manufacturing, where SLM samples consistently have more
martensite than EBM samples.3 Indeed, further
evidence of martensite formation and subsequent
decomposition was recently found for EBM
In summary, we developed a numerical scheme in
which the heat transfer and microstructure
evolution equations are coupled for the additive
manufacturing of Ti6Al4V parts. The simulations have
shown that the heat transfer arising from material
processing is sufficient to induce microstructure
evolution through several layers below the free
surface, and in particular to a depth of up to 10
layers. This result suggests that proper
microstructure control has to be achieved by taking into
account the effect of not only the first scan but also
of the next few in determining the final
microstructure. Formation and dissolution of martensite was
studied in the context of comparing EBM to SLM
processing. Given the two different processing
temperature conditions, it was shown that EBM
manufacturing allows for complete decomposition of
martensite after build, while SLM mostly retains
the martensite. Globally, our modeling represents a
specific tool to understand and predict
microstructure evolution in powder-bed additive
manufacturing, and can help to find the choice of process
parameters to locally control the microstructure
which, in turn, allows the control of the final
mechanical properties of the part.
The authors acknowledge helpful discussions
with Dr. W. Pan and S.M.L. Nai at A*STAR
Singapore Institute of Manufacturing Technology
(SIMTech), and X. Tan and Prof. S.B. Tor at
Nanyang Technological University. This work was
supported by the Agency for Science, Technology
and Research of Singapore through the Industrial
Additive Manufacturing Program (Grants 132 550
4103 and 132 550 4106).
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