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A phase-field model for solid-state selective laser sintering of metallic materials
Accepted Manuscript A phase-field model for solid-state selective laser sintering of metallic materials
Xing Zhang, Yiliang Liao PII: DOI: Reference:
S0032-5910(18)30641-7 doi:10.1016/j.powtec.2018.08.025 PTEC 13610
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
4 May 2018 23 July 2018 8 August 2018
Please cite this article as: Xing Zhang, Yiliang Liao , A phase-field model for solidstate selective laser sintering of metallic materials. Ptec (2018), doi:10.1016/ j.powtec.2018.08.025
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ACCEPTED MANUSCRIPT A Phase-Field Model for Solid-State Selective Laser Sintering of Metallic Materials Xing Zhang,1 Yiliang Liao1,a) 1
Department of Mechanical Engineering, University of Nevada, Reno, Reno, Nevada, 89557 USA Author to whom correspondence should be addressed. Electronic mail: [email protected].
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a)
ACCEPTED MANUSCRIPT
Abstract Selective laser sintering/melting (SLS/SLM) is an additive manufacturing process that uses laser energy to sinter/melt powder particles together to construct solid structures.
Materials
In literature, most modeling efforts have been focused on
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for process control and optimization.
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modeling of microstructure evolution during such processes can be of great importance, especially
In this study, a phase-field (PF) based SLS model is
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microstructure evolution as a result of SLS.
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the microstructure evolution during SLM, while few attempts have been made to study the
developed to predict the evolving of microstructure in the solid-state SLS process.
The effects of
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laser power intensity and scanning speed on microstructure evolution are investigated.
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feasibility and capability of modelling in a large scale are demonstrated.
The
The modeling results are
validated by experimental findings in terms of the neck size between adjacent particles.
This PF
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based SLS model is found to be capable of predicting the neck growth for various metallic
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materials including 316L stainless steel, titanium, and nickel.
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Materials.
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Keywords: Selective Laser Sintering; Materials Modeling; Microstructure Evolution; Metallic
ACCEPTED MANUSCRIPT
1. Introduction Selective laser sintering/melting (SLS/SLM) is as an additive manufacturing process for rapid fabrication of three-dimensional (3D) components with complex geometries, widely used for
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In SLS/SLM, laser beam energy is employed to bind
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metals, ceramics and polymers [1].
powdered materials together through various binding mechanisms: solid state sintering, liquid Among these categories, solid-state
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phase sintering or partial melting, and melt-solidification [2].
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SLS aims at fabricating part by consolidating powders via heating the powders to a temperature below the melting point. This process involves sintering neck formation and mass transformation
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between adjacent powder particles without melting [3].
Compared to conventional sintering
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process, solid-state SLS can easily achieve to a temperature close to the melting point without significantly affecting the surrounding powder, leading to faster sintering rate and smaller grain size
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[4, 5]. This advantage along with high flexibility, controllability and fast heating rate make For solid-state SLS of microparticles, it
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solid-state SLS suitable to various industrial applications.
is generally accepted that this process is not suitable for manufacturing highly densified parts due
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to the short duration time of laser-induced heating effect [6], however, it has a great potential on 3D
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printing of porous structures [7] for specific applications, such as thermal management components [8] and biomedical devices [9].
In addition, recent studies demonstrate the feasibility and
advantage of employing solid-state SLS of nanoparticles to fabricate thin-film flexible electronics [10-12]. However, to date, it still remains a great challenge to understand and control the microstructure evolution during solid-state SLS, which determines the physical and mechanical properties of 3D printed structures, considering that this process is affected by multiple factors such as various laser processing parameters and powder properties.
For instance, Toloch et al. [13] investigated the
sintering neck size during solid-state SLS of titanium powder under different laser power.
Zenou
ACCEPTED MANUSCRIPT et al. [12] fabricated copper thin films by employing a pulse laser to copper nanoparticles in ambient conditions.
It was found that the resistance of as-built films decreased with the increase
of laser power and scanning speed due to denser structure and shortened oxidation period, respectively.
In order to achieve solid-state SLS products with desirable properties, it is of Nevertheless,
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specific importance to control the microstructure evolution during laser processing.
On the other hand, microstructure-based material
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timeframe of laser-induced heating effect.
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it is difficult to directly observe the microstructure evolution during solid-state SLS due to the short
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modeling provides us an alternative approach to understand the process-microstructure relationship during solid-state SLS.
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In recent years, extensive investigations have focused on SLM with binding mechanism of fully melt-solidification or partial melting [14-19], while only few efforts have been put on simulating
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the grain growth of nanoparticles during solid-state SLS using molecular dynamics (MD) method.
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However, this method is restricted by the small simulation area and large computational cost, thus it
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is not feasible for modeling microstructure behaviors during SLS in the micro or meso scale. Moreover, the mechanisms of nanoparticles (< 20 nm) sintering, which involve elastic/plastic
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deformation [20] and considerable atomic forces [21], are fundamentally different from mechanisms of sintering powdered materials in the micro/macro scale.
Clearly, there is a demand
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to develop a computational model to understand, control and eventually optimize the process with powder size from tens of nm to hundreds of μm. In this research, we propose a new PF based model to simulate microstructure behaviors during solid-state SLS of metallic materials.
Laser processing conditions are considered by integrating
PF codes with thermal modeling of continuous heating induced by laser irradiation.
The effects of
laser power intensity and scanning speed on microstructure evolution are investigated. feasibility and capability of modelling in a large scale are demonstrated.
The
The modeling results are
validated by experimental findings in terms of the neck size between adjacent particles. This PF based SLS model is found to be capable of predicting the neck growth for various metallic
ACCEPTED MANUSCRIPT materials including 316L stainless steel, titanium, and nickel. 2. Model Description The proposed solid-state SLS model is established by integrating the PF codes with a thermal model. This thermal model is developed first to obtain the temperature profile in the material as
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With the temperature result as an input, a PF model
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affected by the laser-induced heating effect.
(Multiphysics Object-Oriented Simulation Environment (MOOSE) developed by Idaho National
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Lab’s [22]) is applied to simulate the microstructure evolution.
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2.1 Thermal model
In this study, a 3D thermal model is developed for temperature evolution during SLS.
Fig. 1
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presents the schematic diagram of the simulation domain. The temperature profile T(x,y,z,t) can be
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determined by a general heat conduction equation [23]:
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C pT t
( k e T ),
(1)
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where ρ is the powder bed density, t is time, Cp is the temperature-dependent specific heat capacity,
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and ke is the effective thermal conductivity, which can be calculated by [24]: k e k (1 ) , p
(2)
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where k is the thermal conductivity of bulk material, θ is the porosity, and p is an empirical parameter related to powder properties.
Fig. 1. Schematic of thermal model domain. The environment temperature T0 is applied to the entire area as the initial condition: T ( x , y , z , 0 ) T0 .
(3)
The heat influx via laser irradiation and the heat loss induced by thermal convection and radiation are considered at the top surface.
Note that, since this model does not consider the laser
penetration in a loose powder bed, we focus on the temperature profile at the top surface.
Thus,
ACCEPTED MANUSCRIPT the boundary condition can be defined as [25]: ke
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Q h c (T 0 T z 0 ) (T 0 T z 0 ) , 4
z0
z
4
(4)
where Q is the laser energy flux, the suffix ’z=0’ represents the top surface, hc is the heat
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convection coefficient, ε is the surface emissivity and σ is the Stefan-Boltzmann constant. Other
T n
0,
(5)
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ke
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surfaces are assumed to be adiabatic:
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where n is the normal direction of specific surfaces.
The spatial distribution of laser energy on the target surface is considered to follow the
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Gaussian profile, where the laser intensity is at its highest at the center of the laser beam.
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the heat flux can be written as[26]:
( x vt ) y 2
2P 2
exp(2
2
2
(6)
),
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Q (1 R )
Thus,
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where R is the surface reflectivity, P is the laser power, ω is the effective laser spot radius, and v is the scanning speed.
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2.2 Microstructure model
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With the input of temperature history as predicted by the thermal model, a two-dimensional PF modeling is used to simulate the microstructure evolution during the solid-state SLS process. As compared with other mesoscale simulation tools such as Monte Carlo and Cellular Automaton, PF modeling is exceptional for microstructure behavior simulation since it is not required to explicitly track the surface and grain boundaries or impose boundary conditions.
In this work, the PF model
solves the minimization of total free energy F, which is the driving force of sintering process. According to the literature [27], the total free energy is given by a functional equation: F
V
[ f 0 ( , )
2
2
2
]d V ，
(7)
2
where f0(, η) is the local free energy density for a homogeneous system.
The second and third
ACCEPTED MANUSCRIPT terms describe the gradient energy densities from surfaces and grain boundaries, respectively.
The value of is given as 0 for pore
y, t) is the conserved variable representing the mass density. structures and 1 for particles.
(x,
ηi(x, y, t) is the non-conserved order parameter, standing for
different particle crystallographic orientations, where i =1, 2, …q and q is equal to the number of The value of η can be denoted as η1, η2, …, ηq = (1, 0, ..., 0), (0, 1, ..., 0), …, (0,
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powder particles.
ε and εη are gradient term constants.
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0, ..., 1) for different particles and η = (0, 0, ..., 0) for pores.
f 0 ( , ) A (1 ) B [ 2
2
2
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The local free energy density is defined as a double-well function [28]:
6 (1 ) i 4 ( 2 ) i 3 ( i ) ], 2
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i
3
i
2
2
(8)
i
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where A and B are constants related to grain boundary (GB) energy and surface energy. The constants in equation (7) and (8) can be given as [29, 30]:
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k1 ( 2 s
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k2
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A k 3 (1 2
s
gb
gb
gb
(9)
，
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B k4
) ,
gb
(10)
)/,
(11)
/ ，
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where γs and γgb are the surface energy and GB energy, respectively.
(12) δ is the GB width.
k1, k2, k3,
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and k4 are the constants used to normalize material parameters [29]. In order for the minimization of total free energy F, the corresponding phase-field variable (x, y, t) and order parameter η(x, y, t) need to be solved.
The temporal and spatial evolution of and
η represent the microstructure evolution and can be acquired by solving Cahn-Hillard (CH) and Allen-Cahn (AC) equations [31]: t
·M
i t
L
F
,
(13)
，
(14)
F i
where M and L are coefficients used to describe the atom diffusion mobility and the GB mobility,
ACCEPTED MANUSCRIPT respectively. The neck formation and grain growth during the sintering process are caused by mass transport and/or GB migration [32].
Since the mass transport involves various diffusion mechanisms
including surface, volume and GB diffusion as well as vapor transport, the atom diffusion mobility
vol
h ( ) M
vap
[1 h ( )] M
su rf
(1 ) M
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M M
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coefficient, M, can be calculated as [33]: gb
i
j
,
(15)
The value of M can be estimated based on the work of Ahmed et
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vapor, surface and GB diffusion.
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where h(φ) = φ3(10−15φ+6φ2) and Mvol, Mvap, Msurf, Mgb are the mobility coefficients for volume,
D lV m
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al. [30]: M
l
(16)
，
k BT
M
where the suffix ‘l’ corresponds to different diffusion modes, D is the diffusion coefficients, Vm is The value of D
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the molar volume, kB is the Boltzmann constant, and T is the local temperature.
can be estimated with prefactor Dl0 and activation energy Ql by following the well-known Arrhenius
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relation:
Dl Dl0 exp(
Ql
).
(17)
k BT
[34]:
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The grain boundary mobility coefficient, L, used to characterize GB migration, can be calculated by
L
4 W gb 3
,
(18)
where Wgb is the GB mobility and it also can be estimated by the Arrhenius relation. The temperature profile extracted from the thermal model is incorporated in the PF equations. The parameters for PF simulation are nondimensionlized with respect to the length scale, time scale and grain boundary energy.
Details for solving CH and AC equations by finite element method
have been discussed by Tonks et al. [22].
Here, strong form equations with high order terms are
ACCEPTED MANUSCRIPT converted to weak form equations by introducing a test function. A few assumptions are considered for the developed PF model: 1) Vapor diffusion is neglected in this simulation since its contribution to neck formation or grain growth is less important compared to the other three diffusion mechanisms; 2) The contribution from the thermal gradient
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driving force on microstructure evolution is not incorporated in the current model because only two
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particles within a small area are simulated and the temperature is considered as homogeneous or
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with a small gradient over the area, which will not significantly affect the average grain growth [35].
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It is worth mentioning that the rigid-body motion, which may have significant impact on grain growth, is not implemented in this study due to the limited shrinkage during solid-state SLS, but
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should be considered in the future work [33, 36]. 2.3 Material parameters
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In this study, powder bed porosity θ, reflectivity R, and surface emissivity ε are considered to be Powder bed porosity θ is set to 50% and heat convection
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constants during the entire process.
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coefficient hc is taken as 10 W/(m2·K) [37].
The temperature-dependent thermal conductivities
and heat capacities of different materials [38-40] are summarized in Fig. 2.
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37, 38, 41, 42] used for thermal modeling are listed in Table 1.
Other properties [24,
The material parameters used for
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microstructure evolution modeling of 316L stainless steel [43-47], titanium [48-51], and nickel [52-55] are listed in Table 2, respectively.
Fig. 2. Temperature-dependent material properties of Ti, 316L stainless steel and Ni: (a) thermal conductivities, and (b) heat capacities.
Table 1 Other properties of 316L stainless steel, Ti and Ni used in the temperature simulation. Table 2 Material properties of 316L stainless steel, Ti and Ni used in PF model. 3. Results and Discussion
ACCEPTED MANUSCRIPT 3.1 Effect of laser processing parameters on microstructure evolution during SLS In order to understand the capability of proposed SLS model, simulations are carried out to predict the neck growth between two equal-sized 316L stainless steel particles subjected to solid-state SLS.
Given SLS processing parameters including the laser power of 21 W, spot size of
It is well accepted that sintering phenomena occurs while the processing temperature
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3c, and 3d).
With the thermal input, PF model is used to simulate the neck growth (Fig. 3b,
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shown in Fig. 3a.
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0.8 mm and scanning speed of 1 mm/s, the temperature profile predicted by the thermal model is
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is higher than half of the melting point [2]. Therefore, in this work, PF modeling starts/ends at the time when the processing temperature increases up to/cools down to half of the melting point. As shown in Fig. 3b, the
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The PF computational domain is chosen to be 40 μm × 40 μm.
simulation is initialized with two contact circular particles of 30 μm in diameter.
The red area
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represents the particle concentration, while the blue area represents the void concentration. The In the PF model, with the temperature
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concentration of particle-void interfaces changes smoothly.
rise, the microstructural change takes place to reduce the total free energy, leading to the neck The time evolution of neck size is shown in Fig. 3c and 3d.
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formation and grain growth.
The
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final neck size after laser processing is predicted to be 14.8 μm.
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Fig. 3. Solid-state SLS of two equal-sized 316L stainless steel particles with the laser power of 21 W, spot size of 0.8 mm and scanning speed of 1 mm/s: (a) temperature history predicted by the thermal model, (b), (c), and (d) neck growth simulated by PF model at 4.5 s (the starting point), 5.0 s (the peak temperature), and 5.5 s (the final status), respectively. The scale bar represents 10 μm. The proposed model is capable of capturing the effects of laser processing parameters on the microstructure evolution in terms of grain growth and pore structure evolution.
The effect of laser
power energy on the temperature profile during SLS and the neck size after SLS are predicted as shown in Fig. 4a and 4b, respectively.
It is found that given a constant laser spot size of 0.8 mm
and scanning speed of 1 mm/s, a higher peak processing temperature is achieved by increasing the laser power energy, resulting in a larger neck size after laser processing.
For instance, by
ACCEPTED MANUSCRIPT enhancing the laser power energy from 17 to 25 W, the peak temperature increases from around 1200 to 1500 K, leading to the growth of neck size from 7.9 to 19.6 μm.
According to the
Arrhenius relation between diffusion coefficient and temperature, the enhanced neck growth by increasing laser power energy during SLS is attributed to a greater atom diffusion rate resulting On the other hand, the effect of laser scanning speed on the
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from a higher processing temperature.
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temperature profiles and the corresponding neck sizes are shown in Fig. 5a and 5b, respectively.
For example, by increasing the scanning speed from
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resulting in a smaller neck size after SLS.
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It is observed that a faster laser scanning speed leads to a shorter duration time of laser heating,
0.5 to 8 mm/s, a shortened heating duration time leads to a significant decrease in the neck size
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from 18.7 to 4.2 μm. Obviously, unlike SLM with the common scanning speed of over tens millimeter per second, a slower scanning speed is needed for solid-state SLS in order to provide a
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sufficient heating duration for neck formation.
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Fig. 4. Effect of the laser power energy on microstructure evolution, as predicted by the proposed model: (a) the temperature profiles as affected by laser power energy of 17, 21, and 25 W, and (b) the simulated neck sizes after SLS with various laser power energy.
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Fig. 5. Effect of the laser scanning speed on microstructure evolution, as predicted by the proposed model: (a) the temperature profiles as affected by laser scanning speeds of 0.5, 1, 2, 4, and 8 mm/s, and (b) the simulated neck sizes after SLS with various laser scanning speeds. 3.2 Large-scale simulation The developed model is further employed to a large-scale simulation.
Fig. 6 presents the
evolution of pore configuration and grain size during solid-state SLS of multiple 316L stainless steel particles. simulations.
A laser power of 21 W and a scanning speed of 1 mm/s are chosen for the
Fig. 6a and 6b shows the simulation result of 9 particles with uniform size of 40 μm.
It can be observed that the final neck size reaches ~ 14 μm, while the grains depict similar deformation and large pores remain after processing.
In such case, the mass transport is governed
by surface diffusion and grain boundary diffusion, leading to the sintering neck formation and grain
ACCEPTED MANUSCRIPT growth. However, as the solid-state SLS processes, the neck growth rate decreases because the dihedral angle d tends to reach an equilibrium state [56]. Additionally, the grain coarsening induced by grain boundary migration barely occur due to the equilibrium configuration for all particles [32].
Therefore, the rates of grain growth and densification is very limited.
For
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particles with non-uniform size (average diameter of 40 μm), as shown in Fig. 6c and 6d, grain
As a result, the smaller particles is consumed by larger
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take place due to particle size differences.
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boundary migration toward the curvature center (from the larger particles toward the small ones)
For instance, particle 1 in Fig. 6d is
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ones via volume diffusion as the solid-state SLS processes.
absorbed by its surrounding larger particles and its size decreases from initial 30 μm to 22 μm after
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processing. Moreover, the initial porosity is decreased by adding particles with different sizes, since the smaller ones tend to fill the gap among large ones, leading to more interfaces between
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adjacent particles compared to the powder bed with equal-sized particles.
This results in more
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necking formations and faster densification, which is proved by the significantly decreased pore Furthermore, due to the higher surface area per unit
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size within the area marked with black circle.
volume for the smaller particles, the formation and growth of sintering neck are faster compared to
Therefore, it is necessary to employ powder application process [58] to describe the
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the process.
Obviously, the spatial and size distribution of particles can significantly affect
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large particles [57].
initial state of the powder bed, further improving the practicability of this model.
Fig. 6. Large-scale microstructure evolution during solid-state SLS of 316L stainless steel particles, as predicted by the proposed model: (a) initial status and (b) final status of 9 particles with uniform size of 40 μm; (c) initial status and (d) final status of 9 particles with different sizes (average size of 40 μm). This work demonstrates the feasibility and capability of using PF method to simulate solid-state SLS of multiple powders in a large scale. The model can be used to describe the change in pore configuration within a powder bed accompanied by grain growth, and investigate the effects of laser process parameters and powder properties.
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3.3 Validation of the thermal model Given the lack of data regarding temperature evolution during solid-state SLS, the thermal model is first qualitatively validated by comparing the measured and simulated width of melt pool
stainless steel subjected by SLM.
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Fig. 7 shows the experimental observation and the thermal modeling result of 316L Given a laser power energy of 110 W, a spot diameter of 0.6
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during SLM.
Fig. 7a, indicating the melt pool width of ~600 μm [59].
Based on the liquidius line, a melt pool width is
The simulation result agrees well with the experimental
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predicted to be around 550 μm.
The modeling result of the temperature
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distribution at the top surface is shown in Fig. 7b.
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mm, and a scanning speed of 100 mm/s, the morphology of the sample’s cross-section is shown in
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observation.
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Fig. 7. Comparison of experiment result and temperature model prediction for 316L stainless steel subjected to SLS/SLM: (a) optical micrograph of the sample cross-section [59], adopted with permission from Elsevier, and (b) simulated temperature distribution at the sample surface.
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Fig. 8 shows the comparison between the thermal measurement and our model prediction in Experiments were carried out with a laser power energy of
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case of laser processed Ti sample [40].
2 W, a spot size of 0.05 mm, and a scanning speed of 1 mm/s.
The surface temperature profile
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measured by an infra-red camera shows a maximum value of 2673 K ± 200 K. With the inputs of the same laser processing parameters, the thermal model predicts the peak temperature of around 2700 K, which matches well with experimental data.
Fig. 8. Comparison of temperature model prediction (bold red line) with measured temperature profile (thin black line) along the scanning direction for Ti sample subjected to SLS/SLM. 3.4 Validation of the PF model In order to evaluate the proposed PF model, the simulated evolution of metallic particles during solid-state SLS is compared to experimental data available in literature.
Fig. 9 shows the
ACCEPTED MANUSCRIPT comparison between the experimental observation and model prediction of neck growth in 316L stainless steel powder bed as processed by SLS.
SLS experiments were conducted by University
of Leuven [2, 60], using a pulsed Nd: YAG laser with a pulse width of 10 ms, pulse frequency of 30 Hz, pulse energy of 0.7 J, spot size of 0.8 mm and scanning speed of 0.42 mm/s.
The neck
It is clearly observed in Fig. 9a that the neck length after SLS is about 30 μm.
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(SEM) images.
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formation between the 316L stainless steel particles was observed by scanning electron microscope In
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order to apply the thermal model, the pulsed laser is considered as a continuous wave (CW) laser
pulse frequency.
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by calculating the average laser power as Pavg = E x f, where E is the pulsed laser energy and f is the The predicted temperature evolution is presented in Fig. 9b.
In the PF model,
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based on the SEM image, the initial sizes of two 316L stainless steel particles are chosen to be 65 μm and 50 μm as shown in Fig. 9c. With the temperature input, the time evolution of neck size is The neck size after laser processing is predicted to be around 30.7 μm,
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shown in Fig. 9d and 9e.
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which matches well with the measurement from the SEM image (30 μm).
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Fig. 9. Comparison of PF model prediction with experiment result for solid-state SLS of 316L stainless steel micro-powders: (a) SEM image of the sintering neck between two particles [2], adopted with permission from Emerald Insight, and (b) Simulated temperature history at the center of the sintering track. The PF model prediction of the neck growth between two particles at (c) 10.7 s (the starting point), (d) 12.05 s (the peak temperature), and (e) 13.45 s (the final status). The scale bar represents 20 μm. Fig. 10 compares the experimental findings [13] with model predictions of Ti micro-powder bed subjected to solid-state SLS. SLS experiments.
Ti micro-powders with a diameter of 200-315 μm were used for
Given a laser power energy of 20 W, a spot size of 3.6 mm, and a laser
processing time of 10 s, the cross-section of Ti sample after laser processing is shown in Fig. 10a. The average neck size after laser processing is measured to be around 68 μm. Note that, the necks measured to obtain an average neck size are marked by red circles in Fig. 10a, and the neck length was measured using ImageJ (developed by Wayne Rasband). is shown in Fig. 10b.
The simulated temperature history
The PF simulation is considered as starting at 1155K, which is the α-to-β
ACCEPTED MANUSCRIPT phase transformation temperature, because only β-Ti contributes significantly to the solid-state SLS process since its self-diffusion coefficient is much higher than that of α-Ti [13]. As shown in Fig. 10c, two equal-sized Ti particles with a diameter of 260 μm were used for PF simulation.
The
predicted neck size between two Ti particles after SLS is predicted to be 65.2 μm (as shown in Fig.
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10d), which is in good agreement with experimental measurement.
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Fig. 10. Comparison of PF model prediction with experiment result for solid-state SLS of titanium micro-powders: (a) optical image of the cross-section of the selective laser sintered Ti powders [13], adopted with permission from Emerald Insight, and (b) simulated temperature evolution during SLS. The PF modeling of the neck growth between two particles during SLS: (c) before laser processing, and (d) after laser processing. The scale bar represents 60 μm.
solid-state SLS.
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Fig. 11 compares the experimental result with simulated neck size of Ni powders subjected to The experiments were carried out by Kathuria [3] with a pulsed laser energy of
The sintered structure has a line width of 221 μm and its
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experiments were 30-60 μm in diameter.
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2.1 W, a scanning speed of 2.5 mm/s, and a spot size of 140 μm. The size of Ni powders used for
magnified view is presented in Fig. 10a.
By selecting the necks between particles in the SEM
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image (Fig. 11a) as marked by red circles, an average neck size is measured to be around 14 μm.
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The thermal modeling of temperature history is shown in Fig. 11b.
In the PF model, two
equal-sized particles with a diameter of 45 μm are employed as shown in Fig. 11c. The time
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evolution of neck growth is presented in Fig. 11d and 11e.
The final neck length after laser
processing reaches to 13.1 μm, which agrees well with the modeling result.
Fig. 11. Comparison of PF model prediction with experiment result for solid-state SLS of Ni micro-powders: (a) the magnified view of the sintered structure [3], adopted with permission from Elsevier; and (b) the simulated temperature history at the center area of the sintering track. The PF modeling of the neck growth between two particles at (c) 0.76 s (the starting point), (d) 0.80 s (the peak temperature), and (e) 0.86 s (the final status). The scale bar represents 10 μm. 4. Conclusion In this study, a PF based model is developed to simulate microstructure behaviors during
ACCEPTED MANUSCRIPT solid-state SLS of metallic materials.
Laser processing conditions are considered by integrating
PF codes with thermal modeling of continuous heating induced by laser irradiation.
The effects of
laser power intensity and scanning speed on microstructure evolution are investigated.
This
model is validated by comparing the modeling results with experimental data in terms of neck The model is found to be capable of predicting
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growth between adjacent micro-powders.
The modeling results can provide important insights and guidance for
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solid-state SLS process design, control, and optimization.
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experimental findings.
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microstructure evolution during solid-state SLS by demonstrating good consistence with the
Furthermore, the feasibility and capability of employing the developed model to large-scale The predicted porosity and grain size
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simulation in terms of multiple particles are demonstrated.
by lager area simulation will lead to fabrication of functional porous products such as electronics
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with designed conductivity and thermal management components with desired thermal properties.
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This will be discussed in our further work along with the effects of large temperature gradient and
Acknowledgement:
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size distribution of powder particles.
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The authors appreciate the financial support by start-up funding from the Department of
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Mechanical Engineering at the University of Nevada, Reno. Data Availability: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
ACCEPTED MANUSCRIPT References:
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[1] E. Olakanmi, Selective laser sintering/melting (SLS/SLM) of pure Al, Al–Mg, and Al–Si powders: Effect of processing conditions and powder properties, Journal of Materials Processing Technology, 213 (2013) 1387-1405. [2] J.-P. Kruth, P. Mercelis, J. Van Vaerenbergh, L. Froyen, M. Rombouts, Binding mechanisms in selective laser sintering and selective laser melting, Rapid prototyping journal, 11 (2005) 26-36. [3] Y. Kathuria, Microstructuring by selective laser sintering of metallic powder, Surface and Coatings Technology, 116 (1999) 643-647. [4] Z. Macedo, A. Hernandes, A quantitative analysis of the laser sintering of bismuth titanate ceramics, Materials Letters, 59 (2005) 3456-3461. [5] B. Qian, Z. Shen, Laser sintering of ceramics, Journal of Asian Ceramic Societies, 1 (2013) 315-321. [6] N. Tolochko, S. Mozzharov, T. Laoui, L. Froyen, Selective laser sintering of single-and two-component metal powders, Rapid Prototyping Journal, 9 (2003) 68-78. [7] A. Gusarov, T. Laoui, L. Froyen, V. Titov, Contact thermal conductivity of a powder bed in selective laser sintering, International Journal of Heat and Mass Transfer, 46 (2003) 1103-1109. [8] H. Yasuda, I. Ohnaka, H. Kaziura, Y. Nishiwaki, Fabrication of metallic porous media by semisolid processing using laser irradiation, Materials Transactions, 42 (2001) 309-315. [9] M.M. Dewidar, K.A. Khalil, J. Lim, Processing and mechanical properties of porous 316L stainless steel for biomedical applications, Transactions of Nonferrous Metals Society of China, 17 (2007) 468-473. [10] Q. Nian, M. Callahan, M. Saei, D. Look, H. Efstathiadis, J. Bailey, G.J. Cheng, Large Scale Laser Crystallization of Solution-based Alumina-doped Zinc Oxide (AZO) Nanoinks for Highly Transparent Conductive Electrode, Scientific reports, 5 (2015) 15517. [11] J. Niittynen, E. Sowade, H. Kang, R.R. Baumann, M. Mantysalo, Comparison of laser and intense pulsed light sintering (IPL) for inkjet-printed copper nanoparticle layers, Sci Rep, 5 (2015) 8832. [12] M. Zenou, O. Ermak, A. Saar, Z. Kotler, Laser sintering of copper nanoparticles, Journal of Physics D: Applied Physics, 47 (2014) 025501. [13] N.K. Tolochko, M.K. Arshinov, A.V. Gusarov, V.I. Titov, T. Laoui, L. Froyen, Mechanisms of selective laser sintering and heat transfer in Ti powder, Rapid prototyping journal, 9 (2003) 314-326. [14] B. AlMangour, D. Grzesiak, J. Cheng, Y. Ertas, Thermal behavior of the molten pool, microstructural evolution, and tribological performance during selective laser melting of TiC/316L stainless steel nanocomposites: Experimental and simulation methods, Journal of Materials Processing Technology, 257 (2018) 288-301. [15] F. Verhaeghe, T. Craeghs, J. Heulens, L. Pandelaers, A pragmatic model for selective laser melting with evaporation, Acta Materialia, 57 (2009) 6006-6012. [16] I.A. Roberts, C. Wang, R. Esterlein, M. Stanford, D. Mynors, A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing, International Journal of Machine Tools and Manufacture, 49 (2009) 916-923. [17] S.A. Khairallah, A. Anderson, Mesoscopic simulation model of selective laser melting of stainless steel powder, Journal of Materials Processing Technology, 214 (2014) 2627-2636. [18] L.-X. Lu, N. Sridhar, Y.-W. Zhang, Phase field simulation of powder bed-based additive manufacturing, Acta Materialia, 144 (2018) 801-809. [19] J.-Q. Li, T.-H. Fan, T. Taniguchi, B. Zhang, Phase-field modeling on laser melting of a metallic powder, International Journal of Heat and Mass Transfer, 117 (2018) 412-424. [20] H. Pan, S.H. Ko, C.P. Grigoropoulos, The solid-state neck growth mechanisms in low energy laser sintering of gold nanoparticles: a molecular dynamics simulation study, Journal of Heat Transfer, 130 (2008) 092404. [21] P. Zeng, S. 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Wollants, Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems, Physical Review B, 78 (2008) 024113. [35] M.R. Tonks, Y. Zhang, X. Bai, P.C. Millett, Demonstrating the temperature gradient impact on grain growth in UO2 using the phase field method, Materials Research Letters, 2 (2014) 23-28. [36] S. Biswas, D. Schwen, V. Tomar, Implementation of a phase field model for simulating evolution of two powder particles representing microstructural changes during sintering, Journal of Materials Science, 53 (2018) 5799-5825. [37] A. Hussein, L. Hao, C. Yan, R. Everson, Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting, Materials & Design, 52 (2013) 638-647. [38] F. Liu, Q. Zhang, W. Zhou, J. Zhao, J. Chen, Micro scale 3D FEM simulation on thermal evolution within the porous structure in selective laser sintering, Journal of Materials Processing Technology, 212 (2012) 2058-2065. [39] Z. Hu, M. Saei, G. Tong, D. Lin, Q. Nian, Y. Hu, S. Jin, J. Xu, G.J. Cheng, Numerical simulation of temperature field distribution for laser sintering graphene reinforced nickel matrix nanocomposites, Journal of Alloys and Compounds, 688 (2016) 438-448. [40] S. Kolossov, E. Boillat, R. Glardon, P. Fischer, M. Locher, 3D FE simulation for temperature evolution in the selective laser sintering process, International Journal of Machine Tools and Manufacture, 44 (2004) 117-123. [41] N.K. Tolochko, Y.V. Khlopkov, S.E. Mozzharov, M.B. Ignatiev, T. Laoui, V.I. Titov, Absorptance of powder materials suitable for laser sintering, Rapid Prototyping Journal, 6 (2000) 155-161. [42] L. Dong, J. Correia, N. Barth, S. 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Technology, 288 (2016) 96-102. [59] A. Foroozmehr, M. Badrossamay, E. Foroozmehr, Finite element simulation of selective laser melting process considering optical penetration depth of laser in powder bed, Materials & Design, 89 (2016) 255-263. [60] B. Van Der Schueren, Basic contributions to the development of the selective metal powder sintering process, University of Leuven, Belgium, 1998.
ACCEPTED MANUSCRIPT Table 1 Other properties of 316L stainless steel, Ti and Ni used in the temperature simulation. Surface reflectivity R 0.4 0.23 0.36
Surface emissivity ε 0.8 0.77 0.8
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316L Ti Ni
Bulk density ρ (kg/m3) 7980 4506 8908
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Material
p 1 1 4
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Table 2 Material properties of 316L stainless steel, Ti and Ni used in PF model. Materials 316L Ti Ni Prefactor Dgb0 (cm 2/s) 0.127 90 4.8 GB diffusion Activation energy Qgb (eV) 0.58 1.93 1.71 Prefactor Dsyrf0 (cm 2/s) 4 x 103 0.47 23.9 Surface diffusion
T
1.3 3.58 x 10 -4 1.353 5.53 x 10-8
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GB mobility
2.21 2 2.6 5.53 x 10-8
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Volume diffusion
Activation energy Qsurf (eV) Prefactor Dvol0 (cm 2/s) Activation energy Qvol (eV) Prefactor (m4/J/s)
1.85 0.92 2.88 1.51 x 10-6
ACCEPTED MANUSCRIPT 0.171 2.41 1.06
0.171 2 1.1
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Activation energy (eV) Surface energy γs (J/m2) GB energy γgb (J/m2)
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0.26 1.9 0.87
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Highlights: A phase-field (PF) based selective laser sintering (SLS) model is developed. SLS of 316L stainless steel, titanium, and nickel are simulated. Effects of laser intensity and scanning speed are modeled. Modeling results are validated by experimental data.
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Xing Zhang, Yiliang Liao PII: DOI: Reference:
S0032-5910(18)30641-7 doi:10.1016/j.powtec.2018.08.025 PTEC 13610
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
4 May 2018 23 July 2018 8 August 2018
Please cite this article as: Xing Zhang, Yiliang Liao , A phase-field model for solidstate selective laser sintering of metallic materials. Ptec (2018), doi:10.1016/ j.powtec.2018.08.025
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ACCEPTED MANUSCRIPT A Phase-Field Model for Solid-State Selective Laser Sintering of Metallic Materials Xing Zhang,1 Yiliang Liao1,a) 1
Department of Mechanical Engineering, University of Nevada, Reno, Reno, Nevada, 89557 USA Author to whom correspondence should be addressed. Electronic mail: [email protected].
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a)
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Abstract Selective laser sintering/melting (SLS/SLM) is an additive manufacturing process that uses laser energy to sinter/melt powder particles together to construct solid structures.
Materials
In literature, most modeling efforts have been focused on
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for process control and optimization.
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modeling of microstructure evolution during such processes can be of great importance, especially
In this study, a phase-field (PF) based SLS model is
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microstructure evolution as a result of SLS.
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the microstructure evolution during SLM, while few attempts have been made to study the
developed to predict the evolving of microstructure in the solid-state SLS process.
The effects of
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laser power intensity and scanning speed on microstructure evolution are investigated.
M
feasibility and capability of modelling in a large scale are demonstrated.
The
The modeling results are
validated by experimental findings in terms of the neck size between adjacent particles.
This PF
ED
based SLS model is found to be capable of predicting the neck growth for various metallic
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materials including 316L stainless steel, titanium, and nickel.
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Materials.
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Keywords: Selective Laser Sintering; Materials Modeling; Microstructure Evolution; Metallic
ACCEPTED MANUSCRIPT
1. Introduction Selective laser sintering/melting (SLS/SLM) is as an additive manufacturing process for rapid fabrication of three-dimensional (3D) components with complex geometries, widely used for
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In SLS/SLM, laser beam energy is employed to bind
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metals, ceramics and polymers [1].
powdered materials together through various binding mechanisms: solid state sintering, liquid Among these categories, solid-state
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phase sintering or partial melting, and melt-solidification [2].
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SLS aims at fabricating part by consolidating powders via heating the powders to a temperature below the melting point. This process involves sintering neck formation and mass transformation
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between adjacent powder particles without melting [3].
Compared to conventional sintering
M
process, solid-state SLS can easily achieve to a temperature close to the melting point without significantly affecting the surrounding powder, leading to faster sintering rate and smaller grain size
ED
[4, 5]. This advantage along with high flexibility, controllability and fast heating rate make For solid-state SLS of microparticles, it
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solid-state SLS suitable to various industrial applications.
is generally accepted that this process is not suitable for manufacturing highly densified parts due
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to the short duration time of laser-induced heating effect [6], however, it has a great potential on 3D
AC
printing of porous structures [7] for specific applications, such as thermal management components [8] and biomedical devices [9].
In addition, recent studies demonstrate the feasibility and
advantage of employing solid-state SLS of nanoparticles to fabricate thin-film flexible electronics [10-12]. However, to date, it still remains a great challenge to understand and control the microstructure evolution during solid-state SLS, which determines the physical and mechanical properties of 3D printed structures, considering that this process is affected by multiple factors such as various laser processing parameters and powder properties.
For instance, Toloch et al. [13] investigated the
sintering neck size during solid-state SLS of titanium powder under different laser power.
Zenou
ACCEPTED MANUSCRIPT et al. [12] fabricated copper thin films by employing a pulse laser to copper nanoparticles in ambient conditions.
It was found that the resistance of as-built films decreased with the increase
of laser power and scanning speed due to denser structure and shortened oxidation period, respectively.
In order to achieve solid-state SLS products with desirable properties, it is of Nevertheless,
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specific importance to control the microstructure evolution during laser processing.
On the other hand, microstructure-based material
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timeframe of laser-induced heating effect.
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it is difficult to directly observe the microstructure evolution during solid-state SLS due to the short
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modeling provides us an alternative approach to understand the process-microstructure relationship during solid-state SLS.
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In recent years, extensive investigations have focused on SLM with binding mechanism of fully melt-solidification or partial melting [14-19], while only few efforts have been put on simulating
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the grain growth of nanoparticles during solid-state SLS using molecular dynamics (MD) method.
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However, this method is restricted by the small simulation area and large computational cost, thus it
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is not feasible for modeling microstructure behaviors during SLS in the micro or meso scale. Moreover, the mechanisms of nanoparticles (< 20 nm) sintering, which involve elastic/plastic
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deformation [20] and considerable atomic forces [21], are fundamentally different from mechanisms of sintering powdered materials in the micro/macro scale.
Clearly, there is a demand
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to develop a computational model to understand, control and eventually optimize the process with powder size from tens of nm to hundreds of μm. In this research, we propose a new PF based model to simulate microstructure behaviors during solid-state SLS of metallic materials.
Laser processing conditions are considered by integrating
PF codes with thermal modeling of continuous heating induced by laser irradiation.
The effects of
laser power intensity and scanning speed on microstructure evolution are investigated. feasibility and capability of modelling in a large scale are demonstrated.
The
The modeling results are
validated by experimental findings in terms of the neck size between adjacent particles. This PF based SLS model is found to be capable of predicting the neck growth for various metallic
ACCEPTED MANUSCRIPT materials including 316L stainless steel, titanium, and nickel. 2. Model Description The proposed solid-state SLS model is established by integrating the PF codes with a thermal model. This thermal model is developed first to obtain the temperature profile in the material as
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With the temperature result as an input, a PF model
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affected by the laser-induced heating effect.
(Multiphysics Object-Oriented Simulation Environment (MOOSE) developed by Idaho National
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Lab’s [22]) is applied to simulate the microstructure evolution.
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2.1 Thermal model
In this study, a 3D thermal model is developed for temperature evolution during SLS.
Fig. 1
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presents the schematic diagram of the simulation domain. The temperature profile T(x,y,z,t) can be
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determined by a general heat conduction equation [23]:
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C pT t
( k e T ),
(1)
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where ρ is the powder bed density, t is time, Cp is the temperature-dependent specific heat capacity,
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and ke is the effective thermal conductivity, which can be calculated by [24]: k e k (1 ) , p
(2)
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where k is the thermal conductivity of bulk material, θ is the porosity, and p is an empirical parameter related to powder properties.
Fig. 1. Schematic of thermal model domain. The environment temperature T0 is applied to the entire area as the initial condition: T ( x , y , z , 0 ) T0 .
(3)
The heat influx via laser irradiation and the heat loss induced by thermal convection and radiation are considered at the top surface.
Note that, since this model does not consider the laser
penetration in a loose powder bed, we focus on the temperature profile at the top surface.
Thus,
ACCEPTED MANUSCRIPT the boundary condition can be defined as [25]: ke
T
Q h c (T 0 T z 0 ) (T 0 T z 0 ) , 4
z0
z
4
(4)
where Q is the laser energy flux, the suffix ’z=0’ represents the top surface, hc is the heat
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convection coefficient, ε is the surface emissivity and σ is the Stefan-Boltzmann constant. Other
T n
0,
(5)
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ke
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surfaces are assumed to be adiabatic:
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where n is the normal direction of specific surfaces.
The spatial distribution of laser energy on the target surface is considered to follow the
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Gaussian profile, where the laser intensity is at its highest at the center of the laser beam.
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the heat flux can be written as[26]:
( x vt ) y 2
2P 2
exp(2
2
2
(6)
),
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Q (1 R )
Thus,
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where R is the surface reflectivity, P is the laser power, ω is the effective laser spot radius, and v is the scanning speed.
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2.2 Microstructure model
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With the input of temperature history as predicted by the thermal model, a two-dimensional PF modeling is used to simulate the microstructure evolution during the solid-state SLS process. As compared with other mesoscale simulation tools such as Monte Carlo and Cellular Automaton, PF modeling is exceptional for microstructure behavior simulation since it is not required to explicitly track the surface and grain boundaries or impose boundary conditions.
In this work, the PF model
solves the minimization of total free energy F, which is the driving force of sintering process. According to the literature [27], the total free energy is given by a functional equation: F
V
[ f 0 ( , )
2
2
2
]d V ，
(7)
2
where f0(, η) is the local free energy density for a homogeneous system.
The second and third
ACCEPTED MANUSCRIPT terms describe the gradient energy densities from surfaces and grain boundaries, respectively.
The value of is given as 0 for pore
y, t) is the conserved variable representing the mass density. structures and 1 for particles.
(x,
ηi(x, y, t) is the non-conserved order parameter, standing for
different particle crystallographic orientations, where i =1, 2, …q and q is equal to the number of The value of η can be denoted as η1, η2, …, ηq = (1, 0, ..., 0), (0, 1, ..., 0), …, (0,
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powder particles.
ε and εη are gradient term constants.
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0, ..., 1) for different particles and η = (0, 0, ..., 0) for pores.
f 0 ( , ) A (1 ) B [ 2
2
2
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The local free energy density is defined as a double-well function [28]:
6 (1 ) i 4 ( 2 ) i 3 ( i ) ], 2
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i
3
i
2
2
(8)
i
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where A and B are constants related to grain boundary (GB) energy and surface energy. The constants in equation (7) and (8) can be given as [29, 30]:
M
k1 ( 2 s
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k2
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A k 3 (1 2
s
gb
gb
gb
(9)
，
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B k4
) ,
gb
(10)
)/,
(11)
/ ，
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where γs and γgb are the surface energy and GB energy, respectively.
(12) δ is the GB width.
k1, k2, k3,
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and k4 are the constants used to normalize material parameters [29]. In order for the minimization of total free energy F, the corresponding phase-field variable (x, y, t) and order parameter η(x, y, t) need to be solved.
The temporal and spatial evolution of and
η represent the microstructure evolution and can be acquired by solving Cahn-Hillard (CH) and Allen-Cahn (AC) equations [31]: t
·M
i t
L
F
,
(13)
，
(14)
F i
where M and L are coefficients used to describe the atom diffusion mobility and the GB mobility,
ACCEPTED MANUSCRIPT respectively. The neck formation and grain growth during the sintering process are caused by mass transport and/or GB migration [32].
Since the mass transport involves various diffusion mechanisms
including surface, volume and GB diffusion as well as vapor transport, the atom diffusion mobility
vol
h ( ) M
vap
[1 h ( )] M
su rf
(1 ) M
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M M
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coefficient, M, can be calculated as [33]: gb
i
j
,
(15)
The value of M can be estimated based on the work of Ahmed et
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vapor, surface and GB diffusion.
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where h(φ) = φ3(10−15φ+6φ2) and Mvol, Mvap, Msurf, Mgb are the mobility coefficients for volume,
D lV m
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al. [30]: M
l
(16)
，
k BT
M
where the suffix ‘l’ corresponds to different diffusion modes, D is the diffusion coefficients, Vm is The value of D
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the molar volume, kB is the Boltzmann constant, and T is the local temperature.
can be estimated with prefactor Dl0 and activation energy Ql by following the well-known Arrhenius
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relation:
Dl Dl0 exp(
Ql
).
(17)
k BT
[34]:
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The grain boundary mobility coefficient, L, used to characterize GB migration, can be calculated by
L
4 W gb 3
,
(18)
where Wgb is the GB mobility and it also can be estimated by the Arrhenius relation. The temperature profile extracted from the thermal model is incorporated in the PF equations. The parameters for PF simulation are nondimensionlized with respect to the length scale, time scale and grain boundary energy.
Details for solving CH and AC equations by finite element method
have been discussed by Tonks et al. [22].
Here, strong form equations with high order terms are
ACCEPTED MANUSCRIPT converted to weak form equations by introducing a test function. A few assumptions are considered for the developed PF model: 1) Vapor diffusion is neglected in this simulation since its contribution to neck formation or grain growth is less important compared to the other three diffusion mechanisms; 2) The contribution from the thermal gradient
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driving force on microstructure evolution is not incorporated in the current model because only two
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particles within a small area are simulated and the temperature is considered as homogeneous or
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with a small gradient over the area, which will not significantly affect the average grain growth [35].
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It is worth mentioning that the rigid-body motion, which may have significant impact on grain growth, is not implemented in this study due to the limited shrinkage during solid-state SLS, but
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should be considered in the future work [33, 36]. 2.3 Material parameters
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In this study, powder bed porosity θ, reflectivity R, and surface emissivity ε are considered to be Powder bed porosity θ is set to 50% and heat convection
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constants during the entire process.
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coefficient hc is taken as 10 W/(m2·K) [37].
The temperature-dependent thermal conductivities
and heat capacities of different materials [38-40] are summarized in Fig. 2.
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37, 38, 41, 42] used for thermal modeling are listed in Table 1.
Other properties [24,
The material parameters used for
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microstructure evolution modeling of 316L stainless steel [43-47], titanium [48-51], and nickel [52-55] are listed in Table 2, respectively.
Fig. 2. Temperature-dependent material properties of Ti, 316L stainless steel and Ni: (a) thermal conductivities, and (b) heat capacities.
Table 1 Other properties of 316L stainless steel, Ti and Ni used in the temperature simulation. Table 2 Material properties of 316L stainless steel, Ti and Ni used in PF model. 3. Results and Discussion
ACCEPTED MANUSCRIPT 3.1 Effect of laser processing parameters on microstructure evolution during SLS In order to understand the capability of proposed SLS model, simulations are carried out to predict the neck growth between two equal-sized 316L stainless steel particles subjected to solid-state SLS.
Given SLS processing parameters including the laser power of 21 W, spot size of
It is well accepted that sintering phenomena occurs while the processing temperature
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3c, and 3d).
With the thermal input, PF model is used to simulate the neck growth (Fig. 3b,
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shown in Fig. 3a.
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0.8 mm and scanning speed of 1 mm/s, the temperature profile predicted by the thermal model is
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is higher than half of the melting point [2]. Therefore, in this work, PF modeling starts/ends at the time when the processing temperature increases up to/cools down to half of the melting point. As shown in Fig. 3b, the
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The PF computational domain is chosen to be 40 μm × 40 μm.
simulation is initialized with two contact circular particles of 30 μm in diameter.
The red area
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represents the particle concentration, while the blue area represents the void concentration. The In the PF model, with the temperature
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concentration of particle-void interfaces changes smoothly.
rise, the microstructural change takes place to reduce the total free energy, leading to the neck The time evolution of neck size is shown in Fig. 3c and 3d.
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formation and grain growth.
The
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final neck size after laser processing is predicted to be 14.8 μm.
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Fig. 3. Solid-state SLS of two equal-sized 316L stainless steel particles with the laser power of 21 W, spot size of 0.8 mm and scanning speed of 1 mm/s: (a) temperature history predicted by the thermal model, (b), (c), and (d) neck growth simulated by PF model at 4.5 s (the starting point), 5.0 s (the peak temperature), and 5.5 s (the final status), respectively. The scale bar represents 10 μm. The proposed model is capable of capturing the effects of laser processing parameters on the microstructure evolution in terms of grain growth and pore structure evolution.
The effect of laser
power energy on the temperature profile during SLS and the neck size after SLS are predicted as shown in Fig. 4a and 4b, respectively.
It is found that given a constant laser spot size of 0.8 mm
and scanning speed of 1 mm/s, a higher peak processing temperature is achieved by increasing the laser power energy, resulting in a larger neck size after laser processing.
For instance, by
ACCEPTED MANUSCRIPT enhancing the laser power energy from 17 to 25 W, the peak temperature increases from around 1200 to 1500 K, leading to the growth of neck size from 7.9 to 19.6 μm.
According to the
Arrhenius relation between diffusion coefficient and temperature, the enhanced neck growth by increasing laser power energy during SLS is attributed to a greater atom diffusion rate resulting On the other hand, the effect of laser scanning speed on the
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from a higher processing temperature.
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temperature profiles and the corresponding neck sizes are shown in Fig. 5a and 5b, respectively.
For example, by increasing the scanning speed from
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resulting in a smaller neck size after SLS.
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It is observed that a faster laser scanning speed leads to a shorter duration time of laser heating,
0.5 to 8 mm/s, a shortened heating duration time leads to a significant decrease in the neck size
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from 18.7 to 4.2 μm. Obviously, unlike SLM with the common scanning speed of over tens millimeter per second, a slower scanning speed is needed for solid-state SLS in order to provide a
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sufficient heating duration for neck formation.
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Fig. 4. Effect of the laser power energy on microstructure evolution, as predicted by the proposed model: (a) the temperature profiles as affected by laser power energy of 17, 21, and 25 W, and (b) the simulated neck sizes after SLS with various laser power energy.
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Fig. 5. Effect of the laser scanning speed on microstructure evolution, as predicted by the proposed model: (a) the temperature profiles as affected by laser scanning speeds of 0.5, 1, 2, 4, and 8 mm/s, and (b) the simulated neck sizes after SLS with various laser scanning speeds. 3.2 Large-scale simulation The developed model is further employed to a large-scale simulation.
Fig. 6 presents the
evolution of pore configuration and grain size during solid-state SLS of multiple 316L stainless steel particles. simulations.
A laser power of 21 W and a scanning speed of 1 mm/s are chosen for the
Fig. 6a and 6b shows the simulation result of 9 particles with uniform size of 40 μm.
It can be observed that the final neck size reaches ~ 14 μm, while the grains depict similar deformation and large pores remain after processing.
In such case, the mass transport is governed
by surface diffusion and grain boundary diffusion, leading to the sintering neck formation and grain
ACCEPTED MANUSCRIPT growth. However, as the solid-state SLS processes, the neck growth rate decreases because the dihedral angle d tends to reach an equilibrium state [56]. Additionally, the grain coarsening induced by grain boundary migration barely occur due to the equilibrium configuration for all particles [32].
Therefore, the rates of grain growth and densification is very limited.
For
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particles with non-uniform size (average diameter of 40 μm), as shown in Fig. 6c and 6d, grain
As a result, the smaller particles is consumed by larger
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take place due to particle size differences.
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boundary migration toward the curvature center (from the larger particles toward the small ones)
For instance, particle 1 in Fig. 6d is
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ones via volume diffusion as the solid-state SLS processes.
absorbed by its surrounding larger particles and its size decreases from initial 30 μm to 22 μm after
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processing. Moreover, the initial porosity is decreased by adding particles with different sizes, since the smaller ones tend to fill the gap among large ones, leading to more interfaces between
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adjacent particles compared to the powder bed with equal-sized particles.
This results in more
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necking formations and faster densification, which is proved by the significantly decreased pore Furthermore, due to the higher surface area per unit
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size within the area marked with black circle.
volume for the smaller particles, the formation and growth of sintering neck are faster compared to
Therefore, it is necessary to employ powder application process [58] to describe the
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the process.
Obviously, the spatial and size distribution of particles can significantly affect
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large particles [57].
initial state of the powder bed, further improving the practicability of this model.
Fig. 6. Large-scale microstructure evolution during solid-state SLS of 316L stainless steel particles, as predicted by the proposed model: (a) initial status and (b) final status of 9 particles with uniform size of 40 μm; (c) initial status and (d) final status of 9 particles with different sizes (average size of 40 μm). This work demonstrates the feasibility and capability of using PF method to simulate solid-state SLS of multiple powders in a large scale. The model can be used to describe the change in pore configuration within a powder bed accompanied by grain growth, and investigate the effects of laser process parameters and powder properties.
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3.3 Validation of the thermal model Given the lack of data regarding temperature evolution during solid-state SLS, the thermal model is first qualitatively validated by comparing the measured and simulated width of melt pool
stainless steel subjected by SLM.
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Fig. 7 shows the experimental observation and the thermal modeling result of 316L Given a laser power energy of 110 W, a spot diameter of 0.6
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during SLM.
Fig. 7a, indicating the melt pool width of ~600 μm [59].
Based on the liquidius line, a melt pool width is
The simulation result agrees well with the experimental
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predicted to be around 550 μm.
The modeling result of the temperature
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distribution at the top surface is shown in Fig. 7b.
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mm, and a scanning speed of 100 mm/s, the morphology of the sample’s cross-section is shown in
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observation.
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Fig. 7. Comparison of experiment result and temperature model prediction for 316L stainless steel subjected to SLS/SLM: (a) optical micrograph of the sample cross-section [59], adopted with permission from Elsevier, and (b) simulated temperature distribution at the sample surface.
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Fig. 8 shows the comparison between the thermal measurement and our model prediction in Experiments were carried out with a laser power energy of
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case of laser processed Ti sample [40].
2 W, a spot size of 0.05 mm, and a scanning speed of 1 mm/s.
The surface temperature profile
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measured by an infra-red camera shows a maximum value of 2673 K ± 200 K. With the inputs of the same laser processing parameters, the thermal model predicts the peak temperature of around 2700 K, which matches well with experimental data.
Fig. 8. Comparison of temperature model prediction (bold red line) with measured temperature profile (thin black line) along the scanning direction for Ti sample subjected to SLS/SLM. 3.4 Validation of the PF model In order to evaluate the proposed PF model, the simulated evolution of metallic particles during solid-state SLS is compared to experimental data available in literature.
Fig. 9 shows the
ACCEPTED MANUSCRIPT comparison between the experimental observation and model prediction of neck growth in 316L stainless steel powder bed as processed by SLS.
SLS experiments were conducted by University
of Leuven [2, 60], using a pulsed Nd: YAG laser with a pulse width of 10 ms, pulse frequency of 30 Hz, pulse energy of 0.7 J, spot size of 0.8 mm and scanning speed of 0.42 mm/s.
The neck
It is clearly observed in Fig. 9a that the neck length after SLS is about 30 μm.
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(SEM) images.
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formation between the 316L stainless steel particles was observed by scanning electron microscope In
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order to apply the thermal model, the pulsed laser is considered as a continuous wave (CW) laser
pulse frequency.
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by calculating the average laser power as Pavg = E x f, where E is the pulsed laser energy and f is the The predicted temperature evolution is presented in Fig. 9b.
In the PF model,
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based on the SEM image, the initial sizes of two 316L stainless steel particles are chosen to be 65 μm and 50 μm as shown in Fig. 9c. With the temperature input, the time evolution of neck size is The neck size after laser processing is predicted to be around 30.7 μm,
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shown in Fig. 9d and 9e.
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which matches well with the measurement from the SEM image (30 μm).
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Fig. 9. Comparison of PF model prediction with experiment result for solid-state SLS of 316L stainless steel micro-powders: (a) SEM image of the sintering neck between two particles [2], adopted with permission from Emerald Insight, and (b) Simulated temperature history at the center of the sintering track. The PF model prediction of the neck growth between two particles at (c) 10.7 s (the starting point), (d) 12.05 s (the peak temperature), and (e) 13.45 s (the final status). The scale bar represents 20 μm. Fig. 10 compares the experimental findings [13] with model predictions of Ti micro-powder bed subjected to solid-state SLS. SLS experiments.
Ti micro-powders with a diameter of 200-315 μm were used for
Given a laser power energy of 20 W, a spot size of 3.6 mm, and a laser
processing time of 10 s, the cross-section of Ti sample after laser processing is shown in Fig. 10a. The average neck size after laser processing is measured to be around 68 μm. Note that, the necks measured to obtain an average neck size are marked by red circles in Fig. 10a, and the neck length was measured using ImageJ (developed by Wayne Rasband). is shown in Fig. 10b.
The simulated temperature history
The PF simulation is considered as starting at 1155K, which is the α-to-β
ACCEPTED MANUSCRIPT phase transformation temperature, because only β-Ti contributes significantly to the solid-state SLS process since its self-diffusion coefficient is much higher than that of α-Ti [13]. As shown in Fig. 10c, two equal-sized Ti particles with a diameter of 260 μm were used for PF simulation.
The
predicted neck size between two Ti particles after SLS is predicted to be 65.2 μm (as shown in Fig.
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10d), which is in good agreement with experimental measurement.
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Fig. 10. Comparison of PF model prediction with experiment result for solid-state SLS of titanium micro-powders: (a) optical image of the cross-section of the selective laser sintered Ti powders [13], adopted with permission from Emerald Insight, and (b) simulated temperature evolution during SLS. The PF modeling of the neck growth between two particles during SLS: (c) before laser processing, and (d) after laser processing. The scale bar represents 60 μm.
solid-state SLS.
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Fig. 11 compares the experimental result with simulated neck size of Ni powders subjected to The experiments were carried out by Kathuria [3] with a pulsed laser energy of
The sintered structure has a line width of 221 μm and its
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experiments were 30-60 μm in diameter.
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2.1 W, a scanning speed of 2.5 mm/s, and a spot size of 140 μm. The size of Ni powders used for
magnified view is presented in Fig. 10a.
By selecting the necks between particles in the SEM
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image (Fig. 11a) as marked by red circles, an average neck size is measured to be around 14 μm.
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The thermal modeling of temperature history is shown in Fig. 11b.
In the PF model, two
equal-sized particles with a diameter of 45 μm are employed as shown in Fig. 11c. The time
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evolution of neck growth is presented in Fig. 11d and 11e.
The final neck length after laser
processing reaches to 13.1 μm, which agrees well with the modeling result.
Fig. 11. Comparison of PF model prediction with experiment result for solid-state SLS of Ni micro-powders: (a) the magnified view of the sintered structure [3], adopted with permission from Elsevier; and (b) the simulated temperature history at the center area of the sintering track. The PF modeling of the neck growth between two particles at (c) 0.76 s (the starting point), (d) 0.80 s (the peak temperature), and (e) 0.86 s (the final status). The scale bar represents 10 μm. 4. Conclusion In this study, a PF based model is developed to simulate microstructure behaviors during
ACCEPTED MANUSCRIPT solid-state SLS of metallic materials.
Laser processing conditions are considered by integrating
PF codes with thermal modeling of continuous heating induced by laser irradiation.
The effects of
laser power intensity and scanning speed on microstructure evolution are investigated.
This
model is validated by comparing the modeling results with experimental data in terms of neck The model is found to be capable of predicting
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growth between adjacent micro-powders.
The modeling results can provide important insights and guidance for
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solid-state SLS process design, control, and optimization.
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experimental findings.
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microstructure evolution during solid-state SLS by demonstrating good consistence with the
Furthermore, the feasibility and capability of employing the developed model to large-scale The predicted porosity and grain size
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simulation in terms of multiple particles are demonstrated.
by lager area simulation will lead to fabrication of functional porous products such as electronics
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with designed conductivity and thermal management components with desired thermal properties.
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This will be discussed in our further work along with the effects of large temperature gradient and
Acknowledgement:
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size distribution of powder particles.
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The authors appreciate the financial support by start-up funding from the Department of
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Mechanical Engineering at the University of Nevada, Reno. Data Availability: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
ACCEPTED MANUSCRIPT References:
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ACCEPTED MANUSCRIPT Table 1 Other properties of 316L stainless steel, Ti and Ni used in the temperature simulation. Surface reflectivity R 0.4 0.23 0.36
Surface emissivity ε 0.8 0.77 0.8
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316L Ti Ni
Bulk density ρ (kg/m3) 7980 4506 8908
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p 1 1 4
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Table 2 Material properties of 316L stainless steel, Ti and Ni used in PF model. Materials 316L Ti Ni Prefactor Dgb0 (cm 2/s) 0.127 90 4.8 GB diffusion Activation energy Qgb (eV) 0.58 1.93 1.71 Prefactor Dsyrf0 (cm 2/s) 4 x 103 0.47 23.9 Surface diffusion
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1.3 3.58 x 10 -4 1.353 5.53 x 10-8
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GB mobility
2.21 2 2.6 5.53 x 10-8
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Volume diffusion
Activation energy Qsurf (eV) Prefactor Dvol0 (cm 2/s) Activation energy Qvol (eV) Prefactor (m4/J/s)
1.85 0.92 2.88 1.51 x 10-6
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0.171 2 1.1
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Activation energy (eV) Surface energy γs (J/m2) GB energy γgb (J/m2)
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0.26 1.9 0.87
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Highlights: A phase-field (PF) based selective laser sintering (SLS) model is developed. SLS of 316L stainless steel, titanium, and nickel are simulated. Effects of laser intensity and scanning speed are modeled. Modeling results are validated by experimental data.
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