Download Khorasani2018 Article RheologicalCharacterizationOfP

The International Journal of Advanced Manufacturing Technology (2018) 97:3761–3775
https://doi.org/10.1007/s00170-018-2168-6
ORIGINAL ARTICLE
Rheological characterization of process parameters influence on surface
quality of Ti-6Al-4V parts manufactured by selective laser melting
Amir Mahyar Khorasani 1 & Ian Gibson 1 & Ali Reza Ghaderi 2
Received: 13 February 2018 / Accepted: 10 May 2018 / Published online: 31 May 2018
# Springer-Verlag London Ltd., part of Springer Nature 2018
Abstract
Additive manufacturing is one of the promising production processes, which has the ability to manufacture final shape directly
from computer-aided designs. In this research, the thermal effect of process parameters on the average surface of selective laser
melting (SLM) Ti-6Al-4V is discussed and mathematically characterized. Based on Taguchi L25, the experiment was designed,
and laser power, scan speed, hatch spacing, laser increment pattern angle, and heat treatment in five levels were selected as input
parameters. Interfacial forces including surface tension, Marangoni’s effect, pressure in droplet, capillarity force, work adhesion,
wetting, recoil pressure, drag forces (due to solid-liquid transition) and interaction of surface tension, hydrostatic and vapor
pressures have been characterized mathematically to analyze their effect on surface quality. Results showed higher energy density
and temperature cause lower surface tension and capillary force, generating unstable and lower surface quality. In addition, higher
energy density and temperature increase droplet pressure, internal pressure, recoil pressure, and thermal stress and change the
balance of forces on the surface of the melting pool and reduce surface quality.
Keywords Selective laser melting . Rheology . Thermal gradient . Surface roughness
Nomenclature
C1, C2
dA
dV1
E1
E2
g
h
H
Hs
Iimp
Planck distribution constants
Increase the surface area
Decrease of internal volume
Melting pool energy
Energy of solidified layer
Gravity acceleration
Height of meniscus
Enthalpy
Hatch space
Impregnation criteria for surface energy
* Amir Mahyar Khorasani
[email protected]
Ian Gibson
[email protected]
Ali Reza Ghaderi
[email protected]
1
School of Engineering, Deakin University, Waurn Ponds, Victoria,
Australia
2
Institute for Frontier Materials, Deakin University, 75, Pigdons Road,
Waurn Ponds, Victoria, Australia
Lp
n
P0
Pch
Precoil
Q
R2
Rbub
Rcur
Rdrop
Rg
Sc
Scontact
Ss
T0
Tc
Tmp
U
Uf
Ufb
V0
Vliquid
Laser power
Katayama-Guggenheim factor
Reference value for pressure
Chamber pressure
Recoil pressure
Internal heat
Second radius of meniscus
Bubble radius
Curvature radius
Radius of droplet
Universal gas constant
Contact area of melting pool with solidified
layer
Contact surface of droplet and base
Scan speed
Reference value for temperature
Critical temperature
Titanium melting point temperature
Cohesive energy
Fluid speed
Speed of melted particles at the end of melting
pool
Reference value for volume
Volume of liquid in the melting pool
3762
Wa
We
Wi
Ws
Wsu
Wt
Z
Zb
αL
αv
γ0
γSL,γSG,γLG
γ∗
δ
λ
ρ
Int J Adv Manuf Technol (2018) 97:3761–3775
Work of adhesion
Required work correspond to pull out external
fluid
Initial work to increase the pressure of droplet
Required work correspond to increase internal
area
Other works
Total work
Axial length toward the end of keyholes
Distance of keyhole from top to the bed
Linear coefficient of expansion
Volumetric coefficient of expansion
Reference value for surface tension
Surface tension for solid-liquid, solid-gas and
liquid-gas
Constant surface tension for each liquid
Molecular dimension
Wave length
Density
1 Introduction
Generally, the surface roughness is low in powder bed systems
such as selective laser melting (SLM) and electron beam melting (EBM), but the surface quality in EBM is lower due to
excessive Marangoni’s convection, unstable melting pool, and
falling powder particle on the unstable melting pool [1–4]. It is
reported that surface roughness varies between 1 and 20 μm
depending on process parameters such as layer thickness,
hatch spacing, laser power, scan speed, and particle size
[5–9]. Few investigations were found in the literature which
purely analyzed the surface quality of as-built parts on SLM.
Reducing scanning speed and increasing layer thickness
lead to formation of irregular tracks and lower surface quality.
Also, use of finer powder and layer thickness improve the
surface roughness [10]. The width of melting pool is associated with hatch spacing and is a critical factor in the formation
of Marangoni’s effect and surface quality [11]. Using full factorial design of experiment to analyze the effect of process
parameters on the surface quality of CoCrMo showed that
laser power, hatch spacing and scan speed are the most influential parameters. The surface roughness using contactable
profilometry for single layer printing was obtained as 8 μm.
However, the reported value is based on the cutoff length of
the profilometer needle [11]. Thermal phenomena and scanning strategy were found to be effective factors on the surface
roughness of Hastelloy for up-skin and down-skin surfaces.
The effect of laser power, scan speed, layer thickness, and
sloping angle on surface roughness showed that due to lack
of wettability and Rayleigh instability, if the scan speed exceeds the original equipment manufacturer recommendations,
higher balling effect and lower surface quality results [12]. A
Gaussian process-based model has been used for learning and
prediction of the porosity in SLM of 17-4 PH stainless steels
as a function of process parameters. Cross-validation for all
eight test samples proved the accuracy of this approach to
predict the value of porosity and surface defects is acceptable
[13]. It is reported that [5] to obtain better surface quality,
maximum hatch distance should not exceed the average width
of the continuous track. The value of temperature, thermal
gradient, and subsequently surface quality in SLM is also
associated with scan length.
Particle size distribution has a major influence on the density and surface quality of the printed parts. Spierings et al.
[14] investigated the effect of three different particle sizes and
two layer thicknesses on surface quality and density of AM
parts. The results showed that using optimum powder particle
size and post-processing such as blasting improves the quality
of the surface in AM and granulation improves the surface
quality but is changed due to the spatter nature of the process.
The size of particle diameter and layer thickness should be
proportional to improve adhesion along the step edge and to
fill gaps between consecutive layers and improve surface
quality [15].
Various post-processings such as re-melting, milling, turning, grinding shot peening, or sand blasting have been suggested to improve the quality of as-built samples. For instance,
laser re-melting improved the surface roughness Ra from 15 to
1.4 μm [16] or milling improved it to 6 μm depending on
cutting strategy and parameters [17–20]. However, these
methods increase the cost and manufacturing lead-time in
the production process.
Most of the investigations theoretically mentioned the effect of process parameters on surface quality. However, there
is a lack of rheological characterization literature on thermal
phenomena of the surface of as-built parts. In this research
based on Taguchi L25, Ti-6Al-4V parts were printed and thermal effect of process parameters such as laser power, scan
speed, and hatch space on melting pool and interface-related
phenomena were scrutinized to clarify their effect on the surface of the printed parts. Different phenomena such as surface
tension and Marangoni’s effect, capillary force, the pressure in
droplet, wetting, work adhesion, recoil pressure, drag force/
contraction forces, and interaction of surface tension, hydrodynamic and vapor pressure are discussed in depth.
2 Materials and methods
2.1 Powder material and SLM process
Due to its high strength, good corrosion resistance and lowdensity Ti-6Al-4V is highly suited for production parts in the
biomedical, aerospace, and automotive industries. In this
work, spherical Ti-6Al-4V powder was used as a feed in the
Int J Adv Manuf Technol (2018) 97:3761–3775
printing process. SLM Solutions 125HL equipped with
Yttrium laser and maximum power of 200 W and minimum
spot size 5 μm was used.
2.2 Surface roughness measurement
Samples were printed based on ASM standard E8 for further analysis on tensile properties. Surface roughness
measurement has been carried out using an Alicona
Infinite Focus optical profilometer that is equipped with
5 to 100× zoom. The measurement was performed on asbuilt samples and not post-polishing was implemented on
the samples to keep the original surfaces. To have consistency in the obtained results and regions of 5 × 3 mm
(about 3000 points) and five times in different areas of
the top surface on the samples were scanned to achieve
the value of the surface roughness. Normalized value of
surface parameters was calculated by this device. Based
on ISO 4288 and ISO 11056 standards, a high pass
Gaussian filter was used. Then, Ra values converted to
Sa to have a more general and consistency in results.
2.3 Design of experiment
The important feature in the characterization of different
aspects such as mechanical properties, surface quality,
and dimensional deviations of SLM parts is low repeatability (while is good repeatability for DMD parts [21,
22]) due to the complex interactions between various
process parameters. Therefore, to increase the accuracy
and generality of this research, Taguchi L25 orthogonal
design of experiment (DOE) has been used, and laser
power, scan speed, hatch space, and laser pattern
incrementing angle were selected for input parameters.
Our previous research showed that due to high cooling
rate (103–108 K/s) as-built samples have low ductility,
therefore, according to ASM standards different annealing processes such as stress relieving, mill annealing,
recrystallization and beta annealing have been carried
out to improve mechanical properties for further research
[23–25]. Thus, annealing temperature was added to the
DOE as an independent parameter to analyze the effect of
heat treatment on surface quality and to increase generality of the experiment for each factor five levels were
chosen (Tables 1 and 2).
2.4 Analyzing the effect of process parameters
on the surface
Based on our previous investigations laser power, scan speed
and hatch space affect melting pool and subsequently surface
characteristics of printed parts. Therefore, the effect of the
mentioned parameters is characterized in this section
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Table 1
SLM Constant process parameters
System parameters
Value
Min. scan line/wall thickness
120 μm
Operational beam focus variable
100 μm
Layer thickness
Laser spot diameter
30 μm
0.2 mm
[24–26]. The surface roughness of as-built parts is highly associated with thermal phenomena and behavior of melting
pool which is discussed based on rheological science and phenomena [12].
To analyze the effect of process parameters on the average surface, artificial neural networks (ANN) was used.
Multi-layer perceptron ANN has been used with 5 inputs
according to Table 2 and output was average roughness.
The number of training, validation, and test samples was
17, 3 and 5 respectively. To analyze the generality of the
proposed ANN, five cross validations have been performed;
therefore, all samples were tested and results are illustrated
in Table 3 and Fig. 1.
As shown in Table 3 and Fig. 1, a high accuracy of the
proposed model is proven. To analyze the effect of process
parameters on average roughness, the interaction of effective
process parameters on melting pool including laser power,
scan speed, and hatch space has been drawn.
3 Results and discussions
For analyzing the effective process parameters on melting
pool, the simplifications are:
(I) Molten material is assumed to be incompressible, (II)
the interface has no thickness, (III) the interface is smooth,
(IV) the chamber has constant working pressure, (V) heat
capacitance and thermal conductivity of the melted materials
were constant [21, 22], and (VI) layer thickness was constant
for all 25 samples and therefore neglected.
3.1 Surface tension and Marangoni’s effect
In this research SLM Solutions, 125HL equipped with
Yttrium laser was used. We simplified the laser with black
body, therefore, the radiation energy in temperature “T” by
using Planck distribution is [27–29]:
E ðb;λÞ ðλ; T Þ ¼
C
1 C2
−1
λ5 exp
λT
ð1Þ
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Table 2 Process parameters and
levels
Laser Power
(W)
Scan Speed
(mm/min)
Hatch spacing
(μm)
Scanning pattern
incrementing angle (°)
90
95
600
650
65
70
36
40
20
600
100
105
700
750
75
80
45
60
750
925
110
800
85
75
1050
It should be noted that not all of the laser energy will be
used in melting the powder due to reflection, etc. Importing
process parameters in the Planck distribution and by substitution of energy density in SLM with the radiation energy, we
have [26, 29, 30]:
T mp ¼
C2
C1 SS H S
λln
þ1
LP λ5
ð2Þ
In the bulk of the melt pool, molecules have interaction
with surrounding molecules due to Van der Waals forces. In
interfaces, molecules have half space for interactions with
neighboring molecules. Surface tension is obtained by cohesive energy “U” according to Eq. 3 [30].
γ¼
U
2δ2
ð3Þ
The power of 2 for δ relate to the surface of the molecule.
The developed Eotvos equation for surface tension is called
Katayama-Guggenheim and shows that surface tension is a
direct function of temperature [31, 32].
1
0
B
γ ¼ γ*B
@1−
C
C
2
C
A
C1SS H S
T C λln
þ
1
LP λ5
ð4Þ
A critical point in thermodynamics is the end of phase
equilibrium. This is the point of coexistence of liquid and its
vapor at the end of liquid in the phase equilibrium curve. By
determining reference values (γ0, T0), the surface tension is:
T C −T 0
ð5Þ
γ ¼ γ*
TC
Combining Eqs. 1–3 shows that for linear changes of temperature in relation to surface tension, Eq. 6 is obtained:
γ¼γ
*
2 2
33 n
T C −T 0 4 4
C2
T C 55
−
1−
TC
ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0
P
ð6Þ
Heat treatment
temperature C°
Equation 4 is thermocapillary or Marangoni’s effect
(Marangoni’s convection). Temperature distribution was
highly influenced by the energy density and in the case
of higher laser power and lower scan speed (higher energy
density), the interface of melting pool is locally heated
and according to Eq. 6 surface tension reduced (Fig. 2).
The gradient of surface tension induced at the interface
from the hotter to the cooler area then propagates toward
the bed of the melting pool. The higher the temperature,
the higher the motion of melting pool resulting in greater
irregularity on the surface of the pool. Since the cooling
rate is high in AM, surfaces form quickly and irregularities in the solidified process are maintained [11, 33–35].
Moreover, high energy density enhances densification but
induces fine spherical pores and thermal micro-cracks by
increasing liquid lifetimes and thermal process [36]. If
scan speed increases or laser power decreases, the value
of energy density decreases and less heat generated in the
process thus less micro-fluid flow and instability occurs in
the melting pool forming better surface quality. This trend
was proved by the literature [10, 37–39].
Analyzing hatch space on the surface quality shows
with lower hatch space, higher overlap occurs. This creates a mush area and the gradient of micro-fluid motion
(due to higher viscosity) is zero and no Marangoni’s convection happens and energy density increases and the
chance of formation of keyholes and defects also increases [34]. Moreover, the higher cooling rate on the
surface of the melt pool and reduced overlap leads to
higher heat penetration and increases the chance of the
formation of keyholes and lower surface quality.
3.2 Capillarity force
Capillary force is important in the characterization of
melting pool behavior in micro-scale. To explain the melting pool behavior, we assume the previous hatch and surrounding unmelted powder act as two plates for the melting pool (Fig. 3).
We can simplify the melting pool in terms of fluid
between two parallel plates. Due to low hatch space in
our experiment (60–80 μm), a liquid film tends to be
Int J Adv Manuf Technol (2018) 97:3761–3775
Table 3
3765
Results of the cross-validation
Cross validation
Std. dev.
Max error
Correlation
Cross validation
Std. dev.
Max error
Correlation
1st
2nd
3rd
Train
Test
Recall
Train
Test
Recall
Train
Test
0.01063
0.03022
100
2.11326
3.51448
99.709
2.159
3.482
96.228
0.00557
0.01632
100
2.86936
4.19455
93.884
1.855
2.871
97.061
0.00075
0.002
100
3.10811
3.87853
96.116
3rd
4th
5th
Recall
Train
Test
Recall
Train
Test
1.46058
2.29187
95.276
0.0007
0.00165
100
3.60215
6.15992
99.29
1.56434
2.28229
99.6
0.00095
0.00249
100
2.41102
3.04171
96.897
generated between two parallel plates and is considered to
be adhesive. Capillary force is predominant in microfluids and to minimize free energy a meniscus with round
shape is created. Using Laplace’s law at free interface and
by supposing the first radius of curvature “Rcur,” the second radius of meniscus is “R2” is calculated by:
π
Hs
sin θ−
⇒H s ¼ ð−2R2 cosθÞ
ð7Þ
¼
2R2
2
The minus sign in Eq. 7 shows that the liquid moves down
due to the interaction of capillary and Van der Waals forces. The
pressure in the melting pool is related to hatch spacing, and
therefore, Eq. 8 by applying Laplace’s law is derived [30, 40]:
8
1
1
1 2cosθ
>
>
ΔP
¼
P
−P
¼
γ
−
¼
γ
þ
0
1
>
>
Rcur R2
R
Hs
>
>
>
>
>
< if curvature is concave
>
>
1
1
1 ð2cosθÞ
>
>
−P
¼
γ
þ
¼
γ
−
ΔP
¼
P
>
0
1
>
>
Rcur R2
R
Hs
>
>
:
if curvature is convex
ð8Þ
Due to higher Van der Walls forces in melted metals and
formation of a convex shape, Eq. 8 is dominant. The value of
hatch space is much less than vertical radius and the capillary
pressure in the surface of melting pool by Laplace’s law is
obtained based on Eq. 9 (Fig. 4).
8
−2γcosθ
<
ΔP ¼
ð9Þ
HS
:π
=2 ≪θ≪π
The value of contact angle is in the second quarter of trigonometric circle and therefore the value of melting pool pressure is positive. The capillary force for melting pool between
two parallel plates, including a solidified layer on one side and
powder particle on the other, and considering the hatch space
as the distance between the plates is [30, 40]:
2 2
33n
2cosθ 2 * T C −T 0 4 4
C2
T C 55
−
1−
F≈
πR γ
TC
HS
ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0
P
ð10Þ
By increasing laser power and decreasing scanning speed
(higher energy density), the surface of melting pool has a
higher temperature and due to Marangoni’s convection, the
value of surface tension in Eqs. 4 and 10 decreases. The capillary force reduces therefore the surface of the melt pool has
weaker adhesion to the sidewalls and considering the convex
shape of melted metals the horizontal radius of curvature decreases and rougher surfaces in the staircase are obtained. In
this situation, fast solidification forms surfaces with more distortion and less quality [30, 34].
In lower laser power and higher scanning speed (lower
energy density), the temperature of the surface on the melt
pool is lower and based on Eq. 10, the capillary force
increases and the interaction of intermolecular forces versus wall adhesion move toward equilibrium and surface
becomes smoother. Decreasing contact angle in Fig. 4 is
another reason for decreasing cosθ (from π to π/2) in the
numerator of Eq. 10 and reduction of capillary force.
Using principle of minimum energy, metal liquid
moves downwards in tinner tubes which shows surface
energy in dry walls is lower than wet walls. The impregnation criterion is Iimp = γSG − γSL. The liquid goes down
when γSL > γSG and using Young’s law and equations A1 and A-2 in appendix the height of the meniscus between two parallel plates separated by distance hatch
space is
h¼
2γcosθ
ρgH S
ð11Þ
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Fig. 1 a–c Interaction of laser power, scan speed, and hatch spacing on average roughness. d Samples
Equation 11 shows that increasing hatch space leads to
decreasing contact angle and decreasing value of “h.”
Therefore, the roughness on the surface of melt pool tends to
disappear and smother surfaces were obtained.
radius Rdrop to Rdrop + dRdrop due to increasing internal
volume is [30, 40]:
δwi ¼ −P0 dV 0
ð12Þ
dV 0 ¼ 4πR2drop dRdrop
3.3 Pressure in droplet
The necessary work to pull out the external fluid and the
work corresponding to increase in interfacial area “ws” are:
During SLM process, on account of fully melting of particles, two types of droplets including gas and melted
powder particles exist which can affect the quality of the
surface. In this research, a spherical powder particle was
used and by supposing the melted particle to be
surrounded by liquid, the necessary work to increase
Fig. 2 Marangoni’s effect and surface quality
δwe ¼ −P1 dV 1
ð13Þ
dws ¼ γdA; dA ¼ 8πRdrop dRdrop
ð14Þ
where dV1 is the decrease of external volume proportion
to dV0. At mechanical equilibrium on the surface and bulk
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3767
Fig. 3 Horizontal curvature in capillarity (optical image)
of the melting pool, the total introduced work has zero
value.
P1 ¼ P0 −
2
Rdrop
γ*
2 2
33n
T C −T 0 4 4
C2
T C 55
−
1−
TC
ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0
P
δwt ¼ δwi þ δwe þ δws ¼ 0
ð15Þ
ð18Þ
By combining Eqs. 12–14, the pressure in droplet for bulk
and surface of the melting pool is derived from Eq. 16.
ΔP ¼ P0 −P1 ¼ γ
dA
dV
ð16Þ
The shape of droplet for melted powder particle is spherical
and therefore the internal pressure of a droplet is [30, 38–40]:
ΔP ¼
2γ
Rdrop
ð17Þ
In the case of higher laser power and lower scanning speed,
the accumulated heat in melting pool increases, so the pressure
of droplet according to Eq. 18 also increases:
Fig. 4 Different capillary effects
on melting pool
In addition, higher energy density and temperature leads to
a reduction of surface tension and increasing melted particle
radius and subsequently the pressure of the droplet increases
and leads to bursting droplets from the melting pool, which is
illustrated by Fig. 5.
As it can be seen, the abovementioned mechanism generates some large dents on the surface of the samples and decreases surface quality. In the case of increasing hatch spacing
and decreasing overlap area, Marangoni’s convection reduces
surface temperature and decreases droplet pressure. In lower
hatch space and wider overlap area, the gradient of fluid flow
is zero and accumulated heat results in higher temperature and
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pressure in droplets. This mechanism leads to bursting droplets from the melting pool in the overlap area and reduction of
surface quality (Fig. 5).
3.4 Wetting
Lower surface quality was obtained in lower scan speed and
higher laser power (higher energy density and temperature)
because a liquid spreads in a film if the surface energy is
lowered. Figure 6 shows Young’s law has been derived for
triple line regardless of determining the interactions near the
contact line. Close to triple line, the molecules have different
interaction compared to those in the interfaces. When we increased the scan speed in the range of standard values the laser
track becomes continuous and tends to remove recoil pressure
marks on the topmost surface due to higher gradient of momentum and smaller size of the droplets. Therefore, a line
tension term is added to Young’s law according to Eq. 19
[30, 38–41]:
γ SG ¼ γ SL þ γ LG cosθ þ
γ SLG
Rdrop
ð19Þ
By increasing scan speed the value of “Rdrop” becomes
smaller and with respect to very small “θ” cosθ = 1 then according to Eq. 20 the value of γSG increases:
γ
lim SLG ∼∞ γ SLG ≠0
ð20Þ
Rdrop →0 Rdrop
The wettability of melting pool is defined by the spreading
parameter “S.” According to Eq. 21, the type of spreading can
be film or droplet [30, 38–40]:
8
< S ¼ γ SG −ðγ SL þ γ LG Þ
ð21Þ
If S > 0⇒Film appears
:
If S < 0⇒Droplet appears
Equation 19 shows that by reduction of droplet size the
value of γSG increases and S > 0 so the film of melted titanium
appears on the surface. Lower surface tension and higher wetting results in lower viscosity by taking into account the number of laser pulses and instability of the melting pool. Waves
are generated on the top surface and fast cooling procedure
leads to decreasing surface quality.
Moreover, in the melting pool, bubbles often form along
contact surfaces. The pressure of the bubbles is obtained from
Laplace’s law according to Eq. 22:
P¼
γ
Rcur
ð22Þ
When laser power increases and scan speed decreases, the
temperature of the surface on account of higher energy density
raises and, based on Eq. 21, spreading factor increases S > 0
and the film is formed on the melting pool. In this situation,
Eq. 6 shows that surface tension decreases due to Marangoni’s
effect. Based on the Katayama-Guggenheim relation (Eq. 4)
in critical temperature (boiling temperature), the value of surface tension is zero. However, surface tension has non-zero
value in SLM process since the working temperature will not
go higher than 2250 °C and boiling temperature for Ti-6Al-4V
is around 3560 °C [42]. Increasing wettability from Eqs. 21
and 22 leads to:
lim
Lp →Lphigh
γ
∼∞
Rcur →0 Rcur
ðPÞ ¼ lim
ð23Þ
Therefore, the value of the internal pressures increases radically and the bubbles burst during the process and throw
some particles above solidified surfaces and reduce the surface quality. Figure 7 shows the thrown particles due to hydrophilic contact with the melting pool. In other words, the
interaction of higher internal pressure for bubbles and lower
surface tension due to higher energy density leads to a volcano
effect on the top of the samples. Small balling was found at
low scan speeds and high scan powers due to longer liquid
lifetimes, increased melt volumes, and decreased melt viscosities [12, 43].
Decreasing hatch space leads to increase in the value of
overlap area. When the second hatch is scanned by the laser
in the overlap area, partial melting happens and based on
Katayama-Guggenheim theory, surface tension in solidliquid and liquid-gas increases. The material phase in the overlap area is mush and the gradient of fluid flow in this area is
zero:
*
∇ uf ¼
∂u f ^ ∂u f ^ ∂u f ^
jþ
iþ
k¼0
∂x
∂y
∂z
ð24Þ
Therefore, no Marangoni’s convection happens in the overlap area and surface tension in liquid phase increases:
γ SG < ðγ SL þ γ LG Þ⇒S < 0
ð25Þ
Based on Eq. 25, partial wetting happens which causes
more waviness and rougher surfaces are formed during solidification [9, 34].
3.5 Work of adhesion
In this section, the effect of laser power, scan speed, and
hatch space on work adhesion and surface quality has
been analyzed parametrically. The work of adhesion is
defined for solid/liquid or immiscible liquids. In solid,
liquid interfaces such as melting pool/solidified layer the
combination of work adhesion and Young’s law produces
Young-Dupre’s equations. These relations are used to
Int J Adv Manuf Technol (2018) 97:3761–3775
3769
Fig. 5 Bursting droplet in the surface of the melting pool: (A) colored map and (B) normal map
characterize the effect of laser power, scan speed, and
hatch space on the surface quality.
If the contact of melting pool with the solidified layer is
“SC,” then surface energy is obtained from Eq. 26:
E SL ¼ γ SL S C
ð26Þ
The work that is required to separate the melting pool and
solidified layer is work of adhesion and after separation, the
energy is:
E t ¼ E 1 þ E2 ¼ ðγ 1 þ γ 2 ÞS C
ð27Þ
Now the work of adhesion is obtained according to Eq. 28
[30, 38, 40].
W a ¼ γ 1 þ γ 2 −γ 12
⟹W a ¼ γ LG þ γ SG −γ SL
γ 1 ¼ γ LG ; γ 2 ¼ γ SG ; γ 12 ¼ γ SL
ð28Þ
By drawing different forces exerted on triple line (topmost
surface/melting pool) at equilibrium, the forces must be zero
and along scan direction, the following equation is derived [1,
2] (Fig. 8).
γ LG cosθ ¼ γ SG −γ SL
ð29Þ
The work adhesion for melted and solidified layers from
Eqs. 26 and 27 is obtained by [30, 40]:
Fig. 6 Partial melting in the
surface: (a) more droplet and (b)
more film shape
W a ¼ γ ð1 þ cosθÞ
ð30Þ
In the case of higher laser power and lower scan speed due
to generation and accumulation of higher heat, the value of
γLG decreases and melting pool becomes a film and from Eq.
30 work adhesion decreases. This phenomenon leads to reduction of initial adhesion of melting pool with solidified layer
and due to the movement of laser and instability of melting
pool, melted material flows and the gradient of fluid flow has
non-zero value specifically at the bottom of the melt pool [12].
*
∇ ufb ¼
∂ufb ^ ∂ufb ^ ∂ufb ^
jþ
k≠0
iþ
∂x
∂y
∂z
ð31Þ
Due to this motion, larger waves occur and unmelted powder
particles drop to the melting pool even when top surface of the
melt pool has small movement/fluctuation, which increases the
value of average roughness during fast solidification.
In the case of lower laser power and higher scanning speed,
lower energy density and temperature leads to increase in
surface tension and work adhesion. As a result, more adhesion
and higher stability in melting pool generate better surface
quality.
Increasing hatch space leads to increasing contact surface
between the melting pool and solidified layers. Therefore, the
surface energy increases according to Eqs. 26 and 27. Work of
adhesion is a function of surface energy thus, by increasing
3770
Int J Adv Manuf Technol (2018) 97:3761–3775
Fig. 7 a Hydrophilic surface and small bubbles. b Hydrophobic and larger bubbles. c The effect of bursting of small bubbles on surface quality
surface energy this factor increases and melting pool becomes
more stable and consequently smaller waves and better surface quality were obtained.
3.6 Recoil pressure
The recoil/snapback movement of melted fluid is a common
rheological phenomenon in laser-based production processes
[44]. The source of snapback movement is related to laser
pressure and viscous and elastic characteristics of fluid under
deformation forces. The effect of recoil pressure is quite obvious on the top surface of SLM parts and is obtained according to the following Eq. [44]:
ΔH V 1
1
ð32Þ
−
Precoil ¼ P0 exp
Rg
T V T mp
Recoil pressure in SLM is defined based on process parameters by substituting titanium melting temperature from
Planck dispersion and using Eqs. 2 and 32 and 33:
13
C1SS H S
λln
þ
1
6 ðδQ þ VdPch −δW SU Þ B 1
C7
LP λ5
C7
B −
¼ P0 exp6
4
A5
@T V
Rg
C2
2
Precoil
0
ð33Þ
Fig. 8 Triple contact line on the
surface of the printed part
In SLM by increasing laser power and decreasing scanning
speed (increasing energy density), the argument of a logarithmic function in Eqs. 32 and 33 decreases. In SLM, the surface
pressure from the chamber is constant and by assuming no
additional work goes on inside the chamber “Wsu” the recoil
pressure increases (Eq. 34). Increasing recoil pressure leads to
a more pronounced step effect on the surface of the samples
and decreasing surface quality as shown in Fig. 9.
13
C1SS H S
λln
þ
1
C7
6 δQ B 1
LP λ5
B
C7
¼ P0 exp6
A5
4 Rg @ T V −
C2
2
Precoil
0
ð34Þ
In addition, enthalpy is a function of heat dh = δQ; therefore, according to Eq. 2, increasing energy density leads to
increasing temperature and generated heat on the surface of
melting pool and subsequently recoil pressure increases and
higher stair effect was observed on top of the melting pool.
Also, according to Fig. 10, the volume of displaced material
piled up around the edges of the melt pool increased and lower
surface was observed.
Increasing hatch space generates a greater log term in Eq.
34 and as a result, lower recoil pressure and step effect are
observed in the top surface of the samples.
Int J Adv Manuf Technol (2018) 97:3761–3775
3771
Another reason for increasing the average roughness for
smaller hatch space is associated with the promotion of particle attachment in the overlap of two subsequent hatches.
Larger overlap leads to enabling the previously fabricated
track to absorb more energy and increase the temperature.
This effect is stronger than the cooling of overlap area due
to the heat sink effect. The wider heat affected zone and more
partially melted powder attached to a solid interface is the
result of this phenomenon and increased average roughness
[5, 12].
3.7 Drag force/contraction forces
In powder bed, additive manufacturing the build substrate is
welded to the sample to prevent primary movement and acts
as a temporary base and reduces the degree of freedom.
The linear expansion coefficient of Ti at melting pool at
1600 °C grows about seven times compared to the ambient
temperature (Fig. 10), so the increase in volume is significant
and the following equation is drawn:
T
ΔV
mp
¼ exp ∫T 0 aV ðT ÞdT
ð35Þ
V
For isotropic materials aV = 3aL, however for printed Ti6Al-4V due to anisotropic behavior of the material, the volumetric expansion due to increasing the temperature in melting
pool by combining Eqs. 2 and 35 is:
8
0 C2 1
>
>
C1 SS H S
>
>
B λln LP λ5 þ1
C
< ΔV
¼ expB
ðξaL ðT ÞÞdT C
@∫ T 0
A
V
>
>
>
>
:
ξ>1
ð36Þ
Increasing the laser power and decreasing scan speed tend
to increase the upper interval of integral and change of volume. Also, in higher temperature such as melting pool, the
thermal expansion coefficient is aL(T0) = 7aL(Tmp); therefore,
the volumetric change within the process increase 7ξ. In this
situation, the volume of melted material expand and becomes
bigger. In addition, thermal stress for anisotropic material such
as SLM Ti-6Al-4V is obtained from Eqs. 36 and 37 [46].
σth ¼
σth ¼
Eξα
T mp −T 0
1−ν
Eξα
C1SS H S
ð1−ν Þ λln
þ1
LP λ5
ð37Þ
C S H
C 2 −T 0 λln 1 S 5 S þ 1
LP λ
ð38Þ
From Eq. 38, it can be observed that when the higher energy density is selected (increasing laser power and decreasing
scanning speed and hatch spacing), the value of the argument
in the log term increases and therefore the numerator of the
fraction becomes bigger and denominator gets the smaller
value. As a result, thermal stress greatly increases and with
respect to Eqs. 35 and 37, the higher thermal stress and larger
volumetric expansion on the surface generate a larger rippling
effect on the top surface (Fig. 10b).
In solidification, the initial cooled part of the material is
granular followed by boundary regions (which floated in the
melting volume). By carrying out a cooling process, grain
boundaries are converted to semisolid/mush. When higher
laser power and lower scan speed and hatch spacing are selected, higher energy and thermal stress exerted to the material
according to Eq. 38. Under higher stress and forces, high
thermal gradient in liquid phase [47] and destabilization of
the solidification cause a transition from a planar to cellular
or dendritic solidification. Therefore, grain size becomes
smaller and tensile strength improves up to 25% compared
to wrought materials [24, 25, 42]. Grain boundaries reduce
the thermal and electrical conductivity of the material and this
is more obvious for Ti-6Al-4V due to low thermal conductivity (21.9 W m−1 K−1). Thus, a combination of these four factors comprising low thermal conductivity, small grain size,
low elongation, and high volumetric expansion for Ti-6Al4V, generates higher distortion on the surface and formation
of micro-cracks and cracks in bulk of the material.
According to Eq. 37, increasing energy density (laser power and decreasing hatch space and scan speed) increases the
value of thermal stress, so due to high thermal expansion the
interaction of contraction forces and substrate resistance may
result in cracks and reduce the surface quality.
3.8 Interaction of surface tension, hydrostatic
and vapor pressures
In SLM of metals, keyholes are one of the defects appearing
on whole surface and bulk. In the melting pool, a vapor pressure acts versus hydrostatic force and surface tension on the
interface of liquid/solid so in keyhole walls the vapor pressure
increases by increasing depth of the keyhole and decreasing
the radius [1, 48]. Gasses trapped in the balling region form a
classical keyhole shaped void (Fig. 11).
Hydrostatic pressure and surface tension tend to close the
walls of keyholes, while, vapor pressure acts in opposite and
tends to keep the walls open (Fig. 9). Hydrostatic and vapor
pressures are derived based on Eqs. 39 and 40 [1, 2]:
Phydro ¼ P0 þ ρgzSinθ
Pvapor ¼ P0 þ
γ ðT Þ
þ ρgz
RðzÞ
ð39Þ
ð40Þ
It is known that the working temperature for Ti-6Al-4V is
less than boiling (critical temperature); therefore, the surface
tension has non-zero value and based on Eq. 41, high pressure
is observed at the end of the keyhole:
3772
Int J Adv Manuf Technol (2018) 97:3761–3775
Fig. 9 The effect of recoil pressure on the step effect of SLM parts
8
>
>
γ ðT Þ
>
>
>
lim
∼∞
>
< z→zb RðzÞ
C2
>
≠T c ⇒ γ ðTÞ≠0
>
>
>
C
S
1
SHS
>
>
þ
1
: λln
LP λ5
ð41Þ
Then by considering non-equilibrium equations in the X
direction (normal to build plane):
∑Px ¼ P0 þ
2
γ ðT Þ
þ ρgh
RðzÞ
3
2 2
33n
C2
T C 55
* T C −T 0 4
4
4
−
1−
− γ
−P0 þ ρghSinθ5
TC
ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0
P
ð42Þ
Vapor pressure is higher than hydrostatic and surface tension (Eq. 42); therefore, according to Eqs. 41–43, we have:
Pvapor ≫Phydro þ γ⇒∑Px ≠0
ð43Þ
By decreasing scanning speed and increasing laser power
according to Eqs. 42–44, the value of "Γ” and the chance of
formation of keyholes increase. This phenomenon shows the
head of keyholes stays open and surface quality decrease.
2
2 2
33n 3
γ ðT Þ 4 * T C −T 0 4 4
C2
T C 55 5
1−
Γ¼
− γ
−
TC
RðzÞ
ðT C −T 0 Þλln CL1 S SλH5 S þ 1 T C −T 0
P
ð44Þ
Increasing hatch spacing also leads to generation of a
lower overlap area and is noted that in overlap area the
value of Ra is five to seven times higher than the center
of the track [34]. Higher hatch space also leads to increase in the radial acceleration and speed of melting
flow. Therefore, the speed of melting flow is not zero
and higher conduction occurs on melting pool, while in
overlap area, lower contact and conduction are happening. Consequently, the size of the melt pool increases
and average surface improves [34]. Also, higher hatch
space leads to higher Marangoni’s convection and carrying the heat from the keyhole bottom to the surface then
radially outward and the results are increasing weld pool
width near the top surfaces [34]. The higher hatch spacing, the smaller “Γ" and the chance of formation of keyholes and lower surface roughness reduces. In another
word, lower hatch space and higher overlap area increase
the region with no velocity vectors that is a fertile
ground for the formation of keyholes (Appendix) [1, 2].
Also, the remaining liquid films in the keyhole in the
Fig. 10 a Thermal expansion coefficient versus increasing temperature [45]. b Rippling effect
Int J Adv Manuf Technol (2018) 97:3761–3775
3773
Fig. 11 SEM image for the
interaction of hydrostatic
pressure, surface tension, and
vapor pressure on formation of
keyholes
final stage of solidification are critical to solidification
cracking as it forms a region of extremely low shear
strength [49].
4 Conclusion
One significant aspect of AM is the fact that metal-based
AM is characterized by low repeatability due to the complex and various physical transformations and non-linear
interaction of different process parameters and thermophysical properties of different materials. In the current
work, according to Taguchi L25 SLM Ti-6Al-4V parts
were printed and thermal effect of the process parameters
comprising laser power, scan speed and hatch space on
melting pool, interfaces and average surface were characterized. The effect of different rheological phenomena like
surface tension and Marangoni’s effect, capillary force,
the pressure in droplet, wetting, work adhesion, recoil
pressure, drag force/contraction forces and interaction of
surface tension, hydrodynamic and vapor pressure on average surface analyzed and the following conclusion were
drawn.
Higher temperature leads to lower surface tension and irregularity on the top surface and decreases surface quality.
In higher laser power and lower scan speed, the value of
surface tension decreased and subsequently capillary force
reduced; therefore, horizontal radius of curvature decreases
and a rougher surface is generated.
Higher energy density and temperature increase droplet
pressure and therefore, higher pressure in droplets acts as
boiling effect and splashing particles out of the melting
pool and increases surface roughness.
Higher internal pressure in bubbles and low surface tension
result in a volcano effect on the surface of the samples.
In low laser power and high scan speed, the work adhesion
becomes smaller and the surface of melting pool becomes
unstable and rough.
Recoil pressure is a direct function of energy density.
Higher energy density leads to higher recoil pressure
and step effect on the surface and reduces the surface
quality.
Higher energy density increases thermal stresses and due to
higher thermal expansion of Ti-6Al-4V in higher temperature
the interaction of contraction forces and substrate resistance
generates crack and distortion on the surface of the printed
parts.
Increasing laser power and decreasing scanning speed tend
to increase non-equilibrium forces on the surface of melting
pool and increase the chance of formation of keyholes and
reduction of surface quality.
Better surface quality leads to better layering between each
two subsequent layers and can provide higher density followed by better tensile strength.
Appendix
When liquid moves down to the tube, the system gains potential energy due to hydrostatic force. The balance is:
1
1
ρghV liquid −S contact I ¼ ρghπR2 h−2πRhI
2
2
1
¼ ρgπR2 h2 −2πRhγcosθ
2
E¼
ðA1Þ
The equilibrium evolution of the liquid is derived by:
∂E
2γcosθ
¼ 0⇒h ¼
∂h
ρgH S
ðA2Þ
3774
Int J Adv Manuf Technol (2018) 97:3761–3775
Table 4
Surface roughness values
Laser
power
(W)
Scan
speed
(mm/s)
Hatch
space
(μm)
Pattern
angle
(Deg)
Heat treatment Average
temperature (C) surface
μm
90
600
65
36
20
12.24
90
650
70
40
600
12.24
90
90
700
750
75
80
45
60
750
925
13.10
16.92
90
95
800
600
85
70
72
45
1050
925
19.51
17.14
95
650
75
60
1050
23.31
95
95
700
750
80
85
72
36
20
600
10.93
11.13
95
800
65
40
750
10.86
100
100
600
650
75
80
72
36
600
750
8.61
10.51
100
100
100
700
750
800
85
65
70
40
45
60
925
1050
20
14.27
22.32
11.89
105
105
105
105
105
110
600
650
700
750
800
600
80
85
65
70
75
85
40
45
60
72
36
60
1050
20
600
750
925
750
22.91
10.60
9.21
7.73
15.08
10.05
110
110
110
110
650
700
750
800
65
70
75
80
72
36
40
45
925
1050
20
600
17.45
21.47
12.54
10.16
7.
8.
9.
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
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