Optimization of SLM Process Parameters for Ti6Al4V Medical Implants

TL;DR: In this article, the effect of selective laser melting (SLM) process parameters on the characteristics of Ti6Al4V samples, such as porosity level, surface roughness, elastic modulus and compressive strength (UCS), has been investigated using response surface method.

Abstract: Ti6Al4V alloy has received a great deal of attention in medical applications due to its biomechanical compatibility. However, the human bone stiffness is between 10 and 30 GPa while solid Ti6Al4V is several times stiffer, which would cause stress shielding with the surrounding bone, which can lead to implant and/or the surrounding bone’s failure.,In this work, the effect of selective laser melting (SLM) process parameters on the characteristics of Ti6Al4V samples, such as porosity level, surface roughness, elastic modulus and compressive strength (UCS), has been investigated using response surface method. The examined ranges of process parameters were 35-50 W for laser power, 100-400 mm/s for scan speed and 35-120 µm for hatch spacing. The process parameters have been optimized to obtain structures with properties very close to that in human bones.,The results showed that the porosity percentage of a SLM component could be increased by reducing the laser power and/or increasing the scan speed and hatch spacing. It was also shown that there was a reverse relationship between the porosity level and both the modulus of elasticity and UCS of the SLM part. In addition, the increased laser power was resulted into a substantial decrease of the surface roughness of SLM parts. Results from the optimization study revealed that the interaction between laser process parameters (i.e. laser power, laser speed, and the laser spacing) have the most significant influence on the mechanical properties of fabricated samples. The optimized values for the manufacturing of medical implants were 49 W, 400 mm/s and 99 µm for the laser power, laser speed and laser spacing, respectively. The corresponding porosity, surface roughness, modulus of elasticity and UCS were 23.62 per cent, 8.68 µm, 30 GPa and 522 MPa, respectively.,Previous investigations related to additive manufacturing of Ti alloys have focused on producing fully dense and high-integrity structures. There is a clear gap in literature regarding the simultaneous enhancement and adjustment of pore fraction, surface and mechanical properties of Ti6Al4V SLM components toward biomedical implants. This was the objective of the current study.

Summary

1. INTRODUCTION

• Process-induced variability has huge impacts on the circuit performance in the sub-90nm VLSI technologies [10, 9].
• One important aspect of the variations comes from the chip leakage currents.
• Io f f and threshold voltage Vth as shown below [14], Io f f = Is0e Vgs−Vth nVT (1− e −Vds VT ) (1) where Is0 is a constant related to the device characteristics, VT is the thermal voltage, and n is a constant.
• But this method needs to know the impulse response from all the current sources to all the nodes, which is expensive to compute for a large network.

2. PROBLEM FORMULATION

• The authors first present the model of power grids in this paper.
• The authors then present the modeling issue of leakage current under intra-die variations.
• After this, the authors present the problem that they try to solve.

2.1 Power Grid Network Models

• The power grid networks in this paper are modeled as RC networks with known time-variant current sources, which are obtained by gate level logic simulations of the VLSI systems.
• For a power grid (versus the ground grid), some nodes have known voltage modeled as constant voltage sources.
• For C4 power grids, the known voltage nodes can be internal nodes inside the power grid.
• Given known deterministic vector of current sources, I(t), the node voltages can be obtained by solving the following differential equations, which is formulated using modified nodal analysis (MNA) approach, Gv(t)+C dv(t) dt = I(t) (2) where G is the conductance matrix, C is admittance matrix resulting from capacitive elements.
• V(t) is the vector of time-varying node voltages and branch currents of voltage sources that the authors try to solve.

2.2 Modeling Leakage Current Variations

• The G and C matrices and input currents I(t) depend on the circuit parameters, such as metal wire width, length, thickness on power grids, and transistor parameters, such as channel length, width, gate oxide thickness, etc.
• The authors only consider the log leakage current variation, due to the channel length variations, which is modeled as Gaussian variations [12].
• After that, the authors consider spatial correlation in the intra-die variation.
• Therefore, given the process variations, the MNA for (2) becomes Gv(t)+C dv(t) dt = I(t,ξ(θ)) (3) Note that the input current vector, I(t,ξ(θ)), has both deterministic and random components.

3.1 Concept of Hermite Polynomial Chaos

• In the following, a random variable ξ(θ) is expressed as a function of θ, which is the random event.
• Hermite PC utilizes a series of orthogonal polynomials (with respect to the Gaussian distribution) to facilitate stochastic analysis [16].
• These polynomials are used as the orthogonal basis to decompose a random process in a similar way that sine and cosine functions are used to decompose a periodic signal in Fourier series expansion.

3.2 Simulation Approach Based on Hermite PCs

• In case that v(t,ξ) is unknown random variable vector (with unknown distributions) like node voltages in (3), then the coefficients can be computed by using Galerkin method, which states that the best approximation of v(t,ξ) is obtained when the error ∆(t,ξ), which is defined as ∆(t,ξ) = Gv(t)+C dv(t) dt − I(t,ξ(θ)) (10) is orthogonal to the approximation.
• Once the authors obtain those coefficients, the mean and variance of the random variables can be easily computed as shown later in the section.
• This will be explained in details in the next section.

4. LOG-NORMAL LEAKAGE CURRENT VARIATIONS

• The authors present the new method for representing the lognormal leakage current distributions by using Hermite PCs with one or more independent Gaussian variables representing the channel length or threshold voltage variations.
• The authors method is based on [6] and the authors will show how it can be applied to solve their problems for one or more independent Gaussian variables.

4.1 Hermite Polynomial Chaos representation

• Let g(ξ) be the Gaussian random variable, denoting threshold voltage or device channel length.
• (18) Obviously, for the MOS device leakage current equation (1), leakage current, Io f f = cIl(Vth) = ce −Vth , where the leakage component Il(Vth) is a log-normal random variable.
• To find the other coefficients, the authors can apply (9) on l(ξ).

4.3 Hermite PC with two and more Gaussian variables

• Similarly, for four Gaussian random variables, assume that ξ = [ξ1,ξ2,ξ3,ξ4] is a normalized, uncorrelated Gaussian random variable vector.
• Hence, the desired Hermite PC coefficients can be expressed using the equation (30) above.

5. VARIATIONS IN WIRES AND LEAKAGE CURRENTS

• The authors will consider variations in width (W ), thickness(T ) of wires of power grids, as well as threshold voltage(Vth) in active devices which are reflected in the leakage currents.
• The variation in width W and thickness T will cause variation in conductance matrix G and capactance matrix C while variation in threshold voltage will cause variation in leakage currents.
• As mentioned in previous section, the variation in leakage current resulting can be represented by a second Hermite PC as in equation (26): I(t,ξI) = I0(t)+ I1(t)ξI + I2(t)(ξ2I −1) (33) here, ξi is a normalized Guassian distribution random variable representing variation in threshold voltage.

6. EXPERIMENTAL RESULTS

• This section describes the simulation results of circuits with lognormal leakage current distributions for a number of power grid networks.
• All the proposed methods have been implemented in Matlab.
• All the experimental results are carried out in a Linux system with dual Intel Xeon CPUs with 3.06Ghz and 1GB memory.

6.2 Experiment considering leakage current variation

• Fig.1 shows the node voltage distributions at one node of a ground network with 1720 nodes.
• The standard deviations of the log-normal current sources with one Gaussian variable is 0.1.
• To consider multiple random variables, the authors divide the circuit into several partitions.
• Table 2 shows the speedup of the Hermite PC method over Monte Carlo method with 3000 samples.
• Also, one observation is that the speedup depends on the sampling size in MC method.

6.3 Experiment considering variation in G,C,I

• Considering variation in conductance, capacitor and leakage current at the same time, Fig. 3 and fig.
• 4 show the node voltage distributions at one node of two different ground circuit, Circuit1 and Circuit2, respectively.
• Table 3 shows the CPU speedup of HPC method than MC method.
• The sample time of Monte Carlo is 3500 and the authors can see that it’s more than 100X time faster of proposed method than the Monte Carlo method.
• The advantage is obviously seen in the table.

Figures

Table 2. The range of matrix building parameters.

Table 3. Matrix building parameters with resulting surface roughness, porosity %, elastic modulus and ultimate compressive strength.

Fig 3. Effect of laser power on the surface roughness.

Fig 6. Effect of (a) laser power, (b) scan speed, (c) hatch spacing and (d) the interaction between speed and hatch spacing on the UCS.

Fig 1. Ce

Fig 9. SLM coupons fabricated using the optimized process parameters

Fig 5. Effect of (a) laser power, (b) scan speed and (c) hatch spacing on the elastic modulus.

Table 4.Response surface model coefficients for the surface roughness and porosity fraction.

Fig 8. Predicted optimum laser power and scan speed (at a hatch spacing of 90 µm) for desirable properties of a SLM part suitable for medical implants; (a)elastic modulus (10-30 GPa), (b) maximum porosity %, (c)surface roughness (1-10 µm) and (d) highest UCS.

Fig 4. Effect of (a) laser power, (b) scan speed, (c) hatch spacing and (d) the interaction between speed and hatch spacing on the porosity; (e) and (f) are micrographs of samples 15 and 2 respectively.

Table 5.ANOVA p-values for each of the parameters and parameter interactions for the Ra, porosity %, elastic modulus and UCS.

Fig 2. Design-Expert plot. Predicted vs actual data for different properties of SLM part, (a) modulus of elasticity, (b) porosity, (c) surface roughness and (d) UCS.

Table 1. Ti6Al4V powder size distribution

Full text

University of Birmingham
Optimization of SLM Process Parameters for
Ti6Al4V Medical Implants
El-Sayed, Mahmoud; Ghazy, Mootaz; Yehia, Youssef; Essa, Khamis
DOI:
10.1108/RPJ-05-2018-0112
License:
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Citation for published version (Harvard):
El-Sayed, M, Ghazy, M, Yehia, Y & Essa, K 2018, 'Optimization of SLM Process Parameters for Ti6Al4V
Medical Implants', Rapid Prototyping Journal. https://doi.org/10.1108/RPJ-05-2018-0112
Link to publication on Research at Birmingham portal
Publisher Rights Statement:
This is the Accepted Author's Manuscript for the following article: Mahmoud Elsayed, Mootaz Ghazy, Yehia Youssef, Khamis Essa, (2018)
"Optimization of SLM process parameters for Ti6Al4V medical implants", Rapid Prototyping Journal, https://doi.org/10.1108/RPJ-05-2018-
0112
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Download date: 10. Aug. 2022



Optimization of SLM Process Parameters for Ti6Al4V Medical Implants
Abstract
Ti6Al4V alloy has received a great deal of attention in medical applications due to its
biomechanical compatibility. However, the human bone stiffness is between 10 and 30 GPa
while solid Ti6Al4V is significantly stiffer, which would cause stress shielding with the
surrounding bone which can lead to implant and/or the surrounding bone’s failure. In this
work, the effect of SLM process parameters on the characteristics of Ti6Al4V samples, such
as porosity level, surface roughness, elastic modulus and compressive strength (UCS), has
been investigated using Response Surface Method (RSM). The examined ranges of process
parameters were 35-50 W for laser power, 100-400 mm/s for scan speed and 35-120 µm for
hatch spacing. The results showed that the porosity % of a SLM component could be
increased by reducing the laser power and/or increasing the scan speed and hatch spacing. It
was also shown that there was a reverse relationship between the porosity level and both the
modulus of elasticity and UCS of the SLM part. In addition, the increased laser power
resulted in a substantial decrease of the surface roughness of SLM parts. The process
parameters have been optimized to obtain structures with properties very close to that in
human bones. Results from the optimization study revealed that the interaction between laser
process parameters (i.e. laser power, laser speed, and the laser spacing) have the most
significant influence on the mechanical properties of fabricated samples. The optimized
values for the manufacturing of medical implants were 49 W, 400 mm/s and 99 m for the
laser power, laser speed and laser spacing, respectively. The corresponding porosity, surface
roughness, modulus of elasticity and UCS were 23.62%, 8.68 µm, 30 GPa and 522 MPa,
respectively.
Keywords: Selective laser melting (SLM); Design of Experiment; Ti-6Al-4V; Medical
Implants
1. Introduction
Selective laser melting (SLM) is an additive manufacturing technique that produces near
fully dense metal parts directly from a CAD design by adding layer upon layer [1-4]. The
main concept is based on a laser beam that passes over a thin layer of powder and diffuses it
selectively to the desired shape. Next, a new layer of powder is spread, the platform is
lowered according to the required layer thickness and then the melting process is repeated
until the full part is obtained [5,6]. SLM has many advantages such as producing complex
shapes that are difficult to fabricate via conventional methods, short time from design to
market, and near net shape production which minimizes waste of materials [7,8]. For these
reasons, the SLM process is used in aerospace and biomedical applications such as implants
and prostheses [9,10]. Examples of metal powder used in SLM processes are: titanium alloys,
steels, cobalt, chromium and aluminum alloys [11]. On the other hand, SLM has some
limitations that include the stair step effect which increases surface roughness, and balling
phenomenon which increases both the surface roughness and the porosity of SLM parts [12].

T
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a
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22]. It has
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and t is t
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a
gns is the
s noted as "
,
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fa
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ctors are s
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p
rocesses [
1
6].
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e
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imately 1
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arameters
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6Al4V pa
r
l
owing par
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t
he size
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nction
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ents by
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a
nd the
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t
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ctor is
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own in
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17,18].
u
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perties,
0 GPa.
a
ble for
on the
r
ts have
a
meters

(laser power = 110 W, scan speed = 400 mm/s, scan spacing = 40 µm, and layer thickness =
50 µm). Sun et al. [24] used the Taguchi method to optimize four process parameters: layer
thickness, linear energy density, hatch spacing and scanning strategy. They reported that 80
W laser power, 200 mm/s scan speed, 60 μm hatch spacing, a 20 μm layer thickness and X-Y
inter-layer for scanning strategy was sufficient to achieve fully dense, good quality Ti6Al4V
components. In another study Murr et al. [25] have produced Ti6Al4V parts via SLM for
biomedical implants. It was indicated that SLM was capable of producing good quality parts
with mechanical properties better than wrought and cast Ti6Al4V parts. Vandenbroucke and
Kruth [26] also produced medical and dental parts fromTi6Al4V alloy and tested their
mechanical and chemical properties. The Ti6Al4V produced had achieved 99.98 % density.
However, it should be noted that in the earlier studies such as those by Murr [25] and
Vandenbroucke and Kruth [26], the objective was mainly to produce SLM parts with
minimum porosity in order to achieve mechanical properties that could reach, or even
exceed, those of bulk material. In the work reported by Vandenbroucke and Kruth [26], a
tensile young's modulus of about 94 GPa was obtained. Nevertheless, the elastic modulus of
bones in human body ranges from 10 to 30 GPa. The large difference in moduli between
titanium implants and bones, known as stiffness mismatch, can result in stress shielding,
which has been held responsible for implant loosening and consequently could cause the
patients to require a revision surgery. Two solutions were found to this problem: the first one
was developing new types of titanium alloys that have modulus closer to bones and the
second one was developing porous structure instead of solid structures which reduces
material modulus [27-30].Titanium alloys that have 30% volume porosity can have modulus
similar to human bones. One problem of porous structures is that it decreases toughness and
creates stress concentration around the pores [31].
Furthermore, a medical implant should have high compressive strength to prevent
fractures and improve functional stability. High strength is also required to impede
spring-back both during and after the operation procedure [32,33]. Finally, an implant should
have sufficient surface roughness to improve the ingrowth of the human tissues into it.
Compared to smooth surfaces, textured implants surfaces exhibit more surface area for
integrating with bone via osseointegration process. It was suggested that a surface roughness
in the range from 1 to 10 microns would be required to enhance both the osteoconduction
(in-migration of new bone), and osteoinduction (new bone differentiation) processes [34-36].
Previous investigations related to additive manufacturing of Ti alloys have focused on
producing fully dense and high integrity structures. There is a clear gap in literature regarding
the simultaneous enhancement and adjustment of pore fraction, surface and mechanical
properties of Ti6Al4V SLM components towards biomedical implants. In the present work,
artificial pores have been created in Ti6Al4V parts fabricated via SLM by controlling the
process parameters to achieve surface and mechanical properties suitable for biomedical
applications. The influence of processing parameters by means of laser power, scan speed
and hatch spacing on the surface roughness, porosity content and mechanical properties of
Ti6Al4V components produced by SLM will be investigated. Statistical analysis by means of
Design of Experiments (DoE) and Analysis of Variance (ANOVA) will be adopted to
optimise the SLM process parameters and fabricate custom parts with elastic modulus, UCS
and surface roughness sufficiently close to that of human bones.

2. Experimental Methods
2.1 Materials
Ti6Al4V gas atomized alloy powder was supplied by LPW Technology. Most of the
powder particles had a size range between 19-45m as measured using a laser diffraction
analyzer (Microtrac) following the ASTM B822 standard. The size distribution of powder
used is shown in Table 1.
Table 1. Ti6Al4V powder size distribution
Particle size
(m)
<16 16-22 22-31 31-44 >45
Percentage
(%)
5 10 28 46 11
2.2. Statistical design of experiment (DoE) using response surface
In this study the design of experiment RSM was carried out to generate an experimental
plan with minimum possible trials. ANOVA was utilized to find a relationship between the
input and output parameters, identify the most significant parameters, and find the optimal
setting of those parameters that can achieve the intended objective function. The response
surface “Y” can be expressed by a second order polynomial (regression) equation as shown
in Equation 2:
Yb


∑
b

x


∑
b

x



∑
b

x

x

(2)
where x
i
are the factors input parameters. The terms b
0,
b
i
, b
ii
, and b
ij
are the model
coefficients that depend on the main and interaction effects of the process parameters.
Method of least squares is used to determine the constant coefficients. To perform the design
of experiment, Design-Expert Software Version 7.0.0 (Stat-Ease Inc., Minneapolis, USA)
was used.
The procedure adopted in this study was as the following:
1. Identification of the key process parameters, and setting the upper and lower bound for
each.
2. Selection of the output response.
3. Developing the experimental design matrix.
4. Carrying out the experiments according to the design matrix, and recording the output
response.
5. Developing a mathematical model to correlate the process parameters to the output
response.
6. Optimizing that model using genetic algorithm.
In the current study three factors (process parameters) were considered which are the laser
power, scan speed and hatch spacing. According to the central composite design, and as
described above, each parameter was varied over 5 levels (-α, -1, 0, 1 and α). See Fig 1. In
this work α was considered to be 2 in order to change each factor over five equal levels. Table
2 shows the levels of each factor in this investigation. As shown -α and α represent the
minimum and maximum levels respectively, of each factor. Also, three center points (at the 0
level (middle) of all factors, see Fig1) were considered. The center points are used to provide

Frequently asked questions

Q1. What are the contributions in "University of birmingham optimization of slm process parameters for ti6al4v medical implants" ?

In this work, the effect of SLM process parameters on the characteristics of Ti6Al4V samples, such as porosity level, surface roughness, elastic modulus and compressive strength ( UCS ), has been investigated using Response Surface Method ( RSM ). The examined ranges of process parameters were 35-50 W for laser power, 100-400 mm/s for scan speed and 35-120 μm for hatch spacing. 

Q2. What were the measurements used to determine the quality of the fabricated samples?

Porosity content, surface roughness, elastic modulus and compressive strength (UCS) were measured as outputs to better understand the quality characteristics of the fabricated samples. 

Q3. What is the effect of laser power on surface roughness?

In addition, the increased laser power increases the energy density which improves the wettability of the melt pool, eliminating the differences in surface tension and in turn decreasing the chance of encountering the balling phenomenon which dramatically decreases the side surface roughness [2]. 

Q4. What is the effect of increasing the scan speed and hatch spacing on the melt pool?

Increasing the scan speed and hatch spacing and/or a decrease in the laser power shall reduce the melt pool and lead to incomplete consolidation. 

Q5. What is the effect of low scan speed on the overlapping area of adjacent lines?

Small hatching spacing would increase the overlapping area of adjacent scanning lines, resulting in a complete melting of the powderbetween scanning lines. 

Q6. How many GPa did a structure with a porosity of 43 and 80?

During the manufacturing of Ti6Al4V open-porous scaffolds using SLM, Weißmann and co-authors [43] concluded that a structure with a porosity % between 43 and 80 experienced an elastic modulus in the range from 26.3 to 3.4 GPa and an UCS in the range from 750 to 100 MPa. 

Q7. How many GPa would be predicted for a SLM part?

In the current study it was predicted that at 23.62% porosity the elastics modulus and UCS of the SLM part would be 30 GPa and 522 MPa, respectively. 

Q8. What is the effect of stress shielding on the implant?

Stress shielding prevents the needed stress being transferred from the implant to adjacent bone, which might result in bone loss in the near-vicinity of implants. 

Q9. What is the role of pores in the fabrication of titanium implants?

Their results showed that creating pores in a Ti6Al4V part had a significant role in reducing its stiffness, which could allow the implant to have an elastic modulus that is close to that of human cortical bone. 

Q10. What is the way to make a Ti implant?

In biomedical applications, a Ti implant with structure similar to that in sample 2 is recommended as it has low elastic modulus. 

Q11. What was the effect of decreasing the porosity % on the elastic modulus?

Decreasing the porosity % from 25.43 to 2.94 resulted in a significant increase in the elastic modulus from 17 to 75 GPa, and a comparable rise in the UCS from 388 to 1749 MPa. 

Q12. What is the way to use the implants?

for biomedical application, implants with rough surfaces are preferred to allow tissues to grow inside and integrating them to the hosting bones.