Fluid Structure Interaction Study of Thermal Spray Coating on a Titanium Alloy.
In many biomedical implants titanium alloys are used as biomaterials for hip joints, knee joints, dynamic compression plates (DCP) . The major advantage of titanium alloys is that it is sometimes a shape memory alloy. It can adjust its shape according to physical change in surrounding condition. Also, for normal walking conditions titanium alloys implants show longer fatigue life than stainless steel and cobalt chrome alloys . Friction and wear performance of these alloys are better than other biomaterials. This tribological advantage is beneficial for using titanium alloy in hip joint implants .The surface properties have to be improved for sake of reliability and convenience and is generally coated by thermal spraying. It is the process in which the range of coating thickness is very large . Micro coating can be done by this process, whose effects will be discussed in this paper. Thermal spraying is one of the coating processes which melt the coating material to molten or semi-molten state and deposited on the substrate. Substrate is preheated to certain temperature before coating is done. The processes uses plasma gas and shield gas. Plasma gas is one which passes through orifice and gets ionized whereas shield gas passes through outer tube and prevents oxidation.
There are many parameters such as gas pressure required during spraying process, current required for ionizing plasma gas, gas velocity required to transfer molten material to already prepared substrate which depends upon material to be coated, material on which coating is done i.e. the substrate, melting points of coat and substrate material . Finite Element Simulation of thermal spraying process plays an important role as we can decide the optimum material to be coated on substrate.
This study attempts to quantify residual stresses with varrying coating material composition and drop size of spray. This simulation is done by FSI on LS DYNA which attempts to relate impact and thermal stresses to residual stresses at interaction surface.
Figure 1 shows mechanism of thermal spraying process. Section A shows formation of plasma jet and its interaction with environment. Section B shows entry powder in plasma and its interaction with plasma and section C shows coating formation.
Li et al.  studied effects of plasma spray coating of HA and zirconia on titanium alloy. Graded HA/YSZ coating was effectively delivered utilizing composite powder by barometrical plasma spray coating. The composite covering demonstrates a multilayer structure comprised of YSZ bondcoat, HA + YSZ composite layer and HA topcoat. The composite coating is bioactive and has higher bond quality contrasted with unadulterated HA covering. The crystalline of HA can be expanded utilizing heat treatment.
Wang et al.  did finite element study of multilayer thermal barrier coating process and found relationship among thermal, quenching and residual stresses is given. Results were found out and it is stated that residual stresses are combination of quenching stresses and thermal stresses. Zheng Zhang et al.  studied a coupled adaptive mesh free method (AFM) and finite element method (FEM) for contact analysis of plasma spray. The tangential friction and heat generation is considered in model which discusses the thermo-elastic contact scenario between plane and real rough surface. Coupled AFM and FEM model shows accurate results than uniformly refined model.
Rapid cooling of molten coat material happens, which results in generation of quenching stresses. It can be formulated as below 
[[sigma].sub.q]= [[alpha].sub.c]([T.sub.m] - [T.sub.s])[E.sub.c] (1)
where, [[alpha].sub.c], [E.sub.c], [T.sub.m] and [T.sub.s] are coating thermal expansion coefficient, coating material elastic modulus, sprayed material melting point and substrate temperature respectively.
Thermal stresses are result of mismatch between substrate and coat material surfaces. They can be formulated as
[[sigma].sub.tm] = [Ec/1 - v] [DELTA][alpha][DELTA]T (2)
Residual stresses are combination of quenching and thermal stresses. It can be given as
[sigma] = [[sigma].sub.q] + [[sigma].sub.tm] (3)
This study  concluded that residual stresses increase with simulation time and deposition layer.
Clyne and Gill  did a review on effect of interfacial adhesion in thermal spray coatings. Yttria-balanced out zirconia (YSZ) is used as coating for aeronautical and biomedical applications to give thermal boundary assurance to surfaces presented to high temperatures which are used in inward burning motors . Its central focal points are its stability at high temperatures, low thermal conductivity, and sensibly high thermal extension coefficient of 7 to [10.sup.-5] [K.sup.-1]. Since the coatings are moderately thick (sometimes upto 300 micron) and are presented to big thermal cycles, they must have the capacity to withstand high strains instigated by differential thermal weather development and thermal gradients. Various approaches have been utilized to get a high spallation resistance in YSZ thermal barrier coatings (TBCs) will serve to show the different potential outcomes that are accessible to move forward coating stability. Initially, the synthesis of YSZ is controlled to create a intense, spallation-safe coating. The best outcomes are acquired from a 6 to 8 wt% YSZ, which gives a metastable supersaturated tetragonal structure in the as-splashed state . This structure has been named "nontransformable" in light of its great full face soundness against disintegration into the cubic and monoclinic stages. It has additionally been watched that a lessening of silica debasements expands coatings lifetimes.
Lei Fu et al.  studied effects of YSZ on composite HA/ YSZ coating. The direct reaction can be given as below
[Ca.sub.10][(P[O.sub.4]).sub.6][(OH).sub.2] + Zr[O.sub.2] --> [alpha]-[Ca.sub.3][(P[O.sub.4]).sub.2] + CaZr[O.sub.3] + [H.sub.2]O (4)
This study concluded that significant enhancement in bond strength, fracture toughness and modulus of elasticity happens due to increase of zirconia .
Gua et al. studied YSZ reinforced HA and titanium alloy coating in body fluid simulation. The disintegration conduct in simulated body liquid (SBF) and the pliable grip quality debasement of plasma splashed hydroxyapatitite (HA)/yttria balanced out zirconia (YSZ)/Ti-6Al-4V composite coatings were contemplated. The coatings were found to experience two biointegration forms, i.e., dissolution and the ensuing precipitation of apatite stage. Morphological and stage examinations demonstrated that the disintegration rate of HA/ YSZ/Ti-6Al-4V composite coating was essentially slower than that of the 100% HA coating. The calcium particle focus in SBF affirmed this contention, where the expansion in focus was roughly 0.13mm every day for the initial 7 days in the HA/ YSZ/Ti- 6Al-4V composite coating, while in the HA coating, the comparing rate of increment was 0.43mm every day. Coatings were found to debase correspondingly with the inundation time. Be that as it may, the mechanical properties of HA/YSZ/Ti-6Al-4V composite coatings was found to be much superior to those of unadulterated HA coatings taking after inundation in SBF. The ductile bond strength of the HA/YSZ/ Ti-6Al-4V composite coating decreased by approximately 27.7% following 4 weeks in the SBF, while the diminish in the HA coating was observed to be approximately 78.8% over a similar period.
Khor et al.  studied microstructures of HA/ Y SZ and titanium alloy composite coatings which deals with study of influence of mechanical properties and plasma properties on coating process. This composite coating shows an exact homogeneity and also enhances mechanical properties which are validated by micro-hardness test.
Chun-Cheng Chen et al. found HA/ Titanium composite coating characteristics in-vitro electrochemical test results that composite ceramic coatings are beneficial than monolithic HA coating on the basis of fatigue characteristics, mechanical properties and hardness. Deposition by thermal spray is highly anisotropic and gives very low elastic modulus than denser materials .
This study is an attempt to quantify residual stresses by FSI varying the coating materials and compare these results with existing simulation and experimental results in literature for HA and YSZ coating on Ti-6Al-4V. This simulation is done by FSI on LS DYNA which attempts to relate impact and thermal stresses to residual stresses at interaction surface. The current work on FSI i.e. combination of FEM and finite volume method (FVM) combines both physics and solve them simultaneously to interact with each other and increase accuracy.
Materials and Methods
Ti-6Al-4V is taken as substrate. Material properties are taken with reference to Lei Fu et al.  Various sets of coating materials are taken such as pure HA, pure YSZ and composite mixture of HA + 10-50% YSZ by weight. Also, drop size is varied from 50 micron to 100 micron. Entire simulation is done by Fluid Structure Interaction (FSI) using LS DYNA. All the boundary conditions and interaction conditions are taken from literature , spraying distance as 150 mm, spraying jet velocity as 150 m/s, substrate temperature as 1273 and initial temperature of coating drop is 2473 K . The analysis consisted of two fundamental approaches Finite Element Method (FEM) and Computational Fluid Dynamics (CFD). The motive of using these approaches was to increase accuracy of computational analysis and to simulate the homogeneous coating drop and to predict residual stresses and thermal behaviour (FSI analysis). The computational accuracy needs high performance system but that will prove to be expensive. Another alternative method to achieve this would be by reducing the number of elements involved in the simulation. FEM would not serve the purpose as the mesh involved in the CFD study would be volume mesh. But on the contrary FSI needs a 3D mesh. And the utilization of the multi-physics would introduce interaction elements to model the fluid and the aid to simulate the flow simultaneously to study more than one physics.
User controlled meshes for FSI which deals with study of 2D and 3D quasi-Eulerian formulation for FEM cab be applied for fluid in the pressurized bubble. Rigid body meshes are used to eliminate Hourglass modes and effects. To study FSI approach various literatures regarding FSI analysis in rotating structure applications such as bearings were studied.
A benchmark problem using numerical and analytical analysis on the basis of Navier Stokes equation to study dynamic forces by fluid on seals and bearings. Navier Stokes equation in conservative 3D form is compared with the numerical (L. T. Tam et al. 2009) . Slurry flow is modeled on CFD by considering Navier Stokes equation for all three directions including properties of mud. Two phase Euler-Euler equation is modeled using standard root mean square k-a algorithm with turbulent flow. Author  successfully concluded that particle distribution is asymmetric in vertical plane due to gravity and flow velocity decreases as slurry composition increases. Also, increase of pressure is low at small velocities but, it increases very rapidly at higher velocities S. (K. Lahiri and K. C. Ghant 2010) .Study on CFD and FSI analysis on bearing is done where CFD and FSI approaches are compared and concluded that FSI approach will be more accurate (B. S. Shenoy et al. 2011) .
An arbitrary lagrangian Eulerian (ALE) approach has been elaborated by interacting face and contact nodes. Both formulations are collaborated at elements and particular nodes. It has given the equation for moving Lagrangian mesh as below [17, 18, 19].
[mathematical expression not reproducible] (5)
Also, Eulerian Formulation is given as the momentum equation as Navier Stokes equarion.
[mathematical expression not reproducible].
[mathematical expression not reproducible].
Yuri Bazilevs et al.  have explained element interaction in ALE approach as shown in figure 2, which shows Element node formulation and areas of applying boundary conditions.
LS DYNA Keyword User Manual  explains an ALE card for multi-material group part. For this case 3D solid element is used for drop and substrate material.
Finite Element simulation of thermal spraying mechanism is done with three different stages pre-processing on LS Pre-Post and solving in LS DYNA manager and post-processing on LS Pre-Post. Geometry is modelled on LS Pre-Post platform with suitable constraints and with substrate size as 120*120*120 micron dimensions. Various drop sizes are modelled from 50 to 100 micron diameter for different cases.
Figure 3 shows sample geometry of substrate and 100 micron diameter drop. Firstly one of the surfaces is meshed with density of 40 by 40 nodes at each side then it is offset to another surface by solid map by line as offset path. Droplet meshing is done with general volume mesh which may be either of tetrahedral element or hexagonal element. Generally, droplet meshing size is kept as low as possible because, it may results in accuracy. Firstly apply thermal conditions because, thermal spraying process has two different temperatures one is for droplet and another is for substrate. This temperature difference results into heat flux and ultimately to generation of thermal stresses. Figure 4 shows meshing for substrate and drop.
Impact analysis is done simultaneously with fluid analysis by keeping particle or droplet as a slave and substrate surface as a master in constrained card so that fluid and structural study can be done simultaneously for Fluid Structure Interaction (FSI).. Boundary conditions are applied as velocity 150 m/s. Results are plotted for that thermal analysis separately and then coupled with FSI study. For that purpose Arbitrary Lagragian Eulerian approach is selected with Hourglass effect. Master mesh is selected for substrate mesh and slave mesh is selected for droplet mesh, which is applied in card known as constraints, Lagrange In Solid.
Results and Discussion
This study considered 42 cases by changing drop size and material composition. The residual stresses are tabulated and comparison among them is shown. Fig. 5 shows sample results for 100 micron droplet.
Table 1 shows values of residual stresses generated in case of Pure HA and Pure YSZ coating. As shown in Table 1, the maximum residual stress is found in case of pure YSZ coating for 100 micron diameter drop i.e. 360.62 MPa. For same drop size residual stresses in case of pure HA coating is 226.59 MPa. From this table it is shown that as drop size increases, residual stresses generated increases.
Also residual stresses for various combinations are tabulated in Table 2. Increase in residual stresses by increasing YSZ content and also by increasing drop size can be seen in Table 2.
Figure 6 shows comparison between pure YSZ and pure HA coating and figure 7 shows comparison among various composite coating cases.
By comparing figure 6 and figure 7, if the same drop size is considered residual stresses generated in coating of pure Y SZ is maximum i.e. 360.21 MPa. For same drop size minimum residual stresses found in case of pure HA. Also, from both figures it can be seen that as drop size increases, residual stresses generated increases, and as Y SZ combination increases, residual stresses also increase.
Earlier only FEM is used to evaluate residual stresses in thermal spray process and this doesn't compute the interface temperatures and thereby the associated stresses. This paper deals with FSI analysis to overcome this limitation. Thermal and impact analysis and their effect on each other can be studied simultaneously on same software platform which avoid numerical incompatibility and instabilities. This is the major advantage of FSI. In this study, maximum residual stress for 100 micron diameter drop is 360.62 MPa which is found for pure YSZ coating. An experimental study in literature  found the stresses to be approximately 345 MPa which very near to present simulation results. So, this technique can be an effective tool for computation of residual stresses for a spray process.
As above results stated impact of Yttria Stabilized Zirconia shows maximum impact whereas Hydroxyapatite shows minimum. Composite of Ha and 10% to 50%YSZ (as taken for analysis purpose) shows results in between HA and YSZ but in increasing manner. Hence, we can increase rigidity of HA by mixing suitable amount of YSZ in HA. Hence, addition of amount of YSZ depends upon rigidity and fracture toughness. [10, 11, 12].
Temperature gradient is maximum at contact and will decrease as it passes to edges. Residual stresses are also maximum between inter face bond between substrate and coat material droplet.
Coat material can directly be used as per the application. If substrate would be used for flexibility application, HA coating is preferred, for rigidity YSZ is preferred and for flexibility as well as rigidity composite of both can be used as per rigidity and flexibility is concerned.
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[21.] LS DYNA Keyword User Manual Volume 1 (2016)
Rohit Chaudhari *, Vrushabh Sawant, Davidson Jebaseelan (#), Sreekanth Dondapati
School of Mechanical & Building Sciences, VIT University, Chennai Campus, Chennai 600127 India
Received 8 May 2017; Accepted 11 November 2017; Published online 31 December 2017
* Coresponding author: Dr. Davidson Jebaseelan
Caption: Figure 1: Mechanism of Thermal Spraying Process
Caption: Figure 2: Element designation for ALE code a) Staggered grid with the volume flux defined on its corresponding cell face; (b) Collocated-grid method with additional velocity components defined at cell center; (c) ALE method with additional velocity components defined at cell corner
Caption: Figure 3: Geometry Modelled in LS DYNA
Caption: Figure 4: Meshing for Substrate and Drop
Caption: Figure 5: (a) Inertia stresses on Droplet. (b) Impact stresses on substrate (c) Residual Stresses on Substrate Surface after 5 seconds
Caption: Figure 6: Comparison Between Residual Stresses in case of Pure HA and Pure YSZ.
Caption: Figure 7: Comparison Among Residual Stresses in Various composite cases
Table 1: Residual Stresses for Pure YSZ and Pure HA Drop Size Residual (Min) Stresses (MPa) YSZ HA 50 251.62 123.93 60 270.11 151.78 70 287.25 168.20 80 303.01 187.96 90 335.62 206.07 100 360.21 226.59 Table 2: Residual Stresses for Various Composite Cases Drop Size Residual Stresses (MPa) ([micro]m) HA+10%YSZ HA+20%YSZ HA+30%YSZ HA+40%YSZ HA+50%YSZ 50 154.24 176.39 194.23 204.01 220.08 60 171 00 193.01 212.63 234.24 245.32 70 130.21 202.41 221.15 243.46 254.02 30 201.21 226.47 246.00 266.98 275.98 90 225.36 247.79 266.9S 285.99 295.02 100 255.47 275.00 295.10 303.45 315.01
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|Title Annotation:||Original Article|
|Author:||Chaudhari, Rohit; Sawant, Vrushabh; Jebaseelan, Davidson; Dondapati, Sreekanth|
|Publication:||Trends in Biomaterials and Artificial Organs|
|Date:||Apr 1, 2017|
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