Acta Materialia 55 (2007) 5089–5101

www.elsevier.com/locate/actamat

Residual stresses in high-velocity oxy-fuel thermally sprayed

coatings – Modelling the effect of particle velocity and temperature
during the spraying process
P. Bansal, P.H. Shipway *, S.B. Leen
School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK

Received 13 December 2006; received in revised form 18 May 2007; accepted 22 May 2007
Available online 17 July 2007

Abstract

The application of thick thermally sprayed coatings on metallic parts has been widely accepted as a solution to improve their corro-
sion and wear resistance. Key attributes of these coatings, such as adherence to the substrate, are strongly influenced by the residual
stresses generated during the coating deposition process. In high-velocity oxy-fuel (HVOF) thermal spraying, due to the relatively
low temperature of the particle, significant peening stresses are generated during the impact of molten and semi-molten particles on
the substrate. Whilst models exist for residual stress generation in plasma-based thermal spray processes, finite element (FE) prediction
of residual stress generation for the HVOF process has not been possible due to the increased complexities associated with modelling the
particle impact. A hybrid non-linear explicit–implicit FE methodology is developed here to study the thermomechanical processes asso-
ciated with particle impingement and layer deposition. Attention is focused on the prediction of residual stresses for an SS 316 HVOF
sprayed coating on an SS 316 substrate.
 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: FE; HVOF; SS 316; Residual stress; Particle impact

1. Introduction Residual stress generation in thermally sprayed coatings

has been well researched by various workers [2,5,8–12].
The application of thermally sprayed coatings is a well- Tsui and Clyne [8] suggested that the residual stresses are
established method to improve the wear and corrosion generated from two main sources during thermal spraying.
resistance of components [1,2]. However, coating deposi- First, sprayed molten particles impinging on the substrate
tion using a thermal spray process is inherently associated form flat splats and quench to the substrate temperature
with the generation of residual stresses in the coatings. within a few milliseconds. The underlying substrate con-
These stresses vary in nature and magnitude, and have a strains the thermal contraction of the splats, resulting in
pronounced effect on the mechanical behaviour of the sys- tensile stresses (quenching stresses) in the splats. Secondly,
tem. For example, the strong influence of residual stresses later on, further cooling of the sprayed coating and the
on the wear and fatigue resistance of coatings [2–4] and substrate to the ambient temperature leads to thermal
their resistance to cracking has been reported in the litera- stresses in the coated specimen. This mechanism of residual
ture [5–7]. This identifies the need to design coatings with stress generation is only applicable for a class of thermal
optimized residual stress distributions, which in turn can spray methods where fully molten particles are sprayed
provide improved performance under loading. with low impact velocity; typically, plasma spraying is
one such technique. In contrast, processes such as the
*
Corresponding author. Tel.: +44 115 951 3760; fax: +44 115 951 3800. high-velocity oxy-fuel (HVOF) spray method employ low
E-mail address: philip.shipway@nottingham.ac.uk (P.H. Shipway). spray temperatures and high particle velocities. In such

1359-6454/$30.00  2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2007.05.031
5090 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

processes, the kinetic energy of the impinging particles terizing the behaviour of the gas and sprayed particles by
leads to significant peening of the underlying material (be use of measurement techniques such as laser doppler ane-
it substrate or previously deposited material), thereby influ- mometry, particle image velocimetry and high-speed two-
encing the final state of residual stresses [9]. colour pyrometry [18,21,22]. Different types of thermally
The in situ residual stress generation during the plasma sprayed coatings have now been analyzed and substantial
spray process has been simulated previously using finite information on the link between the sprayed particle char-
element (FE) modelling techniques [5,9]. These models deal acteristics and the process parameters is available
with the thermal effects only and do not include any peen- [18,21,22].
ing stresses for the reasons mentioned above. Recently FE In the present work, the development of a hybrid expli-
modelling has also been used to simulate the impact of cit–implicit FE methodology to simulate the residual stress
solid particles such as may be observed in a range of ther- generation in HVOF sprayed coatings is presented. The
mal spray processes (such cold gas spraying, warm spray- material type and the velocity and temperature of the
ing and HVOF spraying) [13,14]. The impact of a single sprayed particle are used as the key variables to character-
particle has been studied, with the different spray condi- ize the effect of thermal spray process parameters on the
tions simply simulated by changing the particle tempera- final residual stress state in the coating. The methodology
ture; however, the analyses have not yet been extended to presented here is generic in nature since it addresses peen-
predict the residual stresses in these coatings. ing of the target (substrate or previously deposited coating)
Impingement of sprayed particles can also be treated as due to particle impact and subsequent development of
a high-temperature shot-peening process. The shot-peening residual stresses due to phase changes and thermal contrac-
process has been studied extensively using finite element tion. As such, the model can be used across a range of
(FE) modelling [15,16]. This work can provide a methodol- impact velocities and particle temperatures; impact with
ogy which can be extended to simulate the peening phe- both liquid or solid particles can be modelled (simply by
nomenon during thermal spraying. Additionally, useful changing the equations which govern the mechanical prop-
information on the effect of different process and material erties of the particle upon impact). However, at present, the
characteristics on the final residual stress state can be model is unable to model impact of multiphase particles
obtained from these models. For example, Meguid et al. (such as might be encountered in partially molten particles
[16] performed a dynamic elasto-plastic analysis of a single or in particles with two constituents, such as cemented car-
shot impact to study the effect of shot velocity, size and bides) due to the complexities of multiphase flow and the
shape on the plastic zone development upon impact. They lack of mechanical property models for impact of such par-
predicted that the depth of the compressed layer and the ticles. To illustrate the validity of the model, a specific
residual stresses are influenced mainly by the shot shape example of HVOF sprayed SS 316 coatings on SS 316 sub-
and velocity. A three-dimensional FE analysis of a multiple strate is considered since data concerning measured particle
impingement process by the same workers predicted that temperatures, velocities and residual stresses are available
the highest compressive stresses are generated beneath the in the literature. Consequently, the FE-predicted trends
substrate surface on the centre line of the shot [17]. It can be readily compared with experimental results.
was also predicted that the maximum compressive residual
stress and the plastic strains remain comparable for differ- 2. Methodology
ent separation distances between impinging shots. More-
over, multiple shot impacts yielded a more uniform The current work describes the development of an FE
residual stress distribution [17]. methodology to simulate the residual stress generation in
The development of residual stresses during the thermal HVOF sprayed coatings. Experimental measurement of
spray deposition of coatings is strongly affected by both the the residual stresses and relevant coating properties along
material type and the spray process parameters (such as with determination of the key parameters such as tempera-
fuel and oxygen flow rates, pressure and gun design) which ture and velocity of the sprayed particle is beyond the scope
primarily govern impact temperature and velocity [18,19]. of this work. However, for validation, a representative
Production of a reliable coating, therefore, requires precise coating system with measured residual stresses and particle
control over the deposition process and better understand- characteristics was chosen from the literature [21].
ing of the effect of individual process parameters. In recent
years, significant advances have been made in controlling 2.1. HVOF sprayed SS 316 coatings – a representative
and optimizing the process parameters. Several numerical example from the literature
models are now available which can provide a detailed
analysis of heat and mass transfer, together with the gas There is a wide body of literature which reports experi-
and sprayed particle dynamics during thermal spray pro- mental measurements of residual stresses in coatings,
cesses [18,20]. Specifically, it has been shown that the veloc- though few of these papers (i) address materials where
ity and the temperature of the sprayed particles have a the models exist which describe the high-temperature
pronounced effect on the coating properties and its micro- mechanical properties of the particles; (ii) provide detailed
structure [18]. This has led to a growing interest in charac- information required to describe the state of the particles at
 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101 5091

Table 1 Table 2
Spray parameters and the powder properties [21,24] Thermomechanical properties of SS 316 [23,28,29]
Powder feed rate (g min1) 70 Temperature (K) Elastic modulus, E (GPa)
Spray particle temperature (K) 1593 298 193
1500 100
Spray particle velocity (m s1) 520 and 610
1643 75
Median powder particle size (lm) 20–38
Temperature (K) Thermal conductivity, k (W K1 m2)
Torch velocity (mm s1) 700
300 15
800 30
1643 60
impact; or (iii) provide detailed information regarding the
Temperature (K) Thermal expansion coefficient, a (K1)
mechanical properties of the coating. However, it was 273 1.6 · 105
found that a body of work by Totemeier et al. [21,23], con- 972 1.85 · 105
cerning the HVOF deposition of SS 316 coatings on SS 316 1643 3 · 105
substrate using a JP-5000 HVOF system, provided much of Latent heat of fusion (J kg1) 3.3 · 105
the information needed to allow the validity of the FE Density (kg/m3) 8031
model to be examined. Totemeier et al. conducted an Specific heat capacity (J/kg K) 457
extensive study of this coating system and reported exper-
imentally measured residual stresses along with the mea-
sured temperatures and velocities of the sprayed particles
1800
[21]. These particle velocities and temperatures are used
as the inputs to the present FE modelling methodology
1600
to characterize the spray process. The thermal spray pro-
cess parameters (see Table 1) used are also provided
[21,24], along with data concerning the coefficient of ther- 1400
mal expansion of the coating material and its elastic
modulus.
Temperature / K

1200

2.2. Coating deposition mechanism 1000

During a thermal spray process, powder particles car- 800

ried in a stream of a hot carrier gas are propelled towards
a substrate at a high-velocity. Flattening of these particles
600 0.33 Tm
upon impact leads to the formation of splats which are
considered to be the building blocks of the sprayed coating
400
[18,20,25,26]. Possible interaction between the particle and
the gas during the HVOF spray process has been exten-
sively researched by various workers [18,20]. In addition, 200
0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03
the spray characteristics of the JP-5000 spray system have
Time / s
also been studied in detail and it has been shown to pro-
duce a well-defined particle deposition zone approximately Fig. 1. FE-predicted cooling rate of the deposited particle.
29 mm wide with relatively constant particle temperature
and velocity across it [27]. For a wide range of commonly
employed deposition conditions, it can be shown that an it is assumed that the particles deposit in the form of a hex-
individual particle will have cooled to a temperature less agonal lattice, it can be shown that, in this case, the result-
than a third of its absolute melting temperature ing splats are of 58 lm diameter with a centre–centre
(0.33Tm) before another particle is likely to interact with distance of 522 lm. Hence, the assumption of non-interac-
it. Using the deposition data for HVOF spraying of SS 316 tion of particles during deposition is reasonable and indi-
shown in Table 1 and the material properties of the powder cates that a thermally sprayed coating is formed by the
(Table 2 [28,29]), it can be shown that the incident particle consecutive flattening and solidification of individual
flux is around 1.8 · 1010 particles m2 s1. Given that it splats.
can be estimated by FE modelling that an individual parti-
cle will cool to 0.33Tm in around 0.2 ms (Fig. 1), it can then 2.3. FE modelling of residual stress generation
be shown that, within this time-frame, the particle coverage
(assuming a splat diameter of typically 2.0 times the origi- The HVOF spray method is a dynamic deposition pro-
nal particle diameter (29 lm in this case) as observed in the cess involving rapid deformation and solidification of
microstructures of HVOF sprayed stainless steel presented sprayed particles, followed by cooling down of the coated
by Kuroda et al. [24]) is only around 1% of the total area. If specimen to ambient temperature. The peening stresses
5092 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

together with thermal stresses generated during the deposi- 520 and 610 m s1 (Table 1). During impact, much of the
tion process govern the final residual stress state of the kinetic energy of the particle will be transformed into heat.
coated specimen. This emphasizes the importance of study- Hutchings [30] argued that, during impact of a particle with
ing the response of the underlying substrate under impact a metal target during an erosion process, >80% of the origi-
to predict the peening stresses. nal kinetic energy of the particle was transformed into heat,
Particle impact on the substrate using spray velocities in with the rest of the energy being accounted for by the stored
the range of 500–600 m s1 is a highly dynamic event and is energy of plastic deformation, the elastic wave energy and
thus simulated using an explicit finite element method code. the rebound kinetic energy. In a more recent study of
Explicit analysis provides a detailed time history of the cold-spray deposition [13], it was assumed that 90% of the
deformation and stresses during impact and can give an kinetic energy of the particle was dissipated into heat.
estimate of the residual stresses. However, use of explicit Accordingly, in this work, it was assumed that 90% of the
analysis to model the deposition of a number of layers inelastic energy generated during impact was dissipated as
and predict the final residual stress distribution in the spec- heat. Three-node linear displacement and temperature ele-
imen at the ambient temperature is computationally ments were used to discretize the particle and the substrate.
prohibitive. All the displacements on the bottom face of the substrate
In the present work, the resulting residual stresses were were restrained. Symmetry boundary conditions were used
predicted using a hybrid explicit–implicit FE methodology.
The peening stresses generated during impact were deter-
mined using an explicit analysis; in the second stage, these
stresses were introduced in a layer deposition model using
an implicit thermomechanical analysis to predict the accu-
mulated final residual stress state. This hybrid methodol-
ogy is illustrated in Fig. 2.

2.3.1. Explicit particle impact model

A two-dimensional axisymmetric model of a 29 lm
diameter SS 316 particle impacting on an SS 316 substrate
disc of 0.5 mm radius and 0.5 mm depth was generated
using ABAQUS CAE version 6.5.1 (HKS Inc.). A dynamic,
explicit temperature–displacement coupled analysis was
carried out to study the high strain-rate impact process
using ABAQUS/Explicit (HKS Inc.). In the model, spray
conditions were characterized by the particle velocity and
temperature. These parameters were considered as the key
variables in the FE model and analyses were performed Fig. 3. Axisymmetric model of SS 316 particle impact on an SS 316
with the particle temperature of 1593 K and velocities of substrate.

Explicit Particle
Impact Analysis

Implicit Layer
Deposition
Analysis

Fig. 2. Flowchart of the hybrid explicit–implicit methodology used to determine the final residual stress distribution.
 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101 5093

on the left-hand side of the model. Fig. 3 illustrates the FE 4000

.
model of an impinging particle on the substrate. ε = 1× 10 −5 s −1
.
The impact of thermally sprayed particles onto a sub- 3500 ε = 1× 10 −3 s −1
.
strate is a non-linear dynamic contact event. The micro- ε = 1×10 −1 s −1
.
scopic and macroscopic response of the impacting 3000 ε = 1×10 +1 s −1
.
particle and the underlying substrate under such loading ε = 1×10 +3 s −1
.
conditions is strongly affected by the strain, strain rate, ε = 1×10 +5 s −1
2500
temperature and microstructure of the material [31]. Use

Stress / MPa
of an appropriate constitutive equation defining the mate- 2000
rial properties is therefore essential for modelling such pro-
cesses. The constitutive relation proposed by Johnson and 1500
Cook (the J–C model) is widely used in numerical models
involving high strain rates and temperatures [13,32,33], 1000
and its use is generally limited to the impact of solids.
The J–C model is stated as follows [32]: 500
  pl 
e_ Temperature= 298 K
pl n
 ¼ ½A þ Bðe Þ  1 þ C ln
r ð1  ^
hm Þ ð1Þ 0
e_ 0
0 0.2 0.4 0.6 0.8 1
where epl is the equivalent plastic strain, e_ pl is the equivalent Plastic Strain
plastic strain rate, and A, B, C, m, n and e_ 0 are material
parameters measured at or below the transition
3000
temperature. 298 K
^
h is a non-dimensional temperature, defined as: . .
498 K ε = ε0
8 2500 698 K
<0
> for h < htransition
898 K
^ ðhhtransition Þ
h ¼ ðhmelt htransition Þ for htransition 6 h 6 hmelt ð2Þ 1098 K
>
: 2000
1 for h > hmelt 1298 K
Stress / MPa

1498 K
where htransition is the temperature above which thermal
1500
softening is assumed to occur. Since, in the example against
which we have chosen to assess the validity of our model,
the stainless steel particles are below their melting point, 1000
we used the J–C model to describe the mechanical proper-
ties of the materials. It is assumed here that the J–C param-
eters for bulk stainless steel are relevant for this impact 500
model (no J–C parameters for sprayed stainless steel are
available in the literature); also, the thermomechanical 0
properties of the system were also assumed to be the same 0 0.5 1
as that of bulk stainless steel, except where specific data
Plastic Strain
concerning sprayed coatings was available. The thermome-
chanical properties and J–C parameters of SS 316 are listed Fig. 4. Flow stress of SS 316 as a function of plastic strains for (a)
in Tables 2 and 3, respectively. The J–C parameters listed different strain rates and (b) different temperatures according to the J–C
model with the data from Table 3.
in Table 3 have been obtained using a fitting method and
have an average fitting error of dr = 6.66% [34]. Fig. 4

Table 3 illustrates the flow stress of SS 316 for different strains,

Johnson–Cook parameters SS 316 [34] temperatures and strain rates.
J–C parameters SS 316 The general methodology that we are presenting is capa-
ble of modelling cases where the particles are liquid upon
A (MPa) 388
B (MPa) 1901 impact with the substrate. In the case of the particle tem-
perature being greater than its melting point, the J–C
n 0.8722
model of material plasticity assumes the material to have
C 0.02494
a flow stress of zero, and thus use of this model for such
m 0.6567 cases would lead to non-realistic deformed shapes. As such,
Transition temperature (htransition) (K) 298
an alternative material model has to be employed. For
Melting temperature (K) 1643 example, the sprayed particle’s volumetric response can
Reference strain rate ð_e0 Þ (s1) 105
be simulated using an equation of state approach, such
5094 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

as the Mie-Gruneisen equations of state within ABAQUS/ 200

Explicit [35], while its deviatoric behaviour can be charac-
terized via a Newtonian viscous fluid model, also available
within ABAQUS/Explicit [35]. 0
Upon impact, the sprayed particle deforms and spreads
over the substrate, forming a splat. The FE analysis
assumes that, after first contact, the particle remains -200
attached to the substrate. This was implemented by assign-

σrr / MPa
ing a no-separation criterion between the contacting nodes
of the impinging particle and the underlying substrate. The -400
contact was modelled using the penalty function method. A
similar approach has been used successfully in defining
contact during shot-peening processes [15,17]. This contact -600
between the particle and the substrate constrains the
1.5 µm
shrinkage of the solidifying particle, thereby generating
1.0 µm
solidification stresses in the particle. -800
In an explicit analysis, the stable time increment, Dtstable, 0.5 µm

is given as [35]:
Le -1000
Dtstable ¼ ð3Þ 0 0.05 0.1 0.15 0.2
cd
Substrate Thickness / mm
where Le is the smallest element dimension and cd is the
wave speed in the material. The cd of a material is related Fig. 5. Predicted rrr stress profile through the substrate thickness for the
to the elastic modulus E and density q as follows: element sizes of 0.5, 1.0 and 1.5 lm. The r-direction lies in the plane of the
sffiffiffiffi free surface.
E
cd ¼ ð4Þ 2.3.2. Implicit layer deposition model
q
It is not generally feasible to model the deposition of
The requirement for a fine mesh with small elements to complete coating layers on a particle-by-particle basis
capture the detailed stress distributions therefore leads using explicit analysis. Consequently, the approach
to very short maximum allowable time increments which, adopted here is to model a layer-by-layer deposition of
in turn, result in a computationally intensive analysis. In the coating by assuming that the residual stress directly
order to optimize the computational efficiency of the im- under one particle (from Section 2.3.1) applies across the
pact model, smaller elements were used only in the parti- full width of each layer. Consequently, an implicit analysis
cle and along the particle–substrate interface. A mesh of an axisymmetric FE model of a progressively deposited
convergence study was carried out by varying the mesh coating on a thick substrate is employed, with the residual
density in the particle and along the contact interface. stress distribution from the explicit particle analysis being
The final residual stress state in the substrate was em- imposed. In this implicit analysis, the residual stress gener-
ployed as the convergence criteria. Fig. 5 illustrates the ation during coating deposition is predicted using a non-
stress distribution after 100 ns when an SS 316 particle linear, sequentially coupled, thermomechanical FE analysis
at 1593 K is sprayed with an impact velocity of performed in two stages. In the first stage, a heat transfer
610 m s1 onto an SS 316 substrate. It can be seen that analysis is performed to obtain the thermal history of the
the models with 1 and 0.5 lm element sizes predict similar specimen. The time-dependent temperature distribution
residual stress distributions in the underlying substrate: together with the impact stress profile from the explicit
the 0.5 lm element size model predicted a maximum com- analysis are then repeatedly applied for each layer to accu-
pressive stress of 704 MPa at a depth of 9 lm, whereas a mulate the final residual stress distribution, as seen in Fig. 2
compressive stress of 673 MPa was predicted at a depth for layers i = 1–n. The thermomechanical properties of SS
of 10 lm using the 1 lm element size. However, the use of 316 used in the model are listed in Table 2.
smaller elements reduces the Dtstable significantly, thereby The explicit analysis shows that, upon impact, a 29 lm
increasing the analysis time. Particle impact analysis for diameter particle changes into a disc of approximately
a duration of 100 ns using the 1 lm element size requires 10 lm thickness and 80–85 lm diameter. This provides a
only 30 min. On the other hand, it takes approximately splat flattening ratio (ratio of splat diameter to original
15 h to perform a similar analysis using 0.5 lm sized ele- particle diameter) of approximately 3. A similar degree of
ments. To give a reasonable compromise between compu- splat flattening (2–3) is seen in the micrographs of the pol-
tational efficiency and accuracy, the final (converged) ished cross-sections of SS 316 coatings deposited over SS
mesh adopted here uses 1 lm size elements in the particle 316 substrate using the JP 5000 HVOF spray system [24].
and along the contact interface and has 9878 elements In the thermomechanical analysis, coating growth is mod-
and 5142 nodes in total. elled by adding a series of 40 (i.e. n = 40) 10 lm thick layers
 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101 5095

onto a substrate disc of 2.3 mm radius and 1.7 mm depth consecutive layers to account for the gun movement during
(see Fig. 6). The width of each layer is taken to be that the spraying process. Heat transfer between the HVOF jet
of 20 particles which are assumed to be bonded together. and the coating is defined as a surface heat flux of
Fig. 7 shows the FE model with all layers included. The 1 MW m2 in the respective coating top layers [36]. This
heat transfer analyses uses four-node linear diffusive heat heat flux is applied to the top surface for a duration of
transfer elements. The stress analysis uses four-node approximately 41 ms. This period was estimated from the
bilinear, reduced integration plane strain elements with traverse velocity of the spray gun and corresponds to the
hourglass control. Temperature dependency of the conduc- time required by the spray gun to pass over a spray zone
tivity is modelled. The thermal conductivity of the coating of approximately 30 mm. Cooling of the coated specimen
elements is defined using a field variable. Thus, initially all to the ambient temperature by natural convection between
the coating elements are assigned the conductivity of air the coating and the surroundings is also modelled. The
and, to model the deposition of SS 316 particles during elastic moduli and the thermal expansion coefficients of
the spray process, the conductivity of the added elements the SS 316 coatings being considered in this work have
is changed to that of SS 316. Coating growth is then simu- been measured by Totemeier et al. [23] and shown to be
lated by the successive addition of such layers as shown in similar to the bulk material properties; the values employed
Fig. 2. A 10 s delay is permitted between the arrivals of the in the analysis are shown in Table 2. During cooling, defor-
mation in the deposited coating is mainly associated with
the thermal strains. Due to the large time period of the
cooling phase (a few seconds to a few hours, depending
on the component size), the plastic response of the coating
can effectively be assumed to be strain-rate independent.
Hence, we define the stress–strain behaviour for the layer
deposition analysis (implicit analysis) as
rðe; T Þ ¼ rð_e0 ; e; ^hÞ ð5Þ
where r ^ is obtained from Eq. (1). Fig. 8 illustrates
ð_e0 ; e; hÞ
this strain-rate independent flow stress of SS 316 as a func-
tion of temperature for different plastic strain levels.

2.3.2.1. Implementation of residual stress distribution. At a

given depth z, the residual stress from the explicit particle
Fig. 6. Schematic illustration of a thermal spray process and its
impact analysis rres(z) can be approximately implemented
representation in the FE model.

2500
80%
60%
40%
2000 20%
Stress / MPa

1500

1000 increasing
strain

500

0
298 498 698 898 1098 1298 1498 1698
Temperature / K

Fig. 8. Strain-rate independent flow stress of SS 316 as a function of

Fig. 7. Axisymmetric model of layer-by-layer deposition of SS 316 coating temperature for different plastic strain levels using the J–C model with
on SS 316 substrate. e_ ¼ e_ 0 .
5096 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

in the layer deposition model by applying a radial pressure 200

load of p0(z) =  rres(z) to all elements along the radially
outward line at that depth. This procedure is then applied
through the depth of the substrate (for the first coating 0
layer application), giving a through-depth distribution
p0(z) of radial pressure which approximately induces
rres(z). In order to improve the fidelity of the induced resid- -200
ual stress distribution, an iterative scheme with a propor-
tional integral adjustment was used. Hence, if rFE j ðzÞ is

σrr/ MPa
the FE-predicted residual stress associated with an applied -400
(elemental) radial pressure distribution pj(z), then an
improved (iterative) radial pressure distribution pj+1(z) is
given by the following expression: -600
520 ms-1
pjþ1 ðzÞ ¼ pj ðzÞ þ aðrres ðzÞ  rFE
j ðzÞÞ ð6Þ
610 ms-1
where a is taken as 1. Convergence is deemed to have -800

been achieved when the following convergence criterion is

achieved:
Z zr -1000
0 0.05 0.1 0.15 0.2
ðrres ðzÞ  rFE
j ðzÞÞ dz 6 err ð7Þ
0 Substrate Thickness / mm
In the present work, a value of 0.1 is used for err and zr is Fig. 9. FE-predicted final rrr stress distribution through the substrate
taken as 0.2 mm. Effectively, this means that the difference thickness, 400 ns after initial contact.
between the areas under the target and the imposed stress–
depth curves is within 10%. The nodes at the edges were
constrained to attain an accurate initial stress field and surface and transform into circular discs with a variable
were released later during the analysis to yield the de- thickness. Further spreading with significant thinning
formed configuration. The temperature distribution from along the periphery is observed in the particle sprayed at
the explicit analysis was imposed for each added layer by higher velocity.
redefining the boundary conditions in the thermal analysis. Fig. 11 illustrates the FE-predicted change in the splat
radius during impact along with the predicted nodal tem-
3. Results perature at the top of the particle. During the initial stage
of the impact, an increase in the particle temperature is pre-
3.1. Particle impact process dicted and the increase is larger in particles sprayed at
higher velocities. With increasing time, after about
Fig. 9 illustrates the stress fields predicted in the sub- 104 ms, the temperature attains a constant value. Similar
strate upon impact for two different velocities. The behaviour is predicted in the deformation of the particles.
deformed shapes of the SS 316 particles are shown in The splat radius is predicted to increase in the early stage
Fig. 10. Particles upon impact spread over the substrate of the impact and maintains a stable value during the rest

Fig. 10. Deformed shapes of the SS 316 particles sprayed at 1593 K with a particle velocity of (a) 520 m s1 and (b) 610 m s1.
 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101 5097

80 1800

520 ms -1 520 ms-1

70 610 ms-1
610 ms-1 1500

60
1200
Splat Radius / µm

Temperature / K
50

900
40

600
30

20 300

Particle Substrate

10 0
0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 0 0.02 0.04 0.06 0.08
Time / ms Distance / mm

1610 Fig. 12. FE-predicted temperature distribution across the particle and the
520 ms-1 substrate thickness after the impact.

610 ms-1
1606
is predicted to affect a region up to about 30 lm deep. A
greater temperature rise is predicted in the substrate along
the particle–substrate interface when particles are sprayed
Temperature / K

1602
at 610 m s1.
The predicted peening stresses (rrr) induced in the sub-
strate due to impact are illustrated in Fig. 9. The r-direction
1598 is parallel to the free surface. Upon impact, strong com-
pressive stresses are predicted in the substrate up to a depth
of 30 lm. The peening intensity is predicted to increase
1594 with the particle velocity and higher compressive stresses
are predicted when particles are sprayed at 610 m s1.

1590
3.2. Layer deposition analysis
0.E+00 1.E-04 2.E-04 3.E-04 4.E-04
Time / ms The stress and temperature distributions (Figs. 9 and 12)
predicted by the explicit analysis of the impact process were
Fig. 11. FE-predicted change in (a) the splat radius during impact and
introduced in the layer deposition implicit model via the
(b) the nodal temperature at the top of the particle.
process described in the flowchart of Fig. 2. Fig. 13 shows
the predicted rrr profile through the substrate thickness for
of the impact process. No significant change is predicted in the two different spray velocities following the introduction
the particle thickness after about 104 ms. Increasing the of just one layer of coating. Close agreement between
spray velocity to 610 m s1 increases the rate of deforma- the target stress profile and the equilibrium distribution
tion in the early stages of impact. However, the predicted illustrates a satisfactory introduction of the peening stres-
deformation rate gradually decreases and the particle is ses to the implicit layer model. The final residual stress
predicted to attain a final thickness of 10 lm. distributions predicted after the layer-by-layer coating pro-
In the present approach, heat transfer between the par- cess with n = 40 are shown in Fig. 14. The coating surface
ticle and the substrate is modelled by allowing heat conduc- exhibits significant predicted tensile stresses up to a depth
tion at the particle–substrate interface and within the of approximately 15 lm which change at greater depths
particle and the substrate. Fig. 12 depicts the predicted to high compressive stresses. In practice, a network of
temperature distribution across the particle and the sub- microcracks is generally observed on the surface of the
strate thickness 400 ns after initial contact. An increase of thermally deposited coatings. Development of these micro-
approximately 8 K is predicted in the particle upon impact. cracks acts as a mechanism to relax the high tensile stresses
The impact process also imparts heat to the substrate, and generated at the coating surface upon cooling [10].
5098 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

400 profile in HVOF sprayed SS 316 coatings on a steel sub-

strate measured using the layer removal method [37].Com-
pressive stresses of approximately 156 and 277 MPa are
200
predicted in coatings sprayed with the particle velocities
of 520 and 610 m s1, respectively.
0

-200
4. Discussion
σrr / MPa

In addition to predicting the residual stresses in ther-

-400 mally sprayed coatings, the present methodology can also
Explicit - 520 ms -1
be used to gain useful information on the particle impact
-600 process. Fig. 11 provides the deformation and thermal his-
Implicit - 520 ms -1
tory of the sprayed particle during the deposition process.
Explicit - 610 ms -1 No temperature drop is predicted during the period when
-800
Implicit - 610 ms -1 the particle attains a steady final thickness. This indicates
that significant cooling of the particle begins after comple-
-1000 tion of the flattening process. Fan et al. studied stress gen-
0 0.05 0.1 0.15 0.2 eration during impact of a molten Ni particle onto a flat
Substrate Thickness / mm substrate [38]. They reported that the spreading or flatten-
Fig. 13. Predicted rrr profiles through the substrate thickness after the ing time of the droplets was of the order of less than a
addition of one layer of coating in the layer deposition model as compared microsecond, significantly shorter than the estimated solid-
with distributions from the particle impact model. ification time.
The peening stresses (rrr) in the substrate due to impact
are illustrated in Fig. 9. Particle impact is predicted to
1200 induce compressive stresses up to a depth of 30 lm into
520 ms-1
the substrate. The temperature distribution shown in
1000 610 ms-1
Coating Substrate
Fig. 12 indicates that a similar region in the substrate is
800 also predicted to experience an increase in temperature
upon impact. This temperature rise is attributed to the
600 inelastic heat generated due to plastic deformation. This
also explains the greater increase in temperature predicted
σrr / MPa

400
in the substrate when a higher spray velocity is used
200 (Fig. 11).
Fig. 14 shows the residual stress distributions predicted
0 by the FE implicit layer analysis. This final stress state is
-156MPa
governed by the peening and thermal stresses generated
-200
during the deposition process. The effects of these two
-400
-277MPa stresses on the final stress state can be studied in isolation
using the present FE model, as shown in Fig. 15. Differen-
-600 tial cooling and contraction of the coating and the sub-
strate during the deposition process is predicted to
-800
0 0.4 0.8 1.2 1.6 2 generate tensile thermal stresses in the coating. These stres-
Distance / mm ses become compressive at the coating–substrate interface
with the compressive region extending into the substrate.
Fig. 14. Final predicted rrr stress profile through the coating and the Tensile stresses are generally reported in plasma sprayed
substrate thickness for different particle velocities and a particle temper-
ature of 1593 K.
coatings where fully molten particles are sprayed at much
lower velocities, which results in insignificant peening of
the substrate [39]. On the other hand, HVOF sprayed coat-
Increasing the particle velocity is predicted to increase ings are known to exhibit high compressive stresses [3,7].
the compressive stresses in the coating. The compressive The present approach also predicts strong compressive
region is predicted to extend into the substrate to a depth stresses in the deposited coatings, which also highlights
of a few hundred micrometres. The highest compressive the dominant contribution of the peening stresses to the
stresses are predicted at the coating–substrate interface, stress state of HVOF sprayed coatings.
and these stresses rapidly change into high tensile stresses Residual stresses generated during thermal spraying can
in the substrate. The predicted stress distribution in the deform the coated specimen and result in curvature. For a
coated specimen as shown in Fig. 14 is similar to the stress coating under tension, such as a plasma sprayed coating,
 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101 5099

1200 During a thermal spray process, the arrival of a new

Thermal stresses
coating layer over an underlying thin substrate alters the
1000
Residual stresses
stress field of the substrate. Deposition of each layer also
800 changes the overall thickness of the specimen over which
Peening Stresses
the stresses are redistributed. As a result, the final stress
600 distribution becomes dependent on the total thickness of
the deposited coating. Totemeier et al. showed experimen-
400
tally that the residual stresses in an HVOF sprayed Fe3Al
σ / MPa

200 coating on a steel substrate become less compressive with

increased coating thicknesses [21]. Fig. 17 illustrates similar
rr

0 trends in the FE-predicted residual stresses in SS 316 coat-

-200
ings of different thicknesses deposited over an SS 316 sub-
strate. The highest compressive stresses are observed in a
-400 100 lm thick coating, with the 400 lm thick coating being
least compressive.
-600 Coating Substrate
Residual stresses in SS316 coatings have been measured
-800 experimentally by various workers [21,24]. In the current
0 0.4 0.8 1.2 1.6 2 work, the spray conditions used by Totemeier et al. were
Distance / mm included in the FE model to provide a direct comparison
between the measured and FE-predicted residual stresses.
Fig. 15. Predicted thermal, peening and final residual stresses through the
coating and the substrate thickness for a particle velocity of 610 m s1 and
Experimental measurements of the residual stresses were
a temperature of 1593 K from layer deposition model. made using the XRD technique and the application-com-
puted error of the measurements was of the order of
20 MPa [21]. Measured stresses in a 400 lm thick coating
the coating free surface attains a concave curvature [2]. were found to be 130 and 300 MPa for the particle
Compressive stresses in the coatings, on the other hand, spray velocities of 520 and 610 m s1, respectively [21].
render a convex free coating surface [2]. The FE analyses These values agree closely with the FE-predicted stresses
performed here to study the thermal stresses and final stres- of 156 and 277 MPa in the coatings sprayed with the
ses predict such deformed shapes successfully. Fig. 16 particle velocities of 520 and 610 m s1, respectively. Good
shows the resultant bending of the coated specimens with correlation between FE-predicted residual stresses and
tensile thermal stresses and compressive residual stresses deformed particle characteristics and experimentally
in the coating. observed behaviour also provides a useful validation of
the assumptions made in the present FE methodology.
Some of these key assumptions are listed below:

-260

-265

-270

-275
σrr / MPa

-280

-285

-290

-295

-300
0 0.1 0.2 0.3 0.4 0.5
Coating Thickness / mm

Fig. 17. FE-predicted residual stresses in SS 316 coatings of different

Fig. 16. FE-predicted deformed shapes of the coated specimen with (a) ten- thicknesses deposited over SS 316 substrate sprayed at 1593 K and
sile thermal stresses and (b) compressive residual stresses in the coating. 610 m s1.
5100 P. Bansal et al. / Acta Materialia 55 (2007) 5089–5101

Particle impact model: the literature. The results also emphasize the significance of
peening stresses in controlling the final residual stress state
1. 90% of the inelastic energy generated during the impact of the coated specimen. This, in turn, permits the use of the
is dissipated as heat; the remainder is assumed to be dis- key spray parameters to design HVOF sprayed coatings
sipated in other ways (stored energy, elastic waves, etc.). with desired stress states. The development of such a meth-
2. After first contact, the particle remains attached to the odology provides a novel understanding of the effect of the
substrate; there is no particle rebound in the model, process parameters on coating properties (residual stresses)
which equates to 100% deposition efficiency in practice. to assist in designing coatings with improved performance.
However, it is known that, in practice, much lower
deposition efficiencies are observed. Any particle which References
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