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Finite element modeling of solid particle erosion in AISI 4140 steel and

nickeltungsten carbide composite material produced by the laser-based

powder deposition process

Prabu Balu a, Fanrong Kong a, Syed Hamid b, Radovan Kovacevic a,n

a RCAM (Research Center for Advanced Manufacturing), Southern Methodist University, 3101 Dyer St.; Dallas, TX 75205, United Statesb Halliburton, 2601 Beltline Rd.; Carrollton, TX 75006, United States

a r t i c l e i n f o

Article history:

Received 17 September 2012

Received in revised form

6 December 2012

Accepted 17 January 2013Available online 8 February 2013

Keywords:

Solid particle erosion

NiWC composite material

Finite element model

Laser-based powder deposition

a b s t r a c t

A FE dynamic model was developed to study the slurry erosion in NiWC composite material that

considers both Ni and WC separately. The model was verified by the measured erosion rate and the

eroded surface topography. The verified model was used to study the effect of material composition and

different erodent particle characteristics such as impingement angle, velocity and the shape on the

erosion rate, stress distribution and internal energy of the target material. The results show that the

volume fraction of the Ni-matrix determines the energy absorption within the target material and the

WC is responsible for minimizing the erodent attack. It was shown that a soft interlayer can provide

more resistant to erosion in a multilayered NiWC deposit.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Slurry erosion is the major cause of downtime and the

premature failure of components in industries such as oil and

gas and coal mining, as well as in manufactured goods like gas

turbines, rocket nozzles, and boiler tubes [1]. David [2] defined

slurry erosion as Progressive loss of the material from a solid

surface by the action of a mixture of solid particles in liquid in

motion with respect to the solid surface. Slurry erosion involves

complex material removal mechanisms that are governed by a

number of variables such as the material properties of the target

(eroding) and erodent material and erodent particle character-

istics, including morphology, impingement velocity, and angle,

the concentration of erodent in slurry [3]. In general, target

materials show different types of erosion behavior for differenterodent particle characteristics. For example, erosion in most

ductile materials occurs as a result of cutting and ploughing

deformations which are predominant at low impingement angles

(E201 to 301) [4]. On the other hand, erosion in brittle material is

primarily due to crack network formation that occurs at a normal

(901) impingement angle [3]. The complexity of erosion mechanisms

increases by many folds in the case of composite material (e.g.,

NiWC) because of the existence of both brittle (reinforcement: WC)

and ductile (matrix: Ni) materials [5]. Thus, understanding the effectof different variables and their interactions on the erosion behavior

of composite material through experimental techniques is costly,

time consuming, and difficult. Finite element (FE) based numerical

simulation can be used as a time and cost effective tool to estimate

the erosion behavior of components exposed to slurry erosion under

different erosion conditions with a limited number of experiments if

a suitable erosion mechanism is implemented.

A number of analytical and numerical studies have been

performed to explain the erosion mechanisms of different mate-

rials for a wide range of erosion conditions. Over the past two

decades, many numerical simulation-based approaches improved

the understanding of erosion mechanisms and they were used in

selecting the best slurry erosion resistant materials.

Shimizu et al. [6] developed a two-dimensional (2D) finiteelement (FE) based model to study the erosion caused by the

single particle impingement on steel and cast iron. The effect of

impingement angle on erosion was quantified based on the extent

of plastic deformation. They reported that steel and cast iron

show maximum erosion at an impingement angle of 201, 301, and

601, respectively. Bielawski and Beres [7] studied the erosion

resistance of the multilayered coating of titanium nitride through

single particle impingement using a 2D FE model. They reported

that a low magnitude of tensile stress was induced in a two-layer

coating composed of a thin, low-modulus top layer and a thick,

high-modulus bottom layer. Chen and Li [8] established a 2D

micro-scale dynamic model for both ductile and brittle materials

Contents lists available at SciVerse ScienceDirect

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Tribology International

0301-679X/$- see front matter & 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.triboint.2013.01.021

n Corresponding author.

E-mail address: [email protected] (R. Kovacevic).

Tribology International 62 (2013) 1828
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by mapping the material system into a discrete lattice. The effects

of erodent particle characteristics on the erosion of ductile and

brittle material were reported. Further, Chen and Li [9] extended

their model in order to study the erosion behavior of copper/SiC

based metalceramic composite material. The influence of bond

strength at the metal/ceramic interface, volume fraction of

reinforcement particle, and size ratio of reinforcement particle

to erodent particle on erosion rate were considered in their study.

They reported that the small reinforcement particles were moreresistant to erosion than the large ones. Hassani et al. [10]

optimized the architecture (number of layers) of the nano

titanium nitride composite coatings on titanium alloy and stain-

less steel substrate to achieve the excellent erosion resistance

based on a 2D FE model.

Woytowitz and Richman [11] presented a three-dimensional

(3D) numerical model developed to estimate the erosion resis-

tance of copper during the impingement of multi-particles. In

their model the eroded volume was estimated by removing the

failed element from the geometry based on the maximum stress

and strain criteria. Aquaro and Fontani [3] developed a FE based

numerical model to estimate the erosion behavior of ductile

material and brittle material separately. However, the combined

erosion behavior was not discussed in their study. Griffin et al.

[12] studied erosion caused by the multi-particle (five) impinge-

ment on alumina scale/MA956 substrate. In order to incorporate

the actual material removal by erosion, element failure criterion

and element removal technique were used. Eltobgy et al. [1]

simulated the erosion behavior of titanium alloy (Ti6Al4V)

under the action of single and multiple particle impingement.

A non-linear elasticplastic material model including the strain

rate and temperature dependency was considered in their FE

based simulation. Their study emphasized the need to model the

multi-particle impingement to accurately predict the erosion

behavior. Junkar et al. [13] presented a 3D FE based model to

represent the single particle impact from an abrasive water jet

machine. The influence of particle velocity and the impingement

angle on erosion rate was studied. Eshwar and Kovacevic [14]

developed an erosion model based on the material failure criter-

ion using the non-linear FE code ABAQUS/Explicit. The model was

validated based on the measured quantities of the material

removal rate and the depth of penetration. Wang and Yang [15]

studied the erosion behavior of both ductile and brittle materials

at different impingement angles of the erodent particle and its

velocity using a 3D FE model. The model was used to estimate the

residual stress and the total volume of material removed from the

target through multi-particle impingement. Ma et al. [16] devel-

oped a hybrid code based on smoothed particle hydrodynamics

and FE in order to simulate pure water jet penetration on mild

steel. Wang et al. [17] studied the erosion behavior of titanium

(Ti6Al4V) alloy by using a coupled finite element model and

the mesh free technique available in commercial code ANYSY LS-

DYNA. They estimated the dependency of erosion on the impin-gement angle and velocity of the erodent particle. Further, the

change in energy (internal, kinetic, and total) as well as the

residual stress induced in the eroding material due to the

impingement of erodent particle was investigated. The model

was validated with the reported analytical models. However, the

developed model was not validated with experimental data.

After the state-of-the-art review of numerical modeling of

solid particle erosion, it can be concluded that no numerical

assessment has been reported on the erosion behavior of single

and multilayered deposits of NiWC (metalceramic) composite

material formed by laser-based powder deposition on an AISI

4140 steel substrate. Hence, the purpose of this investigation is to

understand the erosion behavior of single and multilayered

NiWC composite material under different erosion conditions

using an experimentally verified ANSYS LS-DYNA based numerical

model.

2. Experimental set-up

Single and multilayered deposits consisting of different com-

positions of nickel (Ni) and tungsten carbide (NT-20, NT-60, and

NT-80) were produced using a 4 kW fiber laser along with the

multi-hopper powder feeding system developed at RCAM [18].

The letters N and T represent the nickel and tungsten carbide

(WC), respectively and the number following letters represents

the mass fraction of the WC in the NiWC deposit. The experi-

mental procedure and the process conditions used to fabricate the

NiWC composite material can be found in [19]. The micrographs

of the single-layer NT-60 deposit and the two-layer NT-60 over

NT-20 deposit are presented in Fig. 1a and b. To measure the

erosion resistance of the fabricated coupons a high pressure water

jet machine was utilized. Fig. 1c shows the specially designed

fixture that can be tilted to any angle between 01 and 901 from the

horizontal axis. The erosion conditions used in this study are

presented in Table 1.

3. Finite element formulation

3.1. Governing equations

Abrasive slurry erosion is a high velocity dynamic event. This

transient dynamic behavior was modeled using the explicit

Fig. 1. (a) and (b) Micrographs of the single-layer NT-60 deposit and the two-layer

NT-60 over NT-20 deposit, respectively; (c) erosion testing facility.

Table 1

Erosion conditions.

Variable Unit Value/range

Abrasive flow rate g/s 4.53

Abrasive material and mesh size Garnet, #80

Impact angle deg 30, 45, 90

Exposure time s 10100

Pump pressure MPa 150

Orifice diameter mm 0.33

Stand-off distance mm 100

Focus tube diameter mm 1.02

Focus tube length mm 76.2

P. Balu et al. / Tribology International 62 (2013) 1828 19



dynamic analysis available at the finite element based commer-

cial code ANSYS LS-DYNA. The laws of conservation of mass,

momentum, and energy are expressed as Eqs. (1)(3) [20].

Conservation of mass is represented by [20]

rV r0 1

where Vis the relative volume, r is the density (current), and r0 isthe reference density.

Conservation of momentum is given by [20]sij,j rfi r xi 2

where sij denotes the Cauchy stress, fi is the body force density,and x i is acceleration.

Finally, conservation of energy is represented by [20]

_E Vsij _e ijpqdij 3

here sij, p, and q represent the deviatoric stresses, and pressure

and bulk viscosity, respectively. The deviatoric stresses (sij ) is

given by [20]

sij sij pqdij 4

where dij is the Kronecker delta. The scheme followed to solve the

governing equations is explained in the ANSYS LS-DYNA Theory

Manual [20] and ANSYS Users Guide [21].

3.2. Model description and conditions (initial and boundary)

In the LS-DYNA FE code, the 3D, Lagrangian, dynamic-explicit

and non-linear analysis was used. The 8-noded, 3D solid brick

element SOLID164 was used to discretize both the substrate and

deposited layer; whereas, both brick as well as quadrilateral

elements were used to discretize the garnet particle. In order to

minimize the computational cost without compromising the accu-

racy of the calculations, it is essential to optimize the geometry and

the element size of the calculation domain. Thus, a number of trial

simulations were performed to identify the effect of coupon

dimensions, constraints, and element size on the equivalent plastic

strain, equivalent stress, and time dependent internal energy. Basedon the sensitivity study, the width and length of the coupon were

set at 3 mm each and an element size of 0.05 mm was chosen. In all

the simulations, the displacement in all three directions was set to

zero at the bottom of the substrate. In a typical dynamic analysis

specification of the initial condition is required to solve the problem.

The initial condition for this analysis was an initial velocity of the

garnet particle, which was estimated based on the known values of

water pressure and the orifice diameter of the water jet as presented

by Junkar et al. [13] and Momber et al. [22].

In the real case, not all of the garnet particles are of same

shape. Vasek et al. [23] showed seven different shapes of garnet

particles. To study the effect of different shapes of the garnet

particles on the erosion behavior, the numerical model incorpo-

rated four basic shapes: cubical, spherical, trigonal, and pentago-nal. The discretized geometry of the different garnet particles is

shown in Fig. 2.

3.2.1. Eroding surface to surface contact algorithm

In a slurry erosion process the erodent particle impinges and

subsequently damages the surface (crater or indent) of the target

material. The repetitive action of the incoming erodent particles

causes successive damage resulting in material removal from the

contact surface. To capture this surface failure, the eroding sur-

face to surface contact (ESTS) algorithm provided in the ANSYS

LS-DYNA was used where the contact between the eroding target

and the erodent particle was defined as master and slave,

respectively [21]. The friction at the contact interface between

the target material and erodent particle was defined by the

Coulomb law of friction, in which, the frictional force Ff is

proportional to the normal force Fn

Ff mFn 5

where m is the proportionality constant (coefficient of friction)which was assumed as 0.4 [20] in the current study. The failure of

the surface element was decided based on the damage parameter

Diel which is defined as [24]

Diel XDepl

ef f=ef r 6

where, Deplef f

is the accumulated incremental effective plastic

strain and efr is the fracture or failure strain of target/erodent

material. It was assumed that the element fails (erodes) due tothe action of erodent particle when the Diel attains a value of 1.

The ESTS algorithm detects the underlying/adjacent surface and

establishes contact with the new surface when any of the contact

surfaces fail.

In this study, the erosion rate was used as a measure of slurry

erosion resistance of the target material (i.e., higher value of

erosion rate signifies a greater vulnerability to erosion). The

erosion rate _E is defined by [24]

_EX

rDielViel

=neMe 7

where, r is the density of the eroded particle (Ni and/or WC), and neand Me, are the number of erodent particles and the mass of erodent

particle, respectively. The material models used in the FE simulation

does not support the failure of element due to excessive distortionthat results in non-convergence of calculation. Hence, the MAT_AD-

D_EROSION feature of LS-DYNA was used which allows for the

deletion of excessively distorted elements from the calculation

domain based on the maximum failure criterion. According to this

feature, when the failure criterion (strain/stress) is encountered at

an integration point, all the components of stress/strain are set to

zero and the material point fails. When all of the material points at

any section of an element fail the element is removed from the

calculation domain [25].

3.3. Material properties

Since the NiWC metal matrix composite material is com-

prised of ductile matrix and brittle reinforcement, the erosionfollows neither ductile nor brittle behavior [5]. The presence of

such dual behavior in a typical composite material can cause a

non-uniform material removal during the action of the erodent

particle [26]. For example, the erosion rate depends on whether

Ni or WC or both are present at the specific location where the

erodent particle impinges. In order to capture this complex

phenomenon, a more realistic erosion model for the composite

material must assign location dependent material properties. For

instance, an erosion model based on the effective mechanical

properties of Ni and WC (average value) of Ni and WC may lead to

an erroneous estimation of the erosion rate. Thus, a novel strategy

is followed in this research where the geometry of the calculation

domain is divided into both the Ni and WC regions depending on

the mass fraction of WC in Ni-matrix (NT-20, NT-40, NT60, and

Fig. 2. Discretized geometry of the garnet particles: (a) cubical; (b) spherical;

(c) trigonal; (d) pentagonal.

P. Balu et al. / Tribology International 62 (2013) 182820
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NT-80). The discretized geometry of the two-layer functionally

graded NiWC composite material, substrate, and erodent particle

is shown in Fig. 3.

In this numerical study four different types of materials

(substrate, matrix, reinforcement, and erodent) were used. The

AISI 4140 steel was considered as substrate and NiWC (metal

ceramic) composite material and garnet was used as coating

material and erodent particle, respectively. For AISI 4140 sub-

strate material, plastic kinematic hardening material model wasconsidered as given in Table 2. For Ni, bilinear isotropic plasticity

was considered as given in Table 3. The material models used for

WC and garnet are presented in Table 4 and Table 5. The failure

criterion based on the maximum strain was imposed for the AISI

4140 steel and Ni, whereas, for the WC and garnet a maximum

tensile stress failure criterion was used (i.e., it was assumed that

the WC fails when it reaches the value of the yield stress).

3.4. Assumptions

Effect of water on material removal is negligible (i.e., only the

garnet particle was considered).

Deposit is defect free (i.e., the presence of defects such as crack

and porosity was ignored).

Deposit is stress free (i.e., the residual stress in the deposited

material was ignored).

Perfect bonding at the interfaces (matrix/reinforcement,

matrix/substrate, and reinforcement/substrate) exists.

Composite material is composed of Ni and WC (i.e., the minor

alloying elements such as silicon and boron were ignored).

The flow diagram of step-by-step procedure used to model the

erosion process in ANSYS LS-DYNA is presented in Fig. 4.

Fig. 3. Discretized 3D FE model of the two-layer NT-60 over NT-20 on AISI 4140 steel and erodent.

Table 2

Plastic kinematic hardening material model for AISI 4140 steel [27].

Modulus of

elasticity, E (MPa)

Density, r

(kg/m3)

Poisson

ratio, n

Yield stress,

sy (MPa)

Tangential

modulus, Et(MPa)

210,000 7850 0.3 792 21,000

Strain rate parameter, C Strain rate parameter, P Fracture strain, efr40 5 0.15

Table 3

Bilinear isotropic plasticity material model for Ni [21,28].

Modulus of

elasticity,E

(MPa)

Density,

r (kg/m

3

)

Poisson

ratio, n

Yield

stress, sy(MPa)

Tangential

modulus,Et

(MPa)

Fracture

strain, efr

180,000 8490 0.31 900 445 0.21

Table 4

Material model for WC [28,29].

Modulus of elasticity, E

(MPa)

Density, r (kg/m3)

Poisson

ratio, nFracture stress, sfr(MPa)

675,000 15,630 0.194 560

Table 5

Material model for garnet particle [13].

Modulus of elasticity, E

(MPa)

Density, r (kg/m3)

Poisson

ratio, nFracture stress, sfr(MPa)

245,000 4000 0.27 500




3.5. Numerical results and discussions

This numerical study explored the erosion behavior of AISI

4140 steel, and also single and multilayered deposits composed of

various mass fractions of WC in the Ni matrix. In particular, the

emphasis was on the stress distribution and erosion rate of AISI

4140 steel and different compositions of NiWC metal matrix

composite material under different erosion conditions such as

garnet particle morphology (size and shape), its angle of impinge-

ment, and its velocity. The following section presents the valida-

tion of this numerical model.

3.5.1. Comparison of the numerical and experimental results

Fig. 5a and b represent the eroded surface topography and the

von Mises equivalent stress distribution of the substrate material

AISI 4140 steel at two different impingement angles, a301anda901, respectively. The erosion conditions used for this simula-tion are as follows: (1) shape of the garnet particle was cubical and

spherical (with four particles in each shape); (2) the size of the

garnet particle was 400 mm; (3) the mass flow rate and the initialvelocity of the garnet particle was 4.53 g/s and 200 m/s, respec-

tively; (4) simulation time was 0.25 ms. The total number of garnet

particles that impinge the target material was calculated based on

the mass flow rate of the garnet particle (considering the particle

shape and size) and the simulation time. From Fig. 5a it can be seen

that at a301 the garnet particles form a groove like deformationon the substrate surface. This long groove type deformation may be

due to the longer contact time of the garnet particle with the target

material at lower impingement angle. When the impingement

angle was increased from 301 to 901, the region of plastic

deformation (indentation width and depth) increased significantly.

An increase in the plastic deformation due to an increased

impingement angle can be attributed to the change in the garnet

particle velocity vector component from near tangential to normal

(perpendicular). A comparison ofFig. 5a and b confirms an increase

in the magnitude of von Mises equivalent stress distribution in the

substrate material. For example, the minimum value of von Mises

equivalent stress of the AISI 4140 at a301 and a901, is 0.75 MPaand 2.1 MPa, respectively.Fig. 4. Flow diagram of the erosion model [24].

Fig. 5. The von-Mises equivalent stress distribution with the topography of the eroded surface of (a) and (b) AISI 4140 steel at impingement angle a301

and a901

.




The von Mises equivalent stress distribution with the eroded

topography of the NT-20 single-layer deposit at two different

impingement angles, a301and a901, respectively is presentedin the Fig. 5c and d. The erosion conditions were the same as in

the previous case. A deposited layer thickness of 0.5 mm was used

in this study. Fig. 5c shows that at a301 the groove likedeformation length is smaller than in the case of AISI 4140 steel

(see Fig. 5a) which confirms that the NT-20 deposit was more

resistant to the erosion damage at a301. As expected, presence

of WC impedes the cutting action of the garnet particle resulting

in higher erosion resistance. At the maximum impingement angle

it was observed that the width of the deformation of NT-20

deposit (see Fig. 5d) is less than in AISI 4140. However, the

erosion resistance of the NT-20 decreased with an increase in the

impingement angle and attained minimum at normal impinge-

ment angle (a901). The trend of increasing value of minimumstress at maximum impingement angle observed in AISI 4140 was

also observed in the NT-20 deposit.

Fig. 6a and b show the eroded surface of the single-layer NT-20

deposit obtained by scanning electron microscope at an impinge-

ment angle a301 and a901, respectively. It was clear from theeroded surface that the lower impingement angle of 301 forms a

groove like shallow crater (see Fig. 6a) and the maximum

impingement angle creates a deep crater. This observation was

consistent with the modeling results (see Fig. 5c and d).

To confirm the accuracy of the model in calculating the erosion

rate, a simulation time of 0.5 ms was used in the following

simulation. The mass flow rate of garnet particle was 4.53 g/s,

and the particle size ranging from 100 mm to 400 mm with fourdifferent shapes (see Fig. 2) were allowed to impinge the xz

plane of the target material at random locations over the

simulation time.

Fig. 7a and b show the comparison of erosion rates between

experimental and numerical calculations for AISI 4140 steel and

the single-layer NT-20 deposit at three different impingement

angles (a301, a451, and a901). The estimated erosion ratefor AISI 4140 steel follows the trend of decreasing magnitude of

measured erosion rate when there was an increase in the

impingement angle. Similarly, the estimated erosion rate of theNT-20 deposit reflected the trend of having a measured erosion

rate at all impingement angles. From these results, it can be stated

that the erosion rate of AISI 4140 steel predicted by the model

was more accurate than that of the NT-20 deposit (i.e., the erosion

rates obtained by both experimental and the model for AISI 4140

are in agreement by approximately 9094%), but the model

under-estimated the erosion rate for NT-20. For example, the

erosion rate obtained by the experiment and numerical modeling

for AISI 4140 at a901 was 6.3 mg/g and 6.9 mg/g, respectively;while the measured and numerically estimated erosion rate of the

NT-20 deposit at a901 was 16.8 mg/g and 13.3 mg/g. Thisunder-estimation of the erosion rate in the case of the NT-20

deposit could be attributed to a number of assumptions made in

the numerical model, such as neglecting the residual stress and

assumptions that no defects existed in the deposited material.

In summary, at lower impingement angle a groove like

deformation was observed in both AISI 4140 steel and NT-20

deposit. However, the length of the groove was limited by the

presence of reinforcement (WC) in the NT20 deposit. For an

increase in impingement angle the area of deformation and the

magnitude of von Mises equivalent stress increased and reached

the maximum value at a901. This was because of the highervalue of normal (perpendicular to target surface) velocity vector

of the garnet particle.

3.5.2. The effect of garnet particle velocity on stress and erosion rate

To study the effect of velocity of garnet particles (Vgp) on stress

and erosion rates, the other erosion conditions such as mass flow

rate and the morphology of garnet particles are maintained as stated

in the description to Fig. 5. Fig. 8a through 8d illustrates the von

Mises equivalent stress distribution of single-layer NT-60 deposits at

two different impingement angles (a151 and a901). Fig. 8acorresponds to the von Mises equivalent stress distribution of the

NT-60 deposit at Vgp200 m/s and at a151 which indicates thatthe area of deformation in both the width and length (x and y)

directions were small. For the same impingement angle (a151),Fig. 6. Eroded surface of single-layer NT-60 deposit at (a) a301 (b) a901.

Fig. 7. Comparison of erosion rate obtained by experiment and numerical modeling at three different impingement angles: (a) AISI 4140 steel; (b) NT-20 single-layer

deposit.




a two fold increase in the velocity of the garnet particle (from

200 m/s to 400 m/s) resulted in a larger area of erosion (seeFig. 8c). The minimum and maximum values of equivalent von

Mises stress from Fig. 8a are 0.10 MPa and 763 MPa, respectively.

Similarly, the minimum and maximum values of equivalent von

Mises stress from Fig. 8c are 0.11 MPa and 834 MPa, respectively.

This shows that an increase in the velocity of garnet particles at a

lower impingement angle significantly increased the peak value

of the stress (localized stress increase) rather than minimum

stress. The von Mises stress distribution corresponding to

Vgp200 m/s and Vgp400 m/s at a901 is shown in Fig. 8band d. An increase in the garnet particle velocity from 200 m/s to

400 m/s resulted in the formation of a new surface (subsurface)

due to the failure of surface elements, which could be observed as

patches of low von Mises stresses. A comparison of Fig. 5d

(NT-20) and Fig. 8b (NT-60) confirms that an increase in the

volume fraction of WC reduces the minimum value of equivalent

von Mises stress from 1.89 MPa to 0.49 MPa.In the slurry erosion process, the internal energy of the target

material raises as the erodent particle impinges on it. This raise in

internal energy may be correlated to the erosion behavior of different

materials for different garnet particle characteristics (morphology,

impingement velocity, angle of impact etc.). The internal energy of

each finite element within the target material can be estimated based

on the six components of stress and strain expressed by [20]

IEnew IEold X6

1

stress incremental strain volume 8

where the left hand side and the first term on the right hand side of

Eq. (8) indicates the internal energy at the current time step, and the

previous time step, respectively.

Fig. 9. The effect of garnet particle velocity on the: (a) time dependent internal energy of the single-layer NT-60 deposit; (b) erosion rate of the AISI 4140 steel and single-

layer NT-20 and NT-60 deposits.

Fig. 8. Effect of velocity of garnet particle (Vgp) on von-Mises equivalent stress distribution in single-layer NT-60 deposit at lower and maximum impingement angles

(a151 and a901): (a) and (b) Vgp 200 m/s; (c) and (d) Vgp400 m/s.

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The time dependent internal energy within the single-layer

NT-60 deposit for a combination of two different garnet particle

velocities (Vgp 200 m/s and 400 m/s) and two different impinge-

ment angles (a151 and a901) is presented in Fig. 9a. Thegarnet particle size in this simulation was 250 mm. As expected,the internal energy of the NT-60 deposit attains a maximum value

of 0.18 J after the impingement of eight garnet particles (cubical

and spherical) at Vgp400 m/s. The curve corresponding to the

time dependent internal energy at Vgp400 m/s and at a151

indicates that the internal energy stored in the deposit was higher

than that for the erosion condition corresponding to Vgp200 m/s

and a 901. This confirms that a combination of low a (151) andhigh Vgp (400 m/s) can cause severe damage to target material

when compared to a combination of maximum a (901) and lowVgp (200 m/s).

The simulated erosion rate of AISI 4140 steel, single-layer

NT-20, and a NT-60 deposit for different velocities (from 100 m/s

to 500 m/s) of garnet particle is shown in Fig. 9b. The garnet

particle size was 250 mm and the other erosion conditions wereidentical to the ones stated in the description corresponding to

Fig. 5. This result reveals that irrespective of the material the

velocity of the garnet particle and the erosion rate are propor-

tional. A closer examination of Fig. 9b indicates that the raise in

erosion rate was sharp___from 100 m/s to 200 m/s with respect to

200 m/s to 500 m/s. This change in slope of erosion rate vs

erodent velocity curve could be due to the failure of the garnet

particle at the higher velocities.

The study shows that the increase in velocity of the garnet

particle increases both the magnitude and the area of equivalent

von Mises stress, time dependent internal energy and the erosion

rate of the target material.

3.5.3. The effect of garnet particle size on stress and erosion rate

The cross-sections of single-layer NT-20 deposit showing the

effect of garnet particle size on the von Mises equivalent stress

distribution is illustrated in Fig. 10a through Fig. 10d. The garnet

particle at a mass flow rate of 2.0 g/s was allowed to impinge the

NT-20 deposit over a time period of 0.25 ms. Based on this, the

number of garnet particles (the total number of erodent particles

impinging on the target material was estimated by dividing the

total mass of the erodent released during the simulation time by

the mass of single particle)were 2 and 15, corresponding to the

size of the garnet particle 500 mm and 250 mm, respectively. Thevelocity of the cubical shaped garnet particle was 300 m/s.

Fig. 10a and Fig. 10b represent the von Mises equivalent stress

distribution after the impingement of 2 and 15 garnet particles at

a151, respectively. Note that a large number of smaller particleimpingements at random locations result in a near uniform

distribution of von Mises equivalent stress. Interestingly, themagnitude of stress in 15-garnet particle impingement is higher

than in 2-garnet particle impingement though the mass of a

garnet particle of 250mm in diameter is almost eight timessmaller than the mass of a garnet particle of 500 mm in diameter.This could be due to the fact that the algebraic sum of the contact

area of the smaller garnet particles that established contact with

the target material was larger than the contact area of the larger

garnet particles. For example, the maximum algebraic sum of the

estimated contact area for the two cubical shaped garnet particles

of 500mm size is 500,000mm2 (500 mm 500 mm 2 mm 500,000 mm2). This confirms that the contact area determinesthe stress distribution in this case rather than the mass of the

particle. A similar trend can be clearly observed at the maximum

impingement angle a901 (see Fig. 10 c and d). A comparison ofFig. 10c and d demonstrates that the larger particle impingement

at a maximum impingement angle resulted an increase in the

depth of the stress distribution.

The relation between the erosion rate and the size of the

garnet particles for three different materials at a901 is displayedin Fig. 11. For a constant velocity of garnet particle (Vgp300 m/s)

an increase in the size of the particle increased the erosion rate of

AISI 4140 steel in all the cases studied here. It is noteworthy that

an increase in the erosion rate of AISI 4140 was lower when the

garnet particle reached a size of 325 mm. The erosion rate of boththe single-layer deposits of NT-20 and NT-60 followed the similar

trend observed in AISI 4140. A closer examination of the single-

layer deposits of NT-20 and NT-60 revealed that the erosion rate

declines with an increase in the garnet particle size after 325 mm.This behavior is predominant in single-layer NT-60 deposit. This

is due to the fact that an increase in the size of the garnet particle

beyond 325 mm causes failure of particles at Vgp300 m/s. Thisfailure, resulting in loss of kinetic energy, subsequently lowers the

Fig. 10. Cross-sections of single-layer NT-20 deposits showing the effect of erodent size on von-Mises equivalent stress distribution: (a) and (b) corresponding to 250 mm

and 500 mm at a151

; (c) and (d) corresponding to 250 mm and 500 mm at a901

.




erosion rate [15]. This effect can be clearly seen in a single-layer

NT-60 deposit due to the higher volume fraction of WC, which in

turn causes more intense fracturing of the garnet particles.

3.5.4. Effect of garnet particle shape on stress and erosion rates

Cross-sections of a single-layer NT-60 deposit showing the

effect of equal size of three different shapes (cubical, spherical,

and trigonal) of garnet particle on the von Mises equivalent stress

distribution at a151

and a901

are presented in Fig. 12athrough 12f. The mass flow rate, velocity, and the size of the

garnet particle were 2 g/s, 300 m/s and 300 mm.Two important observations can be made from these results.

First, the von Mises stress distribution, corresponding to cubical

and spherical shaped garnet particle at a 151 (see Fig. 12a and b),demonstrates that the cubical shaped garnet particle exhibits a

combination of lesser value of peak stress (759 MPa) and higher

value of minimum stress (0.18 MPa), when compared to the latter

(spherical) where the peak stress and the minimum stress values

were 836 MPa and 0.02 MPa. This trend was consistent at a901(see Fig. 12d and e) which confirms that irrespective of the

impingement angle the cubical shaped garnet particle elevates

the overall stress distribution of the target material (deposit)

more effectively than the spherical shaped garnet particle.

The higher value of peak stress observed in the spherical garnet

particle impingement may be due to the point contact (high stress

concentration) nature of it with the target material. Second, the

cubical garnet particle causes more damage to the target material.

The presence of multiple cutting edges in the cubical garnet

particle leads to a deeper penetration into the target material,

subsequently resulting in severe deformation as shown in Fig. 12.

In contrast, though the sharp edge or corner increases both the

stress concentration and the depth of penetration, the value ofpeak stress (at a constant Vgp) depends on the mass of the garnet

particle as well as the location of the impingement (whether the

garnet particle impinges on the matrix or reinforcement particle

or on both). Because the volume of the equal size of the cubical,

spherical, and trigonal shaped garnet particles are different

(Vcubical4Vspherical4Vtrigonal) the mass of these particles are also

different (i.e., mcubical4mspherical4mtrigonal). Hence, it can be

stated that the severe damage in the cubical shaped particle

impingement originates from the difference in mass. This effect

can be seen from the peak stress corresponding to the trigonal

shaped garnet particle (see Fig. 12c and f). Nevertheless, the peak

stress value of the cubical and trigonal shaped garnet particles are

comparable at a901 (see Fig. 12d and f).The depiction of the time dependent energy in respect to the

spherical and cubical shaped garnet particles at a151 and a901(see Fig. 13) reflects the trend observed in the stress distribution.

A maximum internal energy of 0.08 J was incurred after the

impingement of cubical shaped garnet particles. This result confirms

that the raise in energy is directly proportional to the raise in

minimum stress distribution within the target material.

3.5.5. The effect of material composition on stress distribution and

erosion rate

The effect of a soft interlayer on the von Mises equivalent stress

distribution is shown in Fig. 14a and b at a901. The mass flow rate,velocity, and the size of the cubical shaped garnet particle was 2 g/s,

400 m/s, and 300mm. The stress distribution corresponding to thesingle-layer NT-60 deposit (Fig. 14a) indicates that the maximum

and minimum value of stress is 1520 MPa and 1.04 MPa, respec-

tively. Fig. 14b shows the two-layer NT-60 over NT-20 deposits.

An introduction of soft interlayer (NT-20) between the NT-60 andFig. 11. Effect of size of the garnet particle on the erosion rate of the AISI 4140

steel and single-layer deposits of NT-20 and NT-60.

Fig. 12. Cross-sections of single-layer NT-60 deposit showing the effect of erodent shape on von-Mises equivalent stress distribution: (a)(c) corresponding to cubical,

spherical and trigonal shaped garnet particles at a151, respectively; (d)(f) corresponding to cubical, spherical, and trigonal shaped garnet particles at a901,

respectively.



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AISI 4140 steel shows a significant reduction in both the peak stress

(1450 MPa) and minimum stress (0.92 MPa) when compared to the

single-layer NT-60 deposit. The reduction of minimum stress can be

attributed to an increase in the volume of the deposit. It is worth-

while to note that the stress distribution extends in the thickness

direction in the case of the two-layer composite (NT-60 over NT-20)

when compared to the single-layer deposit. This indicates that an

addition of soft interlayer absorbs the energy more effectively,

resulting in the reduction of the peak stress value. A closer examina-tion on the deformation profile at the garnet particle impingement

location delineates that the two-layer deposit (Fig. 14b) deform lesser

than the single-layer deposit (Fig. 14a). This demonstrates that the

stress absorption reduces the severity of deformation.

To show the effect of layer thickness on stress distribution, an

NT-20 deposit of thickness 0.5 mm and 1.0 mm was considered. The

results, corresponding to two different thicknesses at a901, ispresented in Fig. 15. As expected, both the peak stress and minimum

stress in the 0.5 mm thick NT-20 deposit (Fig. 15b) were higher than

those for the 1.0 mm thick NT-20 deposit (Fig. 15b). Note that the

extent of deformation was almost identical in both cases. However,

increasing the layer thickness resulted in local stress reduction as a

result of better energy absorption.

Fig. 16 illustrates the effect of the volume fraction of the WC in

Ni-matrix on the erosion rate at three different impingement

angles (a451, a701, a901). In this study, a simulation time of0.25 ms was used. The mass flow rate of garnet particles was

4.53 g/s and the particle sizes range from 100 mm to 400 mm andfour different shapes (see Fig. 2) were used. The initial velocity of

the garnet particle was 200 m/s. Initially, for all three impinge-

ment angles, the erosion rate decreased with an increase in the

volume fraction of WC and reached a minimum value at 40%

volume fraction of WC. When the volume fraction of the WC was

further increased the erosion rate slowly rose and drastically

increased when the volume fraction of WC reached a value of 70%.

This can be explained by the fact that beyond a critical volume

fraction of the WC particles, the matrix material which acts as an

impact energy shock absorber does not transfer (spread) the

received energy from the garnet particle to the neighboring material.

In other words, an excessive volume of WC particles may provide

more resistance to erosion attack, but the poorer absorption of

energy due to the lack of Ni-matrix result in the accumulation of

internal energy within a very narrow region. This local increase in an

internal energy can raise the magnitude of the local plastic strain,subsequently forming the crack when the plastic strain reaches the

critical plastic strain (or stress) of the Ni/WC. The successive

impingement of garnet particles causes the crack to grow. Finally,

the coalescence of a number of cracks forms the crack network

resulting in the failure of the material [15]. This relationship

between the volume fraction of the WC and the erosion rate is in

good agreement with the experimental result (i.e., the NT-80 deposit

display a higher erosion rate than the NT-60 deposit). Chen and

Li [9] observed this type of erosion behavior in a Cu/SiC composite

material and reported that a 30% volume fraction of SiC in

Cu provided better erosion resistance. A similar observation was

reported in the other composite material such as NiWC [30] and in

H13 steelTiC [31].

Fig. 13. The effect of erodent shapes on the time dependent internal energy of the

single-layer NT-60 deposit.

Fig. 14. Cross-sections show the effect of the interlayer on von-Mises equivalent stress distribution: (a) single-layer NT-60 deposit at a901; (b) two-layer NT-60 over

NT-20 at a901.

Fig. 15. Cross-sections show the effect of layer thickness on von-Mises equivalent

stress distribution at a 901 in NT-20 deposit of thickness: (a) 0.5 mm; (b) 1.0 mm.

Fig. 16. The effect of the volume fraction of the WC in Ni-matrix on erosion rate at

different impingement angles.



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In summary, the simulation results show that the volume

fraction of the Ni-matrix determines the energy absorption within

the target material and the WC is responsible for restraining the

number of damage site caused by the garnet particle.

4. Conclusions

A dynamic model was developed based on the commercial finite

element code ANSYS LS-DYNA in order to study the effect of

different erosion conditions such as garnet particle morphology

(size and shape), angle of impingement, and its velocity on stress

distribution, energy absorption, and the erosion rate of AISI 4140

steel and different compositions of single and multi-layered NiWC

based metal ceramic composite material. The numerical results

provide guidelines for choosing suitable NiWC composition needed

to minimize the erosion over a wide range of erosion conditions. The

following conclusions were drawn based on the results of the

numerical study.

(a) The erosion mechanism for AISI 4140 steel followed typical

ductile properties (ploughing and cutting deformation) while

the mechanism for the NiWC composite material involved

both the ductile and brittle erosion mechanisms dependingon the erosion condition.

(b) Irrespective of the material, a garnet particle with multiple

sharp edges caused more damage to the target material at all

impingement angles.

(c) At a higher velocity of garnet particle (4300 m/s) an increase

in garnet particle size beyond 325 mm resulted in a reductionof erosion rate due to the fracturing of the garnet particle for

the particular material properties of garnet particle studied.

(d) A presence of NT-20 interlayer between the NT-60 layer and

substrate absorbed the impact energy more effectively than a

single-layer of NT-60 on substrate and reduced the extent of

deformation due to the reduction in the peak stress.

(e) The critical volume fraction of WC in Ni-matrix that provided

a minimum erosion rate was in the range of 4050%.(f) The developed model can be used to estimate the erosion

behavior of any (monolithic and/or composite) material

combination in a wide range of erosion conditions using a

suitable material behavior model.

(g) It is concluded that the slurry erosion resistance of the AISI

4140 steel can be significantly enhanced by introducing a

multilayered deposit of NiWC composite material produced

by the laser-based powder deposition process.

Acknowledgement

This work was financially supported by NSF Grant No. IIP-

1034652. The authors acknowledge Mr. Andrzej Socha for his help

in conducting the experiments.

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Prabu Balu_Finite elementmodelingofsolidparticleerosioninAISI4140steeland nickel–tungstencarbidecompositematerialproducedbythelaser-based powder depositionprocess_Tribology international_2005