# Experimental Evaluation of Erosion of Gunmetal under Asymmetrical Shaped Sand Particle

Authors: Mohammad Asaduzzaman Chowdhury; Uttam Kumar Debnath; Dewan Muhammad Nuruzzaman; Md. Monirul Islam
Journal: Advances in Tribology
 (2015)

---

## Abstract

The erosion characteristics of gunmetal have been evaluated practically at different operating conditions. Asymmetrical silica sand (SiO2) is taken into account as erodent within range of 300–600 μm. The impact velocity within 30–50 m/sec, impact angle 15–900, and stand off distance 15–25 mm are inspected as other relevant operating test conditions. The maximum level of erosion is obtained at impact angle 15° which indicates the ductile manner of the tested gunmetal. The higher the impact velocity, the higher the erosion rate as almost linear fashion is observed. Mass loss of gunmetal reduces with the increase of stand-off distance. A dimensional analysis, erosion efficiency (η), and relationship between friction and erosion indicate the prominent correlation. The test results are designated using Taguchi’s and ANOVA concept. S
/
N ratio indicates that there are 1.72% deviations that are estimated between predicted and experimental results. To elaborately analyze the results, ANN and GMDH methods are mentioned. After erosion process of tested composite, the damage propagation on surfaces is examined using SEM for the confirmation of possible nature of wear behavior. The elemental composition of eroded test samples at varying percentage of gunmetal is analyzed by EDX analysis.


---

## Body

## 1. Introduction

Erosion is described as the progressive loss of original material from a solid surface due to mechanical interaction between the surfaces and impinge solid or liquid particle which may be a multicomponent fluid or impinging solid or liquid particles also. Erosive damages of different materials in modern technological systems are very concerning issue for sustainability of the materials with these adverse conditions. In advanced engineering and industrial field, light weight of materials has several applications for minimizing the operating as well as initial investment cost. In different environmental conditions, wind turbine, blower fan blade, hydraulic turbine impellers, and the moving components of ship, aircraft, train, and automobile structure made by different metals and alloys experience the difficulty of impingement of solid particles in the form of erosion. Gunmetal can be used extensively in erosive wear environment for its simple manufacturing technique, suitability for design of different systems and mechanisms, and lower manufacturing cost. Concerning these facts, the gunmetal has been chosen as test samples to examine the erosion resistance at different operating conditions so that the exact nature of erosion can be identified.The researches have been done by the different tribology research groups [1–6] who realized that erosive wear of materials is related to the various factors such as impingement angle, impact velocity, particle size, particle shape, particle type, particle flux, temperature, nozzle geometry, type of materials, hardness of the materials, stand-off distance, test duration, and roughness of the tested materials. Among these factors impingement angle and impact velocity have been recognized as two parameters that noticeably influence the erosion rates of different materials [7]. The erosive behavior of AISI 440C stainless steel and a cermet has been conducted by researchers [8] who observed that both of the materials exhibited noticeable plasticity during impact conditions, but in case of stainless steels which has been characterized by being more ductile in nature. The blending conditions of materials, temperature, pressure, and flow can create the erosive-corrosive wear especially for metal and alloys [9]. Rather than different mechanical properties and operating conditions material hardness has certain amount of role to propagate erosion damage throughout the metals and alloys [10].The previous works [1–10] on metal and alloys varying with different operating and processing conditions as well as mechanical properties and varying percentage of material-combinations on erosion of materials cannot suggest any unique trends of the results. Therefore, the objective of this work is to investigate the erosive wear performance of gunmetal under several test conditions to understand the possible nature of erosion. A dimensional analysis indicates that there is a significant relation between erosion rate and Uttam Number (U. No.). In addition to that, dependency level of theoretical friction coefficient and erosion rate are observed. To analyze the obtained results in board concept, Taguchi, ANOVA, erosion efficiency, ANN, and GMDH approach have been discussed. The morphology of damage surface incorporating possible nature has been analyzed using SEM. The elemental composition of different locations of eroding gunmetal surfaces is obtained by EDX analysis.


## 2. Experimental Details

### 2.1. Materials Properties, Preparation, and Method of Erosion Measurement

The measured mechanical properties of tested gunmetal are listed in Table1. Rectangle type specimens with a size of 50 mm × 30 mm × 5 mm were prepared by utilizing a diamond cutter from injection moulded plaques. Before the erosive wear tests, all specimens were cleaned with acetone. Great care was given to ensure clean surface before and after wear tests. Sand and dust particles were cleaned after erosion test with air blasting and then balanced carefully.Table 1
Mechanical and related properties of gunmetal.
Property
Standard value (S.I.)
Actual or measured data
Units (S.I.)
Density
8719
8710
kg/m3
Tensile yield strength
110
118
MPa
Ultimate tensile strength
220
225
MPa
Hardness
80
85
HBDifferent grain size (300–355, 355–500, and 500–600 microns) with irregular shape (combination of rounded, slightly rounded, and angular) dry quartz type silica sand (hardness 42, 43.2, and 44 MPa, density 1436, 1440, and 1443 kg/m
3) of chemical composition SiO2 was used as an erodent particle. Motor type vibration sieve machine (model: VSS-T, Vinsyst Technologies, ISO 900, India) with measuring range 97 μm to 4 mm was used to measure the particle size.The weight of the samples before and after erosion process was measured by using precision digital electronic balance (model: SP404D, Sciencetech Inc., USA). Erosion rates were calculated from the differences of weight loss by considering unit of timeE
R
=
W
b
e
f
o
r
e
-
W
a
f
t
e
r
/
T
i
m
e.The flow pattern of abrasive particle is related to different factors, such as type of erodent materials, chemical composition, hardness, density, particle shape, and particle size and impact resistance. At the time of the experiment, under lower impact velocity, the pattern of flow of abrasive particle was realized almost similar to the laminar nature but with the increase of velocity laminar as well as turbulent combination of flow pattern being observed. But the changing of impact angles may have some role for characterizing the flow of abrasive particle. In fact, there were different modes of effect of flowing abrasive under different operating conditions. In this context, elastic/plastic deformation by sliding-rubbing grain movement, elastic/plastic deformation by rolling grain movement, chip formation (microcutting) by rubbing grain movement, ridges formation by rubbing and rolling grain movement, and low-cycle fatigue wear were identified. To ensure the exact abrasive flow, more researches can be conducted in future study relevant to experimental and analytical point of view.


### 2.2. Test Apparatus

A sand blast erosive wear testing device was designed and fabricated to understand the erosion process, as shown in Figure1. In this sand blast erosion test rig, sand was ejected from the nozzle by high pressure air to strike the test sample. A geared motor was fixed to a horizontal frame and connected to a cylindrical hollow shaft by a belt and pulley. A hopper was connected to the upper portion of the cylindrical hollow shaft by threads.Figure 1
Schematic diagram of the solid particle erosion rig.An air-sand mixing chamber was connected to the other part of cylindrical hollow shaft, the upper part of which was connected with the compressor with a hose and the lower part attached to a 5 mm converging nozzle. Compressor pressure was controlled by a pressure valve attached to the upper part of the mixing chamber. The motor was run at 60 rpm to transmit sand from the hopper to the mixing chamber at a constant rate via the feed gear. Air and sand were mixed in the mixing chamber and, as a result of high air pressure, sand was ejected through the nozzle at high impingement velocity. A sample holder was fixed in the horizontal plane and was designed to maintain the stand-off distance and to vary the test sample angle from 0 to 90°.


### 2.3. Selection of Number of Observations

The criteria of selection of number of observations of each experiment are the justification of ensuring the accuracy level of tested results. The equation mentioned below is used to validate the selection of number of cycles under certain confidence level within certain accuracy:(1)n=zsAx-2,where n is number of observations that should be taken to provide desired accuracy. Z is Normal deviate for desired confidence level. S
=
∑
x
2
-
∑
x
2
/
n
′
/
n
′
-
1 is estimated standard deviation for the distribution of element time based on observations already made. A is accuracy desired expressed as decimal fraction of true value. x
- is mean of the erosion values, already collected. n
′ is number of observations already made.For the confirmation of accuracy of the test results, the selections of the number of experimental observations were selected using (1). The basis of number of repeatabilities of each experiment at identical test conditions ensures the confidence level within desired accuracy. At the time of designing the number of observations, 95% confidence level within 2% accuracy was considered.


### 2.4. Particles Velocity Measuring Method

The double disc process was adapted to estimate the impingement velocity of solid particles. The method used for calculating particle velocity is illustrated in Figure2. A 15 mm diameter vertical circular stainless steel 304 rod was connected at the top and bottom with 150 mm diameter circular plates and a 1.5 mm hole in the top plate. The high velocity sand was directed on the static top plate hole and, as a consequence, color damage (A) was created on the static lower plate. Then the two horizontal plates were rotated, further color damage (B) was obtained on the lower plate by the sand. The angular displacements of A and B were estimated, and the following formula (2) used to estimate the impingement velocity:(2)V=2πRvLS,where L is the distance between the top and bottom plates, v is the rotational rpm of top and bottom plates, R is the radius from the center of the bottom plate to point B, and S is the angular distance between the two areas of color damage. The impingement velocity calibrations at different pressures are summarized in Table 2.Table 2
The impact velocity calibration at various pressure.
Pressure (bar)
Speed of the rotating disc (rpm)
Linear separation of two marks (mm)
Impact velocity (m/s)
Average impact velocity (m/s)
3.5
6.2
49.61
4700
6.3
48.83
50
6.1
50.42
3
7.4
39.98
4500
7.2
40.88
40
7.4
39.78
2
8.7
30.07
4000
8.5
30.75
30
8.6
30.42Figure 2
Schematic diagram of methodology used for velocity calibration.


### 2.5. ANN Concept

In general, erosive wear is related to variable factors such as impingement velocity, impingement angle, particle size, and stand-off distance. In addition, solid particle flowing parameters are important conditions that affect erosion. Although the solid particle flowing technique has some unknown parameters, these factors should not be ignored, in spite of the difficulty in determining or identifying them. Numerical or finite element techniques can be used to identify hidden factors. However, these techniques tend to be complex, and simple linear regression method does not adequately explain the nonlinearity of the results. Therefore, artificial neural networks (ANN) can be utilized, and ANN models can predict outcomes with a certain level of accuracy, even when the variable relationships are uncertain. In ANN, data-based phenomena are used to predict and examine property-based parameters. Our ANN methodology expresses stored data development, implementation code, and prediction-based outcomes in erosive wear.


### 2.6. NEURAL Analysis

In this analysis, impact velocity, impact angle, erodent size, and stand-off distance are considered the input layer during training. These parameters are distinct and recognized as four input neurons. The database was constructed by considering individual parameters across a range. Actual test data sets were utilized to train the ANN. The database was classified into three regions: (a) validation region, which describes the ANN architecture and accommodates neurons of a distinct layer, (b) a training region, useful for controlling the network weights, and (c) a testing region, relevant for data validation. Input parameters were normalized to the range 0 to 1. Approximately 27 data points were collected to train the neural network. Several ANN structures (Input-Hidden-Output), together with a variable quantity of neurons in the hidden layer, were examined for a fixed cycle, learning rate, error tolerance, momentum parameter, noise factor, and slope parameter. Depending on the minimum number of errors selected, the structure displayed in Table3 was chosen for training the input-output data. The network optimization process (training and testing) was conducted over 2,000,000 cycles, over which error stabilization was achieved. Neuron numbers in the hidden layer were varied and, in the optimized network, found to be 12. The number of cycles selected during training was high enough for rigorous training of the ANN models. Just NN software was used, programmed with a back propagation algorithm, to apply the approach for predicting sample erosion in various test situations. The three-layer neural network with an input layer incorporating 4 input nodes, a hidden layer with 12 neurons, and an output layer with 1 output node is shown in Figure 3.Table 3
Selection of input criterion for training.
Input parameters for training
Values
Error tolerance
0.0002
Learning parameter (β)
0.2
Momentum parameter (α)
0.003
Noise factor (NF)
0.0001
Maximum cycles for simulations
2000000
Slope parameter (£)
0.07
Number of hidden layer neurons
12
Number of input layer neurons (I)
4
Number of output layer neurons (O)
1Figure 3
ANN concept viewing three layers.


### 2.7. Signal-to-Noise (S
/
N) Ratio

The Taguchi concept emphasizes mathematical modeling to reduce time-consumption of experiments and testing by considering parametric optimization when estimating stable erosion under reasonable factors. Detailed explanation and clarification of controllable experiments to identify the ideal considerations in the DOE (design of experiment) is an effective analysis process. The choice of control and fixed parameters is important in DOE, and, in this respect, a large number of factors are incorporated to identify less important variables as early as possible. In previous studies, erosion of polymers and composites was mainly dependent on the impingement velocity; controlling and constant factors are listed in Table4. Considering the L27 (43) orthogonal array design concept, the significance of four variable factors at four different stages are designated.Table 4
Parameters of the setting.
Fixed parameters
Fixed conditions/values
Control factor
Symbols
Nozzle diameter (mm)
5
Velocity of impact
A
Length of nozzle (mm)
55
Angle of impingement
B
Erodent
Silica sand under dry condition
Erodent size
C
Erodent shape
Irregular
Stand-off distance
D
Test temperature
Room temperature
Erodent feed rate gm/sec
4.56
Erodent microhardness (HV)
42–44The first column indicates variable parameters and the corresponding rows show the experimental conditions expressed in Table5 as a blending of parameter levels. Four variable factors at four stages produce 4
3
=
64 runs in a full factorial experiment. On the other hand, Taguchi’s factorial technique minimizes it to 27 runs, providing a better representation of the results.Table 5
Levels for various control factors.
Control factor
Level
Units
I
II
III
1
A: velocity of impact
30
40
50
(m/s)
2
B: angle of impingement
30
60
90
(Deg)
3
C: erodent size
300–355
355–500
500–600
(μm)
4
D: stand-off distance
15
20
25
(mm)The number of tests is characterized as aS
/
N (signal-to-noise) ratio, of which several versions exist based on the type of characteristics. The analyzed ratio related to small amounts of erosive damage in the case of smaller is the better characteristic. Using this approach, this is determined as a logarithmic formulation of the loss function as follows.In the case of less being the improved quality characteristic, this can be estimated using the following formula:(3)SN=-10log⁡1n∑y2,where n is the number of observations and y is the observed data. Less is regarded as the improved characteristic with respect to the S
/
N ratio transformation and is suitable for reducing the erosion rate. The design of the experiment is shown in Table 6, where the second, third, fourth, and fifth columns are designated as impact velocity (1
A), impingement angle (2
B), erodent size (3
C), and stand-off distance (4
D), respectively.Table 6
Orthogonal array for L16 (44) Taguchi design.
L27 (43)
1
A
2
B
3
C
4
D
1
1
1
1
1
2
1
1
2
2
3
1
1
3
3
4
1
2
1
2
5
1
2
2
3
6
1
2
3
1
7
1
3
1
3
8
1
3
2
1
9
1
3
3
2
10
2
1
1
2
11
2
1
2
3
12
2
1
3
1
13
2
2
1
3
14
2
2
2
1
15
2
2
3
2
16
2
3
1
1
17
2
3
2
2
18
2
3
3
3
19
3
1
1
3
20
3
1
2
1
21
3
1
3
2
22
3
2
1
1
23
3
2
2
2
24
3
2
3
3
25
3
3
1
2
26
3
3
2
3
27
3
3
3
1


## 2.1. Materials Properties, Preparation, and Method of Erosion Measurement

The measured mechanical properties of tested gunmetal are listed in Table1. Rectangle type specimens with a size of 50 mm × 30 mm × 5 mm were prepared by utilizing a diamond cutter from injection moulded plaques. Before the erosive wear tests, all specimens were cleaned with acetone. Great care was given to ensure clean surface before and after wear tests. Sand and dust particles were cleaned after erosion test with air blasting and then balanced carefully.Table 1
Mechanical and related properties of gunmetal.
Property
Standard value (S.I.)
Actual or measured data
Units (S.I.)
Density
8719
8710
kg/m3
Tensile yield strength
110
118
MPa
Ultimate tensile strength
220
225
MPa
Hardness
80
85
HBDifferent grain size (300–355, 355–500, and 500–600 microns) with irregular shape (combination of rounded, slightly rounded, and angular) dry quartz type silica sand (hardness 42, 43.2, and 44 MPa, density 1436, 1440, and 1443 kg/m
3) of chemical composition SiO2 was used as an erodent particle. Motor type vibration sieve machine (model: VSS-T, Vinsyst Technologies, ISO 900, India) with measuring range 97 μm to 4 mm was used to measure the particle size.The weight of the samples before and after erosion process was measured by using precision digital electronic balance (model: SP404D, Sciencetech Inc., USA). Erosion rates were calculated from the differences of weight loss by considering unit of timeE
R
=
W
b
e
f
o
r
e
-
W
a
f
t
e
r
/
T
i
m
e.The flow pattern of abrasive particle is related to different factors, such as type of erodent materials, chemical composition, hardness, density, particle shape, and particle size and impact resistance. At the time of the experiment, under lower impact velocity, the pattern of flow of abrasive particle was realized almost similar to the laminar nature but with the increase of velocity laminar as well as turbulent combination of flow pattern being observed. But the changing of impact angles may have some role for characterizing the flow of abrasive particle. In fact, there were different modes of effect of flowing abrasive under different operating conditions. In this context, elastic/plastic deformation by sliding-rubbing grain movement, elastic/plastic deformation by rolling grain movement, chip formation (microcutting) by rubbing grain movement, ridges formation by rubbing and rolling grain movement, and low-cycle fatigue wear were identified. To ensure the exact abrasive flow, more researches can be conducted in future study relevant to experimental and analytical point of view.


## 2.2. Test Apparatus

A sand blast erosive wear testing device was designed and fabricated to understand the erosion process, as shown in Figure1. In this sand blast erosion test rig, sand was ejected from the nozzle by high pressure air to strike the test sample. A geared motor was fixed to a horizontal frame and connected to a cylindrical hollow shaft by a belt and pulley. A hopper was connected to the upper portion of the cylindrical hollow shaft by threads.Figure 1
Schematic diagram of the solid particle erosion rig.An air-sand mixing chamber was connected to the other part of cylindrical hollow shaft, the upper part of which was connected with the compressor with a hose and the lower part attached to a 5 mm converging nozzle. Compressor pressure was controlled by a pressure valve attached to the upper part of the mixing chamber. The motor was run at 60 rpm to transmit sand from the hopper to the mixing chamber at a constant rate via the feed gear. Air and sand were mixed in the mixing chamber and, as a result of high air pressure, sand was ejected through the nozzle at high impingement velocity. A sample holder was fixed in the horizontal plane and was designed to maintain the stand-off distance and to vary the test sample angle from 0 to 90°.


## 2.3. Selection of Number of Observations

The criteria of selection of number of observations of each experiment are the justification of ensuring the accuracy level of tested results. The equation mentioned below is used to validate the selection of number of cycles under certain confidence level within certain accuracy:(1)n=zsAx-2,where n is number of observations that should be taken to provide desired accuracy. Z is Normal deviate for desired confidence level. S
=
∑
x
2
-
∑
x
2
/
n
′
/
n
′
-
1 is estimated standard deviation for the distribution of element time based on observations already made. A is accuracy desired expressed as decimal fraction of true value. x
- is mean of the erosion values, already collected. n
′ is number of observations already made.For the confirmation of accuracy of the test results, the selections of the number of experimental observations were selected using (1). The basis of number of repeatabilities of each experiment at identical test conditions ensures the confidence level within desired accuracy. At the time of designing the number of observations, 95% confidence level within 2% accuracy was considered.


## 2.4. Particles Velocity Measuring Method

The double disc process was adapted to estimate the impingement velocity of solid particles. The method used for calculating particle velocity is illustrated in Figure2. A 15 mm diameter vertical circular stainless steel 304 rod was connected at the top and bottom with 150 mm diameter circular plates and a 1.5 mm hole in the top plate. The high velocity sand was directed on the static top plate hole and, as a consequence, color damage (A) was created on the static lower plate. Then the two horizontal plates were rotated, further color damage (B) was obtained on the lower plate by the sand. The angular displacements of A and B were estimated, and the following formula (2) used to estimate the impingement velocity:(2)V=2πRvLS,where L is the distance between the top and bottom plates, v is the rotational rpm of top and bottom plates, R is the radius from the center of the bottom plate to point B, and S is the angular distance between the two areas of color damage. The impingement velocity calibrations at different pressures are summarized in Table 2.Table 2
The impact velocity calibration at various pressure.
Pressure (bar)
Speed of the rotating disc (rpm)
Linear separation of two marks (mm)
Impact velocity (m/s)
Average impact velocity (m/s)
3.5
6.2
49.61
4700
6.3
48.83
50
6.1
50.42
3
7.4
39.98
4500
7.2
40.88
40
7.4
39.78
2
8.7
30.07
4000
8.5
30.75
30
8.6
30.42Figure 2
Schematic diagram of methodology used for velocity calibration.


## 2.5. ANN Concept

In general, erosive wear is related to variable factors such as impingement velocity, impingement angle, particle size, and stand-off distance. In addition, solid particle flowing parameters are important conditions that affect erosion. Although the solid particle flowing technique has some unknown parameters, these factors should not be ignored, in spite of the difficulty in determining or identifying them. Numerical or finite element techniques can be used to identify hidden factors. However, these techniques tend to be complex, and simple linear regression method does not adequately explain the nonlinearity of the results. Therefore, artificial neural networks (ANN) can be utilized, and ANN models can predict outcomes with a certain level of accuracy, even when the variable relationships are uncertain. In ANN, data-based phenomena are used to predict and examine property-based parameters. Our ANN methodology expresses stored data development, implementation code, and prediction-based outcomes in erosive wear.


## 2.6. NEURAL Analysis

In this analysis, impact velocity, impact angle, erodent size, and stand-off distance are considered the input layer during training. These parameters are distinct and recognized as four input neurons. The database was constructed by considering individual parameters across a range. Actual test data sets were utilized to train the ANN. The database was classified into three regions: (a) validation region, which describes the ANN architecture and accommodates neurons of a distinct layer, (b) a training region, useful for controlling the network weights, and (c) a testing region, relevant for data validation. Input parameters were normalized to the range 0 to 1. Approximately 27 data points were collected to train the neural network. Several ANN structures (Input-Hidden-Output), together with a variable quantity of neurons in the hidden layer, were examined for a fixed cycle, learning rate, error tolerance, momentum parameter, noise factor, and slope parameter. Depending on the minimum number of errors selected, the structure displayed in Table3 was chosen for training the input-output data. The network optimization process (training and testing) was conducted over 2,000,000 cycles, over which error stabilization was achieved. Neuron numbers in the hidden layer were varied and, in the optimized network, found to be 12. The number of cycles selected during training was high enough for rigorous training of the ANN models. Just NN software was used, programmed with a back propagation algorithm, to apply the approach for predicting sample erosion in various test situations. The three-layer neural network with an input layer incorporating 4 input nodes, a hidden layer with 12 neurons, and an output layer with 1 output node is shown in Figure 3.Table 3
Selection of input criterion for training.
Input parameters for training
Values
Error tolerance
0.0002
Learning parameter (β)
0.2
Momentum parameter (α)
0.003
Noise factor (NF)
0.0001
Maximum cycles for simulations
2000000
Slope parameter (£)
0.07
Number of hidden layer neurons
12
Number of input layer neurons (I)
4
Number of output layer neurons (O)
1Figure 3
ANN concept viewing three layers.


## 2.7. Signal-to-Noise (S
/
N) Ratio

The Taguchi concept emphasizes mathematical modeling to reduce time-consumption of experiments and testing by considering parametric optimization when estimating stable erosion under reasonable factors. Detailed explanation and clarification of controllable experiments to identify the ideal considerations in the DOE (design of experiment) is an effective analysis process. The choice of control and fixed parameters is important in DOE, and, in this respect, a large number of factors are incorporated to identify less important variables as early as possible. In previous studies, erosion of polymers and composites was mainly dependent on the impingement velocity; controlling and constant factors are listed in Table4. Considering the L27 (43) orthogonal array design concept, the significance of four variable factors at four different stages are designated.Table 4
Parameters of the setting.
Fixed parameters
Fixed conditions/values
Control factor
Symbols
Nozzle diameter (mm)
5
Velocity of impact
A
Length of nozzle (mm)
55
Angle of impingement
B
Erodent
Silica sand under dry condition
Erodent size
C
Erodent shape
Irregular
Stand-off distance
D
Test temperature
Room temperature
Erodent feed rate gm/sec
4.56
Erodent microhardness (HV)
42–44The first column indicates variable parameters and the corresponding rows show the experimental conditions expressed in Table5 as a blending of parameter levels. Four variable factors at four stages produce 4
3
=
64 runs in a full factorial experiment. On the other hand, Taguchi’s factorial technique minimizes it to 27 runs, providing a better representation of the results.Table 5
Levels for various control factors.
Control factor
Level
Units
I
II
III
1
A: velocity of impact
30
40
50
(m/s)
2
B: angle of impingement
30
60
90
(Deg)
3
C: erodent size
300–355
355–500
500–600
(μm)
4
D: stand-off distance
15
20
25
(mm)The number of tests is characterized as aS
/
N (signal-to-noise) ratio, of which several versions exist based on the type of characteristics. The analyzed ratio related to small amounts of erosive damage in the case of smaller is the better characteristic. Using this approach, this is determined as a logarithmic formulation of the loss function as follows.In the case of less being the improved quality characteristic, this can be estimated using the following formula:(3)SN=-10log⁡1n∑y2,where n is the number of observations and y is the observed data. Less is regarded as the improved characteristic with respect to the S
/
N ratio transformation and is suitable for reducing the erosion rate. The design of the experiment is shown in Table 6, where the second, third, fourth, and fifth columns are designated as impact velocity (1
A), impingement angle (2
B), erodent size (3
C), and stand-off distance (4
D), respectively.Table 6
Orthogonal array for L16 (44) Taguchi design.
L27 (43)
1
A
2
B
3
C
4
D
1
1
1
1
1
2
1
1
2
2
3
1
1
3
3
4
1
2
1
2
5
1
2
2
3
6
1
2
3
1
7
1
3
1
3
8
1
3
2
1
9
1
3
3
2
10
2
1
1
2
11
2
1
2
3
12
2
1
3
1
13
2
2
1
3
14
2
2
2
1
15
2
2
3
2
16
2
3
1
1
17
2
3
2
2
18
2
3
3
3
19
3
1
1
3
20
3
1
2
1
21
3
1
3
2
22
3
2
1
1
23
3
2
2
2
24
3
2
3
3
25
3
3
1
2
26
3
3
2
3
27
3
3
3
1


## 3. Results and Discussion

### 3.1. Influence of Impact Velocity

In erosion, the impingement velocity is related to the sustainability of the material’s life. The test conditions were randomly shaped sand of dimension 300–355, 355–500, and 500–600μm, stand-off distance 15 mm, and impingement angles 15, 30, and 60 degrees at ambient temperature. Under these test environments, erosion rates showed a sharp, increasing trend, with increases in velocity ranging from 30 to 50 m/sec for the tested gunmetal (Figures 4(a), 4(b) and 4(c)). Particles created a high impact of kinetic energy at high velocities, resulting in higher impact effect and greater erosion. In fact, particles occupy tremendous impact of kinetic energy at large velocity causing higher level of impacting effect and results in greater amount of erosion rate. In addition to that with increased velocity the duration between impacts is reduced and energy of the particle is increased which causes higher level of mass loss [17]. At 60-degree impact angle, the kinetic energies of 2052, 2793, 3648, 4617, and 5700 kg-m/sec were estimated for impact velocities of 30, 35, 40, 45, and 50 m/sec, respectively. Temperature variations were propagated throughout the sample surface with increasing velocities. However, due the effect of air-cooling during impaction by the compressor, the temperature increase is small. Nguyen et al. [18], Jha et al. [19], and ElTobgy et al. [20] reported a similar relationship between impingement velocity and erosion rate. Extended thermal characteristics have been observed at high velocities. Temperatures were elevated above ambient temperature level from 8 to 19 degrees for velocity increases between 30 and 50 m/sec. The increase in temperature may, in reality, be small due to rapid displacement of sand from the point of impact as well as cooling from the compressed pressure.Figure 4
Variation of erosion rate with the variation of impact velocity and erodent size (impact angle: (a) 15 degrees, (b) 30 degrees, and (c) 60 degrees and stand-off distance 15 mm).
(a)
(b)
(c)The least-squares fitting of actual data was conducted by applying the power law. Consequently, erodent particle velocities of 30 m/sec, 40 m/sec, and 50 m/sec at impingement angles of 15°, 30°, and 60° were taken in to consideration for these purposes.The relationship between stable erosive wear rate (E) and impingement velocity is stated as a simple power function: (4)E=kvn,where n is the velocity exponent and k is the proportionality constant impact on the other parameters. The influence of impact velocity on erosion rate of metals and alloys has been partially investigated. The velocity exponent (n) in general varies from 2 to 3 and 3 to 5 which indicate that the materials are ductile and brittle in nature, respectively [21]. The other mechanical properties (hardness, ultimate tensile strength, modulus of elasticity, fracture toughness, yield stress, yield strain, rebound resilience, etc.) can be correlated in this way.The fitting parameters are listed in Table7 and as an example the criteria of fitting calculation is expressed in Figures 5(a), 5(b), and 5(c) using GRAPHWIN software. Using the experimental data, calculated velocity exponents are obtained in the range of 0.78–0.91 for gunmetal at different impingement angle. This means that the findings of velocity exponents are found to be much lower than what have been mentioned by the different researchers for conformity of ductile behavior of tested material. In fact, the interesting observation in this study is that, in spite of the fact that the standard range for ductile material is within 2 to 3, it has been observed from the experimental data that the obtained velocity exponent range is true only for certain lower velocities and lower particle size. But at higher impact velocities, different erodent size, or particular shape of erodent, the velocity exponent can be found within the standard range. In this context, it can be realized that velocity exponent range varies with impact velocity, particular shape of erodent, and particle size. In case of coefficient of determination, relationship quality between erosion rate and impact velocity for exponential parameter is found to be stronger (99%) for test samples.Table 7
The power law calculated values at different impingement angles.
Tested material
Impingement angle (α, °)
k
n
R
2
Gunmetal
15
0.007346
0.7841
0.99
30
0.007340
0.7804
0.99
60
0.004123
0.9130
0.99Figure 5
Curve fitting using power law equation for experimental data between erosion rate and impact velocity (test sample: gunmetal: (a) impact angle 15 degrees, (b) impact angle 30 degrees, and (c) impact angle 60 degrees and particle size 500–600).
(a)
(b)
(c)


### 3.2. Influence of Impingement Angle

In order to study the effect of impingement angle on erosion rate, erosion tests were performed by varying the impact velocity from 30 to 50 m/s at impingement angles of 15° to 90° for different particle size. These results are presented in Figures6(a), 6(b), and 6(c) showing the influence of impingement angle on the erosion rate of gunmetal at different impact velocities and particle size. It can be seen that erosion rate is maximum at 15° impingement angle for gunmetal at different impact velocities and particle size studied. At impact angle 15° erosion rates are high and then decrease gradually up to the impingement angle 45°. After that erosion rate increases ranging from 45° to 90°, in general, for all tested samples. The experimental results also show that erosion rates are slightly higher at 60° impingement angle in most cases as compared to 45°, 75°, and 90° impingement angle. It is known that impingement angle is one of the most important parameters for the erosion behavior of materials. In the erosion literature, materials are broadly classified as ductile or brittle, based on the dependence of their erosion rate on impingement angle. The behavior of ductile materials is characterized by maximum erosion rate at low impingement angles (15°–30°). Brittle materials, on the other hand, show maximum erosion under normal impingement angle (90°). Some materials have been shown, however, to exhibit a semiductile behavior with maximum erosion occurring in the angular range 45–60° [22–24]. However, the above classification is not absolute as the erosion behavior of metals and alloys but in reality it strongly depends upon the experimental conditions and mechanical and chemical properties of target materials. In the literature, there are no fixed trends of correlating ductility or brittleness of materials with α
m
a
x or α
m
i
n. It is found that some target materials are characterized in a ductile manner; on the other hand, some show evidence of both ductile and brittle characteristics [23, 25–27]. Nonferrous materials generally exhibit a more ductile response than ferrous materials [28]. The complexity of identifying the nature of alloys and metals as having ductile, semiductile, or brittle behavior makes it challenging for the researchers to summarize unique conclusion. As for example, Parslow et al. [29] reported that the maximum erosion rates are occurring at normal incidence for the copper based alloy and cast iron which ensured the brittle type erosion behavior. Thus, though the use of terms such as failure by “ductile,” “semiductile,” and “brittle” mechanisms is frequent and useful in understanding erosion of materials, it is not strictly true in all cases.Figure 6
Variation of erosion rate with the variation of impingement angle ((a) particle size: 500–600 micron, (b) particle size: 500–600 micron, and (c) particle size: 500–600 micron and stand-off distance: 15 mm).
(a)
(b)
(c)Generally, ductile characteristics are more sensitive to abrasive particles and the maximum erosion lies in the range of 15–30° as a result of microcutting, microploughing and other damage accumulation processes. For brittle materials, mechanisms like plastic deformation and microcracking are the responsible for erosion rate for that property. Depending on the impingement angle, cutting wear is dominant at acute angles while deformation wear is dominant at high impingement angles [30, 31]. It has been well accepted that maximum erosion for ductile material occurs at low angles between 15 and 30° where cutting mechanism dominates, while lower erosion rates are seen for high impingement angles where deformation wear occurs. The reverse is true for brittle material.


### 3.3. Significance of Particle Size on Erosion

Particle size has considerable effect on erosion of gunmetal under various impact velocities for 15-, 30-, and 60-degree impingement angle (Figures7(a), 7(b), and 7(c)). The erosion rate of the tested material tended to increase with erodent size. Previous studies have emphasized the actual and analytical effects of erodent size when considering solid particle erosion of metals, alloys, polymers, and composites. Most results [32–36] show similar trends of erosive loss with respect to erodent size. Sundararajan and Roy [37], Mondal et al. [38], Dundar and Inal [39], and Lynn et al. [40] all performed erosion experiments using a wide range of particle sizes and observed that lower degrees of particle collision efficiency are responsible for reducing erosive wear with lower erodent sizes. They defined collision efficiency n as a ratio of the number of particles striking a unit area of the surface per unit time to the sum of particles incorporated within the volume of suspension swept by that area per unit time [41, 42]. Larger particles experience retardation just before impact due to the overinertial phenomenon. Therefore, their collision efficiency will be close to unity [29].Figure 7
Bar chart showing erosion rate with different particle size ((a) impact angle: 15 degrees, (b) impact angle: 30 degrees, and (c) impact angle: 60 degrees and stand-off distance: 15 mm).
(a)
(b)
(c)On the other hand, smaller particles are more susceptible to retardation before impact. Hence, their collision efficiency and kinetic energy dissipating after impact will be lower, causing a decrease in erosion rate. Several studies have shown that a higher erosion rate occurs with larger particle sizes due to higher energy transfer during impact from particle to target material. The increasing relationship between erosive wear and erodent size is associated with the following: (i) momentary enlargement of particle size and turbulent effect ensure a greater amount of particle striking force on the tested sample as a matter of propagation of indentation damage on the eroded surfaces under repeated action within a short period of time and (ii) in other cases the continuous sticking of expanded abrasive elements may deteriorate the subsurface and initiate fatigue-induced mass loss of surfaces. Generally, momentary particle action, indentation efficiency, and fatigue-initiated mechanisms are significant factors that influence increasing erosion with particle size [37]. In addition, there are some contradictory findings, with some results in practical test conditions showing that material erosion is not affected by particle size. The literature suggests that there may be an optimal level of particle size. The interplay of momentum of the erodent, indentation efficiency, and fatigue assisted erosive wear modes have also been reported by several other researchers.


### 3.4. Influence of Stand-Off Distance

We next examined the effect of the distance between the nozzle and target material on the erosion rate at impact angle 30°, impact velocity 40 m/sec, and three particle sizes. The variation in erosion rate with varying distance is shown in Figure8. It can be seen that the reduction in erosive wear is related to increased distance between nozzle and target material. This is due to the influence of kinetic energy and gravitational force of the sand particle reducing with increasing distance. In addition, when the nozzle and target material are relatively close to each other, particles may strike a small area of the test sample with a high concentration of particle flux but, in the case of large distance, particles may strike a large area of test sample with low concentrations of particle flux. At smaller distances, particles hit the surface as a beam but, with increasing distance, the strike area becomes V-shaped. The eroded impact areas for stand-off distance for 15, 17.5, 20, 22.5, and 25 mm were 63.24, 113.12, 141.47, 171.37, and 237.25 mm2, respectively. In future studies, the concentration of particle flux in relation to stand-off distance should be measured.Figure 8
Erosion rate with different stand-off distance at different particle size (impingement angle: 30 degrees, impact velocity: 40 m/sec).


### 3.5. Dimensional Analysis

Let(5)ER=FV,f,P,D,where E
R is erosion rate, M
T
-
1, V is impact velocity, L
T
-
1, f is sand flow rate, M
T
-
1, P is particle size, L, and D is distance between nozzle and target material, L.Letk be a dimensionless constant; then (5) can be written as follows:(6)ER=kVa·fb·Pc·Dd.Substituting the dimensions of each physical quantity, (5) reduces to(7)MT-1=kLT-1a·MT-1b·Lc·LdorMT-1=kLa+c+d·T-a-b·Mb.Since (5) must be dimensionally homogeneous, equate the powers of M, L, and T and obtain(8)b=1,-a-b=-1or,a=0a+c+d=0or,c=-d.Therefore,(9)ER=kV0·f1·P-d·Ddor,ER=kfDPdor,ER=KDPd,where “d” and “K” are arbitrary constants.The dimensional parameterD
/
P mentioned in (9) is designated the “Uttam Number” and can be expressed in brief as U. No.The relationships between erosion wear (E
R) and U. No. for gunmetal under an impact velocity of 50 m/sec and impact angle 30° are displayed in Figure 9.Figure 9
Erosion rate as function of U. No. for gunmetal.The curves show that erosion rate decreases linearly with increased U. No. and is represented by the following equation:(10)ER=0.142–0.794U.  No.  for  gunmetal.In Figure9, rectangular data points indicate the test observations of erosion rate with U. No. Using these actual data, least-squares equations and correlations were produced using ORIGIN software. The solid lines in the figure indicate trend lines. The correlation coefficient (r) was calculated to obtain −0.67614 for the test material. As a subjective measure of relationship between experimental data with trend line, the mentioned coefficient of correlation signifies that there are moderate negative relationships between erosion rate and Uttam Number. In this perception, it can be summarized that the actual data figure ensures acceptable recognition with the theoretical model.Several models or correlations [11–16] have previously been proposed. Due to their complexity of application and rigorous mathematical procedures, our correlation indicates a simpler way to correlate erosion rate with U. No. using dimensional analysis. Previous and suggested correlations are listed in Table 8. In previous models, mechanical properties are given priority compared to the operating conditions. Our present method is novel in that it ensures the dependency of erosion rate with stand-off distance and particle size, which has not previously been taken into consideration.Table 8
Different models for erosion.
Model number
Equations describing the model
Constants of  the model
Pair of materialswall, erodent
Model [11]
V
E
R
=
m
p
w
y
u
p
2
k
s
1
e
sin
⁡
2
α
-
6
w
y
sin
⁡
α
2
e
=
1.14
Steel St4 sank
s
=
700 MPa
Model [12]
E
R
=
278.90
u
p
100
2.47
cos
⁡
α
2
I
-
e
t
2
+
0.0832
u
p
100
2.344
sin
⁡
α
2
I
-
e
t
2
Steel 410, high silica sand
Model [13]
M
c
=
ρ
t
u
p
2
C
m
p
P
ψ
sin
⁡
2
α
-
2
I
+
m
p
r
p
2
/
I
p
w
y
sin
⁡
α
2
C
=
0.015
w
y
=
6
Steel St4, sand
Model [14]
E
R
=
K
A
f
α
u
p
cos
⁡
α
2
I
-
R
T
2
+
f
V
I
N
K
A
=
3.67
∗
10
-
6
Steel 355, high silica sand
Model [15]
E
R
=
A
u
p
n
f
α
f
α
=
b
α
2
+
c
α Now α
≤
α
0
α
0
=
15
°
Carbon steel, high silica sand
Model 0 [16]
E
R
v
=
0.00000163
u
p
cos
⁡
α
2.5
sin
⁡
α
π
45.4
°
+
0.000000468
u
p
sin
⁡
α
2.5 Now α
≤
22.7
°
Carbon steel, coal dust
Model
E
R
=
(
0.142–0.794
) U. No., where U
=
D
/
P
Gunmetal


### 3.6. Erosion Efficiency

The researchers [43] have established a formula for measuring erosion efficiency (η) mentioned in(11)η=2EHvV2ρsin2α,where E is stable level of erosive wear, HV is the Vickers hardness of impacting element, V is impingement velocity, and ρ is the density of silica sand. Detachment of superficial layer in ideally microploughing effect on crater has been realized without initiation of fracture (indicates nonerosive nature) and signifies zero erosion efficiency. That is, ideally microcutting conditions are assumed to be unity. At the time of generation of erosive wear most likely as a lip and simultaneously the initiation of fracturing characteristics, η can be considered at the level of 0-1. Accordingly, for brittle material, when the erosive wear has been found due to material spelling as well as removal of higher level of chunks (due to interconnection of either lateral or radial cracking facts), in this case η can be assumed to be larger than 100%.The hardness alone is unable to provide sufficient correlation with erosion rate, largely because it determines only the volume displaced by each impact and not really the volume of particle. Thus, a parameter which will reflect the efficiency with which the volume that is displaced is removed should be combined with hardness to obtain a better correlation. The erosion efficiency is obviously one such parameter. This thought has already been reflected in the theoretical model but the evaluation of erosion efficiency can be made only on the basis of experimental data. Hence, the values of erosion efficiencies of these alloy calculated using (6) are summarized in Table 9 along with their hardness values and operating conditions. The hardness values (H
v) and density (ρ) are 42, 43.2, and 44 MPa and 1436, 1440, and 1443 kg/m3 of particle size 300–355, 355–500, and 500–600, respectively. It clearly shows that erosion efficiency is not exclusively a material property but also depends on other operational variables such as impingement angle and impact velocity. The erosion efficiencies of gunmetal under normal impact (η normal) vary from 3.58 to 25.07%, 4.55–33.78%, and 7.31–34.70% for impact velocities 50, 40, and 30 m/s, respectively. The value of η for a particular impact velocity under oblique impact can be obtained simply by multiplying a factor 1/sin2
α with η normal. Similar observation on velocity dependence of erosion efficiency has previously been reported by Arjula et al. [44]. The magnitude of η can be used to characterize the nature and mechanism of erosion. For example, ideal microploughing involving just the displacement of the material from the crater without any fracture (and hence no erosion) will result in η
=
0. In contrast, if the material removal is by ideal microcutting, η
=
1.0 or 100%. If erosion occurs by lip or platelet formation and their fracture by repeated impact, as is usually the case in the case of ductile materials, the magnitude of η will be very low; that is, η
≤
100
%. In the case of brittle materials, erosion occurs usually by sapling and removal of large chunks of materials resulting from the interlinking of lateral or radial cracks and thus η can be expected to be even greater than 100% [44]. According to the categorization made by this author, the erosion efficiencies of the composites under the present study indicate that at low impact speed the erosion response is semiductile (η = 10–100%). On the other hand at relatively higher impact velocity exhibits ductile (η
<
10
%) erosion behavior.Table 9
Erosion efficiency of different operating conditions for gunmetal (experimental design using L27 orthogonal array for Taguchi method analysis).
Exp. number
Impact velocity (m/s)
Density of impactparticle (ρ) kg/m3
Hardness of impact particle (H
v) MPa
Erosion rate(E
R) mg/kg
Erosionefficiency (η)
1
30
1436
42.00
1687.833
34.70975
2
30
1440
43.20
1298.000
33.62469
3
30
1443
44.00
1238.000
30.32633
4
30
1436
42.00
1172.167
9.855353
5
30
1440
43.20
1105.500
13.69071
6
30
1443
44.00
1512.000
8.261464
7
30
1436
42.00
957.833
9.316994
8
30
1440
43.20
1393.667
7.317492
9
30
1443
44.00
1077.667
10.53423
10
40
1436
42.00
1628.667
22.58272
11
40
1440
43.20
1501.333
33.78172
12
40
1443
44.00
2211.167
4.330798
13
40
1436
42.00
297.587
10.04006
14
40
1440
43.20
2002.167
7.844489
15
40
1443
44.00
1540.167
8.246998
16
40
1436
42.00
1699.833
5.106057
17
40
1440
43.20
1357.833
4.556597
18
40
1443
44.00
1193.000
6.517931
19
50
1436
42.00
1791.500
25.07766
20
50
1440
43.20
2605.000
19.85867
21
50
1443
44.00
2031.000
21.86445
22
50
1436
42.00
2347.500
5.924445
23
50
1440
43.20
1846.000
5.523551
24
50
1443
44.00
1694.500
4.961363
25
50
1436
42.00
1597.833
3.588368
26
50
1440
43.20
1491.000
5.301186
27
50
1443
44.00
2168.667
5.278079


### 3.7. Effect of Friction Coefficient

The experiments have shown that at the time of contact of high-velocity solid particles with the tested materials, the impact velocity is assumed to be generated in parallel and normal components (Figure10). In fact, in this case, impact may cause some motion, and some resistance is assumed to be created due to the mechanical properties (such as hardness and tensile strength) of the target material. With this in mind, the friction coefficient was calculated in relation to the angle on theoretical grounds. Applying force analysis and bearing in mind frictional force (F) and tangential force (R), the friction coefficient can be calculated as follows:(12)FX=Fsin⁡θ,F=12mv2,where horizontal force F
X
=
1
/
2
m
v
2
sin
⁡
θ and vertical force are equal to reaction force (13)FY=R=12mv2cos⁡θ.We know that frictional force is equal to F
=
μ
R, μ
=
F
/
R, or μ
=
tan
⁡
θ.Figure 10
Impact velocity in parallel and normal directions.Friction coefficient calculated from the above equation and its corresponding erosion rate at 15–75-degree impact angles and impact velocity 50 m/sec are listed in Table10.Table 10
Friction coefficient and corresponding erosion rate at impact velocity 50 m/sec.
Impingement angle (degree)
Friction coefficient
Corresponding erosion rate at impact velocity 50 m/sec
15
0.268
0.15794
30
0.577
0.15602
45
1
0.14119
60
1.732
0.14569
75
3.732
0.13715In Figures11, 12, and 13 rectangular scatter data show the experimental relationship between erosion rate and the friction coefficient. To justify the experimental relation with theoretical context, liner regression and correlation are developed by using ORIGIN software. Continuous lines shown in these figures indicate the polynomial regression lines. The correlation coefficients are 0.778, 0.820, and 0.9296 for gunmetal, respectively, indicating strong positive relationships between erosion rate and friction coefficients for gunmetal. The experimental and theoretical data and are correlated to an acceptable level.Figure 11
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 50 m/sec.Figure 12
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 40 m/sec.Figure 13
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 30 m/sec.


### 3.8. Steady State Erosion of Gunmetal

In Table11, the first, second, third, fourth, fifth, and sixth columns represent impact velocity, impingement angle, particle size, stand-off distance, erosive wear, and S
/
N ratio, respectively. S
/
N ratio in context of erosive wear rate definitely indicates the arithmetic mean of two replications. Considering all S
/
N ratio of the erosive wear rate, the average level of the entire mentioned S
/
N ratio is calculated as −63.388 dB. Figure 14 shows the graphical presentation of main effect plot of S
/
N ratio emphasizing the consequence of the four varying parameters on erosive wear rate. MINITAB 15 software basically applicable for designing of experimental applicability is employed to analyze the results. This uncomplicated model is needed to predict the performance measurement; in relation to that the probable interrelations among the variable parameters are identified. Under this perception, factorial reflection integrating in an easier manner demonstrates the interaction effects. Analysis of test outcomes is used to make interpretation among the factor combination of A
1, B
3, C
1, and D
3, which contributes to evaluate the least amount of erosive wear rate.Table 11
Variation of erosion rate with different operating conditions for gunmetal (experimental design using L27 orthogonal array for Taguchi method analysis).
Exp. number
Impact velocity 1A (m/s)
Impingement angle 2B (degree)
Particle size3C (μm)
Stand-off distance4D (mm)
Erosion rate (E
R) mg/kg
S
/
N ratio (dB)
1
30
30
300–355
15
1687.833
−64.5466
2
30
30
355–500
20
1298.000
−62.2655
3
30
30
500–600
25
1238.000
−61.8544
4
30
60
300–355
20
1172.167
−61.3798
5
30
60
355–500
25
1105.500
−60.8712
6
30
60
500–600
15
1512.000
−63.591
7
30
90
300–355
25
957.833
−59.6258
8
30
90
355–500
15
1393.667
−62.8832
9
30
90
500–600
20
1077.667
−60.6497
10
40
30
300–355
20
1628.667
−64.2366
11
40
30
355–500
25
1501.333
−63.5295
12
40
30
500–600
15
2211.167
−66.8924
13
40
60
300–355
25
297.587
−49.4723
14
40
60
355–500
15
2002.167
−66.03
15
40
60
500–600
20
1540.167
−63.7514
16
40
90
300–355
15
1699.833
−64.6081
17
40
90
355–500
20
1357.833
−62.6569
18
40
90
500–600
25
1193.000
−61.5328
19
50
30
300–355
25
1791.500
−65.0643
20
50
30
355–500
15
2605.000
−68.3162
21
50
30
500–600
20
2031.000
−66.1542
22
50
60
300–355
15
2347.500
−67.4121
23
50
60
355–500
20
1846.000
−65.3246
24
50
60
500–600
25
1694.500
−64.5808
25
50
90
300–355
20
1597.833
−64.0706
26
50
90
355–500
25
1491.000
−63.4696
27
50
90
500–600
15
2168.667
−66.7239Figure 14
Effect of control factors on erosion rate of gunmetal.Thus, factorial design incorporates a simple means of testing for the presence of the interaction effects. Analysis of the result leads to the conclusion that factor combination ofA
1, B
3, C
1, and D
3 gives minimum erosion rate. The interaction graphs are shown in Figures 15(a), 15(b), and 15(c). As far as minimization of erosion rate is concerned, factors A, B, C, and D have significant effect. It is observed from Figure 15(b) that the interaction in A
×
C shows most significant effect on erosion rate. But the factors A and B individually have greater contribution on output performance, and their combination of interaction with factors A and B is shown in Figure 15(a) and has less effect on erosion rate and the factors B and C individually have greater contribution on output performance, and their combination of interaction with factors B and C is shown in Figure 15(c) and has less effect on erosion rate and then can be neglected for further study.Figure 15
Interaction graph between (a)A
×
B, (b) A
×
C, and (c) B
×
C for erosion rate of gunmetal.
(a)
(b)
(c)Figure16 shows the combination factor of erosion rate with impact velocity and impingement angle. It can clearly be seen that erosion rate increases with increased impact velocity at impact angle 15° due to the maximum particle energy transfer to the tested sample surface and less deformation occurring at the eroded surfaces. Maximum microcutting and ploughing occur at 15-degree impingement angle. The contour plot between impact velocity and impingement angle, impact velocity and erodent size, and impact velocity and stand-off distance is shown in Figure 17, while Figure 18 shows the 3D relationship between erosion rate and impact velocity, impact angle, and standoff distance. Large amounts of material were transferred from the tested surface material due to the impact velocity of 46–48 m/sec at a distance of 22–24 mm. Erodent size is an important factor dictating solid particle erosion rate.Figure 16
Heat map between (a) impact velocity and impingement angle, (b) impact velocity and erodent size, and (c) impact velocity and stand-off distance of gunmetal.
(a)
(b)
(c)Figure 17
Contour plot between (a) impact velocity and impingement angle, (b) impact velocity and erodent size, and (c) impact velocity and stand-off distance of gunmetal.
(a)
(b)
(c)Figure 18
3D Surface plot among erosion rate, impact velocity, impingement angle, and stand-off distance (a, b, c) for gunmetal.
(a)
(b)
(c)


### 3.9. ANOVA and the Effects of Factors of Gunmetal

Analysis of variance (ANOVA) chart is a decision making methodology for exact confirmation of imagining the significance of effecting level of factors considered. In addition to that ANOVA is an analyzing tool to select the order of more meaningful factors. Table12 signifies the analysis of ANOVA to realize the contribution of factors on erosive wear rate. The ANOVA with erosion rate results are listed in Table 12. This analysis was assumed to be considered for a level of significance of 5%, that is, for level of confidence 95%. The last column of the table indicates the order of significance among control factors and interactions. It can be realized from Table 12 that the control factor P
=
0
.
027 has highest static influence of 28.81%, P
=
0
.
045 has an influence of 22.29%, P
=
0
.
218 has an influence of 8.10%, and P
=
0
.
345 has an influence of 5.23% on erosive wear rate of tested material system under observations. The results indicated that the factor (D) that is stand-off distance and impact velocity (A) exerted more effect on the erosion rate, followed by the impingement angle (B) and particle size (C). The effect of combined factors on impact velocity and sand size (A
∗
B) on erosive wear performance played a crucial impact.Table 12
Effects of factors of gunmetal. Analysis of variance forS
/
N, using adjusted SS for tests.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
P
P (%)
A
2
72.266
72.266
36.133
5.45
0.045
22.29
B
2
26.275
26.275
13.137
1.98
0.218
8.10
C
2
16.948
16.948
8.474
1.28
0.345
5.23
D
2
93.402
93.402
46.701
7.04
0.027
28.81
A
∗
B
4
23.756
23.756
5.939
0.90
0.521
7.33
A
∗
C
4
26.060
26.060
6.515
0.98
0.482
8.04
B
∗
C
4
25.747
25.747
6.437
0.97
0.487
7.94
Error
6
39.777
39.777
6.629
12
Total
26
324.231In case of comparative analysis of interaction of different alternative factors,A
∗
C = interaction within impingement velocity ∗ erodent size (P
=
0.482) has less number of P values compared to other two combinations. According to this perception, the factor interaction A
∗
B = velocity of impact ∗ angle of impingement (P
=
0.521) implies lesser significance of contribution on erosive wear rate in comparison with factor interaction B
∗
C = angle of impingement ∗ erodent size (P
=
0.487). Hence, the lower the P values, the higher the significance of contribution on the erosion rate justified. The present analysis shows that four levels of erosive test parameters impact velocity (A) and stand-off distance (D) individually and have both statistical and physical significance (percentage contribution is greater than error) in case of erosion rate of gunmetal. But interaction combinations between different control parameters have statistical significance but do not have physical significance, since error evaluated is more than percentage contribution of these interactions, which is evident from the ANOVA results.


### 3.10. Morphology of Eroded Surfaces

#### 3.10.1. SEM Analysis

Surface Morphology at Different Impingement Angle. Then analysis of surface morphology of gunmetal was examined by using JEOL JSM 7600F Scanning Electron Microscope (country of origin Japan). SEM micrographs of eroded surfaces of gunmetal are appearing in Figures 19(a), 19(b), 19(c), 19(d), 19(e), and 19(f). Figures 19(a) and 19(b) specifies that gunmetal eroded surface at 15° impact angle is worn by the mechanism of microploughing, grooves, displaced material, and large fragments. Extensive ploughing and the resulting lip formation are evident in the micrograph for 15° impingement angle. The direction of ploughing in surface morphologies coincides with the direction of particle motion during sand blasting. This is the angle where the higher amount of erosion has been noted under all test conditions. Materials which show ductile erosion behavior can be easily worn off by microploughing erosion mechanisms caused by the lateral impact of the particles. In Figures 19(c) and 19(d) at 30° impingement angle pitting action and craters have occurred as a result of lower erosion rate of the all tested materials. On the other hand at 60-degree impingement angle plastic deformation, craters, and microcutting action have occurred in Figures 19(e) and 19(f). The reduction in mass loss at higher impact angles, near or at 90° at velocity lower than 50 m/sec, is because there was not too much evidence of sliding action of abrasive particles unlike lower impact angles where the sliding component is significant and increases the mass lost in the material. But the reverse is true in few cases for high impact velocity 50 m/sec due to the quick impacting at short contact time between particle and target surface.Figure 19
SEM micrograph of eroded aluminum alloy at impact angle, (a, b) 15 degrees, (c, d) 30 degrees, and (e, f) 60 degrees.
(a)
(b)
(c)
(d)
(e)
(f)Surface Morphology with Different Impact Velocity. Surface morphology at different impact velocity has been presented in Figures 20(a), 20(b), 20(c), and 20(d) for analyzing the wear mechanism. Figures 20(e) and 20(f) under impact velocity 30 m/sec emphasized the lower erosion rate due to displaced material and putting action. This is because of the low particle energy. Figures 20(c) and 20(d) show that the damage has occurred on the target surface at impact velocity 40 m/sec. In this case the damaged has been done by the influence of craters, pulling action. At higher impact velocity (50 m/sec) due to the effect of crack and ploughing action, higher levels of erosion are obtained as a result of high particle energy (Figures 20(a) and 20(b)).Figure 20
SEM micrograph of eroded gunmetal at impact velocity: (a, b) 50 m/sec, (c, d) 40 m/sec, and (e, f) 30 m/sec.
(a)
(b)
(c)
(d)
(e)
(f)


### 3.11. Analysis of Erosion with Different Percentage of Gunmetal at Different Impact Angles Using Energy Dispersed X-Ray Spectrograph (EDX)

The analysis of energy dispersed X-ray spectrograph (EDX) of gunmetal was done by using JEOL JSM 7600F Scanning Electron Microscope (country of origin Japan). In this method an electron beam of 10–20 KeV strikes at the tested surface that causes X-ray to be emitted from the point of incidence. The emission energy of X-ray depends on the types of materials under observation; that is, the use of X-ray energy emission shows distinct nature depending on soft to hard materials and thus it gives the unavoidable signature in case of some kinds of materials. When an X-ray strikes the detector, it will generate a photoelectron which in turn generates electron hole pairs. A strong electric field attracts the electrons and holes towards the opposite ends of the detector. The size of the pulse thus generated depends on the number of electron hole pairs created, which in turn depends on the energy of the incoming X-ray. In this method however elements with low atomic number are difficult to be detected. The detector which is lithium doped silicon (SiLi) is protected by a beryllium window and operated at liquid nitrogen temperatures.Figures21 and 22 show the amount of silica embedded within the eroded surfaces at impact angle of 15 degrees. Similar observations are found in Figures 23, 24, 25, and 26 for impact angles of 60 and 90 degrees, respectively. The EDX analysis shows that the percentages of embedded silica are increased with the decrease of percentage of copper in gunmetal for all tested angles. The significance of these observations is that the higher the copper composition in gunmetal, the lower the silica engagement within the target surfaces which causes lower erosion rate. The depth at which the particle has been embedded into the material was very small depth from the upper surface. Just beneath the lip, the particle embedded into the material has been observed by other researchers as well [45]. It was assumed that the amount of fragmentation and secondary erosion would be dependent on the particle velocity, impingement angle, particle size, stand-off distance, and different in hardness between the particle and target material. The variation of composition of tin and zinc has some limited role with the variation of erosion rate.Figure 21
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 15-degree impact angle.Figure 22
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 15-degree impact angle.Figure 23
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 60-degree impact angle.Figure 24
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 60-degree impact angle.Figure 25
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 90-degree impact angle.Figure 26
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 90-degree impact angle.The existence of the O and Si atoms in high percentage was the evidence of the embedded erodent garnet particles to the surfaces of the samples. Based upon the EDX analysis results, it was concluded that the erodent particles were embedded to the surfaces of theg during the erosion process. It was concluded that this can be possible because of the ductile behavior of the gunmetal.


### 3.12. Confirmation Experiment for Gunmetal

The end level of Taguchi approach is the validation of experimental observations for analyzing the quality characteristics. The validity of test results is ensured by concerning an arbitrary set of factor level combination and after that it has been compared with the test results. The measuredS
/
N ratio for wear rates is estimated in connection with the predictive equations.The estimatedS
/
N ratio for wear rates can be calculated with the help of following predictive equations:(14)η-=T-+A-2-T-+B-3-T-+C-2-T-+D-1-T-,where η
- is the predicted average; T
- is overall experimental average; A
-
2, B
-
3, C
-
2, and D
-
1 are the mean response for factors at designated levels.By combining like-terms, the equation reduces to(15)η-=A-2+B-3+C-2+D-1-3T-.A new combination of factor levels A
2, B
3, C
2, and D
1 is used to predict deposition rate through prediction equation and it is found to be η
-
=
-
64.866 for each performance measure; an experiment was conducted for different factors combination and compared with the result obtained from the predictive equation.The new generated model is very meaningful for the prediction erosive wear rate to a justifiable accuracy. The calculated deviation (error level) is 1.72% and is obtained in case ofS
/
N ratio of erosive wear rate. The results of experimental confirmation using optimal erosive wear parameters and comparison of the predicted erosion rate with the actual erosion rate using the optimal erosive wear parameters are indicated in Table 13. The improvement in S
/
N ratio from the starting level to optimum level is 0.858 dB. The erosion rate is reduced by almost 10%. Considering this scientific approach, it can be mentioned that erosion rate performance is improved by using Taguchi method. After all, the accuracy level can be improved more precisely in case of increase of the number of measurements. This validation approach incorporates the generation of the mathematical model for the prediction of measures of performance on the basis of knowledge of the input parameters.Table 13
Results of the confirmation experiments for erosion rate of gunmetal.
Optimal control parameters
Initial process parameter
Prediction
Experimental
Improvement in the result
Level
A2, B1, C2, D3
A2, B3, C2, D1
A2, B3, C2, D1
S
/
N ratio for erosion rate (dB)
−64.608
−64.866
−63.750
0.858
Erosion rate (mg/gm)
1699.83
1300.07
1523.80
10.35


## 3.1. Influence of Impact Velocity

In erosion, the impingement velocity is related to the sustainability of the material’s life. The test conditions were randomly shaped sand of dimension 300–355, 355–500, and 500–600μm, stand-off distance 15 mm, and impingement angles 15, 30, and 60 degrees at ambient temperature. Under these test environments, erosion rates showed a sharp, increasing trend, with increases in velocity ranging from 30 to 50 m/sec for the tested gunmetal (Figures 4(a), 4(b) and 4(c)). Particles created a high impact of kinetic energy at high velocities, resulting in higher impact effect and greater erosion. In fact, particles occupy tremendous impact of kinetic energy at large velocity causing higher level of impacting effect and results in greater amount of erosion rate. In addition to that with increased velocity the duration between impacts is reduced and energy of the particle is increased which causes higher level of mass loss [17]. At 60-degree impact angle, the kinetic energies of 2052, 2793, 3648, 4617, and 5700 kg-m/sec were estimated for impact velocities of 30, 35, 40, 45, and 50 m/sec, respectively. Temperature variations were propagated throughout the sample surface with increasing velocities. However, due the effect of air-cooling during impaction by the compressor, the temperature increase is small. Nguyen et al. [18], Jha et al. [19], and ElTobgy et al. [20] reported a similar relationship between impingement velocity and erosion rate. Extended thermal characteristics have been observed at high velocities. Temperatures were elevated above ambient temperature level from 8 to 19 degrees for velocity increases between 30 and 50 m/sec. The increase in temperature may, in reality, be small due to rapid displacement of sand from the point of impact as well as cooling from the compressed pressure.Figure 4
Variation of erosion rate with the variation of impact velocity and erodent size (impact angle: (a) 15 degrees, (b) 30 degrees, and (c) 60 degrees and stand-off distance 15 mm).
(a)
(b)
(c)The least-squares fitting of actual data was conducted by applying the power law. Consequently, erodent particle velocities of 30 m/sec, 40 m/sec, and 50 m/sec at impingement angles of 15°, 30°, and 60° were taken in to consideration for these purposes.The relationship between stable erosive wear rate (E) and impingement velocity is stated as a simple power function: (4)E=kvn,where n is the velocity exponent and k is the proportionality constant impact on the other parameters. The influence of impact velocity on erosion rate of metals and alloys has been partially investigated. The velocity exponent (n) in general varies from 2 to 3 and 3 to 5 which indicate that the materials are ductile and brittle in nature, respectively [21]. The other mechanical properties (hardness, ultimate tensile strength, modulus of elasticity, fracture toughness, yield stress, yield strain, rebound resilience, etc.) can be correlated in this way.The fitting parameters are listed in Table7 and as an example the criteria of fitting calculation is expressed in Figures 5(a), 5(b), and 5(c) using GRAPHWIN software. Using the experimental data, calculated velocity exponents are obtained in the range of 0.78–0.91 for gunmetal at different impingement angle. This means that the findings of velocity exponents are found to be much lower than what have been mentioned by the different researchers for conformity of ductile behavior of tested material. In fact, the interesting observation in this study is that, in spite of the fact that the standard range for ductile material is within 2 to 3, it has been observed from the experimental data that the obtained velocity exponent range is true only for certain lower velocities and lower particle size. But at higher impact velocities, different erodent size, or particular shape of erodent, the velocity exponent can be found within the standard range. In this context, it can be realized that velocity exponent range varies with impact velocity, particular shape of erodent, and particle size. In case of coefficient of determination, relationship quality between erosion rate and impact velocity for exponential parameter is found to be stronger (99%) for test samples.Table 7
The power law calculated values at different impingement angles.
Tested material
Impingement angle (α, °)
k
n
R
2
Gunmetal
15
0.007346
0.7841
0.99
30
0.007340
0.7804
0.99
60
0.004123
0.9130
0.99Figure 5
Curve fitting using power law equation for experimental data between erosion rate and impact velocity (test sample: gunmetal: (a) impact angle 15 degrees, (b) impact angle 30 degrees, and (c) impact angle 60 degrees and particle size 500–600).
(a)
(b)
(c)


## 3.2. Influence of Impingement Angle

In order to study the effect of impingement angle on erosion rate, erosion tests were performed by varying the impact velocity from 30 to 50 m/s at impingement angles of 15° to 90° for different particle size. These results are presented in Figures6(a), 6(b), and 6(c) showing the influence of impingement angle on the erosion rate of gunmetal at different impact velocities and particle size. It can be seen that erosion rate is maximum at 15° impingement angle for gunmetal at different impact velocities and particle size studied. At impact angle 15° erosion rates are high and then decrease gradually up to the impingement angle 45°. After that erosion rate increases ranging from 45° to 90°, in general, for all tested samples. The experimental results also show that erosion rates are slightly higher at 60° impingement angle in most cases as compared to 45°, 75°, and 90° impingement angle. It is known that impingement angle is one of the most important parameters for the erosion behavior of materials. In the erosion literature, materials are broadly classified as ductile or brittle, based on the dependence of their erosion rate on impingement angle. The behavior of ductile materials is characterized by maximum erosion rate at low impingement angles (15°–30°). Brittle materials, on the other hand, show maximum erosion under normal impingement angle (90°). Some materials have been shown, however, to exhibit a semiductile behavior with maximum erosion occurring in the angular range 45–60° [22–24]. However, the above classification is not absolute as the erosion behavior of metals and alloys but in reality it strongly depends upon the experimental conditions and mechanical and chemical properties of target materials. In the literature, there are no fixed trends of correlating ductility or brittleness of materials with α
m
a
x or α
m
i
n. It is found that some target materials are characterized in a ductile manner; on the other hand, some show evidence of both ductile and brittle characteristics [23, 25–27]. Nonferrous materials generally exhibit a more ductile response than ferrous materials [28]. The complexity of identifying the nature of alloys and metals as having ductile, semiductile, or brittle behavior makes it challenging for the researchers to summarize unique conclusion. As for example, Parslow et al. [29] reported that the maximum erosion rates are occurring at normal incidence for the copper based alloy and cast iron which ensured the brittle type erosion behavior. Thus, though the use of terms such as failure by “ductile,” “semiductile,” and “brittle” mechanisms is frequent and useful in understanding erosion of materials, it is not strictly true in all cases.Figure 6
Variation of erosion rate with the variation of impingement angle ((a) particle size: 500–600 micron, (b) particle size: 500–600 micron, and (c) particle size: 500–600 micron and stand-off distance: 15 mm).
(a)
(b)
(c)Generally, ductile characteristics are more sensitive to abrasive particles and the maximum erosion lies in the range of 15–30° as a result of microcutting, microploughing and other damage accumulation processes. For brittle materials, mechanisms like plastic deformation and microcracking are the responsible for erosion rate for that property. Depending on the impingement angle, cutting wear is dominant at acute angles while deformation wear is dominant at high impingement angles [30, 31]. It has been well accepted that maximum erosion for ductile material occurs at low angles between 15 and 30° where cutting mechanism dominates, while lower erosion rates are seen for high impingement angles where deformation wear occurs. The reverse is true for brittle material.


## 3.3. Significance of Particle Size on Erosion

Particle size has considerable effect on erosion of gunmetal under various impact velocities for 15-, 30-, and 60-degree impingement angle (Figures7(a), 7(b), and 7(c)). The erosion rate of the tested material tended to increase with erodent size. Previous studies have emphasized the actual and analytical effects of erodent size when considering solid particle erosion of metals, alloys, polymers, and composites. Most results [32–36] show similar trends of erosive loss with respect to erodent size. Sundararajan and Roy [37], Mondal et al. [38], Dundar and Inal [39], and Lynn et al. [40] all performed erosion experiments using a wide range of particle sizes and observed that lower degrees of particle collision efficiency are responsible for reducing erosive wear with lower erodent sizes. They defined collision efficiency n as a ratio of the number of particles striking a unit area of the surface per unit time to the sum of particles incorporated within the volume of suspension swept by that area per unit time [41, 42]. Larger particles experience retardation just before impact due to the overinertial phenomenon. Therefore, their collision efficiency will be close to unity [29].Figure 7
Bar chart showing erosion rate with different particle size ((a) impact angle: 15 degrees, (b) impact angle: 30 degrees, and (c) impact angle: 60 degrees and stand-off distance: 15 mm).
(a)
(b)
(c)On the other hand, smaller particles are more susceptible to retardation before impact. Hence, their collision efficiency and kinetic energy dissipating after impact will be lower, causing a decrease in erosion rate. Several studies have shown that a higher erosion rate occurs with larger particle sizes due to higher energy transfer during impact from particle to target material. The increasing relationship between erosive wear and erodent size is associated with the following: (i) momentary enlargement of particle size and turbulent effect ensure a greater amount of particle striking force on the tested sample as a matter of propagation of indentation damage on the eroded surfaces under repeated action within a short period of time and (ii) in other cases the continuous sticking of expanded abrasive elements may deteriorate the subsurface and initiate fatigue-induced mass loss of surfaces. Generally, momentary particle action, indentation efficiency, and fatigue-initiated mechanisms are significant factors that influence increasing erosion with particle size [37]. In addition, there are some contradictory findings, with some results in practical test conditions showing that material erosion is not affected by particle size. The literature suggests that there may be an optimal level of particle size. The interplay of momentum of the erodent, indentation efficiency, and fatigue assisted erosive wear modes have also been reported by several other researchers.


## 3.4. Influence of Stand-Off Distance

We next examined the effect of the distance between the nozzle and target material on the erosion rate at impact angle 30°, impact velocity 40 m/sec, and three particle sizes. The variation in erosion rate with varying distance is shown in Figure8. It can be seen that the reduction in erosive wear is related to increased distance between nozzle and target material. This is due to the influence of kinetic energy and gravitational force of the sand particle reducing with increasing distance. In addition, when the nozzle and target material are relatively close to each other, particles may strike a small area of the test sample with a high concentration of particle flux but, in the case of large distance, particles may strike a large area of test sample with low concentrations of particle flux. At smaller distances, particles hit the surface as a beam but, with increasing distance, the strike area becomes V-shaped. The eroded impact areas for stand-off distance for 15, 17.5, 20, 22.5, and 25 mm were 63.24, 113.12, 141.47, 171.37, and 237.25 mm2, respectively. In future studies, the concentration of particle flux in relation to stand-off distance should be measured.Figure 8
Erosion rate with different stand-off distance at different particle size (impingement angle: 30 degrees, impact velocity: 40 m/sec).


## 3.5. Dimensional Analysis

Let(5)ER=FV,f,P,D,where E
R is erosion rate, M
T
-
1, V is impact velocity, L
T
-
1, f is sand flow rate, M
T
-
1, P is particle size, L, and D is distance between nozzle and target material, L.Letk be a dimensionless constant; then (5) can be written as follows:(6)ER=kVa·fb·Pc·Dd.Substituting the dimensions of each physical quantity, (5) reduces to(7)MT-1=kLT-1a·MT-1b·Lc·LdorMT-1=kLa+c+d·T-a-b·Mb.Since (5) must be dimensionally homogeneous, equate the powers of M, L, and T and obtain(8)b=1,-a-b=-1or,a=0a+c+d=0or,c=-d.Therefore,(9)ER=kV0·f1·P-d·Ddor,ER=kfDPdor,ER=KDPd,where “d” and “K” are arbitrary constants.The dimensional parameterD
/
P mentioned in (9) is designated the “Uttam Number” and can be expressed in brief as U. No.The relationships between erosion wear (E
R) and U. No. for gunmetal under an impact velocity of 50 m/sec and impact angle 30° are displayed in Figure 9.Figure 9
Erosion rate as function of U. No. for gunmetal.The curves show that erosion rate decreases linearly with increased U. No. and is represented by the following equation:(10)ER=0.142–0.794U.  No.  for  gunmetal.In Figure9, rectangular data points indicate the test observations of erosion rate with U. No. Using these actual data, least-squares equations and correlations were produced using ORIGIN software. The solid lines in the figure indicate trend lines. The correlation coefficient (r) was calculated to obtain −0.67614 for the test material. As a subjective measure of relationship between experimental data with trend line, the mentioned coefficient of correlation signifies that there are moderate negative relationships between erosion rate and Uttam Number. In this perception, it can be summarized that the actual data figure ensures acceptable recognition with the theoretical model.Several models or correlations [11–16] have previously been proposed. Due to their complexity of application and rigorous mathematical procedures, our correlation indicates a simpler way to correlate erosion rate with U. No. using dimensional analysis. Previous and suggested correlations are listed in Table 8. In previous models, mechanical properties are given priority compared to the operating conditions. Our present method is novel in that it ensures the dependency of erosion rate with stand-off distance and particle size, which has not previously been taken into consideration.Table 8
Different models for erosion.
Model number
Equations describing the model
Constants of  the model
Pair of materialswall, erodent
Model [11]
V
E
R
=
m
p
w
y
u
p
2
k
s
1
e
sin
⁡
2
α
-
6
w
y
sin
⁡
α
2
e
=
1.14
Steel St4 sank
s
=
700 MPa
Model [12]
E
R
=
278.90
u
p
100
2.47
cos
⁡
α
2
I
-
e
t
2
+
0.0832
u
p
100
2.344
sin
⁡
α
2
I
-
e
t
2
Steel 410, high silica sand
Model [13]
M
c
=
ρ
t
u
p
2
C
m
p
P
ψ
sin
⁡
2
α
-
2
I
+
m
p
r
p
2
/
I
p
w
y
sin
⁡
α
2
C
=
0.015
w
y
=
6
Steel St4, sand
Model [14]
E
R
=
K
A
f
α
u
p
cos
⁡
α
2
I
-
R
T
2
+
f
V
I
N
K
A
=
3.67
∗
10
-
6
Steel 355, high silica sand
Model [15]
E
R
=
A
u
p
n
f
α
f
α
=
b
α
2
+
c
α Now α
≤
α
0
α
0
=
15
°
Carbon steel, high silica sand
Model 0 [16]
E
R
v
=
0.00000163
u
p
cos
⁡
α
2.5
sin
⁡
α
π
45.4
°
+
0.000000468
u
p
sin
⁡
α
2.5 Now α
≤
22.7
°
Carbon steel, coal dust
Model
E
R
=
(
0.142–0.794
) U. No., where U
=
D
/
P
Gunmetal


## 3.6. Erosion Efficiency

The researchers [43] have established a formula for measuring erosion efficiency (η) mentioned in(11)η=2EHvV2ρsin2α,where E is stable level of erosive wear, HV is the Vickers hardness of impacting element, V is impingement velocity, and ρ is the density of silica sand. Detachment of superficial layer in ideally microploughing effect on crater has been realized without initiation of fracture (indicates nonerosive nature) and signifies zero erosion efficiency. That is, ideally microcutting conditions are assumed to be unity. At the time of generation of erosive wear most likely as a lip and simultaneously the initiation of fracturing characteristics, η can be considered at the level of 0-1. Accordingly, for brittle material, when the erosive wear has been found due to material spelling as well as removal of higher level of chunks (due to interconnection of either lateral or radial cracking facts), in this case η can be assumed to be larger than 100%.The hardness alone is unable to provide sufficient correlation with erosion rate, largely because it determines only the volume displaced by each impact and not really the volume of particle. Thus, a parameter which will reflect the efficiency with which the volume that is displaced is removed should be combined with hardness to obtain a better correlation. The erosion efficiency is obviously one such parameter. This thought has already been reflected in the theoretical model but the evaluation of erosion efficiency can be made only on the basis of experimental data. Hence, the values of erosion efficiencies of these alloy calculated using (6) are summarized in Table 9 along with their hardness values and operating conditions. The hardness values (H
v) and density (ρ) are 42, 43.2, and 44 MPa and 1436, 1440, and 1443 kg/m3 of particle size 300–355, 355–500, and 500–600, respectively. It clearly shows that erosion efficiency is not exclusively a material property but also depends on other operational variables such as impingement angle and impact velocity. The erosion efficiencies of gunmetal under normal impact (η normal) vary from 3.58 to 25.07%, 4.55–33.78%, and 7.31–34.70% for impact velocities 50, 40, and 30 m/s, respectively. The value of η for a particular impact velocity under oblique impact can be obtained simply by multiplying a factor 1/sin2
α with η normal. Similar observation on velocity dependence of erosion efficiency has previously been reported by Arjula et al. [44]. The magnitude of η can be used to characterize the nature and mechanism of erosion. For example, ideal microploughing involving just the displacement of the material from the crater without any fracture (and hence no erosion) will result in η
=
0. In contrast, if the material removal is by ideal microcutting, η
=
1.0 or 100%. If erosion occurs by lip or platelet formation and their fracture by repeated impact, as is usually the case in the case of ductile materials, the magnitude of η will be very low; that is, η
≤
100
%. In the case of brittle materials, erosion occurs usually by sapling and removal of large chunks of materials resulting from the interlinking of lateral or radial cracks and thus η can be expected to be even greater than 100% [44]. According to the categorization made by this author, the erosion efficiencies of the composites under the present study indicate that at low impact speed the erosion response is semiductile (η = 10–100%). On the other hand at relatively higher impact velocity exhibits ductile (η
<
10
%) erosion behavior.Table 9
Erosion efficiency of different operating conditions for gunmetal (experimental design using L27 orthogonal array for Taguchi method analysis).
Exp. number
Impact velocity (m/s)
Density of impactparticle (ρ) kg/m3
Hardness of impact particle (H
v) MPa
Erosion rate(E
R) mg/kg
Erosionefficiency (η)
1
30
1436
42.00
1687.833
34.70975
2
30
1440
43.20
1298.000
33.62469
3
30
1443
44.00
1238.000
30.32633
4
30
1436
42.00
1172.167
9.855353
5
30
1440
43.20
1105.500
13.69071
6
30
1443
44.00
1512.000
8.261464
7
30
1436
42.00
957.833
9.316994
8
30
1440
43.20
1393.667
7.317492
9
30
1443
44.00
1077.667
10.53423
10
40
1436
42.00
1628.667
22.58272
11
40
1440
43.20
1501.333
33.78172
12
40
1443
44.00
2211.167
4.330798
13
40
1436
42.00
297.587
10.04006
14
40
1440
43.20
2002.167
7.844489
15
40
1443
44.00
1540.167
8.246998
16
40
1436
42.00
1699.833
5.106057
17
40
1440
43.20
1357.833
4.556597
18
40
1443
44.00
1193.000
6.517931
19
50
1436
42.00
1791.500
25.07766
20
50
1440
43.20
2605.000
19.85867
21
50
1443
44.00
2031.000
21.86445
22
50
1436
42.00
2347.500
5.924445
23
50
1440
43.20
1846.000
5.523551
24
50
1443
44.00
1694.500
4.961363
25
50
1436
42.00
1597.833
3.588368
26
50
1440
43.20
1491.000
5.301186
27
50
1443
44.00
2168.667
5.278079


## 3.7. Effect of Friction Coefficient

The experiments have shown that at the time of contact of high-velocity solid particles with the tested materials, the impact velocity is assumed to be generated in parallel and normal components (Figure10). In fact, in this case, impact may cause some motion, and some resistance is assumed to be created due to the mechanical properties (such as hardness and tensile strength) of the target material. With this in mind, the friction coefficient was calculated in relation to the angle on theoretical grounds. Applying force analysis and bearing in mind frictional force (F) and tangential force (R), the friction coefficient can be calculated as follows:(12)FX=Fsin⁡θ,F=12mv2,where horizontal force F
X
=
1
/
2
m
v
2
sin
⁡
θ and vertical force are equal to reaction force (13)FY=R=12mv2cos⁡θ.We know that frictional force is equal to F
=
μ
R, μ
=
F
/
R, or μ
=
tan
⁡
θ.Figure 10
Impact velocity in parallel and normal directions.Friction coefficient calculated from the above equation and its corresponding erosion rate at 15–75-degree impact angles and impact velocity 50 m/sec are listed in Table10.Table 10
Friction coefficient and corresponding erosion rate at impact velocity 50 m/sec.
Impingement angle (degree)
Friction coefficient
Corresponding erosion rate at impact velocity 50 m/sec
15
0.268
0.15794
30
0.577
0.15602
45
1
0.14119
60
1.732
0.14569
75
3.732
0.13715In Figures11, 12, and 13 rectangular scatter data show the experimental relationship between erosion rate and the friction coefficient. To justify the experimental relation with theoretical context, liner regression and correlation are developed by using ORIGIN software. Continuous lines shown in these figures indicate the polynomial regression lines. The correlation coefficients are 0.778, 0.820, and 0.9296 for gunmetal, respectively, indicating strong positive relationships between erosion rate and friction coefficients for gunmetal. The experimental and theoretical data and are correlated to an acceptable level.Figure 11
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 50 m/sec.Figure 12
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 40 m/sec.Figure 13
Erosion rate as function of friction coefficient (F
C) for gunmetal at impact velocity 30 m/sec.


## 3.8. Steady State Erosion of Gunmetal

In Table11, the first, second, third, fourth, fifth, and sixth columns represent impact velocity, impingement angle, particle size, stand-off distance, erosive wear, and S
/
N ratio, respectively. S
/
N ratio in context of erosive wear rate definitely indicates the arithmetic mean of two replications. Considering all S
/
N ratio of the erosive wear rate, the average level of the entire mentioned S
/
N ratio is calculated as −63.388 dB. Figure 14 shows the graphical presentation of main effect plot of S
/
N ratio emphasizing the consequence of the four varying parameters on erosive wear rate. MINITAB 15 software basically applicable for designing of experimental applicability is employed to analyze the results. This uncomplicated model is needed to predict the performance measurement; in relation to that the probable interrelations among the variable parameters are identified. Under this perception, factorial reflection integrating in an easier manner demonstrates the interaction effects. Analysis of test outcomes is used to make interpretation among the factor combination of A
1, B
3, C
1, and D
3, which contributes to evaluate the least amount of erosive wear rate.Table 11
Variation of erosion rate with different operating conditions for gunmetal (experimental design using L27 orthogonal array for Taguchi method analysis).
Exp. number
Impact velocity 1A (m/s)
Impingement angle 2B (degree)
Particle size3C (μm)
Stand-off distance4D (mm)
Erosion rate (E
R) mg/kg
S
/
N ratio (dB)
1
30
30
300–355
15
1687.833
−64.5466
2
30
30
355–500
20
1298.000
−62.2655
3
30
30
500–600
25
1238.000
−61.8544
4
30
60
300–355
20
1172.167
−61.3798
5
30
60
355–500
25
1105.500
−60.8712
6
30
60
500–600
15
1512.000
−63.591
7
30
90
300–355
25
957.833
−59.6258
8
30
90
355–500
15
1393.667
−62.8832
9
30
90
500–600
20
1077.667
−60.6497
10
40
30
300–355
20
1628.667
−64.2366
11
40
30
355–500
25
1501.333
−63.5295
12
40
30
500–600
15
2211.167
−66.8924
13
40
60
300–355
25
297.587
−49.4723
14
40
60
355–500
15
2002.167
−66.03
15
40
60
500–600
20
1540.167
−63.7514
16
40
90
300–355
15
1699.833
−64.6081
17
40
90
355–500
20
1357.833
−62.6569
18
40
90
500–600
25
1193.000
−61.5328
19
50
30
300–355
25
1791.500
−65.0643
20
50
30
355–500
15
2605.000
−68.3162
21
50
30
500–600
20
2031.000
−66.1542
22
50
60
300–355
15
2347.500
−67.4121
23
50
60
355–500
20
1846.000
−65.3246
24
50
60
500–600
25
1694.500
−64.5808
25
50
90
300–355
20
1597.833
−64.0706
26
50
90
355–500
25
1491.000
−63.4696
27
50
90
500–600
15
2168.667
−66.7239Figure 14
Effect of control factors on erosion rate of gunmetal.Thus, factorial design incorporates a simple means of testing for the presence of the interaction effects. Analysis of the result leads to the conclusion that factor combination ofA
1, B
3, C
1, and D
3 gives minimum erosion rate. The interaction graphs are shown in Figures 15(a), 15(b), and 15(c). As far as minimization of erosion rate is concerned, factors A, B, C, and D have significant effect. It is observed from Figure 15(b) that the interaction in A
×
C shows most significant effect on erosion rate. But the factors A and B individually have greater contribution on output performance, and their combination of interaction with factors A and B is shown in Figure 15(a) and has less effect on erosion rate and the factors B and C individually have greater contribution on output performance, and their combination of interaction with factors B and C is shown in Figure 15(c) and has less effect on erosion rate and then can be neglected for further study.Figure 15
Interaction graph between (a)A
×
B, (b) A
×
C, and (c) B
×
C for erosion rate of gunmetal.
(a)
(b)
(c)Figure16 shows the combination factor of erosion rate with impact velocity and impingement angle. It can clearly be seen that erosion rate increases with increased impact velocity at impact angle 15° due to the maximum particle energy transfer to the tested sample surface and less deformation occurring at the eroded surfaces. Maximum microcutting and ploughing occur at 15-degree impingement angle. The contour plot between impact velocity and impingement angle, impact velocity and erodent size, and impact velocity and stand-off distance is shown in Figure 17, while Figure 18 shows the 3D relationship between erosion rate and impact velocity, impact angle, and standoff distance. Large amounts of material were transferred from the tested surface material due to the impact velocity of 46–48 m/sec at a distance of 22–24 mm. Erodent size is an important factor dictating solid particle erosion rate.Figure 16
Heat map between (a) impact velocity and impingement angle, (b) impact velocity and erodent size, and (c) impact velocity and stand-off distance of gunmetal.
(a)
(b)
(c)Figure 17
Contour plot between (a) impact velocity and impingement angle, (b) impact velocity and erodent size, and (c) impact velocity and stand-off distance of gunmetal.
(a)
(b)
(c)Figure 18
3D Surface plot among erosion rate, impact velocity, impingement angle, and stand-off distance (a, b, c) for gunmetal.
(a)
(b)
(c)


## 3.9. ANOVA and the Effects of Factors of Gunmetal

Analysis of variance (ANOVA) chart is a decision making methodology for exact confirmation of imagining the significance of effecting level of factors considered. In addition to that ANOVA is an analyzing tool to select the order of more meaningful factors. Table12 signifies the analysis of ANOVA to realize the contribution of factors on erosive wear rate. The ANOVA with erosion rate results are listed in Table 12. This analysis was assumed to be considered for a level of significance of 5%, that is, for level of confidence 95%. The last column of the table indicates the order of significance among control factors and interactions. It can be realized from Table 12 that the control factor P
=
0
.
027 has highest static influence of 28.81%, P
=
0
.
045 has an influence of 22.29%, P
=
0
.
218 has an influence of 8.10%, and P
=
0
.
345 has an influence of 5.23% on erosive wear rate of tested material system under observations. The results indicated that the factor (D) that is stand-off distance and impact velocity (A) exerted more effect on the erosion rate, followed by the impingement angle (B) and particle size (C). The effect of combined factors on impact velocity and sand size (A
∗
B) on erosive wear performance played a crucial impact.Table 12
Effects of factors of gunmetal. Analysis of variance forS
/
N, using adjusted SS for tests.
Source
DF
Seq. SS
Adj. SS
Adj. MS
F
P
P (%)
A
2
72.266
72.266
36.133
5.45
0.045
22.29
B
2
26.275
26.275
13.137
1.98
0.218
8.10
C
2
16.948
16.948
8.474
1.28
0.345
5.23
D
2
93.402
93.402
46.701
7.04
0.027
28.81
A
∗
B
4
23.756
23.756
5.939
0.90
0.521
7.33
A
∗
C
4
26.060
26.060
6.515
0.98
0.482
8.04
B
∗
C
4
25.747
25.747
6.437
0.97
0.487
7.94
Error
6
39.777
39.777
6.629
12
Total
26
324.231In case of comparative analysis of interaction of different alternative factors,A
∗
C = interaction within impingement velocity ∗ erodent size (P
=
0.482) has less number of P values compared to other two combinations. According to this perception, the factor interaction A
∗
B = velocity of impact ∗ angle of impingement (P
=
0.521) implies lesser significance of contribution on erosive wear rate in comparison with factor interaction B
∗
C = angle of impingement ∗ erodent size (P
=
0.487). Hence, the lower the P values, the higher the significance of contribution on the erosion rate justified. The present analysis shows that four levels of erosive test parameters impact velocity (A) and stand-off distance (D) individually and have both statistical and physical significance (percentage contribution is greater than error) in case of erosion rate of gunmetal. But interaction combinations between different control parameters have statistical significance but do not have physical significance, since error evaluated is more than percentage contribution of these interactions, which is evident from the ANOVA results.


## 3.10. Morphology of Eroded Surfaces

### 3.10.1. SEM Analysis

Surface Morphology at Different Impingement Angle. Then analysis of surface morphology of gunmetal was examined by using JEOL JSM 7600F Scanning Electron Microscope (country of origin Japan). SEM micrographs of eroded surfaces of gunmetal are appearing in Figures 19(a), 19(b), 19(c), 19(d), 19(e), and 19(f). Figures 19(a) and 19(b) specifies that gunmetal eroded surface at 15° impact angle is worn by the mechanism of microploughing, grooves, displaced material, and large fragments. Extensive ploughing and the resulting lip formation are evident in the micrograph for 15° impingement angle. The direction of ploughing in surface morphologies coincides with the direction of particle motion during sand blasting. This is the angle where the higher amount of erosion has been noted under all test conditions. Materials which show ductile erosion behavior can be easily worn off by microploughing erosion mechanisms caused by the lateral impact of the particles. In Figures 19(c) and 19(d) at 30° impingement angle pitting action and craters have occurred as a result of lower erosion rate of the all tested materials. On the other hand at 60-degree impingement angle plastic deformation, craters, and microcutting action have occurred in Figures 19(e) and 19(f). The reduction in mass loss at higher impact angles, near or at 90° at velocity lower than 50 m/sec, is because there was not too much evidence of sliding action of abrasive particles unlike lower impact angles where the sliding component is significant and increases the mass lost in the material. But the reverse is true in few cases for high impact velocity 50 m/sec due to the quick impacting at short contact time between particle and target surface.Figure 19
SEM micrograph of eroded aluminum alloy at impact angle, (a, b) 15 degrees, (c, d) 30 degrees, and (e, f) 60 degrees.
(a)
(b)
(c)
(d)
(e)
(f)Surface Morphology with Different Impact Velocity. Surface morphology at different impact velocity has been presented in Figures 20(a), 20(b), 20(c), and 20(d) for analyzing the wear mechanism. Figures 20(e) and 20(f) under impact velocity 30 m/sec emphasized the lower erosion rate due to displaced material and putting action. This is because of the low particle energy. Figures 20(c) and 20(d) show that the damage has occurred on the target surface at impact velocity 40 m/sec. In this case the damaged has been done by the influence of craters, pulling action. At higher impact velocity (50 m/sec) due to the effect of crack and ploughing action, higher levels of erosion are obtained as a result of high particle energy (Figures 20(a) and 20(b)).Figure 20
SEM micrograph of eroded gunmetal at impact velocity: (a, b) 50 m/sec, (c, d) 40 m/sec, and (e, f) 30 m/sec.
(a)
(b)
(c)
(d)
(e)
(f)


## 3.10.1. SEM Analysis

Surface Morphology at Different Impingement Angle. Then analysis of surface morphology of gunmetal was examined by using JEOL JSM 7600F Scanning Electron Microscope (country of origin Japan). SEM micrographs of eroded surfaces of gunmetal are appearing in Figures 19(a), 19(b), 19(c), 19(d), 19(e), and 19(f). Figures 19(a) and 19(b) specifies that gunmetal eroded surface at 15° impact angle is worn by the mechanism of microploughing, grooves, displaced material, and large fragments. Extensive ploughing and the resulting lip formation are evident in the micrograph for 15° impingement angle. The direction of ploughing in surface morphologies coincides with the direction of particle motion during sand blasting. This is the angle where the higher amount of erosion has been noted under all test conditions. Materials which show ductile erosion behavior can be easily worn off by microploughing erosion mechanisms caused by the lateral impact of the particles. In Figures 19(c) and 19(d) at 30° impingement angle pitting action and craters have occurred as a result of lower erosion rate of the all tested materials. On the other hand at 60-degree impingement angle plastic deformation, craters, and microcutting action have occurred in Figures 19(e) and 19(f). The reduction in mass loss at higher impact angles, near or at 90° at velocity lower than 50 m/sec, is because there was not too much evidence of sliding action of abrasive particles unlike lower impact angles where the sliding component is significant and increases the mass lost in the material. But the reverse is true in few cases for high impact velocity 50 m/sec due to the quick impacting at short contact time between particle and target surface.Figure 19
SEM micrograph of eroded aluminum alloy at impact angle, (a, b) 15 degrees, (c, d) 30 degrees, and (e, f) 60 degrees.
(a)
(b)
(c)
(d)
(e)
(f)Surface Morphology with Different Impact Velocity. Surface morphology at different impact velocity has been presented in Figures 20(a), 20(b), 20(c), and 20(d) for analyzing the wear mechanism. Figures 20(e) and 20(f) under impact velocity 30 m/sec emphasized the lower erosion rate due to displaced material and putting action. This is because of the low particle energy. Figures 20(c) and 20(d) show that the damage has occurred on the target surface at impact velocity 40 m/sec. In this case the damaged has been done by the influence of craters, pulling action. At higher impact velocity (50 m/sec) due to the effect of crack and ploughing action, higher levels of erosion are obtained as a result of high particle energy (Figures 20(a) and 20(b)).Figure 20
SEM micrograph of eroded gunmetal at impact velocity: (a, b) 50 m/sec, (c, d) 40 m/sec, and (e, f) 30 m/sec.
(a)
(b)
(c)
(d)
(e)
(f)


## 3.11. Analysis of Erosion with Different Percentage of Gunmetal at Different Impact Angles Using Energy Dispersed X-Ray Spectrograph (EDX)

The analysis of energy dispersed X-ray spectrograph (EDX) of gunmetal was done by using JEOL JSM 7600F Scanning Electron Microscope (country of origin Japan). In this method an electron beam of 10–20 KeV strikes at the tested surface that causes X-ray to be emitted from the point of incidence. The emission energy of X-ray depends on the types of materials under observation; that is, the use of X-ray energy emission shows distinct nature depending on soft to hard materials and thus it gives the unavoidable signature in case of some kinds of materials. When an X-ray strikes the detector, it will generate a photoelectron which in turn generates electron hole pairs. A strong electric field attracts the electrons and holes towards the opposite ends of the detector. The size of the pulse thus generated depends on the number of electron hole pairs created, which in turn depends on the energy of the incoming X-ray. In this method however elements with low atomic number are difficult to be detected. The detector which is lithium doped silicon (SiLi) is protected by a beryllium window and operated at liquid nitrogen temperatures.Figures21 and 22 show the amount of silica embedded within the eroded surfaces at impact angle of 15 degrees. Similar observations are found in Figures 23, 24, 25, and 26 for impact angles of 60 and 90 degrees, respectively. The EDX analysis shows that the percentages of embedded silica are increased with the decrease of percentage of copper in gunmetal for all tested angles. The significance of these observations is that the higher the copper composition in gunmetal, the lower the silica engagement within the target surfaces which causes lower erosion rate. The depth at which the particle has been embedded into the material was very small depth from the upper surface. Just beneath the lip, the particle embedded into the material has been observed by other researchers as well [45]. It was assumed that the amount of fragmentation and secondary erosion would be dependent on the particle velocity, impingement angle, particle size, stand-off distance, and different in hardness between the particle and target material. The variation of composition of tin and zinc has some limited role with the variation of erosion rate.Figure 21
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 15-degree impact angle.Figure 22
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 15-degree impact angle.Figure 23
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 60-degree impact angle.Figure 24
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 60-degree impact angle.Figure 25
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 90-degree impact angle.Figure 26
Energy dispersed X-ray spectrograph (EDX) aluminum alloy at 90-degree impact angle.The existence of the O and Si atoms in high percentage was the evidence of the embedded erodent garnet particles to the surfaces of the samples. Based upon the EDX analysis results, it was concluded that the erodent particles were embedded to the surfaces of theg during the erosion process. It was concluded that this can be possible because of the ductile behavior of the gunmetal.


## 3.12. Confirmation Experiment for Gunmetal

The end level of Taguchi approach is the validation of experimental observations for analyzing the quality characteristics. The validity of test results is ensured by concerning an arbitrary set of factor level combination and after that it has been compared with the test results. The measuredS
/
N ratio for wear rates is estimated in connection with the predictive equations.The estimatedS
/
N ratio for wear rates can be calculated with the help of following predictive equations:(14)η-=T-+A-2-T-+B-3-T-+C-2-T-+D-1-T-,where η
- is the predicted average; T
- is overall experimental average; A
-
2, B
-
3, C
-
2, and D
-
1 are the mean response for factors at designated levels.By combining like-terms, the equation reduces to(15)η-=A-2+B-3+C-2+D-1-3T-.A new combination of factor levels A
2, B
3, C
2, and D
1 is used to predict deposition rate through prediction equation and it is found to be η
-
=
-
64.866 for each performance measure; an experiment was conducted for different factors combination and compared with the result obtained from the predictive equation.The new generated model is very meaningful for the prediction erosive wear rate to a justifiable accuracy. The calculated deviation (error level) is 1.72% and is obtained in case ofS
/
N ratio of erosive wear rate. The results of experimental confirmation using optimal erosive wear parameters and comparison of the predicted erosion rate with the actual erosion rate using the optimal erosive wear parameters are indicated in Table 13. The improvement in S
/
N ratio from the starting level to optimum level is 0.858 dB. The erosion rate is reduced by almost 10%. Considering this scientific approach, it can be mentioned that erosion rate performance is improved by using Taguchi method. After all, the accuracy level can be improved more precisely in case of increase of the number of measurements. This validation approach incorporates the generation of the mathematical model for the prediction of measures of performance on the basis of knowledge of the input parameters.Table 13
Results of the confirmation experiments for erosion rate of gunmetal.
Optimal control parameters
Initial process parameter
Prediction
Experimental
Improvement in the result
Level
A2, B1, C2, D3
A2, B3, C2, D1
A2, B3, C2, D1
S
/
N ratio for erosion rate (dB)
−64.608
−64.866
−63.750
0.858
Erosion rate (mg/gm)
1699.83
1300.07
1523.80
10.35


## 4. Conclusions

The erosion results of gunmetal have provided some new findings relevant to different operating parameters. The validation of results and correlation of erosion with friction, Uttam Number, artificial neural network, ANOVA, erosion efficiency,S
/
N ratio methodology, GMDH concept have made the realization of novelty of the erosion study of this gunmetal. The morphological analysis provides the evidence of real wear mechanism incorporating displaced materials, grooves, ploughing action, large fragment, pitting action, indentations, crack, folded extruded lip, wear debris, and other related concerning issues for the eroded surface characterization under different impact angles, impact velocity, and stand-off distance. The EDX analysis shows that the percentages of embedded silica are increased with the decrease of percentage of gunmetal for all tested angles. The significance of these observations is that the higher the percentage of copper in gunmetal, the lower the silica engagement within the target surfaces which causes lower erosion rate. Erosion rate is maximum at 15° impingement angle for gunmetal at different impact velocities and particle size. At impact angle 15° erosion rate is high and then decreases gradually up to the impingement angle 45°. After that erosion rate increases ranging from 45° to 90°, in general, for all tested samples. The experimental results also show that erosion rates are slightly higher at 60° impingement angle in most cases as compared to 45°, 75°, and 90° impingement angle. The confirmation of ductile category has been ensured by identifying the highest erosion damage at an angle of 15 degrees. The increase of erosion in such fashion with impact velocity and probable kinetic energy level and temperature propagation through the area of tested surface has some exceptional characteristics of the gunmetal. The power law conception based approach ensures the validity of tested gunmetal group by confirming the value of exponent “n” within range 0.7804 to 0.913 and the rage mostly depends on the impact velocity, particular shape of erodent, and particle size rather than impact angle. The correlation of erosion rate with U. No. and relationship between erosion rate and friction factor provide very good agreement. This correlation can be used as a significant tool for future study. The erodent size and stand-off distance provide new insight into relation of these parameters with erosion rate under clarification of possible trends. The average S
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N ratio −64.866 dB and Taguchi design concept ensure the validation of experimental and theoretical results. The predicted and experimental S
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N ratio fluctuations within range 1.72% and predicted and tested model generated by GMDH and 3D explanations are the promising understanding of this newly tested gunmetal. ANOVA method ensures the identity of main dominating factors distinctly or as an interaction on erosion of the tested gunmetal.It is expected that the analysis of this new or novel concern relating to gunmetal can be used as authentic sources in industry and future researches for the applications of this material in different concerned mechanical and tribological systems.



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*Source: 815179-2015-12-07.xml*