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Erosive Wear Analysis of Mn-Steels

Hammers due to Coal Impact in a High-

Speed Pulverising Mill

By

Md Shahanur Hasan B. Sc in Mechanical Engineering (KUET, Bangladesh), Master of Science in Mechanical

Engineering (CQUniversity, Australia)

Submitted to the Queensland University of Technology, in fulfilment of the

requirements for the degree of Doctor of Philosophy

School of Chemistry, Physics, and Mechanical Engineering

Science and Engineering Faculty

Queensland University of Technology

2018

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill I

Keywords

Material model, Finite element simulation, Tensile test, Compression test, Pressure bar test,

Material fracture, Ductility, Mechanical properties. Erosion wear, Plastic deformation, Failure

strain, Mises stress, Stress Triaxiality, Surface damage, Energy, 3D model, Johnson and Cook

(JC) material model, Abaqus Explicit, Impact damage, Material model parameters, Strain

hardening, Surface hardness, Fractography, Micro-structure.

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill II

Abstract

The coal pulverisation process plays a significant role in thermal power plants to generate

electricity. Large-size coal lumps drop onto the hammer and are crushed and ground into small

particle sizes for effective combustion in power plant burners. Diverse types of pulverizing

mills are used in thermal power plant and related industries. Among them, high-speed hammer

mills are broadly used to pulverise coal.

Hammers are the key machine element of high-speed hammer mills which assist the coal

pulverisation process. Progressive material loss from the hammer occurs due to the mechanical

interactions between the coal particles and the hammer surface. Coal pulveriser industries

implement extensive efforts to combat against premature material loss from the hammer

surface.

This study investigates the erosion wear mechanism of 11% and 14% Mn-steels hammer

through numerical simulation. The behavior of high-manganese steel under large strains and

different strain rates needs to be investigated to predict its response to various dynamic loading

conditions including impact. An empirical constitutive relation developed by Johnson and

Cook (JC) is applied at high strain rate and dynamic loading conditions to determine the flow

stress behavior of Mn-steels during impact.

The deformation behavior of two high-manganese steel cylindrical specimens (11% and 14%

Mn-content) is studied using uniaxial quasi-static tensile tests, split Hopkinson pressure bar

tests at various strain rates and finite element (FE) simulation. These tests are conducted at

room temperature to examine the effects of strain rate, material plasticity and strain hardening

to ultimately determine the JC model parameters and material properties for subsequent use in

FE simulation. Fracture appearance of tensile test specimens is also studied using optical

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill III

microscopy and Scanning Electron Microscope. Results show that 11% Mn-steel exhibits more

toughness, ductility and strain hardening than 14% Mn-steel. The JC model parameters have

been evaluated and represented in tabular form. Tensile tests have been validated by FE

simulation using Abaqus/Explicit and results of more recently published works.

A numerical model is developed using Abaqus® to simulate the solid coal particle impacting

onto the hammer (target). The Abaqus/Explicit® dynamic simulation solver is used for the

analysis in question. The interactions between the solid coal particles and the target Mn-steels

are modelled using the Abaqus/Explicit® element deletion method. The developed stress and

plastic strain are analyzed through simulation of the impact surface. Material erosion wear loss

for both steels is determined under various impacting conditions. Simulation results are

subsequently verified using existing wear theory to validate the FE model.

The consequence of this wide-ranging research study is to develop an erosion wear model that

can be applied in coal pulverizing industries to select the best erosion wear-resistant material

which will reduce operational cost. The national and international benefit would be improved

technology, sustainable economical solution for related industries, Australian coal mining

industries, and worldwide thermal power plants. Hammer manufacturers, design engineers and

casting industries can also benefit from this research outcome.

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill IV

Table of Contents

Keywords ............................................................................................................................................ I

Abstract ............................................................................................................................................. II

Table of Contents .............................................................................................................................. IV

List of Figures ............................................................................................................................... VIII

List of Tables ................................................................................................................................ XIV

List of Abbreviations ..................................................................................................................... XV

Statement of Original Authorship .............................................................................................. XVIII

Acknowledgement ........................................................................................................................ XIX

List of Publications ........................................................................................................................ XX

Chapter 1: Introduction

1.1 Background and Significance ………… ................................................................... 1

1.2 Problem Statement ..................................................................................................... 5

1.3 Aim and Objective of the Study ................................................................................ 7

1.4 Thesis Outline. ........................................................................................................... 8

Chapter 2: Literature Review

2.1 Introduction .............................................................................................................. 10

2.2 Coal Pulverisation Process ...................................................................................... 10

2.2.1 Slow Speed Mills …………………………………………………………... 12

2.2.2 Medium Speed Mills ………………………………………………………. 12

2.2.3 High Speed Hammer Mills …………………………………………………. 13

2.3 Coal Comminution Process …………………………………………………………. 13

2.4 Wear Mechanism in Coal Mills ……………………………………………............... 16

2.4.1 Abrasive Wear ………………………………………………………………. 17

2.4.2 Corrosive Wear ……………………………………………………………... 17

2.4.3 Erosive Wear ………………………………………………………………... 17

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill V

2.5 Parameters Affecting Erosion Wear ………………………………………………... 21

2.5.1 Impact Velocity ……………………………………………………………... 22

2.5.1.1 Particle Kinetic Energy ……………………………………………... 22

2.5.2 Erodent Shape …………………………………………………………….… 23

2.5.3 Impact Angle ………………………………………………………………... 24

2.5.4 Erodent Particle Size …………………………………………………………25

2.5.5 Properties of Erodent Particles and Target Materials ……………….………. 25

2.5.5.1 Erodent Particle Hardness …………………………………….…... 25

2.5.5.2 Surface Hardness and Temperature Effect ….……………………… 26

2.6 Theory of Erosion Mechanism and Measurement Method …………………………. 26

2.7 Erosive Wear Resistance Materials ………………………………………………… 32

2.8 Modelling and Simulation …………………………………………………………... 37

2.8.1 Finite Element Model and Simulation …………………………………….... 37

2.8.1.1 Effect of Erosion Parameters on FE Simulation ……………………. 37

2.8.1.2 Effect of Material Properties on FE Simulation ………………….…. 40

2.9 Johnson-Cook (JC) Material Model Parameter ……………………………………... 44

2.10 Summary of Literature Review ……………………………………………………... 45

Chapter 3: FE Simulation Approach and Methodology

3.1 Introduction ………………………………………………………………………… 47

3.2 Model Development and FE Simulation …………………………............................. 47

3.2.1 Finite Element Package ………………………………………………….…. 47

3.2.2 Finite Element (FE) Concept ………………………………………………... 48

3.2.3 FE Analysis Package ………………………………………………………... 48

3.2.4 Explicit Dynamic Analysis …………………………………………………. 49

3.3 Model Geometry and Boundary Condition ………………………………………… 50

3.3.1 Assembly and Boundary Condition …………………………………………. 53

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill VI

3.3.2 Mesh ………………………………………………………………………… 54

3.4 Material Model ……………………………………………………………............... 55

3.4.1 Johnson–Cook Plasticity Material Model …………. ……............................. 56

3.4.2 Johnson – Cook Failure Model ………………………………....................... 57

3.4.3 Damage Evolution and Element Removal …………………………………... 59

3.5 Summary ……………………………………………………………………………. 62

Chapter 4: Physical Experiment and JC Parameter Determination

4.1 Introduction …………………………………………………………………………. 63

4.2 Quasi-Static Tensile Test …………………………………………………………… 63

4.3 Split Hopkinson Pressure Bar (SHPB) Test ………………………………………… 68

4.4 Simulation of Quasi-Static Tensile Test and Compression Test ...…………..............72

4.5 Numerical Simulation for Determining Stress Triaxiality.…………………..............74

4.6 JC Parameter Determination …………………………………………………………. 79

4.6.1 JC Strength Parameter Determination (A, B, n and C) ......................................... 79

4.6.2 JC Failure Parameters Determination (d1, d2, d3 and d4) ……….......................... 83

4.6.2.1 Determination of d1, d2 and d3 ……………………………………………… 83

4.6.2.2 Determination of d4 ………………………………………………………… 84

4.7 Summary ……………………………………………………………………………. 87

Chapter 5: Metallographic Analysis and Hardness Testing

5.1 Introduction …………………………………………………………………………. 88

5.2 Sample Preparation …………………………………………………………………. 88

5.3 Scanning Electron Microscope (SEM) Fractography ………….................................. 89

5.4 Optical Microscope Fractography ………………………………............................... 92

5.5 Microstructure and Element Analysis ………………………………………………. 95

5.6 Mn-steel Hardness Test ……………………………………………………………... 98

5.7 Microhardness Test ……………………………………………………………….... 99

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill VII

5.8 Summary …...…………………………………………………………………....... 100

Chapter 6: FE Simulation Results Analysis

6.1 Introduction ………………………………………………………………………. 101

6.2 Simulation Result Analysis…………………………………………….....................101

6.2.1 Effect of Erodent Impact Velocity on Erosion Loss ………...........................102

6.2.2 Effect of Erodent Size on Erosion Loss …………………………………… 106

6.2.3 Effect of Erodent Shape on Erosion Loss …………………………………. 110

6.3 Strain Hardening Effect …………………………………………………………… 113

6.4 Erosion Wear Calculation …………………………………………………………. 115

6.5 Model Validation ………………………………………………………….............. 119

6.6 Summary …………………………………………………………………………... 121

Chapter 7: Conclusion and Recommendation

7.1 Conclusion …………………………………………………………………............ 122

7.1.1 Significant of Contribution ………………………………………………… 122

7.1.2 Research Summary ………………………………………………………... 123

7.2 Recommendations …………………………………………..................................... 125

BIBLIOGRAPHY ………………………………………………………………………… 126

APPENDIX A ……………………………………………………………………………... 143

APPENDIX B ……………………………………………………………………………... 144

APPENDIX C ……………………………………………………………………………... 154

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill VIII

List of Figures

Figure 1.1 Coal pulverization flow diagram ……………………………………………... 2

Figure 1.2 Hammer mill used in Power Station …………………………………………...3

Figure 1.3 Cross sectional view of swing hammer ……………………………………… 4

Figure 1.4 Schematic diagram of particle impacting ……………………………………. 4

Figure 1.5 Coal particle impacting on a 3D hammer model ……………………………... 5

Figure 1.6 Unused hammer ……………………………………………………………… 6

Figure 1.7 Eroded hammer ………………………………………………………………. 6

Figure 2.1 High speed hammer mill ……………………………………………………. 13

Figure 2.2 Size reduction process diagram …………………………………………….. 15

Figure 2.3 Abrasive wear mechanism …………………………………………………... 17

Figure 2.4 Erosive wear mechanism …………………………………………………… 18

Figure 2.5 Processes resulting in wear loss of materials due to single or multiple impacts

of particles …………………………………………………………………... 19

Figure 2.6 Impact energy balance model ………………………………………………. 23

Figure 2.7 Particle striking and removing material ……………………………………. 27

Figure 2.8 Von Mises equivalent stress distribution on Ti-alloy target: (a) plastic

deformation, (b) plastic deformation and element failure by micro-ploughing or

cutting process ………………………………………………………………. 38

Figure 2.9 Finite element model ………………………………………………………... 39

Figure 2.10 Typical craters and pile ups formed on the surface resulting from impacts at 30

and 117 m/s impact velocity (a) experiment (b) simulation ………………… 41

Figure 2.11 Simulated surface topography during erosion at 117m/s impact velocity and 30°

impact angle of particles ……………………………………………………. 41

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill IX

Figure 2.12 Discretized 3D FE model of the two-layer NT-60 over NT-20 on AISI 4140

steel …………………………………………………………………………. 42

Figure 3.1 3D model (a) swing hammer (b) Rectangular Mn-steel plate for FE simulation

and (c) spherical shape coal erodent ………………………………………... 51

Figure 3.2 3D model (a) angular shape coal erodent

(b) rectangular shape coal erodent …………………………………………. 51

Figure 3.3 FE simulation flow chart …………………………………………………….52

Figure 3.4 Assembly geometry of spherical coal particle and Mn-steel plate …………. 53

Figure 3.5 Model mesh ………………………………………………………………… 54

Figure 3.6 Schematic of the C3D8R element …………………………………………… 55

Figure 3.7 Stress-strain behaviour of material damage ………………………………… 60

Figure 3.8 Algorithm elasto viscoplastic straining during time step …………………… 61

Figure 4.1 Instron tensile testing machine ……………………………………………… 64

Figure 4.2: a) Unusual shape of hammer and b) Specimen geometry ………………...... 65

Figure 4.3 Tensile test specimen ………………………………………………………. 65

Figure 4.4 Quasi-static tensile test for 11% and 14% Mn-Steel ………………………… 66

Figure 4.5 Load and displacement graph for 11% and 14% Mn-Steel …………………. 67

Figure 4.6 Split Hopkinson Pressure Bar (SHPB) arrangement ………………………… 68

Figure 4.7 Geometry of specimen used for dynamic SHPB test ……………………….. 71

Figure 4.8 True stress-strain evolution at various strain rates for 11% Mn-steel ………. 71

Figure 4.9 True stress-strain evolution at various strain rates for 14% Mn-steel ………. 72

Figure 4.10 a) FE mesh of cylindrical specimen, contour plot b) displacement,

c) reaction force and d) von Mises stress with necking …………………. 73

Figure 4.11 Simulated tensile stress vs strain for 11% and 14% Mn-steel ……………….74

Figure 4.12 Simulated compression stress vs strain for 11% and 14% Mn-steel ………… 74

Figure 4.13 Fracture point of interest ……………………………………………………. 75

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill X

Figure 4.24 Geometry of specimens for FE simulation, a) unnotched, b) 1mm notch radius,

c) 0.75mm radius notch and d) 0.5 mm notch radius ………………………. 76

Figure 4.15 Meshed tensile test specimens: Unnotched, 0.5 mm notch, 0.75 mm notch and

1mm notch …………………………………………………………………... 77

Figure 4.16 Contour plot of FE specimen for 11% Mn-steel showing the equivalent

triaxiality a) unnotched, b) 0.5 mm notched and c) 0.75 mm notched ……… 77

Figure 4.17 Contour plot of FE specimen for 14% Mn-steel showing the equivalent

triaxiality a) unnotched, b) 0.5 mm notched and c) 0.75 mm notched

………………………………………………………………………………. 78

Figure 4.18 Stress triaxiality versus time curves and mean value for the specimens:

unnotched, 1mm notched, 0.75mm notched and 0.5mm notched for 11% Mn-

steel …………………………………………………………………………. 78


unnotched, 0.75mm notched and 0.5mm notched for 14% Mn-steel ………. 79

Figure 4.20 Strain hardening factor ‘B’ and index ‘n’ for 11% Mn-steel …….…………. 80

Figure 4.21 Strain-rate sensitivity coefficient ‘C’ for 11% Mn-steel ………….………… 80

Figure 4.22 Strain-rate sensitivity coefficient ‘C’ for 14% Mn-steel …………….……… 82

Figure 4.23 Strain hardening factor ‘B’ and index ‘n’ for 14% Mn-steel ……….………. 82

Figure 4.24 Strain to fracture vs triaxiality ratio for 11% Mn-steel ………...……………. 83

Figure 4.25 Strain to fracture vs triaxiality ratio for 14% Mn-steel ……………………… 84

Figure 4.26 Strain rate sensitivity for 11% Mn-steel ……………………………………. 85

Figure 4.27 Strain rate sensitivity for 14% Mn-Steel ……………………………………. 86

Figure 5.1 Samples for metallographic analysis ………………………………………... 88

Figure 5.2 Scanning Electron Microscope ……………………………………………… 89

Figure 5.3 SEM micrographs showing ductile fracture in 11% Mn-steel samples (a) and

(b) longitudinal, and (c) and (d) cross-sectional ……………………………. 90

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XI

Figure 5.4 SEM micrographs showing ductile fracture in 14% Mn-steel samples (a) and

(b) longitudinal, and (c) and (d) cross-sectional ……………………………. 91

Figure 5.5 Optical microscope …………………………………………………………. 92

Figure 5.6 Optical micrographs showing ductile fracture in 11% Mn-steel samples at (a)

cross-section before etching and (b) after etching, (c) longitudinal before

etching and (d) after etching ………………………………………………… 93

Figure 5.7 Optical micrographs showing ductile fracture in 14% Mn-steel samples at (a)

cross-sectional before etching and (b) after etching, (c) longitudinal before

etching and (d) after etching ………………………………………………… 94

Figure 5.8 SEM microstructure of 11% Mn-steel alloy ………………………………... 95

Figure 5.9 SEM-EDS analysis of 11% Mn-steel alloy ………………………………… 96

Figure 5.10 XRD patterns of 11% Mn-steel alloy ………………………………………. 96

Figure 5.11 SEM microstructure of 14% Mn-steel alloy ………………………………... 97

Figure 5.12 SEM-EDS analysis of 14% Mn-steel alloy ………………………………… 97

Figure 5.13 XRD patterns of 14% Mn-steel alloy ………………………………………. 98

Figure 5.14 a) Vickers diamond hardness tester, b) Vickers indentation dimension

measurement ………………………………………………………………... 99

Figure 5.15 Digital microhardness tester ………………………………………………. 100

Figure 6.1 Impact velocity vs erosion loss for 11% Mn-steel ………………………….102

Figure 6.2 Impact velocity vs erosion loss for 14% Mn-steel ………………………….102

Figure 6.3 Mises stress for 11% Mn-steel plate impacted by 10mm coal ball at 90º with a

velocity of 275 m/s ………………………………………………………… 103


velocity of 300m/s …………………………………………………………. 104


velocity of 350 m/s ………………………………………………………….104


velocity of 250 m/s ………………………………………………………. 105

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XII


velocity of 300 m/s ………………………………………………………….105


velocity of 350 m/s ………………………………………………………… 106

Figure 6.9 Effect of impacting coal ball size on erosion loss for 11% Mn-steel ……… 107

Figure 6.10 Effect of impacting coal ball size on erosion loss for 14% Mn-steel ……… 107


velocity of 275 m/s ………………………………………………………… 108

Figure 6.12 Mises stress for 11% Mn-steel plate impacted by 10 mm coal ball at 90º with a

velocity of 275 m/s ………………………………………………………… 108


velocity of 275 m/s ………………………………………………………… 109


velocity of 275 m/s ………………………………………………………… 109

Figure 6.15 Influence of erodent shape on erosion loss for 11% Mn-steel ……………… 110

Figure 6.16 Impact position of angular shape coal on Mn-steel plate …………………... 111

Figure 6.17 Impact position of spherical shape coal on Mn-steel plate ………………… 111

Figure 6.18 Mises stress for 11% Mn-steel plate impacted by 20mm size of angular coal

erodent at 90º with a velocity of 275 m/s …………………………………... 112

Figure 6.19 Model energy balance plot ………………………………………………… 113

Figure 6.20 Strain hardening effect due to impact for 11% Mn-steel …………………… 114

Figure 6.21 Strain hardening effect due to impact for 14% Mn-steel …………………… 114

Figure 6.22 Screen shot for target Mn-plate mass in Ton from Abaqus ………………. 115

Figure 6.23 Screen shot for target Mn-plate mass in Ton from Abaqus

after element deletion ……………………………………………………... 116

Figure 6.24 Mises stress for 11% Mn-steel plate impacted by 10 mm coal ball at 90º with a

velocity of 275 m/s ………………………………………………………… 117

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XIII

Figure 6.25 Mises stress for Mn-steel plate impacted by 20 mm coal ball at 90º with a

velocity of 300 m/s ………………………………………………………… 118

Figure 6.26 Mises stress for Mn-steel plate impacted by 20 mm coal ball at 90º with a

velocity of 300 m/s ………………………………………………………… 118

Figure 6.27 Results obtained from FE simulation model vs Bitter model ……………… 120

Figure C-1 Damage initiation criteria for 11% Mn-steel plate impacted by 20mm coal ball

at 90º with a velocity of 275 m/s …………………………………………… 154




at 90º with a velocity of 350m/s …………………………………………… 156





Figure C-6 Damage initiation criteria 11% Mn-steel plate impacted by 20mm coal ball at

15º with a velocity of 350 m/s ……………………………………………… 159

Figure C-7 Mises stress for 11% Mn-steel plate impacted by 20mm coal ball at 15º with a

velocity of 350 m/s ………………………………………………………… 160



Figure C-9 Mises stress for 14% Mn-steel plate impacted by 20mm coal ball at 90º with a

velocity of 350 m/s ………………………………………………………… 162


at 90º with a velocity of 300m/s ……………………………………………. 163


at 90º with a velocity of 250m/s ……………………………………………. 164

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XIV





Figure C-14 Damage initiation criteria 11% Mn-steel plate impacted by 20mm size angular

coal erodent at 90º with a velocity of 275 m/s ……………………………. 167

List of Tables

Table 1.1 Chemical composition of Mn-steel hammer …………………………………. 7

Table 1.2 Coal ash analysis ……………………………………………………………... 7

Table 2.1 Properties of target materials ………………………………………………... 34

Table 2.2 Damage parameters variables for erosion wear due to impact ……………… 45

Table 3.1 Mechanical properties of coal particle ………………………………………. 55

Table 4.1 Mechanical properties of different wt% of manganese steel ………….……. 67

Table 4.2 Strain rate data for 11% Mn-steel …………………………………………... 81

Table 4.3 Strain rate data for 14% Mn-steel …………………………………………… 81

Table 4.4 JC failure parameters in first bracket of equation 3.10 in Chapter 3………… 84

Table 4.5 Material properties and JC parameters for 11% Mn-steel …………………... 86

Table 4.6 Material properties and JC parameters for 14% Mn-steel …………………... 87

Table 4.7 Physical and mechanical properties of coal …………………………………. 87

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XV

List of Abbreviations

Vc [m/sec] Coal particle falling velocity

Vh [m/sec] Hammer speed

Vc/h [m/sec] Resultant impact velocity

N [rpm] Hammer rotational speed

r [mm] Hammer mill radius

E [mass/mass] Erosion rate

C [-] Constant

V [m/sec] Impact velocity

p [-] Velocity exponent

m [gm] Mass

KE [J] Kinetic energy

α [º] Impact angle

Q [mm3] Volume loss

P [MPa] Plastic flow stress

Wd [mm3] Volume loss

M [gm] Erodent mass

K [m/s] Threshold velocity constant

𝜎𝑦 [MPa] Yield stress of target material

𝜌𝑝 [kg/m3] Erodent density

ρt [kg/m3] Target material density

𝛾𝑝 [-] Erodent poission’s ratios

𝛾𝑡 [-] Target material poission’s ratios

Ep [GPa] Erodent modulus of elasticity

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XVI

Et [GPa] Target material modulus of elasticity

ε [J] Energy required to remove per unit volume

ɸ and λ [J] Energy required to remove per unit volume

T [-] Material constant

R [mm] Spherical particle radius

Er [gm/mg] Erosion rate

K1 [-] Material constant

RT [-] Tangential restitution ratio

𝜀𝑐 [-] Critical strain

Δ𝜀𝑝 [-] Plastic strain increment

β [-] Fraction of volume by indentation

JC [-] Johnson and Cook

FE [-] Finite Element

σ [MPa] Flow stress

ε−pl [-] Equivalent plastic strain

ε̇−pl [-] Equivalent plastic strain rate

θ̂ [ºC] Homologous temperature

A [MPa] JC model material strength constant

B [MPa] JC model material strength constant

C [-] JC model material strength constant

n [-] JC model material strength constant

m [-] JC model material strength constant

d1- d2 [-] JC model material fracture strength constant

ωJC [-] Damage variable

∆ε̅f [-] Equivalent plastic strain increment

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XVII

ε̅f [-] Failure strain

p/q [-] Stress triaxiality

SHPB [-] Split Hopkinson Pressure Bar

SR [-] Strain Rate

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XVIII

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet requirements for

an award at this or any other higher education institution. To the best of my knowledge and

belief, the thesis contains no material previously published or written by another person except

where due reference is made.

Signature:

Date: 08/10/2018

QUT Verified Signature

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XIX

Acknowledgements

This is my great pleasure to acknowledge those who have encouraged me and contributed in

many ways during my research study.

I would like to express my deepest and sincere gratitude to my Principal Supervisor Dr Dennis

De Pellegrin for his tireless guidance, wonderful support, and valuable suggestions and

comments throughout my candidature. I am very much proud to work with him and his

professional guidance and encouragement greatly assisted me to achieve my research goals. I

am grateful to Professor Cheng Yan and Dr Wijitha Senadeera for their valuable suggestions

and support.

I would like to convey my special thanks to QUT for the award of a research scholarship and

financial support throughout my study. I am most thankful to the WEARTECH FOUNDRY

for providing me the Mn-steels hammer samples and Gladstone Power Plant to provide me the

eroded hammers. My special thanks to Dr Andrew Brown for his outstanding support to

successfully complete the experimental activities at UNSW Canberra. I am extremely grateful

to QUT-Design and Manufacturing Centre (DMC) and CARF team for their great efforts to

perform experimental activities, and especial thanks to HPC team for their excellent supports

to successfully complete my simulation works.

This thesis could not have been successfully completed without the emotional support of my

wife and my motivating children. Finally, I should offer thanks to my family members for

encouraging and giving me mental support.

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill XX

List of Publications

Publications from this research

Journal Articles (Refereed)

1. Hasan, M.S, De Pellegrin, D., Hargreaves, D and Clegg, R.E, Numerical Investigation

of Hammer Erosive Wear due to Particle Impact. Applied Mechanics & Materials,

2016. ISSN:1662-7482, Vol.846, pp 237-244. Trans Tech Publications, Switzerland.

Journal Submitted (Refereed)

1. Hasan, M.S, De Pellegrin, D., Clegg, R.E and Yan, C, Johnson-Cook Model Parameters

Determination for 11% and 14% Mn-Steel, International Journal of Materials Science and

Engineering: B

Journal in Progress (Refereed)

1. Hasan, M.S, De Pellegrin, D., Clegg, R.E and Yan, C, Numerical Assessment of 11%

Mn-steel Erosion Wear due to Coal Impact, International Journal of Machine Tools and

Manufacturing.

Erosive Wear Analysis of Mn-steels Hammers due to Coal Impact in a High-Speed Pulverising Mill 1

1.1 BACKGROUND AND SIGNIFICANCE

Coal pulverisers are mechanical machine units in which large coal particles are crushed and

ground into sub-75-micron (<0.075 mm) sizes for effective combustion in burners of power

plants. This pulverised coal is conveyed by compressed air to coal burners to burn in the

furnace. Pulverised coal particles react effectively with oxygen in the air-gas stream. Usually,

larger coal particles do not burn out completely and unburned carbon particles keep

accumulating inside the furnace.

In the pulverisation process, the raw coal is dropped from a bunker onto a feeder conveyor belt

as explained in Figure 1.1 and is transported to the coal mill. The coal falls onto a rotating table

inside the mill. Rollers or hammers in the mills crush and grind the coal into powder form and

the fine particles are picked up by primary air. The primary air is heated, so that it can dry the

coal, which initially contains some percentage of moisture [1]. The coal particles are

transported with the air upwards toward the outlet pipes. Heavy particles, whose size is too

large, drop and fall back onto the table for regrinding. Figure 1.1 shows the general flow

diagram of coal pulverising system.

CHAPTER 1: INTRODUCTION


Figure 1.1: Coal pulverisation flow diagram

The industry applications of pulverized coal particles are as follows [1]:

• Pulverised coal combustion in a boiler to generate electricity.

• Pulverised coal injection in cement kiln to produce cement clinker.

• Pulverised coal injection in a blast furnace to assist economic iron making.

• Entrained particle gasification to make syngas for electricity generation.

• Entrained particle gasification to make syngas for chemical production.

There are different types of pulverising mills for grinding coal, such as: slow-speed, medium-

speed and high-speed hammer mills. Among these, the high-speed hammer mill, or impact

mill, is widely used for power generation in Australia and worldwide [1]. As shown in Figures

1.2, 1.3 and 1.4, hammers are fitted on the rotor and coupled with a shaft of the mill. Figure

1.5 shows the 3D model of spherical coal particles impacting on the swing hammer. The shaft

rotates at about 1000 rpm, driven by an electric motor and gear box. The raw coal particles, of

average size 10-20 mm diameter, are dropped onto the rotating hammers which break the coal

into particle sizes by several impacting and dynamic mechanisms. Due to the repeated

Coal conveyed from mine

Raw coal crusher

Raw coal accumulated in bunker

Raw coal feeder

Coal pulveriser mill - Slow speed mill

- Medium speed mill

- High speed

hammer mill

Hot air

Pulverised coal in

furnace for burning


impacting action and mechanical interaction between the hammer surfaces and solid coal

particles, progressive loss of material from the hammer surface gradually occurs through

frequent deformation and cutting action. This phenomenon of material loss is called erosive

wear. The rate of erosive wear depends on parameters such as impact angle, impact velocity,

particle kinetic energy, particle size, particle shape, material hardness, temperature, plastic

deformation, and mechanical properties of materials.

Figure 1.2: Hammer mill used in Power Station


Figure 1.3: Cross-sectional view of swing hammer

Figure 1.4: Schematic diagram of particle impact [2]


The velocity diagram of coal particles impacting the hammers is shown in Figure 1.4. It is

assumed that Vc is the coal particle’s falling velocity, Vh is the hammer speed and Vc/h is the

resultant impact velocity. In the high-speed hammer mill, rotational speed is typically N = 1000

rpm and radius at impact is r = 543 mm; therefore, the hammer velocity is Vh = 57 m/s. The

particle velocity is estimated as Vc = 16.5 m/s, then the resultant velocity is 𝑉𝑐/ℎ= 59 m/s. The

time taken to return the hammer into the previous position for the next impact, is given [2] by

t = 2𝜋𝑟

𝑉ℎ = 0.06 s.

Figure1.5: Coal particle impacting on a 3D hammer model

1.2 PROBLEM STATEMENT

Erosive wear is the utmost dominant wear mechanism in the coal pulverisation process,

especially in hammer mills. This type of material degradation due to impact occurs in many

industries, like: transport, aeronautical, mining, cement, and other related industries. Eroded

and fresh unused hammers were collected from the coal pulveriser mill of a local

manufacturing company, as shown in Figures 1.6 and 1.7 respectively.


Figure1.6: Eroded hammer Figure 1.7 Unused hammer

Figure 1.6 shows a damaged/worn hammer of 2.7 kg weight and Figure 1.7 shows a new unused

hammer of 8 kg weight. It is found that more than 5 kg of material was lost due to erosive wear

phenomena during 8,500 hours of operation. The metal removal rate is calculated to be 0.5

gm/h.

The hammers are made by 11% and 14% Mn-steel of grade AS2074/H1A and manufactured

by WEARTECH FOUNDRY using the casting process, in compliance with Australian

Standard AS 2074 - 2003. Hammers in high-speed mills are eroded due to the repeated coal

particle impacts.

Austenitic manganese steel also called Hadfield’s manganese steel contains around 10 - 14%

Mn with 1 – 1.4% C. After cast, this alloy is rapidly cooling by water quenching from the

temperature of about 1040ºC and homogeneous austenitic is retained. Consequence, alloy

becomes high toughness, strength, ductility, and excellent wear resistance characteristic of

austenitic steel [3].


Chemical composition of hammer alloy is shown in Table 1.1.

Table 1.1: Chemical composition of Mn-Steel hammer [4, 5]

Mn C Si P

11 1 1 0.1

14 1.4 1 0.07

Material degradation of hammer during the pulverising process also depends on the coal

properties. Schumacher [1] found that coal with the presence of sulphur (SO3) and sulphides

like iron pyrite (FeS2) and high moisture content showed high levels of erosive wear on the

hammer. Similarly, Juniper [6] pointed out that silica (SiO2) content coal enhances the tendency

towards erosive wear in the coal pulverisation mill.

Table 1.2: Coal Ash Analysis [7]

SiO2 Al2O3 Fe2O3 CaO MgO Na2O K2O TiO2 Mn3O4 P2O5 SO3

72.3% 23.3% 0.9% 4.07% 0.2% 0.1% 0.3% 1.4% 0.1% 0.1% 0.1%

1.3 AIM AND OBJECTIVE OF THE STUDY

The aim of this research is to investigate the hammer erosion wear behavior for both 11% and

14% Mn-steels and offer a finite element erosion wear model to predict the material erosive

behavior. As a result, industry will select proper manganese steel hammer to save time and

money of coal pulverisation process. This study investigates two main aspects: Mn-steels

material model parameters and finite element erosion wear model.

Some specific objectives of this research are summarized to achieve the goal:

➢ Obtain mechanical properties and material model parameters for both Mn-steels.


➢ Determine the fracture strength, ductility, strain hardening effect and micrographic

analysis for both Mn-steels.

➢ Develop a finite element model to simulate the coal impact on the Mn-steels for erosion

wear assessment and material loss estimation.

➢ Determine dominant stress and strain components due to impact causing surface

damage and material removal from the hammer.

➢ Investigate theoretically the erosion wear loss from the hammer and compare with the

simulation results.

1.4 THESIS OUTLINE

The thesis has seven chapters. Chapter 1 describes the background and significance of the coal

pulverisation process and erosive wear of Mn-steels due to repeated impact of coal erodent on

the hammer. Chapter 1 also presents the objective of the study and thesis outline.

Chapter 2 presents the relevant background information on coal pulverisation phenomena,

material wear during pulverization and related erosive wear theory. The effects of impact

parameters on hammer erosive wear are described. The finite element (FE) simulation process

is discussed to find the impact erosion of the materials.

Chapter 3 represents the FE simulation method, theories of Abaqus Explicit dynamics analysis.

It discusses the Johnson-Cook material models for plasticity and failure, and damage evolution

due to impact. It also presents the simulation model and detailed procedure for determining

hammer erosive wear due to coal erodent impact.


Chapter 4 presents the Quasi-static tensile test and Split Hopkinson Pressure Bar (SHPB) test

for both 11% and 14% Mn-steels. It describes the Johnson-Cook model parameter

determination procedure using tensile tests and simulation results.

Chapter 5 outlines the hardness test for both Mn-steels. It also describes the micrographic,

microstructure and elemental analysis using SEM and optical microscopy at the tensile failure

zones.

Chapter 6 presents the simulation results for 11% and 14% Mn-steels. The results predict the

amount of material removal due to coal erodent impact. Simulation results are displayed in the

graphical form in terms of erosion loss with impact speed, erodent shape and size, and energy.

Simulated results are compared with the published results and theory.

Chapter 7 presents the overall summary of the research and concluding remarks. It also includes

further recommendations for the erosion wear analysis of Mn-steels and other erosion resistant

material to improve hammer performance.


2.1 INTRODUCTION

Wear in the coal pulverisation process plays a crucial role in evaluating the coal pulverising

mill’s performance. Raw coal sourced from the mine site is crushed and ground into small

particle sizes ranging from 50 to 75 µm for better combustion performance. Pulverised coal

particles are required to be reduced in size to a specified limit before they can be fed into the

burner for intense and complete combustion inside the boiler.

The coal particles size reduction process in power plants is a physical process that accounts for

up to half of the operational costs of the plant [8]. Mill wear occurs during the coal pulverising

process and some machine elements are especially affected, such as the hammers, rotating

shaft, beater plate and tube mill liners. As a result, coal pulverising industries incur high

operating costs to combat mill wear. The literature review in this chapter focuses on coal

pulverising phenomena, the causes of mill wear, related wear theories and finite element

simulation for the assessment of erosive wear of hammers made of Mn-steels.

2.2 COAL PULVERISATION PROCESS

Diverse types of equipment are used to pulverise coal into small particles such as hammer

mills, roller mills, ball mills and stirred ball mills. These mills experience abrasion,

compression or impact phenomena. Particularly, hammer mills are used for both compression

and impact mechanisms to produce smaller size coal particles as the coal grinding process

involves strong impact between rotating hammers and falling coal particles [9].

Zulfiquar et al [10] have observed that both ball and vertical spindle mills were widely used in

coal fired power plants. Some coal fired power plants reportedly used hammer mills which also

CHAPTER 2: LITERATURE REVIEW


have the potential of grinding biomass fuels. Apart from ball, hammer, and vertical spindle

mills, knife mills were also included in this section as they are more suitable for bio-mass fuels

because of their cutting blades.

High-rank coals contain more carbon and energy than low-rank coal and tend to have low

moisture content and require the finest grinding; they are usually ground in tube/ball mills

although vertical spindle mills may also be used. Low rank coals tend to have high moisture

content and are usually ground in hammer mills [11]. High-volatile coal pulverizing in ball

mills provides an excellent combustion performance compared to any other coal grinder [12].

Day et al. [13] studied the hammer mill to fragment soft (coal) and hard (iron ore) materials.

They examined the effects of feed rate and rotor speed in terms of reduction ratio, energy

expenditure, and particle size using a hammer mill. It was found that high rotor speed with low

feed rate exhibits better hammer mill performance. Also, it was found that hammer mills

perform better in terms of lower wear rate with hard coal particles. Similarly, Austin [14] found

that high-speed hammer mills break the coal into smaller particle sizes by high velocity impact

with the hammer.

According to speed, coal pulverisers in power plants can be classified into three major

groups [11]:

• slow speed mills, e.g. tube mills,

• medium speed mills, e.g. vertical spindle mills and

• high speed mills, e.g. hammer mills.

These mills are briefly described in the following section.


2.2.1 SLOW SPEED MILLS

In a slow speed mill, a horizontal cylindrical drum rotates at about 17 rpm. Within this drum,

there is a charge of balls from 50 to 20 mm in diameter. Coal lumps are fed into the mill and a

cascade of balls from the mill rotation breaks up the lumps. This process is not completed in a

single pass and oversize materials are returned to the mill via a classifier for further grinding

to achieve the required particle size for combustion. The mills may be double-ended to increase

capacity. Important coal properties are calorific value, moisture content, particle size and

content of volatile matter. This type of mill does not handle high moisture content coal well

and capacity falls about 3% for every 1% increase in moisture content [8].

2.2.2 MEDIUM SPEED MILLS

In a medium speed mill, a horizontal table rotates at about 50 rpm. Rollers or balls lie in a track

on the table and are pressed down onto a bed of coal on the table by the application of spring

or hydraulic force. As the table rotates, it draws coal under a roller or ball where the grinding

takes place. About 5% of the material is reduced to the desired product size per pass under a

roller or ball, with the oversize particles recycled for further grinding. Partly ground coal passes

up through the mill body with carrier air, passing through a series of classification zones, with

the required size coal particles passing out of the mill while oversize particles return to the

grinding zone. The mill is primarily used for grinding black coal and mill capacity can be up

to 100 ton per hour. This type of mill can handle coals with medium moisture content and

medium abrasiveness [8].


2.2.3 HIGH SPEED HAMMER MILLS

In a high-speed mill, as displayed in Figure 2.1, hammers are fitted on the rotor and coupled

with a shaft which rotates at about 1000 rpm. Raw coal is impacted at high velocity by the

rotating hammers which break the coal into various particle sizes by multiple impacts. High

speed mills can handle high moisture content well, but excessive wear takes place with high-

abrasiveness coals [8].

Figure 2.1: High speed hammer mill

2.3 COAL COMMINUTION PROCESS

Coal particle comminution processes are an important part in many industrial systems. Almost

all industrial plants require their raw feed to undergo a size reduction process either as a pre-

processing operation or for post-processing of the product. Mills not only reduce the size of the

solids, but also yield a product with the required size distribution. For this reason, mills are

usually equipped with a mesh screen or other size classification units. In solid fuel combustion


systems, the comminution process is essential to obtain a uniform size of particles for better

combustion performance [10].

Material comminution processes depend on many factors including particle properties such as

hardness, density, moisture and mineral matter, as well as machine variables such as, grinding

pressure, roller gap, and type of the roller [8, 15-17]. In addition, aerodynamics of the mill (e.g.

particle entrainment by air and particle flow on the rotating table) and its classifier system

introduce additional influential parameters in the overall comminution process. Pulverised coal

particles in the furnace are required to be reduced in size to a specified limit before they can be

fed into the burners for intense and complete combustion inside the boiler [8].

A renewed study of power plant milling system is required to implement coal and biomass co-

firing technique because much of the available information is related to coal comminution

rather than its blends with biomass fuels. The potential problems of using biomass in existing

milling systems have been identified in a number of past studies [18] [19].

There are four basic types of comminution mechanism in the coal pulverising mill [1]:

a) Impact

b) Attrition

c) Compression

d) Shear

These comminution mechanisms are briefly discussed below.

a) Impact: This is a sharp instantaneous contact of one moving object on another.

Hammer mills in coal pulverising process follow this impact mechanism to break and

grind coal into the desired particle size.


The action of impact occurs in two main ways: i) gravity impact and ii) dynamic impact.

i) Gravity impact occurs in coal handling plant when coal is dropped onto the hard

hammer surface for grinding into smaller particle sizes.

ii) In dynamic impact, coal is struck by a hammer in an unrestrained environment. This

mechanism follows Newton’s second law of motion, with particles accelerating

away from the impact and usually taking part in numerous other impacts.

b) Attrition: Attrition occurs when two hard surfaces slide relative to each other with coal

particles in between. Figure 2.2 shows the attrition process.

c) Compression: This comminution process occurs when coal particles are entrapped

between two hard surfaces and pressure is applied to break the particles.

d) Shear: When one hard surface moves toward the coal particles located on another

stationary hard surface particle breaks by appliying load. Figure 2.2 shows the

phenomena.

Figure 2.2: Size reduction process diagram

Takeuchi et al [20] analysed the pulveriser system observing that the rotating hammers of the

pulveriser create fluid flow between a concavo-convex stator. Coal impacts against pulveriser

walls and hammers and is finally ground into the different particle sizes. The properties of


particles are affected by fluid flow in the pulveriser system. During the pulverising process,

wear occurs on the machine elements, which is discussed in detail in the following section.

2.4 WEAR MECHANISM IN COAL MILLS

Wear in coal mills plays a significant role when evaluating mill performance including

maintenance costs. Wear is characterized as a process of surface damage due to mechanical

interactions between metals and coal particles. There are many parts or machine elements in

the coal pulveriser such as: hammers, beater plate, fuel pipe bend, classifier, splitters, shaft,

and rotor; these are all affected by wear which can severely affect the performance of the

pulverisation process.

There are some factors that may affect wear in coal grinding mills [21]:

1. Moisture content in coal (high moisture content may enhance the corrosion/erosion

mechanism).

2. Presence of sulphur (SO3) and sulphides like iron pyrite (FeS2).

3. Low grindability coals.

4. Wear material selection (particularly grinding media).

5. Load circulation (Increased grinding for a given output).

6. Material hardness and particle impacting speed

Juniper [6] has pointed out that silica (SiO2) content in coal is enhances tendency towards wear

in coal mills. Creelman et al [21] found three types of wear in coal mills during the pulverisation

process such as, a) abrasive, b) corrosive and c) erosive wear.


2.4.1 ABRASIVE WEAR

Abrasive wear occurs when a hard-rough surface slides across a softer surface. Abrasive wear

is found in ball/tube mills and in vertical spindle mills. There is a difference between two body

and three body abrasive wear mechanism. Two body tends to be ten times worse than three

body. Figure 2.3 shows the abrasive wear phenomena.

Figure 2.3: Abrasive wear mechanism

2.4.2 CORROSIVE WEAR

When a metal specimen comes into contact with a corrosive environment, corrosive wear

occurs due to a chemical reaction between the material, oxygen and moisture present in the air.

Under these conditions, weak oxide films may grow quickly and be worn away quickly by the

action of erosive wear. In pulverising mills oxide films are formed on the iron parts due to the

abundant airflow and presence of moisture in the coal. Wear is enhanced by a combination of

corrosion and erosion that takes away material from the metal surface.

2.4.3 EROSIVE WEAR

Erosive wear is caused by high-velocity impact of hard solid particles against the surface of an

object. Materials from the surface are gradually removed by the coal particles impacting on the

object through repeated deformations and cutting actions. Erosive wear is the utmost dominant

wear mechanism in the coal pulverisation process, especially in hammer mills. About one third


of coal pulverisation mills are hammer mills and these mills are also widely used worldwide to

pulverise coal for electricity generation.

Figure 2.4: Erosive wear mechanism

Zum Gahr [22] raises the following factors that affect the mechanism of erosive wear.

• Angular particles can remove material by micro-cutting while they strike the target

surface at small grazing angles.

• Temperature effects can be superimposed due to high impact energies and friction

forces induced by adhesion between the particles and the target.

• The ratio of particle hardness and target material hardness.

• Surface cracking becomes important with increasing impingement angle, particle size,

particle velocity and the increasing brittleness of the target material.

• More erosion rate was observed on brittle materials than on ductile materials.

Bakker [23] illustrated the six different types of erosive wear phenomena, shown in Figure

2.5, due to impacting actions such as a) micro-cutting and micro-ploughing, b) surface

cracking, c) extrusion of material at the exit end of impact craters, d) surface and subsurface


fatigue cracks due to repeated impact, e) formation of thin platelets due to extrusion and

forging by repeated impact and f) formation of platelets by a backward extrusion process.

Figure 2.5: Processes resulting in wear loss of materials due to single or multiple

impacts of particles [23].

Furthermore, Hutchings and Winter [24] defined erosion as “an abrasive wear process in which

the repeated impact of small particles on the target entrained in a moving fluid against a surface

results in the removal of material from that surface”.

In addition, Stachowiak [25] investigated that removal of materials in erosive wear involved

different mechanisms. For ductile alloys, material removal was caused by the micro-cutting

and micro-ploughing of the solid particles, as shown in Figure 2.5 (a). For brittle materials such

as ceramics, wear occurs by energy transfer from impacting solid particles to the surface of the

target materials. This process will induce material deformation, crack initiation and


propagation, as shown in Figure 2.5 (e), (f) and (b). As a result, the materials pieces detach

from the surface.

Similarly, Aquaro [26] studied that erosion of ductile materials occurs due to the mechanism

of micro extrusion, forging, fracture and plastic deformation by the repeated impact of particles

on the materials. For ductile materials, maximum erosion was obtained at the impact angle of

20-30°, whereas lowest erosion was found at 90° impact angle.

There are different variables affecting erosion [27]:

a) Dynamic of impingement:

• Particle velocity

• Angle of impact

• Particle concentration

b) Impacting particle variables:

• Particle shape

• Particle density

• Particle size

c) Material variables (work piece and particles)

• Young’s modulus

• Poisson’s ratio

• Plastic behaviour

• Failure behaviour

This study concentrates on the measurement of erosive wear rather than abrasive and corrosive

wear. As discussed, abrasive wear occurs during the sliding actions between the hard surface


and soft coal particles. There are minor abrasive wear effects found during particles impacting

on a hammer, as extremely short sliding motion occurs and executes within a short time

interval. However, corrosive wear happens in the machine elements of coal grinding mills and

negligible amount of material loss tends to occur. Therefore, this study only focuses on the

effect of erosive wear on hammer due to coal particle impact. The effects of impact parameters

on erosive wear are discussed in the following section.

2.5 PARAMETERS AFFECTING EROSIVE WEAR

Balasubramaniyam [28] considered various factors affecting the erosion process such as the

variations in the physical, mechanical, chemical, thermal and dynamic behaviour of both

erodent particles and target eroding materials. The major parameters that affect the erosion of

materials are listed below.

1) Impact velocity

2) Impact Angle

3) Erodent Shape

4) Erodent Size

5) Material properties of erodent and target

6) Temperature

Gahr [29] determined that the erosive wear mechanism strongly hinges on the impact angle,

particle size, impact velocity, target material properties including hardness. Due to the

impacting of solid particles, erosive wear on material surfaces leads to different events such as

adhesion, abrasion, deformation, heating, surface fatigue and fracture. Aquaro and Fontani [27]

studied and categorized the three types of variables affecting erosive wear such as a)

impingement variables: particle velocity, impact angle and particle concentration, b) particle


variables: particle shape, particle density and particle size, and c) material variable: mechanical

properties like Young’s modulus, Poisson’s ratio, hardness and toughness.

All these variables influence the manifestation of erosive wear. Some of the variable

parameters are discussed in the following section.

2.5.1 IMPACT VELOCITY

Impact velocity of erodent particles is the most important controlling factor on metal erosion

rate. High rate of erosion occurs at higher particle impacting velocity. The erosion rate (E) of

a material was defined as the ratio of weight loss suffered by the eroding material to the weight

loss of erodent particles causing the loss. Erosion rate velocity dependence is characterized by

the velocity exponent p given by [30, 31]:

𝐸 = 𝐶𝑉𝑝 ................................................................................................................. (2.1)

where, C is a constant and V is the impact velocity p is the velocity exponent. The value of

velocity exponent is in the range of 2 – 3 for ductile materials.

Similarly, Zum Gahr [22] and Bakker [23] examined and concluded that particle impacting

velocity was one of the leading factors generating the erosion wear on the hammer of coal

pulverising mills. In this case, the fuel pulverising system was designed to keep the impacting

velocity below 25 m/s.

2.5.1.1 PARTICLE KINETIC ENERGY

When coal particles impact on metal alloys for pulverisation, stored energy in the particles

depends on the diameter and density at the points of contact between the target alloy and the

particles. Kinetic energy is utilised to deform the alloy surface and subsequently remove the


material from the surface. Hardness, strength, and shape of particles are the most responsible

factors influencing the efficiency of erosive wear. Hard, high strength and sharp edged particles

are more capable of transmitting relatively high amounts of energy over small areas causing

rapid material erosion [32]. The following relation models the kinetic energy of a particle.

KE = 1

2 𝑚𝑉2 ……………………………………………………………………………. (2.3)

Where, KE is the kinetic energy, m is mass of particle and V is the particle impact velocity.

Hutchings [33] and Balasubramaniyam [28] suggested an energy balance theory for a single

normal impact of spherical erosive particles shown in Figure 2.6.

Figure 2.6: Impact energy balance model.

2.5.2 ERODENT SHAPE

Erodent particle shape directly affects the erosive wear. Different shape of coal from mine site

are pulverized. Researchers analyzed their impact erosion by the modelling of three types of

erodent shape like spherical, angular and rectangular. Material removal due to erosive wear by


spherical shaped particles occurs by ploughing deformation on the sides of hills and by removal

of flakes of material from the valleys [34]. On the other hand, Tilly [30] and Goodwin et al

[35] found that erosion rate increases with increasing particle sizes. Similarly, Chen and Li’s

[36] analysis, with the help of numerical simulation, showed that maximum erosion loss occurs

by the impacting of angular-shape particles. Spherical shape particle impacts with point contact

and angular particle impacts with line of contact. Ramesh [37] and Liebhard [38] found their

analysis that angular shape particle with line of impact action erode more material than

spherical shape erodent with point contact.

2.5.3 IMPACT ANGLE

Impact angle is an angle between the target material and the trajectory of the erodent. As coal

particles impact, angle is one of the key factors for erosive wear in coal pulverisation mills; it

has been found that maximum erosive wear occurs at the impact angle of between 15° and 30°

for ductile materials. However, maximum erosive wear is found at the impact angle of 55° to

90° for brittle materials like ceramics [39], [28], [40], [41], [42], [43]. In addition, Grant and

Tabakoff [44] and Shimizu [45] experimentally found that optimum material erosion occurred

at the impact angle of 20°-30° from material surface for ductile materials. However, it has been

found in some cases that greater erosion occurs for ceramic materials at the higher impact angle

of 45° - 60°. Also target material erosion rate depends on the coal impacting velocity, shape

and size [46].

Therefore, impact angle is the most satisfactory pointer of the erosion mechanism. It is

concluded that ductile materials exhibit a higher erosion rate at 20° impact angle. Whereas,

maximum erosion rate occurs in brittle materials at the impact angle of 90° [27].


2.5.4 ERODENT PARTICLE SIZE

Large particles are more prone to fragmenting and thus tend to create additional damage

compared to small-size particles. Angular-shape particles cause more erosive than the spherical

particles [38]. Erosion rate increases with increasing particle size, along with rising particle

impacting velocity [44]. However, erosion rate depends on the impact energy. Higher rate of

erosion occurs with high impact energy as energy depends upon the particle mass and

impacting velocity.

Yerramareddy and Bahadur [47] experimentally found that erosion rate increased up to particle

size of 200µm and then erosion values remained constant. Furthermore, Balasubramaniyam

[28] observed that volume loss of target materials due to the impact of different sizes erodent

particles increased nonlinearly with increasing particle size until the failure region reached the

metal interface layer and then volume loss increased linearly.

2.5.5 PROPERTIES OF ERODENT PARTICLES AND TARGET MATERIALS

2.5.5.1 ERODENT PARTICLE HARDNESS

The erosion mechanism in the coal mills depends on the material properties of both coal

particles and target materials. When coal particles are harder than target materials, the rate of

erosion drastically increases. However, less erosion on target materials is found when the target

material is harder than the coal particles [48]. Material hardness and fracture toughness are

very important mechanical properties which influence the abrasive and erosive wear resistance

of materials like high-chromium white cast iron, cast basalt and alumina ceramic [49]. Target

material hardness is an influential factor that dominates the metal erosion mechanism [50].


2.5.5.2 SURFACE HARDNESS AND TEMPERATURE

EFFECTS

Surface hardness is the most important parameter to represent the variation of material erosion

rate. Surface hardness and tensile toughness are the key material properties determining impact

erosion resistance due to high fracture strength. Sheldon [51] advised that surface hardness was

more suitable variable for characterizing the erosion of either ductile or brittle materials. Oka

[52] advised that erosion rate varies with varying material surface hardness and found that

erosion damage depends on the impact velocity and target material surface hardness. Tilly [53]

suggested that ductile materials have a greater tendency to resist erosion wear with higher

material surface hardness. Levin et al [54] examined that materials with high hardness and

tensile toughness at high strain rates exhibits good erosion wear resistance.

Young [55] pointed out various effects of temperature on erosion. The study showed that

erosion rate was increased for Grade 310 stainless steel when the temperature rose from 25°C

to 975°C. Hockey et al [56] proved that plastic flow processes occurred during the erosion of

brittle materials; the erosion rate of glass, silicon nitride and aluminium oxide were measured

as a function of temperature and impact angle where silicon carbide particles were selected as

the eroding agent.

2.6 THEORY OF EROSION MECHANISM AND MEASUREMENT METHOD

Material degradation or weight loss of ductile materials occurs by a process of plastic

deformation in which material is removed by the cutting action generated by the eroding

particle. During the erosion process on ductile materials, numerous particles strike the surface.

Of these, a few leave without cutting, while others cut the surface and remove material in the

manner similar to the tooth of a milling cutter [40].


Finnie [33] developed the mathematical equations for single particle impact on ductile

materials.

Figure 2.7: Particle striking and removing material [40].

Material volume loss (Q) was determined by the impacting of a single particle of mass (m),

velocity (V) and angle (α) from following equation.

𝑄 = 𝑚𝑉2

𝑃𝜑𝐾(sin2𝛼 −

6

𝐾sin2𝛼) if tan 𝛼 ≤

𝐾

6

…………….. (2.4)

𝑄 = 𝑚𝑉2

𝑃𝜑𝐾(

𝐾 cos2𝛼

6) if tan 𝛼 ≥

𝐾

6

Where, P is the plastic flow stress due to impact, φ is the ratio of depth of contact (l) to depth

of cut (yt).


Finnie conducted experiments to find the values of K and φ. Subsequently the single particle

mass ‘m’ was replaced by multi-particle mass M, and finally equation (2.4) could be rewritten

as follows [40]:

𝑄 = 𝑀𝑉2

8𝑃(sin2𝛼 − 3sin2𝛼) α ≤ 18.5°

……………………. (2.5)

𝑄 = 𝑀𝑉2

24𝑃cos2𝛼 α ≥ 18.5°

The final form of the equation by Finnie agrees with the statement that “the predicted erosion

loss was directly proportional to the total kinetic energy of the particle and inversely

proportional to the minimum flow stress of the target material”. Finnie also advised that these

equations were applicable for low impact angle up to 45° and smooth surfaces [40].

Bitter modified Finnie’s original equation to obtain better match for experimental data. Bitter’s

model [57] is based on the assumption that the loss of material is the material lost due to plastic

deformation. During the impact, plastic deformation Wd occurs after the material elastic limit

is exceeded, and the surface layer is destroyed as fragments of it are removed. Equation 2.6

presents the material loss calculation due to impact.

𝑊𝑑 =1

2

𝑀(𝑉 sin 𝛼−𝐾)2

𝜀 …………………………………………………………………… (2.6)

Where, 𝑾𝒅 is erosion volume loss, M and V are the impacting particle mass and velocity

respectively, α is the particle impact angle, K is the threshold velocity constant which can be

calculated from mechanical and physical properties as given by equation 2.7, and ε is the energy

needed to remove a unit volume of target material due to impact deformation.


𝐾 =1.54𝜎𝑦

5/2

√𝜌𝑝[

1−𝛾𝑝2

𝐸𝑝+

1−𝛾𝑡2

𝐸𝑡]

2

……………………………………………………………… (2.7)

Here, 𝜎𝑦 is the yield stress of the target, 𝜌𝑝 is the impact erodent density, 𝛾𝑝 and 𝛾𝑡 are the

Poission’s ratios, and Ep and Et are the moduli of elasticity of the erodent and target material

respectively.

Later, Neilson and Gilchrist [58] proposed a simplified equation from Bitter’s model for the

ductile erosive wear due to plastic deformation and cutting actions by taking account the elastic

and plastic properties of the particle and specimen. Their model is given in equation 2.8.

𝑊𝑑 = 1

2 𝑀𝑉2 cos2(𝛼) sin (𝑛𝛼)

ɸ +

1

2𝑀(𝑉 sin(𝛼)−𝐾)2

𝜆……………………………………………… (2.8)

Where,

ɸ is the energy needed to remove the unit volume of target material by deformation wear

λ is also the energy needed to remove a unit volume of target material by cutting wear.

Sheldon and Finnie [59] found a good correlation between the amount of erosion produced by

particles impacting normal to the target brittle material and statistical description of the strength

of brittle materials. The volume of material removed by a given number of particles was

predicted as following equation;

𝑄 = 𝑇 𝑅𝑓1 (𝑚) 𝑉𝑓2(𝑚) ……………………………………………………………………. (2.9)

Where,

Q = volume of material removed


T = Material constant

R = radius of a sphere with weight equal to the particle

f1, f2 (m) = prescribed function of m, the flow parameter of the Weibull fracture

strength distribution.

Grant and Tabakoff [44] developed an empirical equation for the erosion of 2024 ductile

aluminium alloy as follows;

𝐸𝑟 = 𝐾1 𝑓 (𝛽1 ) 𝑉12 𝑐𝑜𝑠2 𝛽1 (1 − 𝑅𝑇

2) + 𝑓 (𝑉𝑙𝑛 ) ……………………………………. (2.10)

Where,

𝐸𝑟 = Erosion rate

K1 = material constant

𝑓 (𝛽1 ) = empirical function of particle impact angle

V = particle velocity

RT = tangential restitution ratio

Vln = component of erosion due to the normal component of velocity.

The empirical constants for quartz impacting an aluminium alloy through the erosive

experimental test are:

K1 = 3.67 x 10-6, K12 = 0.585 and K3 = 9.0 x 10-12


Hutchings [33] proposed that material removal by impacts occurred when the maximum plastic

strain within the fragment reached a critical value. He considered the target to be struck by a

large number of particles and distributed at random over the surface with the same velocity and

caused the plastic deformation in target material. He assumed that the whole volume plastically

deformed by each impacting sphere subjected to a plastic strain increment Δ𝜀𝑝 of the same

magnitude. After N impacts, the expectation value of the resultant strain at any point may be

shown Δ𝜀𝑝 N1/2. If Nf is the mean number of impacts, the critical strain (𝜀𝑐) is given following

expression.

𝜀𝑐 = Δ𝜀𝑝 N1/2 ……………………………………………………………………………. (2.11)

Hutchings investigated that the metal volume, which was plastically deformed around an

indentation, was some fraction α of the volume of indentation. Therefore, material volume loss

was αmv2/2P and after Nf impact volume loss may be illustrated as αmv2/2PNf. If the target

material density is ρ and erosion rate Er is defined as the mass loss from the target per unit mass

of impacting particles is given by

𝐸𝑟 =𝛼𝜌𝑣2

2𝑃𝑁𝑓 ………………………………………………………………………………. (2.12)

Final form of Hutchings’s equation for the erosion loss is

Er = 0.033 𝛽𝜌𝑡𝜎1/2 𝑣3

𝜀𝑐2𝑃3/2 ……………………………………………………………………. (2.13)

Where β is the fraction of volume of indentation which is plastically deformed, 𝜀𝑐 is the critical

strain, P is the constant pressure of resistance by the target material for indentation, ρt is target

material density and ρp is the density of the particle.


Hutchings’s derivation for evaluating erosion damage due to impact is applicable only for

normal impacts and spherical particles.

2.7 EROSIVE WEAR RESISTANT MATERIALS

Wear resistant materials have the ability to absorb the strain and are capable of resisting the

strain propagation without the initiation of fracture process [60]. ŚCIESZKA et al [49]

performed the impact wear test using raw lignite coal (brown coal) on several alloys of beater

plates such as 25% Cr Cast Iron (Martensite), 25% Cr Cast Iron (Austentic), 12% Cr Tool Steel,

12% Mn Steel, 12% Mn Steel (Highveld) and High Carbon tool Steel. They evaluated the

performance of beater plates based on erosion factor by their experiments. Finally, they found

that life expectancy of beater plate was drastically increased by 14 times using 25% Cr Cast

Iron (Martensite) instead of high carbon tool steel.

The manganese (Mn) element in steel alloys increases the strength and hardness and reduces

the brittleness effect by forming manganese sulphide. Higher amount of manganese generates

austenitic steel which improves the wear and abrasion resistance. Chromium along with

manganese increase the hardness, toughness and wear resistance [61, 62]. Kim et al [63]

investigated that the addition of less than 5% manganese did not affect the high temperature

wear behavior, but wear resistance improved by adding more than 10% manganese for Fe –

20Cr – 1C – 1Si alloy. It has been suggested that TiN reinforced high manganese steel increased

the wear resistance of base metal [64]. Some researchers [65-67] and [68] found that 11 – 14%

manganese content Hadfield steels are widely used as railroads, grinding mill liners, crusher

jaws and cones, impact hammer and bullet proof helmets because of the higher wear resistance

properties of manganese alloy.


Hardfacing high-chromium cast iron alloy (brittle material) were used for erosive wear test by

impacting silica sand and alumina particles at angles in the range 15 - 90°. The peak rate of

erosion was found in the angle range of 60 - 90°.

Erosion wear tests were performed on three types of high chromium white cast irons with a

variation in carbide volume fraction at impact angle of 90° using WC-Co spheres and alumina

particles. Higher rate of erosion was produced by WC-Co spheres rather than alumina particles

[69].

Levin et al [70] conducted erosion testing on several Ni-based, Co-based and Fe-based alloys

(Inconel-625, Hastelloy-C22, Haynes-B3, Haynes-230, and 316L SS) by impacting brown

alumina (96% Al2O3, 3% TiO2) particles at an impact angle of 90° and 40 m/s impact velocity.

The study concluded that plastic deformation decreased with increasing material hardness.

Erosion test was performed on ductile AISI 440C stainless steel and hard brittle WC-Co cermet

materials using angular shape alumina (Al2O3) particles. Particles were impacted at the velocity

of 60 m/s and three different impact angles of 20°, 50° and 90°. It has been found that WC- Co

cermets showed excellent erosion resistance compared to stainless steel under the same impact

conditions [31].

Physical erosion tests were performed on 12 different target materials by impacting at various

angles, velocities, and particle sizes. A list of materials is summarised in Table 2.1 [71].

Physical testing was carried out using gas jet erosion ASTM standard erosion method (ASTM

G76 – 07).


Table 2.1: Properties of target materials

Material and

abbreviation

Surface roughness,

Rq (µm)

Density ρ (g/cm3) Vickers Hardness (HV)

A1018 Carbon

Steel with Nickel

Plating (Ni Plate)

0.249±0.004 8.83 746±0

A 240 Type 2205

Duplex Stainless

Steel (2205)

0.062±0.012 7.87 262±1

17-4 PH Stainless

Steel (17-4PH)

0.131±0.011 7.73 352±3

Type 316L

Stainless Steel

(316L)

0.057±005 7.87 164±2

A53 Gr. B Steel

(A53-B)

0.138±004 7.83 157±1

A240 Type 410

Stainless Steel

(410)

0.407±0.007 7.77 152±1

A105 Carbon

Steel Forging

(A105)

0.141±0.025 7.84 161±1

A515 Gr. 70

Norm (A515-70)

0.088±0.002 7.86 164±0

Alloy 625 Plate

(1-625)

0.157±0.03 8.43 227±2

Stellite 12 (St12) 0.086±0.0008 8.38 492±3

Stellite 6B (St6b) 0.030±0.003 8.52 361±2

Tungsten Carbide,

88% WC and 12%

Cobalt Binder

(WC)

0.431±0.001 14.20 1029±6

The authors found from the test that the rate of erosion increases with increasing particle impact

velocity and particle size. Decreasing erosion rate was observed at the impingement angle

ranging from 55° - 90° for all 12 materials. Finally, the excellent erosion resistant materials

were found to be tungsten carbide (WC) and Stellite 12. However, the poor erosion resistant

materials were nickel plated A1018 carbon steel and A240 type 410 stainless steel plates [71].


Besides the impact wear test on different alloys, slurry erosive tests were carried out on various

alloys to evaluate the best erosive wear resistant material. Katsich [72] performed erosive wear

tests at elevated temperature on three types of alloys, such as:

a) M2 tool steel alloy of Fe – Cr – C containing Mo, V and W,

b) hardfacing alloy of Fe – Cr – C containing Nb, Mo, B and W and

c) hardfacing alloy of Fe – Cr – C containing of Nb, Mo, V, and W.

The study stated that particle cracking and particle pulling out were the key material removal

mechanism for alloy (c) at elevated temperature, whereas in alloy (b) brittle chipping of

carbides, carbo-borides, and matrix cause material removal. Lip-formation and their fracture

along the adiabatic shear band is the material removal mechanism for alloy (a). They also

analysed and found that erosion efficiency of the alloys increases with increasing temperature.

However, alloys (b) and (c) exhibit temperature independent erosion efficiency under normal

impact.

Sivaprasad [73] studied the erosive wear behavior of aluminium alloy (Al6063) reinforced by

TiB2 in varying 5 and 10% weight percentage composite metal matrix. They conducted slurry

erosive tests in the laboratory using silica sand particles and examined the surface by SEM

after the test. Finally, the authors found that erosive wear rate was decreased by increasing TiB2

in both analyses.

Slurry erosive wear tests were carried out on Al-Si alloy (12 wt% Si) reinforced by varying

weight percentages of fly ash in a distilled water-silica sand medium for up to 14 hours. It was

found that erosive wear resistance increased for this metal-matrix composite aluminium alloy

with increasing fly ash particle content [74]. A similar alloy of Al-Si (11.8 wt% Si) reinforced


by SiC was examined in saline water and acid environments for evaluating slurry erosive wear

with sand. Authors found that wear resistance increased on increasing of SiC content. Wear

rate also increased with increasing sand content [75]. Furthermore, related slurry erosive tests

were performed on Al-Cu alloy (4.5 wt% Cu) mixed with different percentages of fly ash,

finding less metal erosion with the increasing fly ash content [76].

Four alloys were selected for erosive wear testing in a slurry system consisting of water-sand

media. Two aluminium alloys of Alloy 380 (die cast) and 6061T-6511 (extruded grade) and

two high chromium white iron alloys of high-Cr content (sand cast) with 25.8% of Cr and G75

high-Cr (centrifugal cast) with 27.4% of Cr were tested. The study found that the rate of erosion

is increased with increasing particle size for all four alloys and high-Cr white irons exhibits

wear resistance 27-140 times higher than of the aluminium alloys [77].

Parida et al [78] analysed the coal pulverizer mill shaft of EN 25 steel material. They found

that fatigue cracking started from the keyway area, especially from the top edge. They also

discussed the causes of failure. Inappropriate heat treatment leading to elongated manganese

sulphide drastically reduces the shaft material’s ductility and toughness leading to premature

material failure. The study recommended that the shaft material specification should consist of

not only a minimum strength criterion like hardness, but also must include a toughness

parameter.

There are some key mechanical properties of erosion wear resistance materials which are

directly affects the erosion mechanism. Properties are material yield stress, tensile stress,

fracture strain, strain hardening, ductility, hardness and modulus of elasticity.


2.8 MODELLING AND SIMULATION

Modelling and simulation are normally performed to obtain research information without

testing in real life. Simulation technology belongs to the tool set of engineers of all application

domains and has been included in the body of knowledge of engineering management.

Computer modelling and simulation are being implemented to identify material failure modes,

reduce the number of experiments and development costs [79].

2.8.1 FINITE ELEMENT MODEL AND SIMULATION

Finite element models have been developed to investigate the complex behavior of solid

particles impacting onto target materials. The statistical nature of the impacts results in varying

degrees of stress and strain, strain rates, plastic deformation, crater depth, material failure

modes and material loss. A significant amount of technical information can be found on this

subject in the literature, some of which is presented in the following review.

2.8.1.1 EFFECT OF EROSION PARAMETERS ON FE SIMULATION

Many authors have developed finite element models of erosive wear due to particle impact at

different velocities, angles, particle size and shape. Researchers found that, for ductile

materials, maximum erosion occurs at an impact angle between 30 and 35° [80, 81]. Similarly,

Chen and Li [36] found from their finite element simulations that maximum erosion loss

happened at 30° impact angle for ductile materials, and 90° impact angle for brittle materials.

Their study also revealed that the impacted material target zone failed when its deformation

strain exceeded the critical value for the given material. High rates of erosive wear occurred

with impact by sharp-edged particles [6].


Wang and Yang [81] developed a finite element model of erosive wear to simulate the effects

of impact angle, impact velocity and particle penetration. They used silicon carbide particles

with density of 3200 kg/m3 and size of 120 µm and the target material of Ti-6Al-4V. Figure

2.8 shows the simulation results including plastic deformation and surface damage due to

impact.

Figure 2.8: Von Mises equivalent stress distribution on Ti-alloy target: (a) plastic

deformation, (b) plastic deformation and element failure by micro-ploughing or cutting

process [81].

They found that maximum erosion rate occurred at 30° impact angle [81]. Similarly, ElTobgy

and Elbestawi [80] conducted similar erosive wear simulation on the Ti-alloy (Ti-6Al-4V)


with hardness of 35 HRC by the impacting of mild steel ball. Figure 2.9 shows the 3D model

with impacting solid spherical ball.

Figure 2.9: Finite element model [80]

The study found maximum erosion wear at angles ranging from 30 - 35° and the rate of erosion

increased with increasing particle size [80]. Similarly, Kumar and Shukla [82] conducted an

explicit finite element analysis (FEA) using ANSYS modelling steel particles impacting on

titanium alloy (Ti-6Al-4V) to evaluate the erosive characteristics of the material. They found

the maximum erosion rate at the impact angle of 45° with 180 m/s impact velocity. The target

specimen deformation increased when particles with higher amounts of energy and momentum

impacted at higher velocity and impact angle.

Wang and Yang [83] developed an erosive model using finite element analysis by the

impacting of a steel sphere ball (500µm size) at different angles and velocity on the target

material Ti-6Al-4V. The study found that erosion rate increased with the increasing of

impacting velocity. It was observed that the kinetic energy of impacting particles is transferred

to the target material. During erosion, particle kinetic energy reduces while the target material

internal energy increases.


2.8.1.2 EFFECT OF MATERIAL PROPERTIES ON FE SIMULATION

Mechanical properties of materials are the key influential factor for impact erosion. Plastic

deformation, crater depth and material removal depend on the variation of impact parameters.

Material damage occurs when strains reach the material fracture strain.

Chen and Li [36] found from their finite element simulation that maximum erosion loss

occurred at 30° impact angle for ductile materials, and 90° impact angle for brittle materials.

The study suggested that the impacting particles caused failure when the strain exceeded the

critical value of material.

Woytowitz and Richman [84] investigated the damage that occurs, through FE modelling,

when multiple spherical alumina particles impact on a copper target at the velocity of 25 m/s.

It was found that maximum damage occurred at 200 particles impacting through cyclic

deformation compared to 10 and 100 particles.

Shimizu et al [45] analysed the erosion wear through finite element simulation by the impact

of steel particles on SS400 steel specimen. The study found the highest plastic strain at the

protruded portions at impact angles of 20° - 30°, which led to higher erosion rate, while

minimum plastic strain value was found at the angle of 60°.

Takaffoli and Papini [85] conducted extensive laboratory experiments and Finite Element

Analysis (FEA) using solid particles of 150µm nominal diameter granular aluminium oxide

impacting on the target materials of Al6061 – T6 aluminium alloy. Due to particle impacting

actions, crater depth formation and surface damage are shown in Figures 2.10 and 2.11.


Figure 2.10: Typical craters and pile ups formed on the surface resulting from impacts at 30°

and 117 m/s impact velocity (a) experiment (b) simulation [85].

Figure 2.11: Simulated surface topography during erosion at 117m/s impact velocity

and 30° impact angle of particles [86].

Their study found (from laboratory test and finite element simulation analysis) that maximum

volumetric erosion rate happened at the impact angle of approximately 30° [86].

Later Takaffoli and Papini conducted simulation analysis on crater depth due to impacting of

single angular particle of heat treated AISI A2 tool steel with hardness 750 BHN and density


7800 kg/m3 on the target material of Al6061-T6 with harness 90 BHN and density 2800 kg/m3.

When solid particles were impacted onto metals, acavity was formed on the metal surface that

was called the crater depth. Maximum crater depth was observed at the normal impact

direction. High rate of erosive wear occurred with the impact of sharp-edge particles [87].

In addition, Balu et al [88] developed a 3D finite element (FE) model of solid particle impacting

on AISI 4140 steel and nickel-tungsten carbide composite materials for erosion measurement.

Single and multilayered deposits of different compositions of nickel (Ni) and tungsten carbide

(NT-20, NT-60 and NT-80) were deposited on AISI 4140 steel substrate for the simulation as

shown in Figure 2.12.

Figure 2.12: Discretized 3D FE model of the two-layer NT-60 over NT-20 on AISI 4140

steel.

The failure criterion based on the maximum strain was imposed for the AISI 4140 steel and Ni.

However, maximum tensile stress was used as a failure criterion for the tungsten carbide and


solid erodent particles. Tungsten carbide therefore fails when it reaches the value of the yield

stress. The study found a lower rate of erosion at higher particle impacting velocity (>300m/s)

and larger particle size beyond 325 µm due to the fracturing of erodent particle for the particular

material properties. In addition, the presence of NT-20 interlayer between the NT-60 layer and

substrate absorbed the impact energy more effectively than a single layer of NT-60 on the

substrate and reduced the extent of deformation due to the reduction in the peak stress.

Wang and Shi [89] validated the Johnson – Cook plasticity and damage model for the impacting

of steel and alumina on the target material Ti-6Al-4V using the explicit finite element code

with Abaqus/explicit software. Crater depth was measured and simulated by using finite

element code with impacting solid ball at the velocity of around 245 m/s and 45° impact angle.

Similar crater depths were found in both experimental and FE simulation tests. Similarly,

Cenna et al [90] conducted erosion tests through the impacting of spherical chromium steel

balls (dia 500µm) and zirconia particles (dia 90-100µm) on mild steel and aluminium surfaces,

and measured the crater depth using a Laser Scanning Confocal Microscope (LSCM). They

found low crater depth at 30° impact angle and at lower impact velocity of 60 m/s.

Yarrapareddy and Kovacevic [91] established an erosion model based on the material failure

criterion using the non-linear FE code Abaqus/Explicit. The model was validated with the

physical experiment of material removal rate and the depth of penetration. Ma and Guo [92]

developed a hybrid code based on SPH and FEA to simulate pure water jet penetration on mild

steel. Elalem and Li [93] presented a dynamic simulation model using the explicit formulation

in FEM. The model included strain hardening and material failure.


2.9 JOHNSON-COOK (JC) MATERIAL MODEL PARAMETER

Many authors have used the JC material model for damage analysis under impact loading

conditions by determining the model parameters [94-99]. This model is very popular due to the

simple form of the equation and its availability in Abaqus®. A few tests like tensile and SHPB

(Split Hopkinson Pressure Bar) need to be done to evaluate the JC material model parameters

and, once obtained, these parameters can be used as input parameters in Abaqus FEA.

The Johnson-Cook plasticity material model has been applied to determine the penetration

performance for military vehicle doors where the bullet impacted at velocities of 500, 1000 and

1500 m/s. It has been found from the explicit finite element simulation that 2 mm thickness

AISI 4340 steel showed full penetration [100].

Kennan and Buentello [101, 102] conducted several tests with the split-Hopkinson bar

apparatus at different strain rates and tensile tests on mild steel to obtain the true stress-strain

curves. The authors created logarithmic relations between stress and strain in the plastic region

of quasi-static tensile test and Hopkinson bar test data to obtain the Johnson – Cook (JC) model

parameters. Many authors have attempted similar approaches to obtain the JC model

parameters for various metals. Milani et al [103] performed quasi-static tensile tests and SHPB

compression experiments with varying temperature and strain rate on Ti-6Al-4V alloy to

determine the JC model parameters.

Schreiber [79] performed quasi-static compression and SHPB compression tests to determine

the JC model parameters of AISI 4340 and HF-1 steels. Banerjee et al [104] carried out the

series of tensile tests with varying strain rate and temperature to determine the JC strength and

failure parameters for medium carbon armour steel.


2.10 SUMMARY OF LITERATURE REVIEW

In order to identify research problems and investigate possible solutions, an extensive literature

survey has been conducted through the years from 1957 to 2016. Based on this, the following

summary has been made:

Pulverisation phenomena that break the coal into fine particle sizes have been identified from

the literature. The coal pulverisation process presents many technical problems and factors

which directly affect the process. As a result, mill breakdown occurs which incurs high

maintenance and production costs. Mill wear is one of the significant factors that adversely

influence the coal grinding process.

Different erosive wear damage parameters have been discussed which are directly responsible

for the machine element’s wear in coal pulverising mills, as shown in Table 2.2.

Table 2.2: Damage parameters variables for erosion wear due to impact.

Erodent Particle Variable Particle impingement variables Material variable

• Particle shape

• Particle density

• Particle size

• Particle velocity

• Impact angle

• Particle Concentration

Mechanical properties:

Young modulus,

Poisson’s ratio,

hardness, toughness,

plastic strain, yields

stress, tensile stress.

Most of the studies in the literature attempt to evaluate the effect of erosive wear damage

parameters on different alloys, suggesting the condition of material loss due to impact, and to

compare their tested alloys with erosion resistant materials. Limited attempts have been made

to detect the real life erosive wear problems due to coal particle impacting actions for the


purpose of improving beater plate material in high speed hammer mill and to improve tube mill

liner lifetime, slurry erosion due to coal ash impact.

As found in the literature survey, the hammer is the vital machine element in high speed coal

pulverising mills to break coal for burning to generate steam for power generation industries

and other relevant operations. No study has been performed to analyse the erosion wear

phenomena due to coal impact on manganese steels. Hammers are often made using Mn-steel

alloy of 11% and 14% manganese content. This study fills up the gap by investigating in detail

the mechanical properties and erosion wear mechanism of 11% and 14% Mn-steel. Finally, this

study offers to industry to select best erosion wear resistance Mn-steel material to save money

and labor in coal pulverization process.

The Johnson–Cook (JC) material model is used in Abaqus simulation to determine the erosion

loss of Mn-steels. But, JC material model constants for the Mn-steels are not available in the

published literature. These need to be determined from the experimental data of quasi-static

tensile test, Split Hopkinson Pressure Bar and Abaqus finite element simulation, as discussed

in Chapter 3.


CHAPTER 3: FE SIMULATION APPROACH AND METHODOLOGY

3.1 INTRODUCTION

This chapter presents Finite Element (FE) model development to simulate solid erodent

impacting on ductile Mn-steels for erosion wear analysis. Material loss estimation of Mn-steel

plate due to impact of solid coal erodent is needed to determine a detailed erosive wear

assessment. This study has been made in an effort to develop a FE model and to enable

prediction of material loss under specific operating conditions. The model is developed using

Abaqus Explicit FE simulation solver. Abaqus is needed to input the physical and mechanical

properties of both Mn-steels and coal in the FE simulation. It is needed to assign the material

model parameters for both Mn-steels which will estimate the flow stress and fracture strain

during coal impact on to Mn-steel. Johnson – Cook (JC) developed a material model to

determine the stresses and fracture strains and this JC model is incorporated in Abaqus.

3.2 MODEL DEVELOPMENT AND FE SIMULATION

3.2.1 FINITE ELEMENT PACKAGE

Abaqus finite element package is selected for this study. It is generally used to model material’s

mechanical behaviour. Abaqus is commercially available with two solvers for time dependent

dynamic system: Abaqus Standard and Abaqus Explicit [105]. Abaqus Explicit is extensively

used for simulating dynamic time dependent problems, such as erosive wear, impact, blasts,

and fracture mechanism. Many models have been built using Abaqus to solve high strain rate

problems as presented in the literature [80, 106-112]. The Abaqus/Explicit solver is useful for

this study as it deals with time dependent material behaviour and different strain rates at high

velocities.


3.2.2 FINITE ELEMENT (FE) CONCEPT

FE is the technique of analysis to approximate the solutions to structural problems as an

alternative to finding the analytical solution where the unknown quantities are obtained from

mathematical functions valid at an infinite number of locations in the object under study. As

an alternative, numerical methods provide only approximate values of the unknown quantities

at discrete points in the object [105].

Normally, a FE model splits a structure into a discrete number of finite elements. These

elements are composed of various points called nodes. Each of these nodes connects to

adjoining nodes to create a web throughout the structure. This web is called a mesh. The mesh

is programmed with all necessary information to simulate how the structure will react to the

applied conditions. During the analysis, all element functions are combined to produce a set of

simultaneous algebraic equations. The number of functions depends on the number of

elements. The solution of these large-order systems of equations provides the approximate

solution to the structural problem [113]. This study is created 3D model of Mn-steel plate and

divided the plate into small number of elements which is also called mesh. When erodent coal

is impacted onto the Mn-steel plate, Abaqus simulate the impacting phenomena and calculate

the stress-strain, material damage and progressive material loss in every element by using

explicit formulations and JC material model. Consequently, damaged elements are removed

from the Mn-steel plate and mass of these removed elements will be the erosion wear loss due

to impact.

3.2.3 FE ANALYSIS PACKAGE

Finite Element Analysis (FEA) is programmed to solve large order systems of equations to

simulate the effects of applied dynamic loads, vibrations, fatigue, and heat transfer. Abaqus


FEA package is useful to simulate scenarios subject to high stress and strain applications like

impact on metal objects as studied in this research [105].

3.2.4 EXPLICIT DYNAMIC ANALYSIS

The explicit dynamic analysis in Abaqus FE is based on the application of an explicit

integration rule combined with the use of diagonal element mass matrices. The explicit

integration through time is carried by using many small time increments [105].

Modelling of the erosion process is performed using a general-purpose finite element solver

ABAQUS/EXPLICIT version 6.14.2. This simulation solver is suitable for the modelling of

brief, transient dynamic events like impact and blast problems. This study is on the dynamic

analysis of particles impacting on metals which satisfies the Abaqus/Explicit solver

requirements.

The analysis engaged is a Lagrangian formulation detailing the momentum equation as shown

in Eq. 3.1.

𝑀𝑈 ̈ = 𝐹𝑒𝑥𝑡 − 𝐹𝑖𝑛𝑡 …………………………………………………………………… (3.1)

Where M is the lumped mass matrix, 𝑼 ̈ is the nodal acceleration at each time step, Fext is the

externally applied load for each node and Fint is the internal force. This set of equations is

solved using explicit time integration with the central difference method employing a lump

mass matrix which improves the computational efficiency considerably [114].

The equations of motion for the body displacement, velocity and acceleration are integrated

using the explicit central difference integration rule:

𝑢(𝑖+1) = 𝑢𝑖 + ∆𝑡(𝑖+1)�̇�(𝑖+1/2)…………………………………………………………….(3.2)


�̇�(𝑖+1/2) = �̇�(𝑖−1/2) + ∆𝑡(𝑖+1)+∆𝑡(𝑖)

2�̈�(𝑖) …………………………………………………. (3.3)

�̈�(𝑖) = 𝑀−1 . (𝐹(𝑖) − 𝑃(𝑖)) …………………………………………………………… (3.4)

Where u is the displacement, �̇� is velocity, �̈� is acceleration, i is the increment number, i±1/2

are the mid-increment values, t is time, M is the diagonal mass matrix, F is the applied load

vector, and P is the internal force vector [105]. The internal vector is given by:

𝑃 = ∫ 𝐵𝑇0

𝑉∶ 𝜎 𝑑𝑉 …………………………………………………………………….. (3.5)

Where B is a strain displacement, and V is the volume of the material at the current point in

time [105].

The explicit integration gains computational efficiency through the use of the diagonal element

mass matrix, M, since the inversion of it is M-1. M-1 is used to compute the accelerations at the

beginning of the increment [105].

The explicit integration is based on the fact that the kinematic state can be evaluated using

known velocity, �̇�(𝒊−𝟏/𝟐) , and acceleration, �̈�(𝒊). To start the integration the initial value of the

mean velocity, �̇�(−𝟏

𝟐), needs to be defined. This value is defined in Abaqus by default as [105]:

�̇�(−1/2) = �̇�(0) + ∆𝑡(0)

2�̈�(0) …………………………………………………………….. (3.6)

3.3 MODEL GEOMETRY AND BOUNDARY CONDITION

The simulation model consists of two parts. One is Mn-steel plate of size 30 x 30 x 5mm and

other is a coal ball of 20 mm diameter. A coal erodent is impacted on the Mn-steel plate.

Angular type coal particle of size 20 mm is also selected for the numerical simulation.


Abaqus/Explicit numerically determines the Mn-steel damage and progressive material loss

due to impact. The flow chart in Figure 3.3 shows a summary of simulation procedure.

Figure 3.1: 3D model (a) swing hammer (b) Rectangular Mn-steel plate for FE

simulation.

Figure 3.2: 3D model (a) spherical shape coal erodent (b) angular shape coal

erodent.

a b

a b


NO YES

Figure 3.3: FE simulation flow chart

Start

Pre-processing by

Abaqus/CAE

- Model geometry

- Material properties

- Meshing

- Boundary conditions

- Contact algorithm

- Output request

Third party

pre-processor

for geometry

Simulation by Abaqus/Explicit

- Numerical calculation using

explicit dynamics formulations

Run

successfully

Success

Input file:

job.inp

Output files:

Job.odb, job.dat,

job.res, job.fil


3.3.1 ASSEMBLY AND BOUNDARY CONDITION

The Mn-steel plate and coal ball are assembled as shown in Figure 3.4 and both come in contact

using the Abaqus contact algorithm. The coal particle impacts on to the Mn-steel plate at

different velocities, sizes, shapes and angle. The Mn-steel plate is encastred at the base where

all displacement and rotation along the three axes are set equal to zero. In the contact, the coal

particle surface is considered as the master surface while the Mn-steel plate surface is the slave

surface.

Figure 3.4: Assembly geometry of spherical coal particle and Mn-steel plate


3.3.2 MESH

This simulation model is divided into two main parts, one is Mn-steel plate and other one is

coal particle. Coal particle virtually impacts on to the Mn-steel plate and material from Mn-

steel is removed or damaged or deformed due to the impact action. A fine mesh of the Mn-steel

plate is necessary for accurate results to be obtained. Fine mesh size is found 0.25mm by the

mesh convergence study. When particle impact on to the Mn-steel plate with big mesh size,

less erosion happened. And erosion gradually increase with reducing mesh size. Finally, found

no further increase of erosion after reducing 0.25mm mesh size.

Figure 3.5: Model mesh

The Mn-steel plate is composed about 300,000 elements of 0.25 mm length. The element type

is C3D8R. This is a continuum 3-Dimensional 8-node linear hexahedral element which uses

reduced integration. This type of mesh element is developed for 3D simulations of continuous

solids. Eight-node linear hexahedral elements means that each element consists of 8 nodes

arranged as shown in Figure 3.6.


Figure 3.6: Schematic of the C3D8R element [115]

Reduced integration is selected for the model instead of full because it may increase the

accuracy of the FE simulation results. Hour-glass control is selected to control the zero-energy

modes. Zero energy modes are those that, regardless of the deformation of element, their

integration points do not experience any strain. In the literature, successful FE models [80, 101,

107, 108, 112, 116] demonstrate that this is an appropriate type of element for use in high strain

rate simulations.

3.4 MATERIAL MODEL

This study analyses both 11% and 14% Mn-steel erosion wear due to impact of coal particles

using FE simulation. Physical and mechanical properties of coal particles are available in the

literature and shown in Table 3.1 [117-119].

Table 3.1: Mechanical properties of coal particle

Coal Physical and

Mechanical Properties

Density (kg/m3) 1600

Young’s Modulus, E

(MPa)

3500

Poisson’s Ratio 0.33


The material properties of Mn-steels (11% and 14%) are not readily available in the literature.

Therefore, these have been obtained through quasi-static tensile test, compression test and FE

simulation, which are described in Chapter 4.

The statistical nature of the impacts results in varying degrees of stress-strain, strain rates,

plastic deformation, material failure modes and progressive material loss. Stress and strain are

developed when coal erodent impacts on the Mn-steel plate. In the FE simulation, JC material

model calculates the flow stress and fracture strain developed by the coal impact. When stress

exceeds the material yield limit and strain value reaches the fracture strain, Mn-steel plastic

deformation occurs. As a result, progressive damage of Mn-steel happens and subsequently

fragment of material removed. JC material model in Abaqus FE simulation calculates the

stress-strain and material damage during impact or dynamic loading. JC material model is

applied by researchers [80, 89, 102, 120] in their FE simulation to predict material wear. This

study selects the Johnson-Cook (JC) material model to determine the material erosion wear

loss due to particle impact on Mn-steel. The JC model is available in Abaqus and deals with

high strain material failure and progressive damage due to impact loading. The JC material

model is described in the following section.

3.4.1 JOHNSON–COOK PLASTICITY MATERIAL MODEL

The JC plasticity model was developed by G R Johnson and W H Cook in 1983 [95]. This

model is suitable for high strain rate deformation of ferrous and non-ferrous materials and deals

with the material failure and progressive damage due to dynamic loads applied to the metal.

This empirical model is available in ABAQUS and is widely used in the simulation and analysis

of material dynamic failure. Eq. 3.7 is the JC hardening model which defines the dynamic flow

stress [95-97, 105]:


𝜎 = [𝐴 + 𝐵(𝜀−𝑝𝑙)𝑛] [1 + 𝐶𝑙𝑛 (�̇�−𝑝𝑙

�̇�0)] (1 − 𝜃𝑚) …………………………………….. (3.7)

where, 𝝈 is the yield stress, 𝜺−𝒑𝒍 is the equivalent plastic strain, �̇�−𝒑𝒍 is the equivalent plastic

strain rate, �̂� is the homologous temperature, A is the initial yield stress, B is the hardening

modulus, C is the strain rate dependent coefficient, n is the work hardening exponent and m is

the thermal softening coefficient.

The first brackets of the equation 3.7 represent the static yield stress and parameters A, B and

n can be found from the quasi-static tensile tests at room temperature, as discussed in

subsequent section. The second set of brackets represents the effect of strain rate and the

coefficient ‘C’ can be determined by a combination of quasi-static tensile test and Split

Hopkinson Pressure Bar (SHPB) test at various strain rates. The third brackets characterise the

temperature. This study is limited to isothermal room temperature conditions; therefore, the

thermal softening coefficient ‘m’ will not be determined.

3.4.2 JOHNSON – COOK FAILURE MODEL

The Johnson - Cook (JC) failure model is a cumulative damage model that takes into account

the dynamic load and strain to fracture The JC model extends the fracture criterion proposed

by Hancock and Mackenzie to make the failure strain sensitive to stress triaxiality, temperature,

strain rate and fracture strain [95, 121].

The JC failure criterion is suitable for high strain rate deformation of metals for dynamic

monotonous impact loading. The model assumes that damage accumulates in the material

element during plastic straining which accelerates immediately when the damage reaches a

critical value.


𝝎𝑱𝑪 is defined as a damage variable which varies between 0 (material not damaged) and 1

(material fully damaged). The criterion is based on the value of equivalent plastic strain at

element integration points. JC assumed failure occurs when the damage parameter 𝝎𝑱𝑪 reaches

or exceeds 1 [105]. The variable 𝝎𝑱𝑪 is described as

𝜔𝐽𝐶 = ∑∆�̇̅�𝑓

�̅�𝑓 ………………………………………………………………………… (3.8)

Where ∆�̅�𝒇 is the increment of the equivalent plastic strain and �̅�𝒇 is the strain at failure re-

evaluated at each time increment [105].

The general expression for the fracture strain at failure is as follows:

𝜀�̅� = [[𝑑1 + 𝑑2𝑒𝑥𝑝 (𝑑3𝑝

𝑞)] [1 + 𝑑4𝑙𝑛 (

�̇̅�𝑝

�̇̅�0)] (1 + 𝑑5𝜃) ……………………………… (3.9)

Where �̇̅�𝒑 is the plastic strain rate, �̇̅�𝟎 is the reference strain rate, and d1 through d5 are

the model’s fracture constants.

The first set of brackets represents the strain to fracture as a function of stress triaxiality. The

term p/q is the triaxiality and also called the hydrostatic tensile stress. It is defined as the ratio

of the hydrostatic pressure, p, over the Von Mises stress, q. The JC fracture parameters d2 and

d3 are based on the triaxiality. The second set of brackets represents the effect of increased

strain rate on the material ductility. The third set of brackets represents the thermal softening

as a function of the homologous temperature [105].

From the mentioned failure models, it can be said that the JC failure model is suitable in the

dynamic loading situations with various strain rates. This is a simple form of equation, with

easy to find fracture constants and supported in Abaqus. This study will determine the JC


failure parameters by experiment and FE simulation of 11% and 14% Mn-Steel which is

described in following sections.

3.4.3 DAMAGE EVOLUTION AND ELEMENT REMOVAL

Within Abaqus, damage evolution of ductile materials assumes that the progressive

degradation of the material stiffness defines material response, leading to failure. For this

model, fracture energy per unit area, Gf, is used as an input for damage evolution based on

energy dissipated during the damage process. Instantaneous failure occurs when Gf = 0. It

causes a sudden drop in stress at the material point that can lead to dynamic instabilities [101].

First, we assume an exponential evolution of the damage variable, d:

𝑑 = 1 − exp (− ∫�̅�𝑦�̇�𝑝𝑙

𝐺𝑓

𝑢𝑝𝑙

0) …………………………………………………………… (3.10)

This equation ensures that the energy dissipated during the damage evolution process is equal

to 𝐺𝑓. In Abaqus/Explicit, damage variable, d = 1 when the dissipated energy reaches a value

of 0.99𝐺𝑓.

Elements are deleted from mesh after reaching the damage initiation point and stress decreases

according to following equation:

𝜎 = 𝜎(1 − 𝐷) …………………………………………………………………… (3.11)

Where σ is the flow stress, �̅� is JC flow stress due to an undamaged response, and D is the

damage evolution criterion variable. This variable represents the material stiffness degradation

at the integration point. When D = 0, the material has no stiffness degradation. When D = 1,

the material stiffness is completely degraded and fracture is assumed to occur [101]. For this

erosion wear model, the element is deleted from the mesh once fracture has occurred.


Abaqus/Explicit is able to simulate a ductile material stress-strain response as shown in Figure

3.7. This figure shows that the material response due to dynamic load is initially linear elastic

(section a-b), followed by plastic yielding with strain hardening (section b-c). The material

damage initiates at point c and beyond. There is a reduction of load carrying ability until

reaching rupture at point d. The material is therefore failed at point d.

Figure 3.7: Stress-strain behavior of material damage

The flow chart in Figure 3.8 employs many equations described previously in this chapter.

Abaqus FE simulation for erosion wear using dynamic explicit integration can be implemented

with this visco-plastic algorithm in conjunction with JC plasticity models. This flow chart gives

an idea how the equations work within Abaqus FE simulation.

Where M is the mass matrix, F is the external load matrix, P is the internal nodal forces, ε is

the individual element strain, B is a strain-displacement matrix, DE is the elasticity matrix, εe

is the elastic strain, �̅�𝒚 is the yield stress, εvp is the plastic strain, �̇̅�𝒗𝒑 is the equivalent

viscoplastic strain rate, �̇̅�𝟎 is the reference strain rate, A is the initial yield stress, B is the

hardening modulus, C is the strain rate dependent coefficient, n is the work hardening exponent,

𝜀𝑓 is JC failure strain, p is the pressure stress, q is the Von Mises stress, and d1 to d5 are the JC

model parameters.


Figure 3.8: Algorithm of elasto viscoplastic straining during time step [102]

𝒖(𝒊+𝟏) = 𝒖𝒊 + ∆𝒕(𝒊+𝟏)�̇�(𝒊+𝟏/𝟐)

�̇�(𝒊+𝟏/𝟐) = �̇�(𝒊−𝟏/𝟐) + ∆𝒕(𝒊+𝟏) + ∆𝒕(𝒊)

𝟐�̈�(𝒊)

�̈�(𝒊) = 𝑴−𝟏 . (𝑭(𝒊) − 𝑷(𝒊))

Explicit Dynamic Analysis

𝑷 = ∫ 𝑩𝑻𝟎

𝑽

∶ 𝝈 𝒅𝑽

Internal Forces

[𝜺𝒗𝒑](𝒊+𝟏)

= [𝜺𝒗𝒑](𝒊)

+ √𝟐

𝟑[�̇�𝒗𝒑]

(𝒊+𝟏/𝟐)∶ [�̇�𝒗𝒑]

(𝒊+𝟏/𝟐) ∆𝒕(𝒊+𝟏/𝟐)

𝝈 = [𝑨 + 𝑩(𝜺−𝒑𝒍)𝒏] [𝟏 + 𝑪𝒍𝒏 (

�̇�−𝒑𝒍

�̇�𝟎

)] (𝟏 − �̂�𝒎)

�̅�𝟎 = [𝑨 + 𝑩(𝜺−𝒑𝒍)𝒏](𝟏 − �̂�𝒎)

�̅�𝒇 = [[𝒅𝟏 + 𝒅𝟐𝒆𝒙𝒑 (𝒅𝟑

𝒑

𝒒)] [𝟏 + 𝒅𝟒𝒍𝒏 (

�̇̅�𝒑

�̇̅�𝟎

)] (𝟏 + 𝒅𝟓�̂�)

𝝈 ≥ �̅�𝟎

𝝎𝑱𝑪 = ∑∆�̇̅�𝒇

�̅�𝒇 𝝈(𝒊+𝟏) = �̅�(𝟏 − 𝑫𝒅𝒂𝒎𝒂𝒈𝒆)

�̇̅�𝒗𝒑(𝒊+𝟏/𝟐)

= �̇�𝟎 𝒆𝒙𝒑 [𝟏

𝑪(

�̅�𝒚

�̅�𝟎− 𝟏)]

𝜺 = 𝑩𝒖(𝒊)

[𝜺𝒆] = 𝜺 − [𝜺𝒗𝒑](𝒊)

𝝈𝒆 = 𝑫𝒆[𝜺𝒆]

Individual Element Strain

Elastic Strain

Elastic Stress

JC Flow and Static Stress

Flow Rule Condition

Equivalent Plastic Strain

JC Dynamic Fracture Strain

Equivalent Plastic Strain Rate

Yes

yield occurred

�̇̅�𝒗𝒑(𝒊+𝟏/𝟐)

= 𝟎

No yield occurred

Yes

damage occurred

𝝈(𝒊+𝟏) = �̅�𝒚

No damage occurred

𝒖(𝒊+𝟏), �̇�(𝒊+𝟏/𝟐), �̈�(𝒊)

𝜺𝒗𝒑(𝒊+𝟏)

, �̇̅�𝒗𝒑(𝒊+𝟏/𝟐)

𝝈(𝒊+𝟏)

𝒕𝒊 + ∆𝒕


3.5 SUMMARY

Research methodology is divided into two parts. First part is described the Abaqus FE

simulation procedure of coal impacting on Mn-steel plate. 3D model of coal erodent and Mn-

steel plate are created using Abaqus. Fine mesh is generated in Mn-steel plate for accurate

results. Boundary conditions are applied on bottom of the plate to make sure that all degrees of

freedom are zero during coal erodent impacting on Mn-steel plate. JC material model is

described in the second part of this methodology chapter as Abaqus will evalute the material

damage and element deletion using the JC plasticity materrial model. Therefore, JC model

parameters are needed to determine which will be the input parameters in Abaqus FE

simulation. Chapter 4 is described to determine the JC model parameters by experiments and

FE simulation.


4.1 INTRODUCTION

This chapter deals with the determination of JC model parameters. JC strength parameters (as

shown in Equation 3.7) depend on the material yield stress, strain hardening and strain rate

which can be obtained through the quasi-static tensile tests and Split Hopkinson Pressure Bar

(SHPB) tests at different strain rates. Finite element simulations for tensile and compression

tests are performed to determine the stress triaxiality at the specimen centre. This stress

triaxiality will help to obtain the JC failure parameters. Physical tensile testing results of both

Mn-steels are verified with the published results and compare with the simulated tensile and

compression test results.

4.2 QUASI-STATIC TENSILE TEST

Quasi-static tests are performed on an Instron tensile testing machine to evaluate the elastic

and plastic material properties for JC model parameters of 11% and 14% Mn-steel shown in

Figure 4.1. These JC parameters would be the numerical input values for the material models

in Abaqus FE simulations. Cylindrical specimens for tensile test are manufactured using wire

cut machining from the unusual shape of hammer shown in Figure 4.2 (a). Specimen geometry

is designed in compliance with the Australian Standard of AS 1391 – 2007, as illustrated in

Figure 4.2 (b). Each specimen is mounted in the Instron grippers using threaded adapter and

the testing parameters are set using Bluehill software. Instron jaw movement speed with

mounted specimen keeps as much as low to get better results, as higher speed fails the specimen

suddenly. The tests are performed at a speed of 1 mm/min. Specimens are loaded with the

Instron until failure and a stress-strain relationship is obtained from the test data. 11% Mn-steel

CHAPTER 4: PHYSICAL EXPERIMENT AND JC PARAMETER

DETERMINATION


and 14% Mn-steel at quasi-static strain, in which the engineering stress-strain values are

converted to true stress-strain using Equations (4.1) and (4.2) [122].

𝜀𝑡𝑟𝑢𝑒 = ln(1 + 𝜀𝑒𝑛𝑔.) ..……………………………………………………………….. (4.1)

𝜎𝑡𝑟𝑢𝑒 = 𝜎𝑒𝑛𝑔.(1 + 𝜀𝑒𝑛𝑔.)……………………………………………………………… (4.2)

Figure 4.1: Instron tensile testing machine


Figure 4.2: a) Unusual shape of hammer and b) Specimen geometry

Figure 4.3: Tensile test specimen

a

b


0

200

400

600

800

1000

1200

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Tru

e S

tres

s (M

Pa)

True Strain

11% Mn-Steel 14% Mn-Steel

It was observed during tensile testing that 11% Mn-steel failed at strain of 0.32 and elongated

up to 27.25 mm. Similar linear strain hardening was observed for 14% Mn-steel, which failed

earlier at 0.16 strain and elongation of only 13.6 mm as shown in Figures 4.4 and 4.5. The 11%

Mn-steel specimen body showed a more pronounced undulating surface during the test. Both

Mn-steels exhibited sharp linear strain hardening where stress increases to drive the plastic

deformation. Around 14 kN force was needed to cause failure of the 11% Mn-steel, whereas

only 11 kN load was needed to cause failure of the 14% Mn-steel. Therefore, it can be said that

11% Mn-steel is more ductile, tough and has the ability to withstand more dynamic load than

14% Mn-steel. This ductility is also analysed in the metallographic analysis of tensile tested

specimens in the following Chapter 5.

Figure 4.4: Quasi-static tensile test for 11% and 14% Mn-Steel


Figure 4.5: Load and displacement graph for 11% and 14% Mn-Steel

Table 4.1: Mechanical properties of different wt% of manganese steel

Material Young’s

Modulus

(GPa)

Yield

Strength

(0.2%

offset)

(MPa)

Tensile

Stress at

Maximum

load (MPa)

Elongation

(%)

Reference

12.5% Mn-steel 190 350 800-1000 >35 [68]

13% Mn-steel - 350-380 800-940 30-40 [123]

11% Mn-steel 170 375 975 32 Present

work

14% Mn-steel 180 390 675 16 Present

work

16% Mn-steel - 970 1384 37 [124]

25% Mn-steel - 977 1100 35 [125]

30.5% Mn-steel - 990 1180 42 [126]

0

2000

4000

6000

8000

10000

12000

14000

16000

0 5 10 15 20 25 30

Load

(N

)

Displacement (mm)

11% Mn-Steel 14% Mn-Steel


It can be seen in Table 4.1 that material properties of 11% and 14% of Mn-steel are in good

agreement with the published literature. However, fracture strain of 14% Mn-steel is low

because it has lower tendency of ductility. It is found that carbon content in 14% Mn-steel is

more than 1.2%.

Bayraktar [65] analysed that ductility, strain hardening and tensile stress are reduced

drastically if carbon content of any alloys is more than 1.2%. Carbon content of 14% Mn-steel

is 1.4% which reduced the mechanical strength and ductility of material. Further ductility

analysis is performed in Chapter 5.

4.3 SPLIT HOPKINSON PRESSURE BAR (SHPB) TEST

Stress waves develop and propagate through the material while pressure or impact is applied.

However, these waves are ignored at static or quasi-static testing at very low strain rate.

Therefore, stress waves are only considered for high-velocity impact dynamic studies. The

SHPB technique is used to acquire high strain rate properties of materials through the

measurement of stress waves created by a high-speed impact against the material.

The Hopkinson Pressure Bar was developed by Bertram Hopkinson in 1914 to measure stress

pulse propagation in a metal bar [127]. This apparatus is capable of measuring the stress and

strain by incorporating oscilloscopes with electrical condenser units to measure the pressure

wave propagation in the bars [128].

Figure 4.6: Split Hopkinson Pressure Bar (SHPB) arrangement [129]


A SHPB consists of three bars and a specimen is placed between two long bars called incident

bar and transmission bar as shown in Figure 4.6. The striker bar impacts position A of the

incident bar at a velocity that generates a stress wave that propagates through the incident bar

at the material’s speed of sound. The specimen is compressed between point B of the incident

bar and point C of the transmission bar. The pulse is transmitted through the test specimen

without a significant loss of wave intensity. This incident wave then passes through to the

transmission bar.

The waves are partly reflected into the input bar and partly transmitted through the specimen

and into the transmission bar. The reflected portion travels as a tension wave with strain, 𝜀𝑟(𝑡),

and is measured by strain gauge S1. The compressive strain, 𝜀𝑡(𝑡), accompanying the

transmitted wave is recorded in the output bar strain gauge S2 [130].

The compressive stress wave/pulse is assumed to be developed as 𝜎 =1

2𝜌𝐶𝑉, where, 𝜌 is the

material density of the bar, C is the material wave speed and V is the striker bar impact velocity.

The wave speed can be calculated by 𝐶 = √𝐸

𝜌 . The stress, strain rate and strain can be

calculated from the reflected and transmitted waves using following equations [127]:

Stress,𝜎 =𝐸𝐴0

2𝐴(𝜀𝑖(𝑡) + 𝜀𝑡(𝑡) + 𝜀𝑟(𝑡)) .……………………………………………. (4.4)

Strain rate,𝜀̇ =𝑑𝜀

𝑑𝑡=-

𝐶(𝜀𝑡−𝜀𝑖+𝜀𝑟)

𝐿 ……………………………………………………………. (4.5)

Strain, 𝜀(𝑡) = − 𝐶

𝐿∫ −

𝐶(𝜀𝑡(𝑡)−𝜀𝑖(𝑡)+𝜀𝑟(𝑡))

𝐿

𝑡

0 𝑑𝑡 …………………………………… (4.6)

It is assumed that specimen deforms uniformly. The strains in the incident bar are equal to the

strain in the transmitter bar. Therefore,


𝜀𝑖(𝑡) + 𝜀𝑟(𝑡) = 𝜀𝑡(𝑡) …………………………………………………………………… (4.7)

In this case, stress, strain rate and strain can be expressed in the following form:

𝜎 = 𝐸𝐴0

2𝐴(𝜀𝑡(𝑡)) ………………………………………………………………………… (4.8)

𝜀̇ = 𝑑𝜀(𝑡)

𝑑𝑡 =-

2𝐶

𝐿𝜀𝑟(𝑡) ………………………………………………………….................. (4.9)

𝜀(𝑡) = − 2𝐶

𝐿∫ 𝜀𝑟(𝑡)𝑑𝑡

𝑡

0 ……………………………………………………………….. (4.10)

The SHPB test was conducted between two types of manganese (Mn) alloys: 11% and 14%.

Four cylindrical sized specimens of each alloy were manufactured from the hammer obtained

from the coal pulverizing industry.

The specimens were made according to the apparatus requirements. Lengthwise, 0.01 mm

tolerance is maintained to make the striking surface flat for uniform impact, as illustrated in

Figure 4.7.

The incident and transmission bars have a diameter of 12.7 mm and the yield strength of 2413

MPa. The striker bar of length 228.6 mm and diameter of 12.7 mm hits the incident bar,

generating a 4907.56 m/s wave speed along the specimen. The test specimen is compressed

between the incident and transmission bars. Different loads are applied on Mn-steels which

create different stress wave along the specimen. And SHPB acquire different strain rate

depending on applied load. Different strain rate effect along the specimen shows the Mn-steels

failure behavior. Four consecutive tests were conducted at different strain rates for each Mn-

alloy. Experimental results are described further on.


-200

0

200

400

600

800

1000

1200

1400

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Tru

e S

tres

s (M

pa)

True Strain

SR 440 SR 1800 SR 980 SR 2150

Figure 4.7: Geometry of specimen used for dynamic SHPB test

Figure 4.8: True stress-strain evolution at various strain rates for 11% Mn-steel


Figure 4.9: True stress-strain evolution at various strain rates for 14% Mn-steel

4.4 SIMULATION OF QUASI-STATIC TENSILE TEST AND COMPRESSION

TEST

Simulation of the quasi-static tensile test is performed using the commercial FE code

Abaqus/6.14-2/ Explicit Solver to verify the simulation results with the experimental data. A

3D axisymmetric model of the tensile specimen is created on Abaqus/CAE. Material elastic

and plastic properties from the physical tensile test are used in Abaqus as input parameters

(refer to Table 4.1). Material density of 7900 kg/m3 and Poisson’s ratio of 0.29 are used for

both 11% and 14% Mn-steel.

The FE mesh model and deformed mesh of the cylindrical specimen at necking are shown in

Figure 4.10. The specimen is modelled using 4-node bilinear axisymmetric quadrilateral

element (CAX4R) with reduced integration and hourglass control. For the boundary

conditions, one end of the specimen is fixed, and the other end is free to measure the

-200

0

200

400

600

800

1000

1200

1400

0 0.005 0.01 0.015 0.02 0.025 0.03

Tru

e S

tres

s (M

Pa)

True Strain

SR 280 SR 1670 SR 615 SR 870


displacement. Reaction forces are measured from the fixed end to determine the load. The FE-

simulated stress-strain curve is compared with the experimental observations. Reasonably good

agreement is observed with respect to stress-strain relationship as shown in Figure 4.4 and

Figure 4.11.

Figure 4.10: a) FE mesh of cylindrical specimen, contour plot b) displacement, c) reaction

force and d) von Mises stress with necking.

d

a

b

c


0

200

400

600

800

1000

1200

-0.1 0 0.1 0.2 0.3 0.4

Str

ess

(MP

a)

Strain

11% Mn-steel

0

200

400

600

800

-0.1 0 0.1 0.2

Str

ess

(MP

a)

Strain

14% Mn-steel

0

200

400

600

800

1000

1200

-0.1 0 0.1 0.2 0.3 0.4

Str

ess

(MP

a)

Strain

11% Mn-steel

0

200

400

600

800

-0.05 0 0.05 0.1 0.15 0.2

Str

ess

(MP

a)

Strain

14% Mn-steel

Figure 4.11: Simulated tensile stress vs strain for 11% and 14% Mn-steel

Figure 4.12: Simulated compression stress vs strain for 11% and 14% Mn-steel

4.5 NUMERICAL SIMULATION FOR DETERMINING STRESS TRIAXIALITY

Stress triaxiality (η) is the ratio of the stress in a body based on the hydrostatic stress (𝜎ℎ) and

the Von Mises (𝜎) equivalent stress. It can be expresses in the following form.

𝜂 = 𝜎ℎ

�̅� ………………………………………………………………………………… (4.11)


Hydrostatic stress and Von Mises stress can be calculated using following equations [131]:

𝜎ℎ = 1

3 (𝜎1 + 𝜎2 + 𝜎3) …………………………………………………………………. (4.12)

And, Von Mises stress can be calculated using following equation:

𝜎 = √1

2 [(𝜎1 − 𝜎2)2 + (𝜎2 − 𝜎3)2 + (𝜎3 − 𝜎1)2] …………………………………… (4.13)

Where 𝜎1, 𝜎2 and 𝜎3 are the principle stresses.

When material is necking, volume of inside necking zone is strained in tension in the direction

of principle stress 𝜎1, and compresses in two other transverse directions as diameter of

specimen is reduced by the necking phenomena. This creates higher hydrostatic stress which

leads to higher stress triaxiality [132]. Stress triaxiality is an important parameter for ductile

fracture material.

Fracture theory assumes that the failure will occur due to the coalescence of voids at the centre

point of specimen shown in Figure 4.13. For this reason, Johnson and Cook developed a failure

criterion based on the stress state and plastic strain at fracture projected in this interior point

[102].

Figure 4.13: Fracture point of interest [116]

To obtain the JC failure parameters refer to equation 3.10 in Chapter 3, it is needed to find out

the triaxiality at the centre point of specimen. However, there is no instrument which will


measure the triaxiality. This can only be obtained from FE simulation. Four specimens are

selected for the axisymmetric tensile test simulation shown in Figure 4.14.

Stress triaxiality for both Mn-steels needs to be determined for the evaluation of JC fracture

parameters. A numerical simulation of tensile test is performed using Abaqus/6.14-2/ Explicit

Solver to determine the stress triaxiality at the centre of specimens. A 3D axisymmetric model

of tensile specimens is created on Abaqus/CAE, as shown in Figure 4.15 with unnotched, 0.5

mm notch, 0.75 mm notch and 1mm notch. Mechanical properties of Mn-steels found from the

physical tensile testing are used in the numerical simulation to determine the stress triaxiality

at the centre element of cylindrical specimens.

Figure 4.14: Geometry of specimens for FE simulation, a) unnotched, b) 1mm notch radius,

c) 0.75mm radius notch and d) 0.5 mm notch radius.

a

b

c

d


Figure 4.15: Meshed tensile test specimens: Unnotched, 0.5 mm notch, 0.75 mm notch and

1mm notch.

Contour plots for both Mn-steels are shown in Figures 4.16 and 4.17 with plastic deformations.

Triaxiality against time and average triaxiality values at the centre point of specimens have

been achieved through the FE simulation and graphically represented in Figures 4.18 and 4.19.

Figure 4.16 Contour plot of FE specimen for 11% Mn-steel showing the equivalent triaxiality

a) unnotched, b) 0.5 mm notched and c) 0.75 mm notched.

a c b


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.2 0.4 0.6 0.8 1 1.2

Str

ess

Tri

axia

lity

Time (s)

Unnotched

Average Unnotched

0.75mm Notched

Average 0.75mm

1mm Notched

Average 1mm

0.5mm Notched

Average 0.5mm

Figure 4.17 Contour plot of FE specimen for 14% Mn-steel showing the equivalent triaxiality

a) unnotched, b) 0.5 mm notched and c) 0.75 mm notched.

Figure 4.18. Stress triaxiality versus time curves and mean value for the specimens:

unnotched, 1mm notch, 0.75mm notched and 0.5mm notched for 11% Mn-steel

Nicola [133], Yingbin [134], Jinkook [135] and T. Børvik [136] performed tensile test

simulation using Abaqus with cylindrical specimens at different notching to find the stress

triaxiality. They conducted FE simulation with different ductile materials and found the stress

triaxiality value in the range of 0.33 to 1.6m for ductile materials.

b a c


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

Str

ess

Tri

axia

lity

Time (s)

Unnotched

Average Unnotched

0.75mm Notched

Average 0.75mm

0.5mm Notched

Average 0.5mm

1mm Notched

Average 1mm

This study found the average value of stress triaxiality for ductile 11% Mn-steel 0.41, 1.05,

0.46 and 0.33 and ductile 14% Mn-steel 0.93, 0.908, 0.422 and 0.38) which are in the range of

published works.


unnotched, 1mm notch, 0.75mm notched and 0.5mm notched for 14% Mn-steel.

4.6 JC PARAMETER DETERMINATION

4.6.1 JC STRENGTH PARAMETER DETERMINATION (A, B, n and C)

The JC model parameter A is determined from the stress strain curve as the value of yield stress

in Figure 4.4. This value was determined by applying a 0.2% offset yield limit rule, giving A

= 375 MPa. To determine the strain hardening factor, B, and strain hardening index, n, the

plastic region of stress strain curve is defined in terms of the Effective Stress Difference (ESD)

and the plastic strain. The ESD can be calculated by subtracting the yield stress from the total

stress. The plastic strain can also be calculated as the total strain minus the elastic strain.

Plotting the logarithm of ESD and plastic strain allows a linear fit to be applied, as shown in


y = 0.0928x + 1.0002

R² = 0.9959

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 1 2 3 4 5 6 7 8 9

Dynam

ic S

tres

s/S

tati

c S

tres

s

Ln (Strain Rate)

y = 0.3161x + 3.0911

R² = 0.9027

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

-2 -1.5 -1 -0.5 0

Log S

tres

s (M

Pa)

Log Strain

Figure 4.20. Kennan and Buentello [101, 102] determine the JC model parameters applying

this method. This study follows their method to evaluate the JC parameters for 11% and 14%

Mn-steel.

Figure 4.20: Strain hardening factor ‘B’ and index ‘n’ for 11% Mn-steel

The JC strain hardening factor B is determined by the intersection of the log-plot with y-axis

and the intersecting value from Figure 4.20 is 3.0911. Converting the logarithmic value gives,

B=103.0911 = 1233 MPa. The JC strain hardening index, n, is the slope of logarithmic plots.

Therefore, n = 0.316.

Figure 4.21: Strain-rate sensitivity coefficient ‘C’ for 11% Mn-steel


The strain rate sensitivity parameter, C, can be found from SHPB test conducted with various

strain rates of 1 s-1, 440 s-1, 980 s-1, 1800 s-1 and 2150-1 at room temperature. There are a few

steps that need to be followed to find the value of ‘C’ [102] [101], as follows.

(a) Select a value of strain at the plastic region from the stress-strain curves in Figure

4.8. Plastic strain 0.03 is selected for the 11% Mn-steel.

(b) From the experiments at different strain rate, a series of points is created by dividing

the JC dynamic stress at the strain of interest by the static stress.

(c) Plot on a logarithmic scale the ratio of dynamic stress to the static stress versus the

strain rate the data shown in Table 3.

(d) Apply the least-squares fit to the test points and obtain the slope of the least square

fit, which is the value of ‘C’, as shown in Figure 4.21 and with value obtained being

0.092.

Table 4.2: Strain rate data for 11% Mn-Steel.

Table 4.3: Strain rate data for 14% Mn-steel

Strain Rate Stress (MPa)at Plastic

strain = 0.02

Ln (Strain Rate) Dynamic Stress/Static

Stress

1 450 0 1

280 695 5.6347 1.5444

615 800 6.6846 1.7777

870 692 6.5395 1.5377

1670 728 6.5903 1.6177

Strain Rate Stress (MPa) at Plastic

strain = 0.03

Ln (Strain Rate) Dynamic Stress/Static Stress

1 435 0 1

440 675 6.0867 1.5517

980 724 6.88 1.6643

1800 742 7.4955 1.70574

2150 735 7.67322 1.68965


y = 0.1753x + 2.944

R² = 0.9274

2.55

2.6

2.65

2.7

2.75

2.8

2.85

-2.5 -2 -1.5 -1 -0.5 0

Log S

tres

s

Log Strain

y = 0.098x + 0.9968

R² = 0.9231

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6 7 8

Dynam

ic S

tres

s/S

tati

c S

tres

s

Ln (Strain)

A similar approach has been applied to determine the value of ‘C’ for 14% Mn-steel using

Figure 4.22 and Table 4.3 and with value obtained being 0.098.

Figure 4.22: Strain-rate sensitivity coefficient ‘C’ for 14% Mn-steel

Figure 4.23: Strain hardening factor ‘B’ and index ‘n’ for 14% Mn-steel.


y = 0.3073e-0.632x

R² = 0.7454

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2

Str

ain t

o F

ract

ure

Stress Triaxiality

Series1

4.6.2 JC FAILURE PARAMETERS DETERMINATION (d1, d2, d3 and d4)

4.6.2.1 DETERMINATION OF d1, d2 and d3

Parameter d1 is the necking initiation strain [104]. Parameters d2 and d3 can be evaluated using

the triaxiality [110, 137]. Numerical simulation is performed using quasi-static tensile test data

to achieve the relation between stress triaxiality and failure strain. Constants d2 and d3 can be

found from the failure strain vs stress triaxiality graph by exponential curve fitting.

Necking initiation strain for both 11% and 14% Mn-steel are found of (d1=0.015) and

(d1=0.023) respectively.

Next, the strain to fracture against stress triaxiality is plotted in Figure 4.24 and the JC failure

parameters is obtained from the best curve fit for both Mn-steels shown in Table 4.4.

Figure 4.24: Strain to fracture vs triaxiality ratio for 11% Mn-steel.


y = 0.2062e-1.201x

R² = 0.771

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fra

cture

Str

ain

Average Triaxialitty

14% Mn-steel Expon. (14% Mn-steel) Expon. (14% Mn-steel)

Figure 4.25: Strain to fracture vs triaxiality ratio for 14% Mn-steel

Table 4.4: JC failure parameters in first bracket of equation 3.9 in Chapter 3

Material d1 d2 d3

11% Mn-Steel 0.015 0.266 -0.63

14% Mn-Steel 0.023 0.206 -1.2

4.6.2.2 DETERMINATION OF d4

This is a strain rate dependent parameter presented in the second bracket of the JC failure

equation 3.9. Hammer [110] obtained this parameter from strain rate dependent experiments.

He normalized the fracture strains at reference temperature and assuming the average triaxiality

(p/q). Then normalized strain used to obtain the strain rate dependent parameter.

Strain rate parameter is given by:

�̅�𝑓

𝜀𝑟 = [1 + 𝑑4𝐿𝑛 (

�̇̅�𝑝

�̇̅�0)]


y = -5E-08x + 0.0221

R² = 0.779

0.02198

0.022

0.02202

0.02204

0.02206

0.02208

0.0221

0.02212

0 500 1000 1500 2000 2500

Norm

aliz

ed F

ract

ure

Str

ain

Strain Rate

where 𝜀𝑟 = [𝑑1 + 𝑑2 𝑒𝑥𝑝 (𝑑3𝑝

𝑞)] [1 + 𝑑5 (

𝑇−𝑇0

𝑇𝑚−𝑇0)] ……………………………………. (11)

𝜀𝑟 can be calculated by putting already obtained parameters d1, d2 and d3, and average triaxiality

for 11% Mn-Steel.

𝜀𝑟 = [0.015 + 0.58 𝑒𝑥𝑝(−2.89 𝑥 0.61)][1 + 0]= 1.59

The values of fracture strain of the four different strain rates were divided by 1.59 to normalize

them and then the normalized fracture strain against strain rate was plotted. The value of d4 can

be found by the curve fitting from Figure 4.26 and finally d4 = 0.0221 is obtained.

Figure 4.26: Strain rate sensitivity for 11% Mn-steel

Similarly, for 14% Mn-Steel, 𝜀𝑟 = [0.023 + 0.244 𝑒𝑥𝑝(−2.37 𝑥 0.74)][1 + 0]= 0.686 and

dividing the fracture strain at different strain rate by this value and plotted the normalized

fracture strain against strain rate in Figure 4.27 and get the value of d4 = 0.028.


y = 3E-06x + 0.0285R² = 0.8751

0.0285

0.029

0.0295

0.03

0.0305

0.031

0.0315

0.032

0.0325

0.033

0.0335

0.034

0 200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed F

ract

ure

Str

ain

Strain Rate

Figure 4.27: Strain rate sensitivity for 14% Mn-Steel

Finally, JC strength and failure parameters for both Mn-steels are presented in Table 4.5 and

4.6 respectively.

Table 4.5: Material properties and JC parameters for 11% Mn-steel

Mechanical and Physical

Properties

Density (Kg/m3) 7900 (7.9e-9 ton/mm3)

Young Modulus, E (GPa) 170 (170000 MPa)


Johnson-Cook Strength

Constant

A (MPa) 375

B (MPa) 1233

N 0.316

C 0.092

M -

Johnson-Cook Fracture

Constant

d1 0.015

d2 0.266

d3 -0.63

d4 0.0221

d5 -


Table 4.6: Material properties and JC parameters for 14% Mn-steel

Mechanical and Physical

Properties

Density (Kg/m3) 7900

Young Modulus, E (GPa) 190


Johnson-Cook Strength

Constant

A (MPa) 390

B (MPa) 880

N 0.175

C 0.098

m -

Johnson-Cook Fracture

Constant

d1 0.023

d2 0.206

d3 -1.2

d4 0.028

d5 -

Table 4.7: Physical and mechanical properties of coal [117-119]

Coal Physical and

Mechanical Properties

Density (Kg/m3) 1600

Young Modulus, E (MPa) 3500


4.7 SUMMARY

Mechanical properties like yield stress, tensile stress, failure strain, strain hardening and

modulus of elasticity of both Mn-steels have been obtained by tensile testing experiments.

Tensile test results have been validated with published results and FE simulation. 11% Mn-

steel showed more ductile behavior than 14% Mn-steel. Split Hopkinson Pressure Bar test has

been performed by creating stress wave with the impacting of various loads. Stress-vs strain

rate relations have been achieved which helped to determine JC material model parameters. JC

material model parameters of both Mn-steels have been determined through the best curve

fitting from the tensile and SPHB testing and FE simulation, and finally presented in tabular

form. These parameters are the input of Abaqus numerical simulation for erosion wear model

for the 11% and 14% Mn-steels. FE simulation results of erosion wear loss due to coal erodent

impact for the both Mn-steels are discussed in Chapter 6.


5.1 INTRODUCTION

The results of tensile test presented in Chapter 4 observed that 11% Mn-steel has the more

ductile tendency than 14% Mn-steel. Microscopic analysis is performed for both Mn-steels at

the tensile failure zone to further study ductility and failure mechanisms. Material ductility or

toughness and failure behavior are the key responsible properties of erosion wear assessment.

Microstructural analysis and X-ray diffraction (XRD) are performed on both Mn-steels tensile

specimens to identify the phase. Vicker Hardness and microhardness tests were also performed

on both 11% and 14% Mn-steels. Microstructural phase and hardness are also responsible

properties to predict the erosion wear behavior of Mn-steel.

5.2 SAMPLE PREPARATION

Two samples for each Mn-steel were prepared from the tensile specimens. The samples were

cut along cross-sectional and longitudinal directions at the fracture zone. Both samples were

polished and etched with 3% Nital etchant for SEM and optical microscopic analyses as shown

in Figure 5.1.

Figure 5.1: Samples for metallographic analysis

CHAPTER 5: METALLOGRAPHIC ANALYSIS AND HARDNESS

TESTING

Cross-sectional

Longitudinal


5.3 SCANNING ELECTRON MICROSCOPE (SEM) FRACTOGRAPHY

Micrographs of the fracture surfaces of tensile specimens are conducted in a SEM, model JEOL

JSM-7001F, as shown in Figure 5.2.

Figure 5.2: Scanning Electron Microscope


Figures 5.3 and 5.4 show the SEM micrographs of the fractured surface at tensile failure zone

in both cross-sectional and longitudinal planes for both Mn-steels. Micro-void coalescence and

micro-cracks appear in all pictures. However, a tearing tendency is observed for 11% Mn-steel

specimens when compared to 14% Mn-steel. Fractures along with micro-cracks are found for

14% Mn-steel. Few researchers Bayraktar [65] and Kim [63] performed the micrographic

analysis in tensile failure zone and found the micro-void and crack at the failure zone.

Figure 5.3: SEM micrographs showing ductile fracture in 11% Mn-steel samples (a) and (b)

longitudinal, and (c) and (d) cross-sectional

a b

d c

Micro-void

Micro-crack


Avramovic-Cingara [138] performed SEM analysis in tensile failure zone of DP600 steel and

found the similar results of micro-void growth and crack initiation at fracture zone. Janet [139],

Kahn [140], Pinho [141] and Carboni [142] found the similar scenario at the tensile failure

zone.

Figure 5.4: SEM micrographs showing ductile fracture in 14% Mn-steel samples (a) and (b)

longitudinal, and (c) and (d) cross-sectional

Micro-void

a b

d c


5.4 OPTICAL MICROSCOPE FRACTOGRAPHY

Optical micrographs were captured for both 11% and 14 % Mn-steel samples before and after

etching on the microscope of model LEICA DMi 8A.

Figure 5.5: Optical microscope

The optical microscopic images are shown in Figures 5.6 and 5.7 for both steels at tensile

failure zone. A typical ductile rupture is observed in all cases, which occurs by cracking, tearing

and fracture. However, more cracking and tearing tendency appear to be finer in 11% Mn-steel

(Figure 5.6 a, b c and d) as compared with the specimens of 14% Mn-steel (Figure 5.7 a, b, c


and d). Tasan [143], Ray [144] and [145] analysed the ductile damaged and found micro-crack

and micro-void at tensile failure vicinity.

Figure 5.6: Optical micrographs showing ductile fracture in 11% Mn-steel samples at (a) cross-

section before etching and (b) after etching, (c) longitudinal before etching and (d) after

etching.

a b

c d

Crack growth

Fracture with tearing


Figure 5.7: Optical micrographs showing ductile fracture in 14% Mn-steel samples at (a) cross-

sectional before etching and (b) after etching, (c) longitudinal before etching and (d) after

etching

Figure 5.7 for 14% Mn-steel shows the micro-crack formation and material fracture due to

tensile load. However, material failure with tearing and more crack growth is observed in

Figure 5.6 of 11% Mn-steel. It is clear from the microscopic analysis that Mn-steels failure or

fracture mechanism is different for both steels. This difference is already observed in tensile

testing. Therefore, this can also be the evidence of higher ductility observed of 11% Mn-steel.

d c

b a

Micro-crack

Fracture


5.5 MICROSTRUCTURE AND ELEMENT ANALYSIS

Microstructural analysis and X-ray diffraction (XRD) are performed on both 11% and 14%

Mn-steel polished specimens to identify the phases. Figure 5.8 and Figure 5.11 show the SEM

micrographs for both Mn-steels. It is seen that microstructure consist of single crystal austenite

grains. Single phase steel is the evidence of erosion wear resistance material. However,

corrosion pits of grain boundaries observed in Figure 5.11 for 14% Mn-steel. XRD patterns

of both steels are presented in Figure 5.10 and Figure 5.14. The Mn-steels alloy are observed

fully single crystal austenitic phase. Similarly, austenitic phase is obtained for high manganese

(10 % to 14% Mn content) steel by ASTM handbook [3], Jun-ki [63], Emin Bayraktar [65] and

Mejia [146].

Figure 5.8: SEM microstructure of 11% Mn-steel alloy

SEM-EDS analysis of both Mn-steels surfaces depicted in Figures 5.9 for 11% Mn-steel and

Figures 5.12 for 14% Mn-steel. Significant quantities of oxygen and aluminium observed in

11% Mn-steel surface as seen in Figure 5.9 compare to 14% Mn-steel elemental analysis in

Figures 5.12. Alumina slurry polishing material is used to polish the specimens and higher

amount of aluminium and oxygen contamination found in 11% Mn-steel samples.


-100.00

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

0.00 20.00 40.00 60.00 80.00 100.00

Inte

nsi

ty (

a.u.)

Diffraction angle 2Ө (degree)

Austenitic

Figure 5.9: SEM-EDS analysis of 11% Mn-steel alloy

Figure 5.10: XRD patterns of 11% Mn-steel alloy


Figure 5.11: SEM microstructure of 14% Mn-steel alloy

Figure 5.12: SEM-EDS analysis of 14% Mn-steel alloy


-100.00

0.00

100.00

200.00

300.00

400.00

500.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

Inte

nsi

ty (

a.u.)

Diffraction angle 2Ө (degrees)

Austenitic

Figure 5.13: XRD patterns of 14% Mn-steel alloy

5.6 Mn-STEEL HARDNESS TEST

Material hardness is measured at different positions on the Mn-steels samples using a Vickers

hardness tester (Vickers 452 SVD). Samples were manufactured from the hammer of 11% and

14% Mn-Steel. Hardness measurements and sample preparations were performed according to

Standard ASTM E384 [147]. In the Vickers hardness tester, a pyramid-form diamond indenter

applied a load on the sample surface of 50 kg-f (HV50) for a time duration of between 10 and

15 seconds.

Vicker hardness of Mn-steels can be determined using equation 5.3

𝐻𝑉 =2𝐹 sin

136°

2

𝑑2 …………………………………………………………………….. (5.3)

Where, F is the load in kg-f and d is the arithmetic mean of two diagonals d1 and d2 of the

impression, and HV = Vickers hardness.


Equation 5.3 can therefore be used to calculate the hardness value which in this case is

automatically calculated and appears on the equipment’s screen. Five different position were

chosen on each sample and the average value of Vickers hardness was found to be 205HV50

for 11% Mn-Steel and 220HV50 for 14% Mn-steel. Therefore, the hardness values for both

Mn-steels are quite close.

Figure 5.14: a) Vickers diamond hardness tester, b) Vickers indentation dimension

measurement

5.7 MICROHARDNESS TEST

Microhardness test is performed on the polished metallographic samples as shown in Figure

5.1 for both 11% and 14% Mn-steel. A pyramid-form diamond indenter applied a load on the

sample surface of 200 gm (HV0.2). This test is conducted by Digital Microhardness Tester of

model MXT70 shown in Figure 5.15. Five different points were chosen on each sample for

pyramid indenter and average value of microhardness was found to be 215 HV0.2 for 11% Mn-

steel and 226 HV0.2 for 14% Mn-steel.


Figure 5.15: Digital microhardness tester

5.8 SUMMARY

Micrographic analysis reveals that 11% Mn-steel is more ductile than 14% Mn-steel. This is

also observed in tensile test experiments. Phase analysis by SEM and XRD is identified single

crystal austenitic phase for both Mn-steels. It is found in mechanical engineering handbook [3]

that austenitic manganese steel is characterized as high strength, high ductility and excellent

resistance to wear. Elemental analysis proved that wt% manganese content in the Mn-steel

alloy. Hardness test is performed to compare the both Mn-steels hardness ability which is the

key property of erosion wear resistance materials. However, the hardness for both steels is quite

close with higher hardness found for 14% Mn-steel and even close to the value of

microhardness.


6.1 INTRODUCTION

The FE simulation model and method have been discussed in Chapter 3. The Johnson and Cook

(JC) plasticity material model has been selected for simulation as it is incorporated in Abaqus.

The JC material model parameters for both Mn-steels (11% and 14% Mn-steel) are determined

and presented in Chapter 4 as shown in Table 4.5. These values are used in Abaqus as input

parameters for achieving erosion wear loss of Mn-steels due to coal particle impact with

different speeds, sizes, and shapes. Erosion wear comparison of 11% and 14% Mn-steel are

discussed under the same impact condition. Simulation results are compared with wear theory

and published results for the purpose of model validation.

6.2 SIMULATION RESULT ANALYSIS

When erodent particles impact on to the target Mn-steel plate surface, some elements are only

plastically deformed with no material or element removal, which causes the target material to

strain-harden. Some elements plastically deform to the point that the element is removed from

the strain hardened zone as a result of the impact. This removed material is counted as erosion

wear loss. Mn-steels erosion wear results, based on the finite element model, are presented in

terms of the following parameters for both 11% and 14% Mn-steels:

❖ Impact velocity of coal erodent

❖ Size of coal erodent

❖ Shape of coal erodent

❖ Angular impact of coal erodent

CHAPTER 6: FE SIMULATION RESULTS ANALYSIS


6.2.1 EFFECT OF ERODENT IMPACT VELOCITY ON EROSION LOSS

Coal erodent size of 20 mm diameter impacting at 90º angle on to the target Mn-steel plate at

different speeds are simulated using Abaqus Explicit analysis. Four different velocities are

chosen to achieve the material erosion loss variation.

Figure 6.1: Impact velocity vs erosion loss for 11% Mn-steel

Figure 6.2: Impact velocity vs erosion loss for 14% Mn-steel

Erosion Loss = CV2.6924

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 50 100 150 200 250 300 350 400

Ero

sion

Loss

(gm

)

Impact Velocity (m/s)

Erosion Loss = CV2.3267

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 50 100 150 200 250 300 350 400

Ero

sion

Loss

(gm

)



A plot of material erosion loss against the impact velocity is depicted in Figures 6.1 and 6.2 for

both materials. Erosion loss increases with the impact velocity because of the increased kinetic

energy content of the coal particle. This leads to more material loss of Mn-steel plates for the

same-mass of the impacting coal ball.

The velocity exponent obtained from the graph in Figure 6.1 is 2.69 for 11% Mn-steel and 2.32

for 14% Mn-steel, which is in the range of velocity exponent values for ductile erosion

predicted in the erosion wear theories. A velocity exponent of 2 for ductile metals is proposed

by Finnie [148], 2.5 by Hashish [149] and Sheldon [150] determined experimentally the

velocity exponent to be in the range of 2 – 3 for the ductile materials. The amount of material

loss observed is greater for 14% Mn-steel than 11% Mn-steel under the same impact

parameters. Contour plots from Abaqus FE simulation with the variation of impact velocity are

shown following Figures. Elements are deleted from the Mn-steel plate due to impact. Mass of

deleted elements is the erosion loss which is calculated by subtracting the impacted plate from

original plate.

Figure 6.3: Mises stress for 11% Mn-steel plate impacted by 20mm coal ball at 90º with a

velocity of 275 m/s



velocity of 300m/s


velocity of 350 m/s



velocity of 250 m/s


velocity of 300 m/s



velocity of 350 m/s

6.2.2 EFFECT OF ERODENT SIZE ON EROSION LOSS

Analysis is performed for coal ball of diameters 10mm, 14mm and 20mm, at 275m/s impact

velocity with 90º impact angle. The plot of erosion loss against the erodent diameter is shown

in Figures 6.9 and 6.10 for both Mn-steels respectively. Erosion loss increases with higher

erodent size as coal ball mass, kinetic energy and surface area all increase with increasing

diameter. The erosion loss is proportional to the impacting mass which leads to the constant

erosion loss. Tilly and Scott [151] and Goodwin et al. [35] found similar trends in their studies,

revealing that erosion loss increased with increasing erodent sizes. Abaqus FE simulation

contour plots are depicted in Figures 6.11 to 6.14 of 14mm and 10mm coal erodent ball for

both Mn-steels.


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 10 15 20 25

Ero

sion

loss

(gm

)

Coal ball diameter (mm)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25

Ero

sion

loss

(gm

)

Coal ball diameter (mm)

Figure 6.9: Effect of impacting coal ball size on erosion loss for 11% Mn-steel

Figure 6.10: Effect of impacting coal ball size on erosion loss for 14% Mn-steel

Figures 6.9 and 6.10 show that there is no erosion wear loss of 10mm coal ball impacting at

275m/s velocity. Because, 10mm coal ball has lower mass compare to 14mm and 20mm ball

which create lower kinetic energy at impacting zone. At this condition, very little damaged of


target materials (Mn-steels) surface are observed. But no material has been removed from the

surface as shown in Figure 6.12 and 6.13.


velocity of 275 m/s

Figure 6.12: Mises stress for 11% Mn-steel plate impacted by 10 mm coal ball at 90º with a

velocity of 275 m/s



velocity of 275 m/s


velocity of 275 m/s


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Angular Circular

Ero

sion

loss

(gm

)

Erodent Shape

6.2.3 EFFECT OF ERODENT SHAPE ON EROSION LOSS

The shape of erodent determines the contact area between the erodent and target Mn-steel

surface during impact. Material removal depends on this contact area and kinetic energy

applied to the surface. Two different erodent shapes are considered for this simulation by

keeping the same impact velocity and angle of impact as 275 m/s and 90º respectively.

Spherical ball with 20mm diameter and 20mm size of angular shape erodent are nearly same

mass of 6.7 gm and 6.4 gm respectively. But angular shape erodent has the more area of contact

with the target Mn-steel surface than spherical shape erodent. More contact area with nearly

similar kinetic energy impacting creates more erosion loss as shown in Figure 6.15. Finnie

[148], Chen and Li [36], Liebhard [38] and Ramesh [37] find their impact erosion analysis that

angular shape erodent has the more tendency to occur more erosion than spherical erodent at

the same impacting conditions.

Figure 6.15: Influence of erodent shape on erosion loss for 11% Mn-steel


Figure 6.16: Impact position of angular shape coal on Mn-steel plate

Figure 6.17: Impact position of spherical shape coal on Mn-steel plate


Figure 6.18: Mises stress for 11% Mn-steel plate impacted by 20mm size of angular coal

erodent at 90º with a velocity of 275 m/s

A typical energy balance plot of current model is shown in Figure 6.19 at the impact condition

of 275 m/s velocity and 90-degree impact angle of 20 mm diameter erodent coal. The erosion

wear simulation due to impact for the current work is an energy conserved system. The total

energy in this model should remain same for any time which is equal to the initial kinetic energy

of erodent. Theoretical kinetic energy of a 20 mm diameter coal ball is found to be 253343 J,

while the simulated kinetic energy was 250955 J indicating that the values are indeed close. In

Figure 6.19, it is shown that the kinetic energy comes down and the internal energy goes up

during the erodent coal impact at the Mn-steel target surface. Default hourglass energy added

which is also shown in Figure 6.19.


Figure 6.19: Model energy balance plot

6.3 STRAIN HARDENING EFFECT

When the coal erodent impacts on to the target Mn-steel, plastic deformation and plastically

deformed surface layer may form in the impact region, giving rise to increased yield strength

at the impact zone due to strain hardening effects. Upon further deformation, the yield strength

at the surface of the material approaches the fracture strength and additional strain eventually

leads to material failure. At this point, the surface material is brittle and subsequent impacts

lead to material fragmentation and detachment. The JC material model described in Chapter 3

explains this phenomenon. Figures 6.20 and 6.21 depict the stress versus strain response of the

two different manganese steel materials and element failure in the FE simulation due to impact

of the coal erodent on to the Mn-steel may be predicted from this information.

-50000

0

50000

100000

150000

200000

250000

300000

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012

Ener

gie

s (J

)

Time (S)

Damage Dissipation Energy Hourglass Energy

Internal Energy Kinetic Energy


0

100

200

300

400

500

600

700

-0.05 0 0.05 0.1 0.15 0.2

Str

ess

(MP

a)

Strain

Figure 6.20: Strain hardening effect due to impact for 11% Mn-steel

Figure 6.21: Strain hardening effect due to impact for 14% Mn-steel

It may be clearly observed that failure strain and strain hardening effect due to impact are in

good agreement with physical tensile test experimental results described in Chapter 4.

0

200

400

600

800

1000

1200

-0.1 0 0.1 0.2 0.3 0.4

Str

ess

(MP

a)

Strain


6.4 EROSION WEAR CALCULATION

When coal impact on the Mn-steel plate, some elements in FE simulation, which satisfy the

damage condition, are deleted from the plate. Erosion wear or material loss in the FE simulation

is calculated by the mass difference between the plate of before and after element deletion. For

this sample calculation, it is considered the impact condition of impact velocity 300 m/s, impact

angle 15º, erodent coal ball diameter 20 mm. Figure 6.22 presents the Mn-steel plate screen

shot from the Abaqus with no element deletion and the plate mass is 35.6 gm. After impact

some elements are deleted, and mass of Mn-steel plate is 34.96 gm as displaced in Figure 6.23.

Therefore, Erosion loss = 35.6 – 34.9647 = 0.6353 gm.

Figure 6.22: Screen shot for target Mn-plate mass in Ton from Abaqus


Figure 6.23: Screen shot for target Mn-plate mass in Ton from Abaqus after element deletion


When coal impacts on to the Mn-steel plate, higher misses stress and strain developed at the

centre of impacting zone. Plastic deformation occurs when developed mises stress and strain

reach the material yield stress and fracture strain. Figure 6.24 is the example of showing mises

stress distribution where 10mm coal ball is impacted with 275 m/s speed.

Figure 6.24: Mises stress for 11% Mn-steel plate impacted by 10 mm coal ball at 90º with a

velocity of 275 m/s

On the other hand, coal ball of diameter 20mm is impacted with 300 m/s speed creates higher

mises stress and strain at the impacting zone. As a result, some elements at the impacting zone

are satisfied the damage condition and destroyed geometry of the elements present in the Mn-

steel plate as shown in Figure 6.25. Material loss is calculated after removing the destroyed

geometry from the plate as shown in Figure 6.26. Therefore, center point elements with higher

mises stress are deleted from the plate. For this reason, lower mises stress is showing the centre

of impact.


Figure 6.25: Mises stress for Mn-steel plate impacted by 20 mm coal ball at 90º with a velocity

of 300 m/s

Figure 6.26: Mises stress for Mn-steel plate impacted by 20 mm coal ball at 90º with a velocity

of 300 m/s


6.5 MODEL VALIDATION

FE simulation results are discussed at different impact conditions. A) Effect of erodent impact

velocity on erosion loss; velocity exponents from the Figures 6.1 and 6.2 are 2.69 and 2.32

which are in the range of 2 – 3 for ductile materials compared with published works. B) Effect

of erodent size on erosion loss; few authors proved that erosion loss is increased with increasing

erodent size for any materials. This study found the similar trend with published works. C)

Effect of erodent shape on erosion loss; several authors analysed that angular shape erodent

occur more erosion loss than spherical shape erodent for any ductile materials at the same

impacting conditions. This study found that general trend is same with the published works.

However, the amount of material removed due to coal erodent impact with different speed also

needs to be validated. There are two ways of simulated results verification. One is by physical

experimentation and the other involves applying existing erosion wear theory.

Physical experimental set up for coal impact on the Mn-steels is very expensive. Therefore, in

this instance, the simulated erosion wear is validated with the erosion wear theory using Mn-

steel material properties and impact conditions. There exist several erosion wear theories

available and these are discussed in Chapter 2. Among them, the Bitter model is selected for

the validation as it deals with ductile impact erosion and is simple to calculate using mechanical

and physical properties of the materials concerned.

Bitter modified Finnie’s original equation to obtain better match for experimental data. Bitter

model [57] is based on the assumption that the loss of material is the material lost due to plastic

deformation. During the impact, plastic deformation Wd occurs when the material elastic limit

is exceeded, and the surface layer is destroyed as fragments of it are removed. Equation 6.1

presents the material loss calculation due to impact.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

275 300 350

Ero

sion

Loss

(gm

)


FE Simulation

Bitter Model

𝑊𝑑 =1

2


𝜀 …………………………………………………………… (6.1)

Where, 𝑾𝒅 is erosion loss in volume, M and V are the impacting particle mass and velocity

respectively, α is the particle impact angle, K is the threshold velocity constant which can be

calculated from mechanical and physical properties as given by equation 6.1, and ε is the energy

needed to remove a unit volume of target material due to impact deformation.

𝐾 =1.54𝜎𝑦

5/2

√𝜌𝑝[

1−𝛾𝑝2

𝐸𝑝+

1−𝛾𝑡2

𝐸𝑡]

2

………………………………………………………… (2.7)

Where, 𝝈𝒚 is the yield stress of target, 𝝆𝒑 is the impact erodent density, 𝜸𝒑 and 𝜸𝒕 are the

Poission’s ratios, and Ep and Et are the moduli of elasticity of the erodent and target material

respectively.

Results of Mn-steel erosion wear from the FE simulation and Bitter model are displayed in

Figure 6.27. Three types of impact velocity (275, 300 and 350m/s) are selected for the impact

of 20mm diameter coal ball on to the Mn-steel plate at 15º impact angle.

Figure 6.27: Results obtained from FE simulation model vs Bitter model


6.6 SUMMARY

The erosion wear loss for Mn-steel is obtained from the Abaqus FE simulation model. It is

found that 11% Mn-steel has the lower tendency of material erosion due to coal impact compare

to 14% Mn-steel. Therefore 11% Mn-steel is good erosion wear resistance material compare

to 14% Mn-steel. The FE simulation results are compared with the Bitter’s theoretical wear

model. The results obtained from the both models are in very good agreement. Therefore, the

FE erosion wear model is verified with the erosion wear theoretical model.


7.1 CONCLUSION

From the results and discussion in this thesis, it is seen that the specific aim and objectives of

this research have been achieved. This study provided a comprehensive new set of results for

the 11% and 14% Mn-steels erosion wear loss due to impact of coal erodent at certain impact

conditions for the first time. JC material model parameters and mechanical properties have

been determined from the quasi-static tensile test and Split Hopkinson Pressure Bar test. The

nature of material failure or fracture obtained in tensile tests showed that 11% Mn-steel exhibits

more ductility and similar evidence was found in SEM and optical microscopic analysis at the

tensile failure zone. A 3D FE simulation model has been developed using Abaqus to predict

the erosion wear behavior of Mn-steels due to coal impact. Erosion wear loss due to impact at

different conditions have been achieved for both steels. The results showed that 11% Mn-steel

have the less erosion wear than 14% Mn-steel at same impact condition.

7.1.1 SIGNIFICANT OF CONTRIBUTION

➢ There are good prospects for innovating erosion wear models to predict the material

loss of Mn-steels due to impact. Mn-steels are widely used in coal pulverizing industries

and other industry applications as erosion wear resistant materials. It is a big drawback

that Mn-steels erosive wear resistance capability has not yet been fully developed. This

study has developed erosive wear models to assess the impact erosive wear on Mn-

steels (11% and 14%) by determining the mechanical properties and JC material model

parameters.

CHAPTER 7: CONCLUSION AND RECOMMENDATION


➢ The study found that 14% Mn-steel have lower fracture strain, low strain hardening

and ductility, and higher tendency of material loss due to coal impact compare to the

11% Mn-steel.

➢ This simulated erosion wear model can easily be used to predict the impact erosion

wear behaviour of any engineering materials by putting the mechanical properties and

material model parameters as the input of Abaqus.

➢ This innovative erosion wear model and Mn-steels (11% and 14%) properties give a

clear idea for scientists, engineers, and stakeholders to select right Mn-steel and open a

door for further erosion study of different wt% of Mn-steel to save money in industry

operating cost.

7.1.2 RESEARCH SUMMARY

➢ Mechanical properties like yield stress, modulus of elasticity and hardness are quite

close for both Mn-steels, however tensile stress, ductility and failure strain found

higher in 11% Mn-steel compare to 14% Mn-steel from the tensile test.

➢ SEM and optical micrographic analysis at tensile failure zone also proved the

presence of higher ductility in 11% Mn-steel compare to 14% Mn-steel.

➢ Single crystal austenitic phase is found from SEM and XRD analysis on both Mn-

steels tensile specimens which is the evidence of erosion wear resistance materials,

consistence with observation of [3].

➢ FE Erosion wear model invented that Mn-steel with high tensile stress, failure strain

and ductility occur less erosion wear due to impact. Therefore, 11% Mn-steel is

more erosion wear resistance material compare to 14% Mn-steel.

➢ Vickers hardness test on both steels depicted the close hardness value which was

205HV50 for 11% Mn-Steel and 220HV50 for 14% Mn-steel. Microhardness test


results also showed the quite similar value of 215 HV0.2 and 226 HV0.2 for both

steels respectively.

➢ Quasi-static tensile test has been verified against recently published data and FE

simulation, with results matching very closely.

➢ The JC material model constants and failure parameters for both 11% and 14% Mn-

steel have been determined through uniaxial tensile tests, compression tests and FE

simulation conducted over a range of strain rates and room temperature.

➢ The obtained JC strength parameters have been used as input parameters in Abaqus

FE simulation for the erosion wear analysis arising from coal erodent impact.

➢ The FE results of erosion wear model have been displayed in terms of material loss

in gm against the impact velocity, erodent size and erodent shape. Simulated results

were compared with theoretical and published results and found to be in good

agreement.

➢ The erosion wear analysis was performed using several velocities of 200 m/s, 275

m/s, 300 m/s and 350 m/s for 11% Mn-steel and 200 m/s, 250 m/s, 300 m/s and 350

m/s for 14% Mn-steel. The 20 mm diameter coal erodent was impacted on to the

target Mn-steels at 90º impact angle. It was found for both steels that material loss

increased with the increase in erodent velocity as higher velocity creates more

kinetic energy. The velocity exponent obtained from FE model was 2.69 for 11%

Mn-steel and 2.32 for 14% Mn-steel, which were in good agreement with the

published works.

➢ Erosion loss variation with the erodent size of 10 mm, 14 mm and 20 mm was

studied by keeping the same velocity and impact angle of 275 m/s and 90º


respectively for both steels. Erosion loss of Mn-steels increase with the size of

particle, which is also consistent with the published literature.

➢ The shape of erodent with erosion loss was studied at constant velocity of 275 m/s

and 90º impact angle. The FE simulation was performed with two different shapes

in which one is point contact with spherical and other one is line contact with

angular. The erosion loss was more when Mn-steel plate was impacted by the

erodent with line contact than point contact. Therefore, area of contact with the

target Mn-steel surface is more in line contact than point contact.

7.2 RECOMMENDATIONS

Further research is proposed to advance the present research:

➢ This study is limited to assess impact erosion for 11% and 14% Mn-steels. It is

recommended to perform further study of different wt% Mn-steels to predict the impact

erosion and find the best combination of Mn-steel for coal pulverising industries.

➢ There are other erosion wear resistance materials like Stellites, Titanium, alumina alloy,

stainless steel, and others. This developed model can be used to predict the erosion wear

of these alloys only by determining the JC model’s parameters.

➢ This study of erosion wear model is considered single erodent impact. Multi-particles

impacting can be considered to assess the overall material erosive wear behaviour.

➢ This study of erosion wear model is limited at room temperature. However, there are

some situations in real life that impact erosion may occur in high temperature. So, it

can be further extending of research to consider temperature effects of the erosion wear

model.


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APPENDIX A

EROSION WEAR CALCULATION USING BITTER’S MODEL

Impact velocity, V = 275, 300 and 350 m/s

Impact angle, α = 15deg

Coal ball mass of 20mm diameter = 6.7x10-3 kg

Energy ‘ε’ to remove per unit of target material is calculated from the stress strain diagram in

Chapter 4, Figure 4. is 219.2x106 J.

𝑊𝑑 =1

2


𝜀

Calculating velocity threshold constant ‘K’ using material properties refer to Table 4.5, 4.6 and

4.7

𝐾 =1.54𝜎𝑦

5/2

√𝜌𝑝

[1 − 𝛾𝑝

2

𝐸𝑝+

1 − 𝛾𝑡2

𝐸𝑡]

2

𝐾 =1.54(375𝑥106)5/2

√1600[1 − 0.332

170𝑥109+

1 − 0.292

3.5𝑥109]

2

K= 7.13 m/s


Erosion wear, 𝑊𝑑 =6.7𝑥10−3(275 𝑠𝑖𝑛15−7.13)2

2𝑥219.2𝑥106

Erosion wear = 0.49 gm at 275m/s impact velocity

Similarly, erosion wear is calculated at impact velocity of 300 and 350 m/s of 0.6gm and

0.84gm respectively.

APPENDIX B

SAMPLE INPUT FILE FOR ABAQUS EXPLICIT ANALYSIS

Sample input file for 11% Mn-steel

20mm coal ball impacted onto 11% Mn-steel plate at 90deg with a 300m/s velocity

*Heading

** Job name: Coal11Mn300Big Model name: Model-1

** Generated by: Abaqus/CAE 6.14-2

*Preprint, echo=NO, model=NO, history=NO, contact=NO

**

** PARTS

**

*Part, name="Big Plate"

*End Assembly

**

** ELEMENT CONTROLS

**

*Section Controls, name=EC-1, ELEMENT DELETION=YES

1., 1., 1.

**

** MATERIALS

**

*Material, name=Coal


*Density

1.6e-09,

*Elastic

3500., 0.33

*Material, name=Mn-Steel

*Damage Initiation, criterion=JOHNSON COOK

0.015, 0.266, -0.58, 0.0224, 0., 0., 0., 1.

*Damage Evolution, type=ENERGY, softening=EXPONENTIAL

15.,

*Density

7.9e-09,

*Elastic

170000., 0.29

*Plastic, hardening=JOHNSON COOK

375., 1233., 0.316, 0., 0., 0.

*Rate Dependent, type=JOHNSON COOK

0.092,1.

**

** INTERACTION PROPERTIES

**

*Surface Interaction, name=IntProp-1

**

** PREDEFINED FIELDS

**

** Name: Predefined Field-1 Type: Velocity

*Initial Conditions, type=VELOCITY

Set-7, 1, 0.

Set-7, 2, -300000.

Set-7, 3, 0.

** ----------------------------------------------------------------

**

** STEP: Step-1

**

*Step, name=Step-1, nlgeom=YES


*Dynamic, Explicit

, 0.001

*Bulk Viscosity

0.06, 1.2

**

** BOUNDARY CONDITIONS

**

** Name: BC-1 Type: Displacement/Rotation

*Boundary

Set-8, 1, 1

Set-8, 2, 2

Set-8, 3, 3

**

** INTERACTIONS

**

** Interaction: Int-1

*Contact, op=NEW

*Contact Inclusions, ALL EXTERIOR

*Contact Property Assignment

, , IntProp-1

**

** OUTPUT REQUESTS

**

*Restart, write, number interval=1, time marks=NO

**

** FIELD OUTPUT: F-Output-1

**

*Output, field

*Node Output

A, RF, U, V

*Element Output, directions=YES

DMICRT, EVOL, LE, MISES, PE, PEEQ, S

*Contact Output

CSTRESS,


**

** HISTORY OUTPUT: H-Output-1

**

*Output, history, variable=PRESELECT

*End Step

Sample input file for 14% Mn-steel

20mm coal ball impacted onto 14% Mn-steel plate at 90deg with a 300m/s velocity

*Heading

** Job name: Coal14Mn300Big Model name: Model-1



**

** PARTS

**

*Part, name="Big Plate"

*End Assembly

**

** ELEMENT CONTROLS

**


1., 1., 1.

**

** MATERIALS

**


*Density

1.6e-09,

*Elastic

3500., 0.33




0.023, 0.206, -1.2, 0.0285, 0., 0., 0., 1.


15.,

*Density

7.9e-09,

*Elastic

190000., 0.29


390., 880., 0.175, 0., 0., 0.


0.098,1.

**


**


**


**



Set-7, 1, 0.

Set-7, 2, -300000.

Set-7, 3, 0.

** ----------------------------------------------------------------

**

** STEP: Step-1

**


*Dynamic, Explicit

, 0.001

*Bulk Viscosity

0.06, 1.2

**



**


*Boundary

Set-8, 1, 1

Set-8, 2, 2

Set-8, 3, 3

**

** INTERACTIONS

**


*Contact, op=NEW



, , IntProp-1

**

** OUTPUT REQUESTS

**


**


**

*Output, field

*Node Output

A, RF, U, V



*Contact Output

CSTRESS,

**


**


*End Step


Sample input file for 11% Mn-steel angular impact

Heading

** Job name: Coal11Mn15An275Big Model name: Model-1



** PARTS

*Part, name="Big Plate

*Nset, nset=Set-7, instance=Coal-1, generate

1, 2937, 1

*Elset, elset=Set-7, instance=Coal-1, generate

1, 2560, 1

*End Assembly

** ELEMENT CONTROLS


1., 1., 1.

**

** MATERIALS

**


*Density

1.6e-09,

*Elastic

3500., 0.33



0.015, 0.266, -0.58, 0.0.0224, 0., 0., 0., 1.



15.,

*Density

7.9e-09,

*Elastic

170000., 0.29


375., 1233., 0.316, 0., 0., 0.


0.092,1.






Set-7, 1, 0.

Set-7, 2, -275000.

Set-7, 3, 0.

** ----------------------------------------------------------------

**

** STEP: Step-1

**


*Dynamic, Explicit

, 0.001

*Bulk Viscosity


0.06, 1.2

**


**


*Boundary

Set-6, 1, 1

Set-6, 2, 2

Set-6, 3, 3

**

** INTERACTIONS

**


*Contact, op=NEW



, , IntProp-1

**

** OUTPUT REQUESTS

**


**


**

*Output, field

*Node Output


A, RF, U, V



*Contact Output

CSTRESS,

**


**


*End Step


APPENDIX C

FE SIMULATION CONTOUR PLOTS FOR BOTH 11% AND 14% Mn-STEEL

Figure C-1: Damage initiation criteria for 11% Mn-steel plate impacted by 20mm coal ball at

90º with a velocity of 275 m/s



90º with a velocity of 350m/s


Figure C-6: Damage initiation criteria 11% Mn-steel plate impacted by 20mm coal ball at 15º

with a velocity of 350 m/s


Figure C-7: Mises stress for 11% Mn-steel plate impacted by 20mm coal ball at 15º with a

velocity of 350 m/s


Figure C-9: Mises stress for 14% Mn-steel plate impacted by 20mm coal ball at 90º with a

velocity of 350 m/s


Figure C-14: Damage initiation criteria 11% Mn-steel plate impacted by 20mm size angular

coal erodent at 90º with a velocity of 275 m/s

erosive wear analysis of mn-steels hammers due to coal impact … shahanur_hasan... ·...

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