SIMULATING RESIDUAL STRESS IN MACHINING;

FROM POST PROCESS MEASUREMENT TO

PRE-PROCESS PREDICTIONS

A Thesis Submitted to

The School of Industrial Engineering and Management of

KTH Royal Institute of Technology

In Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

In Production Engineering and Management

By

Joanne Proudian

Supervised By:

Professor Arne Melander

Doctor Niclas Stenberg

August 2012

Stockholm

ACKNOWLEDGEMENTS

I would like to thank the people who made this research possible.

First, I would like to thank Professor Arne Melander and Dr. Niclas Stenberg for giving me the

opportunity to be part of this research effort, and also would like to thank them for their guidance

and support throughout the whole thesis time.

Appreciation and Gratitude are due to Zaki Abu Ghazaleh for his support and love throughout

the journey.

I would like to thank all my friends here and abroad for their support. Also, I want to thank my

family; my mother, my father and my sisters for their continuous support and encouragement

throughout my stay at KTH.

Last but not least, I can only say thank you Lord for everything you have done through my life

and proclaim, “Thus far the LORD has helped me.”

1

ABSTRACT

Metal cutting is a widely used manufacturing technique in the industry and has been the

focus of many research and studies in both academic and industrial fields. Prediction of induced

residual stresses in a machined component is essential in a component’s fatigue life and surface

integrity approximation. Furthermore, it plays a significant role in optimizing cutting process

conditions as well as cutting tool geometries. Research has found that using experimental

techniques in measuring residual stresses in a machined component is both time consuming and

expensive as a method. In the attempt of eliminating the post process measuring drawbacks, the

finite element modeling and simulation has proven its efficiency, as a tool, in predicting

mechanical and thermal variables, hence, providing a pre-process prediction of variables which

may prevent future component failures.

This thesis uses the finite element method to study, model and simulate orthogonal metal

cutting using the commercial software DEFORM. Orthogonal cutting simulations of 20NiCrMo5

steel are performed and simulation results are validated against experimental data. The influence

of the feed rate, cutting speed and rake angle variations on the induced residual stress are

investigated and analyzed. Simulation results offer an insight into cutting parameters and tool

geometry influence on the induced residual stresses. Based on the simulation results, cutting

speed and rake angle showed a trend when varying the parameters on the induced residual stress;

however more investigation is needed in determining a trend for the feed rate influence.

2

TABLE OF CONTENTS

LIST OF FIGURES 5

LIST OF TABLES 9

LIST OF SYMBOLS 10

CHAPTER 1 INTRODUCTION 12

1.1 STATEMENT OF THE PROBLEM 13

1.2 BACKGROUND AND NEED 14

1.3 PURPOSE OF THE STUDY 15

1.4 RESEARCH QUESTIONS 15

1.5 SIGNIFICANCE TO THE FIELD 16

CHAPTER 2 LITERATURE REVIEW 17

2.1 RESEARCH ON ORTHOGONAL MACHINE CUTTING 17

2.2 RESEARCH ON THE FORMATION OF RESIDUAL STRESS

IN MACHINING 19

2.3 RESEARCH ON THE USE OF FINITE ELEMENT METHOD IN THE

SIMULATION OF MACHINING PROCESSES 20

CHAPTER 3 BASIC CONCEPTS OF MACHINING PROCESS 26

3.1 ORTHOGONAL CUTTING VARIABLES 27

3.2 DEFORMATION ZONES 28

3.3 FORCES IN METAL CUTTING 29

3.4 CHIP FORMATION IN METAL CUTTING 30

3

3.5 SHEAR PLANE, VARIABLES AND FORCES IN METAL CUTTING 31

3.5.1 CHIP THICKNESS RATIO 31

3.5.2 SHEAR ANGLE 32

3.5.3 SHEAR PLANE FORCES 33

3.6 TEMPERATURE IN METAL CUTTING 33

CHAPTER 4 FINITE ELEMENT SIMULATION OF METAL CUTTING 34

4.1MESHING 34

4.2 FINITE ELEMENT MODEL FORMULATION 34

4.2.1 LAGRANGIAN 35

4.2.2 EULERIAN 36

4.2.3 ARBITRARY LAGRANGIAN EULERIAN 36

4.2.4 UPDATED LAGRANGIAN 37

4.3 ASPECTS OF MODELING IN FEM SIMULATION 38

4.4 WORK MATERIAL CONSTITUTIVE MODEL 39

4.4.1 JOHNSON COOK MATERIAL MODEL 40

4.5 FRACTURE CRITERIA 40

4.6 FRICTION MODEL 41

4.6.1 COULOMB FRICTION MODEL 42

4.6.2 CONSTANT SHEAR MODEL 42

4.6.3 STICKING AND SLIDING ZONE MODEL 42

CHAPTER 5 PRESENT MODEL AND SIMULATION OF METAL CUTTING 44

5.1 FINITE ELEMENT PACKAGE AND UTILIZATION 44

5.2 TIME INTEGRATION SCHEME 45

4

5.3 TOOL MODELING 47

5.4 WORK PIECE MODELING 48

5.4.1 MATERIAL PHYSICAL PROPERTY 49

5.5 SYSTEM MODELING 51

CHAPTER 6 RESULTS AND DISCUSSION 56

6.1 INTRODUCTION 56

6.2 MODEL CALIBRATION 56

6.2.1 DETERMINATION OF PARAMETERS 56

6.2.2 DATA COLLECTION 58

6.2.3 MESH DISTRIBUTION 62

6.3 FEED RATE ANALYSIS 64

6.3.1 FEED RATE SIMULATION COMPARISON 84

6.4 CUTTING SPEED ANALYSIS 88

6.5 RAKE ANGLE ANALYSIS 92

6.6 TEMPERATURE ANALYSIS 95

6.7 3D ANALYSIS 98

CHAPTER 7 FUTURE WORK 108

CHAPTER 8 CONCLUSION 109

REFERENCES 111

5

LIST OF FIGURES

Page #

Figure 3.1: (a) A full view of a typical machining process, and (b) Cross-sectional

view of a typical machining process…………………………………………….......26

Figure 3.2: Types of cutting: (a) Orthogonal cutting, (b) Oblique cutting ……………………...27

Figure 3.3: Variables in orthogonal cutting……………………………………………………...28

Figure 3.4: Deformation zones in metal cutting…………………………………………………28

Figure 3.5: Forces generated during orthogonal cutting process………………………………...29

Figure 3.6: Chip samples: (a) Discontinuous, (b) Continuous, (c) Continuous with

Built-up edge. (Source: Childs, et al. 2000)………………………………….….…..30

Figure 3.7: Relation between the shear angle and the chip thickness……………………….…...32

Figure 3.8: Merchant’s orthogonal force diagram……………………………………………….33

Figure 4.1: An explanatory demonstration of the Eulerian, Langrangian

and ALE formulations…………………………………………………………….….37

Figure 4.2: Stress distribution on rake face……………………………………………………...43

Figure 5.1: (a) 2D view of the cutting tool, (b) 3D view of the cutting tool…………….....……48

Figure 5.2: Johnson – Cook flow curve………………………………………………..………...49

Figure 5.3: Work piece model in 2D simulation……………………………………....................50

Figure 5.4: Work piece model in 3D simulation (a) simplified model (b) curved model……….51

Figure 5.5: Work piece boundary constrains in 2D simulations…………………………………52

Figure 5.6: (a) Tool movement simulation in 2D model, (b) Tool movement

simulation in 3D model……………………………………………………………...53

Figure 5.7: Contact generation between the tool and the work piece in (a) 2D model simulation,

(b) 3D model simulation……………………………….……………………………54

Figure 5.8: Remeshing procedure at cutting zone……………………………………………….55

Figure 6.1: Chip morphology obtained by the simulations listed in Table 6.1………………….58

Figure 6.2: Data Collection Process……………………………………………………………..59

6

LIST OF FIGURES (CONTINUED)

Figure 6.3: Work piece after being relaxed……………………………………………………...60

Figure 6.4: Residual stresses in x, z, & y directions before and after relaxing graphs…………..61

Figure 6.5: Simulated mesh densities (a) coarse mesh, (b) semi-coarse mesh and (c) fine mesh.62

Figure 6.6: Circumferential residual stress compared across the mesh distributions……………63

Figure 6.7: Axial residual stress compared across the mesh distributions………………………63

Figure 6.8: Feed rate 0.2mm/rev simulation……………………………………………………..65

Figure 6.9: Scattered Circumferential residual stresses in feed rate 0.2mm/rev test…………….65

Figure 6.10: Graph with upper and lower standard deviations from the mean values of

Circumferential residual stresses in feed rate 0.2 mm/rev test…………..………...66

Figure 6.11: Circumferential residual stresses in feed rate 0.2mm/rev test……………………...67

Figure 6.12: Scattered Axial residual stresses in feed rate 0.2mm/rev test……………………...67

Figure 6.13: Graph with upper and lower standard deviations from the mean values of

Axial residual stresses in feed rate 0.2 mm/rev test………………….…..………...68

Figure 6.14: Axial residual stresses in feed rate 0.2 mm/rev test…………………………..……68

Figure 6.15: Two points of residual stress evolution………………………………………..…...69

Figure 6.16: Circumferential residual stress evolution at the two points………………………..70

Figure 6.17: Axial residual stress evolution at the two points…………………………………...71

Figure 6.18: Feed rate 0.45mm/rev simulation…………………………………………………..72

Figure 6.19: Scattered Circumferential residual stresses in feed rate 0.45mm/rev test………….72

Figure 6.20: Graph with upper and lower standard deviations from the mean values of

Circumferential residual stresses in feed rate 0.45 mm/rev test………..……….....73

Figure 6.21: Circumferential residual stresses in feed rate 0.45mm/rev test…………………….73

Figure 6.22: Scattered Axial residual stresses in feed rate 0.45mm/rev test…………………….74

Figure 6.23: Graph with upper and lower standard deviations from the mean values of

Axial residual stresses in feed rate 0.45 mm/rev test…………..…………………..75

7

LIST OF FIGURES (CONTINUED)

Figure 6.24: Axial residual stresses in feed rate 0.45mm/rev test……………………………….75

Figure 6.25: Feed rate 0.8 mm/rev simulation…………………………………………………...76

Figure 6.26: Scattered Circumferential residual stresses in feed rate 0.8 mm/rev test…………..77

Figure 6.27: Graph with upper and lower standard deviations from the mean values of

Circumferential residual stresses in feed rate 0.8 mm/rev test………………...…..77

Figure 6.28: Circumferential residual stresses in feed rate 0.8 mm/rev test……………………..78

Figure 6.29: Scattered Axial residual stresses in feed rate 0.8 mm/rev test……………………..78

Figure 6.30: Graph with upper and lower standard deviations from the mean values of

Axial residual stresses in feed rate 0.8 mm/rev test…………..……………………79

Figure 6.31: Axial residual stresses in feed rate 0.8 mm/rev test………………………………..79

Figure 6.32: Feed rate 0.2 mm/rev comparison with Prasad study………………………………81

Figure 6.33: Feed rate 0.45 mm/rev comparison with Prasad study……………………………..82

Figure 6.34: Feed rate 0.8 mm/rev comparison with Prasad study………………………………83

Figure 6.35: Feed rate simulations……………………………………………………………….84

Figure 6.36: Circumferential residual stresses in feed rate simulations…………………………85

Figure 6.37: Circumferential residual stresses experimentally measured in feed rate tests…….85

Figure 6.38: Axial residual stresses in feed rate simulations…………………………………….86

Figure 6.39: Axial residual stresses experimentally measured in feed rate tests………………...87

Figure 6.40: Cutting Speed simulations………………………………………………………….88

Figure 6.41: Circumferential residual stresses in cutting speed simulations…………………….89

Figure 6.42: Axial residual stresses in cutting speed simulations……………………………….90

Figure 6.43: Radial residual stresses in cutting speed simulations………………………………90

Figure 6.44: Temperature distribution in cutting speed simulations…………………………….91

Figure 6.45: Tool rake angle analysis simulations…………………………………………….....92

Figure 6.46: Circumferential residual stresses in tool rake angle simulations…………………..93

8

LIST OF FIGURES (CONTINUED)

Figure 6.47: Axial residual stresses in tool rake angle simulations……………………………...94

Figure 6.48: Relationship between various DEFORM modules………………………………...95

Figure 6.49: Temperature distributions in simulation……………………………………………96

Figure 6.50: Temperature distribution in cutting speed 400 m/min test after

component is relaxed………………………………………………………………97

Figure 6.51: Feed rate 0.2 mm/rev in 3D simulation…………………………………………….98

Figure 6.52: Slicing of work piece in 3D simulations…………………………………………...99

Figure 6.53: State variable graph distribution in 3D simulations………………………………..99

Figure 6.54: Scattered circumferential residual stresses in feed rate 0.2 mm/rev 3D test……...100

Figure 6.55: Circumferential residual stresses in feed rate 0.2 mm/rev 3D test………………..100

Figure 6.56: Scattered axial residual stresses in feed rate 0.2 mm/rev 3D test…………………101

Figure 6.57: Axial residual stresses in feed rate 0.2 mm/rev 3D test…………………………..101

Figure 6.58: Feed rate 0.45 mm/rev in 3D simulation………………………………………….102

Figure 6.59: Scattered circumferential residual stresses in feed rate 0.45 mm/rev 3D test…….103

Figure 6.60: Circumferential residual stresses in feed rate 0.45 mm/rev 3D test………………103

Figure 6.61: Scattered axial residual stresses in feed rate 0.45 mm/rev 3D test………………..104

Figure 6.62: Axial residual stresses in feed rate 0.45 mm/rev 3D test…………………………104

Figure 6.63: Feed rate 0.8 mm/rev in 3D simulation…………………………………………...105

Figure 6.64: Scattered circumferential residual stresses in feed rate 0.8 mm/rev 3D test……...105

Figure 6.65: Circumferential residual stresses in feed rate 0.8 mm/rev 3D test………………..106

Figure 6.66: Scattered axial residual stresses in feed rate 0.8 mm/rev 3D test………………....106

Figure 6.67: Axial residual stresses in feed rate 0.8 mm/rev 3D test…………………………..107

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LIST OF TABLES

Page #

Table 5.1: Geometric variables of the cutting tool………………………………………………37

Table 5.2: Tool material physical property data…………………………………………………37

Table 5.3: Johnson – Cook constitutive material model constants………………………………38

Table 5.4: Work piece material physical property data………………………………………….39

Table 5.5: Cutting Conditions Variations………………………………………………………..41

Table 6.1: Design of Experiments list …………………………………………………………...47

Table 6.2: Mesh Type Description……………………………………………………………….52

Table 6.3: chip thickness measured for the feed rate simulations……………………………….84

Table 6.4: chip thickness measured for the cutting speed simulations………………………….89

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LIST OF SYMBOLS

Symbol Description

Yield Stress

Hardening Modulus

c Clearance Angle

Damping Matrix

Strain Rate Constant

d Depth of Cut

f Feed Rate

Vector of Nodal forces equivalent to the element internal Stresses

Fc Cutting Force

Ff Frictional Force

Fn Normal Force

Normal Force on the Shear Plane

Shear Force

Ft Thrust Force

Coefficient of Friction in Shear Model

Thermal softening coefficient

Mass Matrix

Hardening coefficient

r Chip Thickness Ratio

Vector of Externally applied Nodal Loads

to Undeformed Chip Thickness

tc Chip Thickness

Instantaneous Temperature

Melting Temperature

Room Temperature

Homologous Temperature

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LIST OF SYMBOLS (CONTINUED)

Symbol Description

Vector of Nodal Displacements

V Cutting Speed

Greek Symbols

α Rake Angle

Equivalent plastic strain

Effective Strain

Fracture Strain

Dimensionless plastic strain rate

µ Coefficient of Friction in Coulomb’s Law

Normal Stress

Effective Stress

Maximum Principal Tensile Stress

Frictional Stress

Shear Angle

Strength model exponent

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1. INTRODUCTION

Machining in general, is a term used to describe the removal of material from a work

piece. Machining processes include, but are not limited to, turning, milling, grinding, drilling and

broaching. These processes are known for being complex. Plastic deformation, thermal stresses

and phase transformation add a major role of complexity to machining processes. In general, the

actual separation of the material from the work piece leaves out a component that, more often

than not, shall directly be put to use in critical applications. Complexities in the machining

process alter the quality and performance of the machined component which are directly related

to surface integrity. Surface integrity include the topological parameters (surface roughness and

other characteristic surface topographic features), mechanical properties (residual stresses,

hardness, etc.), and metallurgical states of the work material during processing (phase

transformation, microstructure and related property variations, etc.) [1]. This relation is not only

at the surface level but also to certain depths.

Nearly every component in use has undergone a machining process at some point within

its manufacturing cycle. During such processes, engineering components are subjected to

stresses and strains of variable magnitudes and nature. The stresses produced as a result of

machining processes (i.e.: mechanical working of the material, heat treatment, chemical

treatment, joining procedure …etc.,) are called residual stresses. The significance and criticality

of residual stresses comes from their significant effect on the fatigue life of machined

components [2].

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1.1 STATEMENT OF THE PROBLEM

Throughout the machining industry, interest in the turning operation is increasing as the

technology replaces more grinding and other finishing operations due to the benefits of cost

reduction and raise in productivity. However, the measure of complexity is significant due to the

diversity of physical phenomena involved, such as, large elastic-plastic deformation, complicated

contact/friction conditions, thermo-mechanical coupling and chip separation mechanisms [3].

For various applications, the properties of a part's surface are central for the functional

behaviour of the machined component. Residual and applied stresses have been associated with

structural failures of the machined components.

Residual stresses are by-products of machining processes and unfortunately cannot be

ignored. When a component’s surface integrity is evaluated, residual stresses are often

considered to be one of the most critical parameters to assess the quality of the machined surface,

with the objective to reach high reliability levels. Residual stresses in a work piece are merely a

function of its material processing and machining history [4]. According to their nature, residual

stresses can enhance or impair the functional behavior of a machined part. In the vicinity of the

machined surface, tensile residual stresses have negative effects on fatigue and fracture

resistance and stress corrosion. This can lead to a substantial reduction in the component’s life

[5]. Residual stresses in the machined surface layers are affected by the cutting tool, work

material, cutting regime parameters (for example: cutting speed, depth of cut and feed) and

contact conditions at the tool-chip and tool-work piece interfaces.

14

1.2 BACKGROUND AND NEED

For years, material removal processes have been used to achieve dimensional accuracy

and surface integrity of various products. The presence of residual stresses, induced by these

processes, is a major factor to consider in the attempt to conserve a part’s fatigue life. Therefore,

the task of developing a methodology capable of predicting residual stress induced by machining

is of great value.

Huge amounts of efforts have been made by researches to develop analytical,

experimental and numerical models in order to predict the post process induced residual stresses

in a work piece [6]. However, all methodologies come in shy to express the cutting process

parameters and tool geometry parameters as functions to determine the machined residual stress

profile; in order to manage the process to achieve the desired residual stress profile.

Nonetheless, questions still arise concerning the causes and the mechanisms of generating

residual stress in machining and how to control the cutting conditions and parameters in order to

achieve a desirable residual stress state.

Most applied methods for measuring residual stresses are destructive measurement

techniques involving a layer removal (either mechanically or chemically) or hole-drilling. The

X-ray technique is probably the most highly developed non-destructive measurement technique

available today [2]. For this reason, it is a task of great importance to develop a reliable method

for measuring residual stresses and comprehending the level of information they can provide. In

recent years, research attempts of developing surface integrity predictive models were made by

the use of analytical methods and finite element simulations.

15

1.3 PURPOSE OF THE STUDY

The aim of this thesis is to create an accurate numerical simulation model for the

prediction of induced residual stresses in a work piece that undergoes a typical turning machine

operation. DEFORM, [7], a commercial and state of the art computer program is used to provide

2D as well as full three-dimensional (3D) simulations of the turning operation.

The results of the numerical simulations are experimentally validated with the

experimental results that took place at SWEREA KIMAB’s labs and at SCANIA’s production

line [8].

Every engineering based process has certain limitations and obstacles that add to its level

of complexity; understanding these limitations could provide a wide range of solutions and

possibly save time and money. Therefore, this thesis addresses the major obstacles and

limitations that emerged during turning process simulations. The scope of this project will cover

only the range of cutting work conditions, cutting tool geometry, and work piece and tool

material tested experimentally. Finally, the thesis will increase the level of industrial awareness

about the significance of predicting the residual stress distribution in a machined component.

1.4 RESEARCH QUESTIONS

Can Finite Element modeling be a practical and efficient tool to accurately predict the residual

stresses in the turning machine operation?

16

1.5 SIGNIFICANCE TO THE FIELD

The conclusion of this thesis will have a major and robust impact on the industry as a

whole. The accurate prediction of residual stresses could become an opportunity undertaken by

tool manufacturers in improving cutting tool design prior to manufacture and field testing and for

manufacturers; users of cutting tools, in selecting the optimum working conditions and

evaluating the effect of them on tools life and on the quality of the final part. Not taking the

prediction of the residual stresses in consideration may be a threat to these stakeholders leading

to high level of waste in time and money.

17

2. LITERATURE REVIEW

Residual stresses induced by machining processes, is a growing area of research where

interest in the prediction of these stresses and the know-how they are created in order to take

preventive measures and avoid and manage its occurrence is increasing. Efforts have been made

to study metal cutting processes and understand the physical phenomenon of the formation of

residual stresses. And to take the literature knowledge into another realm, research has shifted its

focus from measuring post process residual stresses into discovering techniques of predicting

pre-process residual stresses mainly by using Finite Element Methods as the mean of achieving

this scientific purpose.

The literature review will address three areas related to the ability of creating numerical

simulations that accurately predicts the residual stresses induced by the turning process in the

machined work piece. The first section will address research related to the understanding of

orthogonal machine cutting. The second section will focus on research studies about the

formation of residual stresses in machining. Finally, the third section will discuss research

related to the use of Finite Element Method in simulating machining processes.

2.1 RESEARCH ON ORTHOGONAL MACHINE CUTTING

Research in the field of machining processes has been advancing over the years in order

to provide more literate and experimental understanding to aid present and future developments.

Analytical models have been developed for the purpose of explaining the mechanics of metal

cutting process. One of the earliest orthogonal cutting models referred to by John T. Carroll III

and John S. Strenkowski [9], was developed by Ernst and Merchant. In order to relate the shear

plane angle to the tool rake angle and the rake angle coefficient of friction, they used the energy

18

approach. In 1951, Lee and Shaffer developed a more advanced model. They proposed a shear-

angle model based on the slip-line field theory. The model assumed a rigid-perfectly plastic

material behaviour and a straight shear plane. Kudo introduced a curved shear plane to the slip-

line model to account for the controlled contact between curved chip and straight tool face.

Between the 1959 and 1961, Palmer and Oxley and Oxley et al. included the effect of work

hardening and strain-rate effects in their proposed analytical models. Doyle et al. in 1979 studied

the effect of interfacial friction between the chip and the tool. The effect of local heating in metal

cutting was analysed by Trigger and Chao [as cited in reference 10].

Several books have been written about machining processes, M.Vaz Jr., et al. [3], and

Cenk KILIÇASLAN [11] in his master thesis referred to these books and some of them are;

Fundamentals of Machining and Machine Tools by G. Boothroyd and W.A. Knight (1989)

covers mechanical and production engineering perspectives. Metal Machining: Theory and

Applications by T.H.C. Childs et al. (2000) provides a discussion of the theory and application of

metal machining. More general introductory knowledge can be found in the text book;

Manufactruing Engineering and Technologhy by Kalpakjian, et al. (2006).

Studying the machining process in an experimental approach has proved to be expensive

and time consuming due to the wide range of parameters to be considered in tool geometry,

materials, cutting conditions, etc. Especially when trying to understand the surface integrity and

residual stress generation phenomenon in machining. These complexities lead to develop

alternative approaches such as numerical simulations. Among the analytical and numerical

methods developed, the finite element method proved to be the most widely favoured method of

use.

19

2.2 RESEARCH ON THE FORMATION OF RESIDUAL STRESSES IN MACHINING

A main research issue with huge efforts put into; is the understanding of the mechanisms

of residual stress formation and its implications. Henriksen [as cited in references 10, 12 and 13]

conducted a series of tests to understand residual stresses and found that grain deformation of the

surface layer generates residual stresses. Therefore, attributing mechanical deformation as the

main reason for residual stress generation and considering the thermal stresses due to heat

generation to have a negligible role. He also found that in ductile materials, residual stresses

were usually of a tensile nature while in brittle materials, they are of a compressive nature.

Okushima and Kakino [as cited in references 10, 12, 13, 14], questioned Henrikson’s hypothesis

of residual stress generation by relating the temperature distribution and thermal effects as main

causes of residual stresses. However, no agreement was observed between the calculated results

and the experimental results. In their study, Liu and Barash [as cited in references 12, 14, 15, and

16] validated Henrikson’s conclusions. Three quantitative measures were identified by their

studies to define the mechanical state of a machined layer. They also found that there was no

relation between the linear thermal expansions on the machined layer on residual stress

distribution. Liu and Barash showed that a main cause of producing both tensile and compressive

residual stresses in machining was the mechanical deformation of the work piece surface.

Kono et al. and Tonshoff et al. [as cited in references 10, 14] agreed on residual stresses

being dependent on the cutting speed. Matsumoto et al. and Wu and Matsumoto et al. [as cited in

references 10, 14] observed that material hardness has a significant effect on the residual stress

distribution that remains in the machined part, their results agreed well with the experimental

data trends. Konig et al. [as cited in references 10, 14] indicated that the formation and

development of residual stresses is attributed to the friction in metal cutting. Schreiber and

20

Schlicht [as cited in reference 14] confirmed that the magnitude and the distribution of the

residual stresses are greatly influenced by the mechanical properties of the work piece material.

Brinksmeier and Scholtes [as cited in reference 13] found that tensile residual stresses and the

depth of the stressed area is likely to increase with the feed rate.

Brinksmeier [as cited in references 13 and 17] found that the tool edge condition

influences the residual stress profile. M’Saoubi et al. [as cited in references 12, 15 and 18]

verified experimentally a correlation between cutting tool temperature and the in-depth profile of

residual stresses.

The studies on residual stresses in machined parts and the efforts put into understanding

the mechanism of its formation has provided important insights in the comprehension of this

phenomenon and on issues such as residual stress distribution, mechanical and cutting properties

attribution and the effect of tool edge. However, the mechanism of residual stress generation is

still not completely understood and more studies are needed.

2.3 RESEARCH ON THE USE OF FINITE ELEMENT METHOD IN THE SIMULATION OF

MACHINING PROCESSES

Finite element simulations are considered a widespread and strong tool in the study of

metal cutting. Due to its comprehensive ability, finite element simulations take into account large

complexities that come upon metal cutting (i.e. large deformation, strain rate effect, tool-chip

contact and friction, local heating and temperature effect, different boundary and loading

conditions). Usui and Shirakashi [as cited in references 10 and 11] developed one of the early

finite element models of metal cutting. In their model they assumed a rate-independent

deformation and used a geometric criterion for chip separation. Iwata et al. [as cited in reference

10] assumed a rigid-plastic behaviour of the material in the proposed FEM model, including in

21

the study the effect of friction between the tool and chip. The study didn’t cover the thermal

effect in machining. Tyan and Yang [as cited in references 10 and 19] were the first to propose

the use of the Eulerian formulation in steady-state metal cutting simulation.

Till late 1990s, the majority of researchers generated their own FEM codes to use in their

studies. Due to the long computational hours of simulations and high memory capacity needed,

the use of FEM was limited and if used, 2D simulations were dominant. However, over the last

20 years, developments in technology (hardware and FE codes) dramatically increased,

overcoming to an extent the limitations faced in modelling and computational difficulties.

Commercially available software packages became more in use [20, 21]. These packages

included NIKE-2D, DEFORM, FORGE2D, ABAQUS/standard, ABAQUS/Explicit,

ANSYS/LS-DYNA, ALGOR and FLUENT.

Carroll and Strenkowski [9] used the general purpose software; NIKE2D for reviewing

two orthogonal cutting models; an updated Lagrangian model and a Eulerian model. The models

were applied to single point diamond turning. Both computer models compared favourably with

experimental work. Strenkowski and Moon [as cited in references 10, 15 and 18] proposed a

steady-state Eulerian orthogonal cutting model. No residual stresses were calculated due to

neglecting the material elasticity in the simulation.

Lin and Lin [as cited in reference 10] proposed a model based on a coupled thermo-

elastic-plastic behaviour with large deformation based on an updated Lagrangian FEM model,

and used a strain energy density criterion for chip separation. Hashemi et al. [22] studied fracture

mechanics to simulate chip separation and developed a fracture algorithm to automatically split

the elemental nodes as the tool penetrates the work piece. The chip geometry predictions agreed

well with the experimental results. Marusich and Ortiz [23] developed a Lagrangian finite

22

element model of orthogonal high-speed machining with continuous remeshing and adaptive

meshing. In their study, Cerreti et al. [24] investigated chip separation in orthogonal cutting

using the commercial code DEFORM 2D. They defined a damage criterion which deleted

elements exceeding the critical damage value. Ceretti et al. concluded their study by the need to

gather more experimental data in order to refine the model and accurately define the critical

damage value. Shih [25] developed a model to analyse the orthogonal metal cutting with

continuous chip formation, using a Eulerian description. Shih found that the lack of complete

material properties and friction parameters directly impacts the accuracy of the finite element

simulation. Also, Shih [26] studied the effect of the rake angle in the cutting processes. In his

doctoral thesis, Kalhori [27] investigated different modelling approaches for the chip separation.

The physical model of chip separation was found to be more suitable in simulation. Yang and

Liu [28] proposed a new stress-based polynomial model of friction behaviour in machining;

linking the normal stress with the shear stress in a function to obtain a friction coefficient.

Unfortunately, no experimental data was available to verify the results.

Zouhar and Piska [21] conducted their studies with cutting tools of different geometry.

Mohammadpour et al. [15] investigated the effect of machining parameters on residual stresses

in orthogonal cutting. The study concluded that the maximum tensile residual stresses increased

with increasing the cutting speed and feed rate. In his master thesis, Cenk KILIÇASLAN [11]

studied the ability to predict the cutting variables by modelling the orthogonal metal cutting

using different constitutive material models, friction models and tool geometries. Ceretti et al.

[29] studied orthogonal metal cutting under different cutting conditions.

Özel and Altan [30] presented a methodology to determine work piece flow stress and

friction at chip-tool interface using measured data as a reference to calibrate the model. In his

23

later studies, Özel [20] investigated further the effects of tool-chip interfacial friction models on

the FE simulations. Results showed that the friction modeling at the tool-chip interface has

significant influence on the FE simulation predictions and that the friction models developed

from the experimentally measured normal and frictional stresses at the tool rake face resulted in

most favorable predictions. Shi et al. [31] studied the effect of friction on the thermo-mechanical

quantities in the orthogonal metal cutting process, performing a series of simulations varying the

tool rake angle and friction coefficients. Bil et al. [32] compared three different simulation

models of orthogonal metal cutting process with experimental data. The study showed that no

one model achieved a satisfactory correlation with all the measured process parameters. Filice

[33] investigated the effect of the friction model implemented in 2D simulation of orthogonal

cutting and whether a “best” model can be identified. Mechanical results were found to be

insensitive to the friction model, while, friction was a more relevant issue in the thermal analysis.

Cherouat et al. [34] used an adaptive remeshing procedure in 2D simulations of metal forming

processes. In a very recent study, Zhang et al. [35] proposed a 3D model with advanced adaptive

remeshing procedure which well simulated the material removal orthogonal cutting process.

Few studies are found in literature, which mainly focus on using FEM in predicting

residual stresses. Liu and Guo [14] studied the effect of sequential cuts and tool-chip friction on

residual stresses, using the explicit finite element code; ABAQUS. It was observed that by

optimizing the second cut, tensile residual stresses from the first cut can be turned into

compressive. Shet and Deng [19] and Shi et al. [31] investigated the frictional interaction along

the tool-chip interface and a range of rake angles. In their latest work, Shet and Deng [10]

concluded that the tool-chip friction and tool rake angle have nonlinear effects on residual

stresses and strains. Outeiro et al. [36] investigated the influence of the cutting parameters on the

24

residual stress induced in turning of AISI 316L steel. Specifically focusing on cutting forces,

cutting speed and the process feed rate. Salio et al. [18] simulated turning in turbine disks, using

nonlinear finite element code MSC.Marc. The study gave insights on the selection of cutting

parameters and the predicted and experimental residual stresses were found to be in satisfactory

agreement. In later studies, Outeiro et al. [37] studied the effect of tool geometry and cutting

parameters on residual stress distribution induced by orthogonal cutting. The study showed that

the uncut chip thickness had the strongest influence on residual stresses and that residual stresses

increase with most of the cutting parameters and cutting tool edge radius. Wang et al. [38]

investigated the variations of residual stresses in the machined surface layer. The results showed

that high cutting speed is a main factor affecting the residual stress. In his dissertation, Carl

Hanna [39] developed a novel approach of extracting the cutting parameters and tool geometry

from a desired or required residual stress profile. The results proved that the approach gives

realistic recommendations of parameters in order to end with the desired residual stress in the

machined part. Liang and Su [17] presented a predictive model for residual stress in orthogonal

cutting. The model presented, captured the trends of generated residual stress as well as

magnitudes. Miguélez et al. [5] investigated the generation of residual stresses in orthogonal

metal cutting using an ALE finite element approach. The study concluded that tensile stresses are

the result of both thermal and mechanical effects.

Prasad [40] used an FE model to simulate the machining induced residual stress in the

work material. Prasad used an Arbitrary Lagrangian Eulerian (ALE) adaptive meshing FEM to

simulate the model by the commercial FE code; ABAQUS. His findings and results are going to

be used by this thesis to compare with the author’s results.

25

The studies previously stated, have provided good understanding and insight of the metal

cutting process, residual stress formation and finite element method being a method used in

predicting residual stress pre-process machining. As research takes more interest in predicting

the residual stress induced in the machined part surface, there will be opportunities to advance

these predictive methods. Generated Finite Element codes can be said generally achieves its

purpose in predicting residual stresses to an extent, but its main drawback is in its simulation

time requirement which is not adaptable for process optimization. A sound interpretation of the

mechanism of residual stress generation is still missing, and the derived models are purely

empirical. This drawback limits the ability to generalize the application of the results and models

reached by FE codes on the wide range of materials used. The research is limited to the materials

investigated in the papers published and in order to apply the model, further experimentation and

estimation of parameters are needed. Therefore unfortunately, residual stress modelling currently

is still at the experimental phase, and few industrial applications are being made.

26

3. BASIC CONCEPTS OF MACHINING PROCESS

Machining is the process of removing material from a work piece in the form of chips.

The process consists of a sharp cutting tool that cuts through a blank material to leave the work

piece with the desired dimensions and shape. The process generates shear deformation in the

work piece to form a chip; and as the chip is removed, the newly machined surface is exposed. A

typical machining process is illustrated in Figure 3.1.

(a) (b)

Figure 3.1 (a) A full view of a typical machining process, and

(b) Cross-sectional view of a typical machining process.

There are two types of the metal cutting process used in the industry: orthogonal and

oblique cutting. In orthogonal cutting, the chips are removed from the work piece by a cutting

edge perpendicular to the direction of motion. In oblique cutting, the tool’s cutting edge cuts

through the work piece material with an inclination angle, inclined relatively to the cutting

direction, as shown in Figure 3.2.

27

Figure 3.2 Types of cutting: (a) Orthogonal cutting, (b) Oblique cutting

Despite the fact that oblique metal cutting operations are extensively used in the industry,

orthogonal cutting proved throughout research, that it is simpler to model and can provide good

approximations.

3.1 ORTHOGONAL CUTTING VARIABLES

In a typical orthogonal cutting operation, specifically turning, the work piece is rotated at

a certain velocity called the cutting speed (V), in one revolution of the work piece (a bar in this

case), the tool advances in an axial distance f (the feed rate) to reduce the work piece radius by

an amount d (the depth of cut) also known by to as the undeformed chip thickness and tc is the

chip thickness. The rake face is the face where the formed chip and tool come in contact. Rake

angle (α) is an angle between the rake face and the chip formed. The clearance face is a surface

which the tool passes over the machined surface. Clearance angle (c) also known as the relief

angle is an angle between newly machined surface and the clearance face. These variables

determine the characteristics of the process and are shown in Figure 3.3.

28

Figure 3.3 Variables in orthogonal cutting

3.2 DEFORMATION ZONES

In the metal cutting process, there are three main deformation zones, as shown in Figure 3.4.;

Primary shear zone (A-B): In this region, the chip is formed mainly as the cutting edge of

the tool cuts through the work piece. Deformation takes place in the material in this zone

by a concentrated shearing process.

Secondary shear zone (A-C): From A to C, i.e. the rake face, the chip and the tool are in

contact. A frictional stress and heat due to the plastic deformation is generated on the

rake face. Also, material flow occurs in this zone.

Tertiary shear zone (A-D): Deformation may occur in this zone, when the clearance face

of the tool rubs the newly machined surface.

Figure 3.4 Deformation zones in metal cutting

29

3.2 FORCES IN METAL CUTTING

A classical orthogonal cutting model is assumed to have plane-strain deformation

conditions. A typical representation of the process model is shown in Figure 3.5.

Figure 3.5 Forces generated during orthogonal cutting process

An important aspect of the cutting process, are the forces acting on the tool. The earliest

and simplest model to understand the cutting process is Merchant’s model. The cutting forces

vary with the cutting tool angles. The cutting force, Fc, is the component of the force acting on

the rake face of the tool. This is usually the largest of the force components. The frictional force,

Ff, is the force due to friction along the rake angle. Ft, is the thrust force, this force is in the

direction of feed motion. Another component of the force is the normal force, Fn. This force is the

smallest of the force components and tends to push the tool away from the work piece in a radial

direction [41].

In orthogonal metal cutting, the force components are geometrically related by the

following equations;

(3.1)

(3.2)

30

3.4 CHIP FORMATION IN METAL CUTTING

The chip varies in shape and size throughout the industrial machining processes. Shearing

of the material in the primary shear zone leads to the formation of the chips. In metal cutting

processes, three types of chips occur: Discontinuous chips, continuous chips and continuous

chips with built-up edge (BUE), as shown in Figure 3.6.

(a) (b) (c)

Figure 3.6 Chip samples: (a) Discontinuous, (b) Continuous, (c) Continuous with

Built-up edge

Discontinuous chip occurs in cutting brittle materials such as cast iron or when machine

cutting some of the ductile metals under low cutting speeds. Machine vibration or tool chatter are

also probable causes to this type of chip formation. Discontinuous chip has the advantage of the

ease of being cleared from the cutting area. Continuous chip is produced when cutting ductile

metals with high speeds. Better surface finish is usually related to this type of chips and is

considered ideal for cutting operations. Continuous chip with built-up edge is formed when low

carbon steels are machined cut with high speed steel cutting tools but under low cutting speeds.

Built-up edge results in having poor surface finish machined components and it shortens the tool

life. Built-up edge chip can be eliminated by increasing the cutting speeds used in the machining

process.

31

Childs et al. in their book Metal Machining theory and applications [42] mentioned the

main factors affecting the chip flow to be; the rake angle of the tool, the friction between the chip

and the tool and the work hardening of the work material as it forms the chip.

3.5 SHEAR PLANE, VARIABLES AND FORCES IN METAL CUTTING

During the metal cutting process, the material is severely compressed in the area in front

of the cutting tool. This compression of the material causes high temperature shear, and the

plastic flow. When the strain in the work piece exceeds a critical value of the material, the

particles will shear forming the chip, which moves up along the rake face of the tool. The

process is repeated as the cutting tool moves further in the work piece, forming a chip. The plane

which the element shears is called the shear plane, i.e. the primary shear zone.

The chip formation is dependent on the work piece material primarily, but also on the

cutting conditions and tool edge parameters.

3.5.1 CHIP THICKNESS RATIO

The ratio of the chip thickness to the undeformed chip thickness i.e. the feed rate, is

called the chip thickness ratio. The chip thickness ratio is a good indicator of the efficiency of the

process. The lower the chip thickness ratio, the lower the force and heat generated in the process.

Also, the higher the efficiency of the process.

The chip thickness ratio is expressed by the following formulation,

(3.3)

Where r is the chip thickness ratio, is the chip thickness and is the undeformed chip

thickness.

32

3.5.2 SHEAR ANGLE

The shear plane is tilted at a certain angle relative to the cutting direction. The shear

angle is not clearly defined; however studies have been made to calculate the angle. By using the

chip thickness ratio, the shear angle is assumed to be obtained by the following equation,

(3.4)

Where is the shear angle and is the rake angle. The relation between the shear angle and chip

thickness is shown in Figure 3.7.

Figure 3.7 Relation between the shear angle and the chip thickness

Many authors throughout the literature studied the primary shear zone and different shear

angle relationships have been obtained. Three of the simpler relationships were presented by

Ernst and Merchant, Lee and Shaffer and Kullberg.

33

3.5.3 SHEAR PLANE FORCES

Figure 3.8 Merchant’s orthogonal force diagram

Figure 3.8 presents the Merchant’s orthogonal force diagram at the primary shear zone.

From this figure the shear force and the normal force on the shear plane can be

formulated in the below equations;

(3.5)

(3.6)

3.6 TEMPERATURE IN METAL CUTTING

During the metal cutting process, high temperatures are generated along the tool – chip

interface. High temperature influence many components of the cutting process, including; the

rate of the cutting tool wear, the strength of the work piece material, chip formation mechanics,

surface integrity, etc.

The main sources generating the high temperatures are the intensive plastic deformation

occurring at the shear plane and the frictional heat generated at the tool faces either by contacting

the chip or rubbing the newly machined surface.

34

4. FINITE ELEMENT SIMULATION OF METAL CUTTING

Numerical simulation of machining processes can be traced back to the early seventies

when finite element models for continuous chip formation were proposed. The advent of fast

computers and development of new techniques to model large plastic deformations have favored

machining simulation.

The Finite Element method could be briefly defined as a method which divides the

problem into small parts called elements that can be solved in relation to each other.

4.1 MESHING

Meshing is the procedure of dividing a simulated continuous region into smaller discrete

regions called elements in the finite element analysis. During the metal cutting process, severe

distortions take place to the initial designed mesh which may lead to difficulties in the

convergence of the problem and in numerical errors. In order to deal with this often recurring

problem, a new finite element mesh is generated in the attempt of reducing the distortion of the

elements affected by the deformation. This solution is called adaptive mesh procedure.

4.2 FINITE ELEMENT MODEL FORMULATION

When considering the use of finite element method to simulate metal cutting, basic

aspects should be addressed. Finite element formulations are based on either implicit or explicit

schemes. Implicit scheme is largely used in metal cutting. This scheme requires convergence of

the integration at every time step. Even though this requirement provides better accuracy, the

implicit scheme encounters a higher level of complexity while dealing with discontinuous chip

formation and restrictive contact conditions. On the other hand, explicit schemes solve

35

uncoupled equation system based on information from previous steps. Explicit scheme has also

been employed in metal cutting problems involving high non-linearity complex friction-contact

conditions [43].

There are two main formulations used in finite element simulation of metal cutting,

namely; Lagrangian and Eulerian. As more research focused on the finite element simulations,

researchers developed two new formulations based on the former methods combining the basic

advantages of the classical formulations; Arbitrary Lagrangian Eulerian and the updated

Lagrangian formulation.

4.2.1 LAGRANGIAN FORMULATION

The Lagrangian formulation assumes that the finite element mesh is attached to the work

piece material and follows its deformation; i.e. computing the stresses and strains incrementally

and updating the nodal coordinates at the end of each step increment. Lagrangian formulation is

widely used due to its ability of chip formation and determining the chip geometry as a function

of cutting parameters, plastic deformation process and material properties. Therefore, no

geometric chip criterion in shape and boundaries is required prior the simulation.

Although many advantages are related to the use of the Lagrangian formulation, the

approach has also shortcomings. The severe plastic deformation taking place in the material

causes element distortion. Therefore, requiring mesh regeneration often. Also, a chip separation

criterion should be defined. Estimating the parameters in the criterion is a difficult job, due to the

lack of data and studies covering the whole range of material. The shortcomings of the

Lagrangian formulation is assumed to be eliminated by the use of an updated Lagrangian

formulation with mesh adaptivity or automatic remeshing technique.

36

4.2.2 EULERIAN FORMULATION

The Eulerian formulation, assumes the finite element mesh is fixed in space and the

material flow through the element faces eliminating the possibility of element distortion

throughout the process. Allowing steady state machining to be simulated, requiring fewer

elements for the analysis, and thereby reducing computation time. The Eulerian based models do

not need a separation criterion to be defined for chip fracture.

However, the drawback of the Eulerian formulation is the need of prior knowledge of the

boundaries and chip geometry; from chip thickness, the chip-tool contact length and contact

conditions. This requirement limits the application range of the metal cutting simulation as the

defined parameters should be kept constant throughout the analysis. In order to overcome this

drawback, some studies adopted an iterative procedure to adjust the chip geometry and the tool-

chip contact length.

4.2.3 ARBITRARY LAGRANGIAN – EULERIAN FORMULATION

In the attempt of combining the best features of the classical formulations, an approach

known as Arbitrary Lagrangian – Eulerian formulation (ALE) is proposed. In this approach, the

Lagrangian and Eulerian steps are applied sequentially. For displacements, the mesh follows the

material flow and the problem is solved in Lagrangian step, while for velocities, the mesh is

repositioned and the problem is solved in Eulerian step.

The combined formulation is utilized in the simulation to avoid the severe element

distortion which is a typical problem of Lagrangian approaches, as well as the frequent

remeshing. Where, the Eulerian approach is utilized around the tool tip area where cutting

37

process occurs. And the chip is formed as a function of the plastic deformation taking place in

the material.

A demonstrative explanation of the Eulerian, Lagrangian and ALE formulation is shown

in Figure 4.1

Figure 4.1 An explanatory demonstration of the Eulerian,

Langrangian and ALE formulations

4.1.4 UPDATED LAGRANGIAN FORMULATION

In the attempt of overcoming the drawbacks of the classical Lagrangian formulation, an

updated Lagrangian formulation was developed. In this approach, the element distortion problem

is solved by the mesh adaptivity and automatic remeshing technique. The element local

coordinates of the FE mesh and local reference frame are continuously updated. The updated

Lagrangian formulation is therefore suitable when large deformations are employed.

38

The main shortcoming of the proposed formulation is the long computation time needed

to finish the simulation.

4.3 ASPECTS OF MODELING IN FEM SIMULATION

The research question addressed in this study is whether a numerical simulation, FE

modeling code is able to accurately predict the residual stress induced in a machined surface. The

simulation of machining represents a challenging task, with many aspects related to machining

still not very clear and not so easy to simulate. In order to have reliable results and have accurate

predictions of the residual stress distribution in a machined surface, the most essential aspects to

model in the FEM simulation for cutting are; work material model, chip separation criteria or

fracture criterion and friction model.

1. The work material model should satisfactorily represent elastic plastic and thermo-

mechanical behaviour of the work material deformations observed during machining process.

Accurate and reliable flow stress models are considered highly necessary to represent work

material constitutive behaviour under high-speed cutting conditions.

2. The physical process simulation around the tool cutting edge should not be distorted by the

chip separation criteria in the FEM model especially when dominant tool edge geometry such

as a round edge or a chamfered edge is present. From a process point of view, the fracture

criterion, when employed, allows the prediction of the chip geometry, however, it influences

the prediction of the forces and other parameters.

3. In order to account for the additional heat generation and stress development, the interfacial

friction characteristics on the tool–chip and tool-work piece contacts should be modelled

with high accuracy.

39

Moreover, it is worth mentioning that friction is one of the hardest phenomena to simulate in

machining. As stated by Özel and Zeren [44], friction in metal cutting plays an important role

in thermo-mechanical chip flow and integrity of the machined work surface.

Accurate simulation predictions of the stress and temperature distributions can be

obtained when an applicable work material flow stress model, a suitable fracture criterion, and a

proper friction model are determined for the tool-chip interface. Further simulation trials can also

be designed in order to identify optimum tool edge geometry and cutting process conditions for

the most desirable surface integrity, longest tool life and highest productivity.

The success and reliability of numerical codes are largely dependent upon the correct

selection of mechanical and thermo-physical properties of the work material as well as the

contact conditions and tool work piece interface. It is regarded as a critical step if acceptable

accuracy of residual stress is to be predicted. Finally, as mentioned by Cerretti et al. [45] in his

paper, “When using FE programs, the final result depends on the input data”.

4.4 WORK MATERIAL CONSTITUTIVE MODEL

The modeling of the flow stress in the work piece material is one of the most important

aspects in considering the simulation of a metal cutting process. Flow stress is the instantaneous

value of yield stress and is represented mathematically by constitutive equations depending on

strain, strain-rate and temperature. From the most widely used constitutive material models are

Oxley, Johnson – Cook and Zerilli – Armstrong. In the literature review, studies have favored the

use of Johnson – Cook constitutive material model and among these are Umbrello et al. [46],

Özel and Zeren [44], Outeiro et al. [37] and Liang and Su [17].

40

4.4.1 JOHNSON - COOK MATERIAL MODEL

Johnson – Cook [47] is a constitutive material model which accommodates to large

strains, high strain rates and high temperatures. The model developed was intended and is well

suited for computational work due to its use of variables which are readily available in most

applicable FE computer codes. Torsion tests over a wide range of strain rates, static tensile tests,

dynamic Hopkinson bar tensile tests and Hopkinson bar tests at elevated temperatures are run to

obtain the data required for the material constants.

The Johnson – Cook constitutive material model is expressed as

( ) ( (

)) (

)

( ) (4.1)

Where ( )

( )

Where is the equivalent plastic strain, ( ) is the dimensionless plastic strain rate, and is

the homologous temperature. The five material constants are A, B, n, C and m. The expression in

the first set of brackets gives the stress as a function of strain. The expressions in the second and

third sets of brackets represent the effects of strain rate and temperature, respectively [47]. is

the yield stress and and represent the effects of strain hardening. Where , is the strain rate

constant. is the instantaneous temperature, is the room temperature, and is the

melting temperature of a given material.

4.5 FRACTURE CRITERIA

In machining processes, large deformations take place, the prediction and control of the

material fracture is a critical issue. In order to investigate the surface finish and integrity of the

produced parts, the damage and fracture of the material should be predicted. In the numerical

41

model, fracture has been simulated by either deleting the mesh elements that have been subjected

to high deformation and stress or by the separation of the elements. A critical damage value is

defined for a specific fracture criterion and when this value is satisfied, fracture takes place.

Therefore, the definition of this damage value is of crucial importance. However, it is not easily

measured or predicted.

Many efforts were found in literature with the attempt to establish a fracture criterion in

order to calculate the limits of formability and be applied in simulating the different materials. In

this study, Normalized Cockcroft and Latham’s ductile fracture is used. This fracture criterion is

applied to a wide range of loading conditions and machining processes, due to its ease of

numerical calculation.

The fracture criterion is expressed by the following formulation,

∫

(4.2)

Where is the maximum principal tensile stress, and the fracture strain. The effective stress

and effective strain are represented by and , respectively. At every element of the work

piece, the fracture damage is evaluated. Fracture occurs when the critical value defined by the

user is satisfied.

4.6 FRICTION MODELS

Since the beginning of the studies on the machining process, huge effort and time has

been spent in research focused on friction models used to simulate this process. Throughout this

time, models have been proposed and tested all over the world and the conclusion of these

studies could be summarized as follows.

42

4.6.1 COULOMB FRICTION MODEL

In the early metal cutting analysis, the simple Coulomb friction model was considered on

the whole contact zone of tool-chip interface. The frictional stresses are assumed proportional to

the normal stresses, using a constant coefficient of friction µ.

The model is defined as

(4.3)

Here, is the frictional stress and is the normal stress.

4.6.2 CONSTANT SHEAR MODEL

The constant shear model is another well-known friction model, where a constant

frictional stress is assumed on the rake face, neglecting the low stress variations of with .

The frictional stress is equal to a fixed percentage of the shear flow stress of the working

material . The model is expressed by the following formulation

(4.4)

Where m is the friction factor.

4.6.3 STICKING ZONE AND SLIDING ZONE MODEL

A more realistic model proposed by Zorev [as cited by references 20 and 33] considered

the rake face of the tool as divided into two friction regions. The first region, the sticking zone,

the normal stress is very large and the frictional stress is assumed to be constant and equal to the

shear flow stress of the material itself. The second region, the sliding zone, on the contrary, the

normal stress is small. Therefore, the model proposes that the normal stress decreases from the

tool edge to the point where the chip separates from the tool. As shown in Figure 4.2.

43

Figure 4.2 Stress distribution on rake face

The sticking zone is modeled by the constant shear friction model and the sliding zone is

modeled by the Coulomb friction model.

The model can be expressed by the following formulations

( ) ( )

( ) (4.5)

Felice et al. [33] concluded in his study on the analysis of friction modeling in orthogonal

machining, that the main mechanical results as in forces, contact length, … etc. are practically

not sensitive to friction model, only by small differences. However, the friction model is most

relevant in thermal analysis. As for Özel [20] studied the influence of friction models on finite

element simulation of machining and noted that the friction models has a significant influence on

the prediction of chip geometry, forces and stresses on the tool. And the friction models that are

based on the measured normal and frictional stresses on the tool rake face are more accurate in

their predictions.

44

5. PRESENT MODEL AND SIMULATION OF METAL CUTTING

5.1 FINITE ELEMENT PACKAGE AND UTILIZATION

In this study, the Finite Element Method software DEFORM, which is based on an

updated Lagrangian formulation that employs implicit integration method designed for large

deformation simulations, is used to simulate the metal cutting process.

Design Environment for Forming (DEFORM) is a Finite Element Method (FEM) based

process simulation system designed to analyze various forming and heat treatment processes

used by metal forming and related industries. By simulating manufacturing processes on a

computer, this advanced tool allows designers and engineers to:

Reduce the need for costly shop floor trials and redesign of tooling and processes

Improve tool and die design to reduce production and material costs

Shorten lead time in bringing a new product to market

Unlike general purpose FEM codes, DEFORM is tailored for deformation modeling. A

user friendly graphical user interface (GUI) provides easy data preparation and analysis;

simplifying the data input and post processing, so engineers can focus on forming, not on

learning a cumbersome computer system. The strength of DEFORM and a key component is the

ability of its automatic, optimized remeshing system tailored for large deformation problems.

The system generates a very dense grid of nodes near the tool tip in order to handle the large

gradients of strain, strain-rate and temperature. This approach is highly effective in simulating

the metal cutting process for no chip separation criterion is needed to be defined. Therefore, the

chip is formed step by step through the simulation as the tool advances in the work piece with

minimum number of remeshes.

45

DEFORM has an extensive material database for many common alloys including steels,

aluminums, titaniums, and super-alloys and is capable of handling user defined material data

input for any material not included in the material database. Deform is able to handle rigid,

elastic, and thermo-viscoplastic material models, which are ideally suited for large deformation

modelling. As well as, elastic-plastic material model for residual stress and spring back

problems. The software can generate self-contact boundary condition with robust remeshing

allowing a simulation to continue to completion even after a lap or fold has formed. In addition,

to its fracture initiation and crack propagation models based on well-known damage factors

which allows the modelling of shearing, blanking, piercing, and machining in 2D and 3D [7].

The range of modules and models the DEFORM software provides meets the simulation

requirements of this study.

5.2 TIME INTEGRATION SCHEME

The governing finite element equations to be solved are

( ) ( ) (5.1)

(plus initial conditions)

Where is the mass matrix, is the damping matrix, is the vector of nodal displacements

(including rotations), denotes the vector of nodal forces equivalent to the element internal

stresses, is the vector of externally applied nodal loads and a time derivative is denoted by an

overdot. The force matrix ( ) depends on the displacements and time, whereas the mass ( ) and

damping ( ) matrices are assumed to be constant, however, this assumption can be removed

[48].

Newton-Raphson time integration scheme is used by DEFORM to obtain a converged

solution in elastic-plastic material simulation models. In 1669, Newton gave a version of the

46

method and in 1690; Raphson generalized and presented the method. Both mathematicians used

the same concept and both algorithms gave the same numerical results [49]. Nowadays, this

method is widely used due to its effectiveness and efficiency.

In the Newton-Raphson method, an initial guess of the root is needed to start the iterative

process. Convergence is a primary issue in this method, it is not guaranteed but if it does

converge, it does faster than the other methods.

The Newton-Raphson method is based on the principle of generating the next iteration

calculating the tangent stiffness matrix of the initial guess of the root to give an improved

estimate of the root. The process is repeated until a root within a desirable tolerance is reached.

In a single Newton-Raphson iteration, a root of ( )is to be found, by a given estimate to

the root, say , by the following

( )

( ) (5.2)

Once is obtained, may be computed using

( )

( ) (5.3)

The process is repeated until the root is obtained.

A drawback of the method is in the ill-conditioning of the tangent stiffness matrix near

the critical point, this will lead to divergence in the computer analysis and no solution found.

47

5.3 TOOL MODELING

Since, the tool wear and effect of machining on the cutting tool are not within the scope

of this study, therefore, the tool is considered as a rigid body throughout the simulations. The

geometric variables of the tool are given in Table 5.1

Table 5.1 Geometric variables of the cutting tool

Rake Angle, α (o) Clearance Angle, c (

o)

Tool Nose Radius

(mm)

Tool Edge Radius

(mm)

+6 +6 1.2 0.02

In the analysis, the tool is selected to be of Tungsten Carbide (WC) material loaded from

the software’s library. The tool material physical property data are listed in table 5.2.

Table 5.2 Tool material physical property data

Property WC Tool

Density (kg/m3) 15

Poisson’s ratio 0.3

Young’s Modulus (GPa) 800

Thermal Conductivity (W/moC) 46

Specific Heat (J/kg/oC) 203

Thermal Expansion (µm/ moC) 4.7

No mesh is generated or thermal analysis calculated for the tool, due to the selection of

the rigid object type to simulate it throughout the study. A 2D and 3D view of the tool are shown

in Figure 5.1.

48

(a) (b)

Figure 5.1 (a) 2D view of the cutting tool, (b) 3D view of the cutting tool

5.4 Work piece Modeling

In the current study, Finite Element simulation modeling of 20NiCrMo5 steel in annealed

condition is studied. The Johnson – Cook material model will be used in order to represent the

material investigated in the study. The Johnson – Cook model constants used for this study were

obtained experimentally by machining tests in the Swerea KIMAB lab and evaluated by Håkan

Thoors according to Prasad [40] which results are going to be used in this study. The Johnson –

Cook model constants are listed in Table 5.3.

Table 5.3 Johnson – Cook constitutive material model constants

Material 20NiCrMo5 steel

490 600 0.015

0.21 0.6 0

1 20 1900

49

The flow curve for the Johnson – Cook constitutive material model is shown in Figure 5.2.

Figure 5.2 Johnson – Cook flow curve

5.4.1 MATERIAL PHYSICAL PROPERTY

20NiCrMo5 steel material is mainly used in pinion manufacturing for heavy torque

transmission in trucks. Throughout the study, the work piece material used will be fixed and the

work piece is considered of elastic-plastic type material in order to measure the residual stresses

induced in the machining process. The work piece material physical property data are listed in

Table 5.4.

Table 5.4 Work piece material physical property data

Property 20NiCrMo5 steel

Density (kg/m3) 7.8

Poisson’s ratio 0.3

Young’s Modulus (GPa) 210

Thermal Conductivity (W/moC) 47.7

Specific Heat (J/kg/oC) 556

Thermal Expansion (µm/ moC) 1.2

50

The finite element mesh of the work piece is modeled for the 2D simulations using

quadrilateral elements. The number of nodes and elements vary throughout the tests, as the

author tries to compare between coarse, semi – fine and fine meshes. The work piece created is

of 5 mm width and 2 mm height. The author used the feature of mesh windows in order to form a

very dense mesh at the cutting zone along the path of the tool, in order to reduce the calculation

time and obtain more accurate results.

The typical 2D simulation model for the work piece is shown in Figure 5.3.

Figure 5.3 Work piece model in 2D simulation

As for the 3D simulations, the finite element mesh of the work piece is modeled using

around 25000 tetrahedral elements. The work piece geometry is generated by the machining

wizard, using the 3D simplified turning operation model. The mesh is equally distributed

throughout the work piece.

The typical 3D simulations for the work piece in simplified and curved models are shown in

Figure 5.4.

51

(a)

(b)

Figure 5.4 Work piece model in 3D simulation (a) simplified model (b) curved model

5.5 SYSTEM MODELING

Several simulations are tested with varying cutting conditions, in order to study the effect

of each on the residual stresses induced in the machined component by machining. The cutting

conditions are listed in Table 5.5.

Table 5.5 Cutting Conditions Variations

Cutting Condition Variations

Cutting Velocity,

Vc (m/min) 40 100 260 400

Feed Rate, f

(mm/rev) 0.2 0.45 0.8

Rake Angle, α (o) +6 0 -6

52

For the boundary conditions, velocity constraints are applied to the work piece in 2D

simulations at its left and bottom surfaces, restricting the work piece in the x and y direction,

respectively. As in 3D simulations, the work piece is constrained in the X, Y and Z directions.

The boundary constrains in 2D simulations are shown in Figure5.5.

Figure 5.5 Work piece boundary constrains in 2D simulations

The tool is moved against the work piece by applying a constant cutting velocity. In 2D

simulations the tool moves in the -X direction, as for the 3D simulations the tool moves in the

+Y direction, as shown in Figure 5.6.

53

(a)

(b)

Figure 5.6 (a) Tool movement simulation in 2D model,

(b) Tool movement simulation in 3D model

From the essential definitions when simulating a machining process, is the definition of

the contact between the work piece and the tool. The tool is selected as a master object and the

work piece is defined as the slave object. The friction type is also defined, and in the current

study, the author chose Coulomb model of friction with a friction coefficient of 0.3 to simulate

the friction between the tool and the work piece. By defining the contact and friction model,

contact is generated, as shown in Figure 5.7.

54

(a)

(b)

Figure 5.7 Contact generation between the tool and the work piece in

(a) 2D model simulation, (b) 3D model simulation

In the current study, the Normalized Cockcroft and Latham fracture criteria is chosen by

the author to simulate chip separation. The value of fracture is set to be 0.6 throughout the whole

study. This value has been selected by trials to find the closest chip morphology compared with

the experimental results. A softening percentage of 0.5% is used in the fracture criteria, to allow

a drop in the flow stress to a small percentage from its original value, in order to maintain a good

element boundary definition rather than having deleted elements by using the fracture routine.

55

The analysis uses the updated Lagrangian model formulation with the automatic

remeshing method. When the software detects element distortion, a new mesh is generated, as

shown in Figure 5.8.

Figure 5.8 Remeshing procedure at cutting zone

56

CHAPTER 6 RESULTS AND DISCUSSION

6.1 INTRODUCTION

In this chapter, the results of the finite element simulations performed by DEFORM are

presented. In the beginning, simulations are run to determine the parameters; the fracture criteria

critical value and the coefficient of friction, and a sufficient mesh density to represent the work

piece. The best estimating results compared to the experimental data are going to be used

throughout the study. The study of M. Werke et al. [8] is going to be used as the reference for the

experimental data used by the author to validate the results of this study. Afterwards, the feed rate,

cutting speed and rake angle variations are going to be studied and their effect on the resulting

residual stress distribution induced in the machined component. Temperature of cutting is

investigated as well as the study proceeds.

6.2 MODEL CALIBRATION

6.2.1 DETERMINATION OF PARAMETERS

The definition of the Normalized Cockcroft and Latham fracture criteria critical value

and Coulombs law coefficient of friction is a major basic step in order to establish the correct

model to simulate the machining process.

The correct model is verified with the chip thickness obtained experimentally with

cutting conditions; 260 m/min cutting speed, 0.2 mm/rev feed rate (represented as depth of cut in

2D simulations). The chip thickness obtained experimentally measured to be 0.312 mm.

Table 6.1 lists the design of experiments; varying the fracture criteria critical values and

coefficient of friction, which are simulated to reach the best combination to model the machining

process.

57

Table 6.1 Design of Experiments list

Test No. Normalized Cockcroft and

Latham critical value

Coulombs Law friction

coefficient

1 0.4 0.4

2 0.5 0.4

3 0.6 0.4

4 0.6 0.5

5 0.6 0.6

6 0.6 0.3

7 0.6 0.2

Figures 6.1 (a) to (f) show the chip morphology obtained by the simulations listed in

Table 6.1.

The chip geometry results are best estimated in Test number (6) when the Normalized

Cockcroft and Latham fracture criteria critical value is 0.6 and Coulombs law coefficient of

friction is 0.3 with a chip thickness of 0.41 mm. It is interesting to note, from the simulations it is

observed that the fracture criteria governs the chip form, and that the coefficient of friction has

effect on the chip thickness; as the coefficient value decreases, the chip thickness is as well

decreased. This observation could be explained for the Normalized Cockcroft and Latham

fracture criteria, by having a higher fracture threshold (i.e. 0.6) a more ductile and smooth chip is

formed; unlike at lower thresholds the chip formed is edgy and not uniform. As for the

Coulombs law, the higher the coefficient of friction selection, the friction stresses generated on

the tool-chip interface increases, causing material prevention and the chip to stick.

58

(a) Test 1 (b) Test 2 (c) Test 3

(d) Test 4 (e)Test 5 (f) Test 6

(f) Test 7

Figure 6.1chip morphology obtained by the simulations listed in Table 6.1

6.2.2 DATA COLLECTION

Mechanical and thermal parameters of the machining process; residual stress and

temperature, are calculated along the work piece in the simulation. The data collection was

performed by dividing the area the tool machined into 10 different points equally distanced and

for each point the data is collected for 9 points of depth reaching up to 0.21 mm. The data

59

collected is then averaged and graphed. This data collection process is repeated throughout the

study. Figure 6.2 represents the data collection process.

Figure 6.2 Data Collection Process

By the definition of residual stress; it is the stress remaining in the machined component

after all the external loads are removed; the component being relaxed [39]. Therefore, when the

data for residual stress was collected, it was taken in consideration for a time to elapse in order to

remove the cutting tool outward of the work piece to relax the component in means of strains and

stresses respectively. Figure 6.3 shows a work piece after being relaxed.

Point 1 Point 2 Point 3 Point 4 Point 5 Point 6 Point 7 Point 8 Point 9 Point 10

60

Figure 6.3 Work piece after being relaxed

During the study, the residual stresses in circumferential, axial and radial directions have

been gathered. The difference between before and after the relaxing of the work piece is shown

by the graphs in Figure 6.4.

From the graphs it is observed that in general, residual stresses tend to have lower

compressive stress when relaxed as seen in Figure 6.4 (a) and (b) and higher tensile stresses as in

Figure 6.4 (c) depending on the nature of the residual stress. Graphically, the curve of the

relaxed residual stresses is above the residual stress curve before being relaxed, this is true till

the depth of around 0.1 mm is reached, the curves intersect and the opposite becomes true. The

intersect of curves could be due to the surface layers (i.e. the surface 0.1 mm) being compressed

more when the tool is in cutting and when it is relaxed the stresses affect the deeper depths to

maintain equilibrium. This is a phenomenon that is observed throughout the whole tests run by

the author.

61

(a) Residual stress in circumferential direction (x)

(b) Residual stress in axial direction (z)

(c) Residual stress in radial direction (y)

Figure 6.4 Residual stresses before and after relaxing graphs

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(M

Pa)

Depth in workpiece (mm)

Residual StressinCircumferentialdirection (x)after relaxing

Residual StressinCircumferentialdirection (x)before relaxing

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-15

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-5

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5

0 0.1 0.2 0.3

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(M

Pa)

Depth in workpiece (mm)

Residual Stressin Axial direction(z) after relaxing

Residual stressin Axial direction(z) beforerelaxing

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3

Rad

ial R

esid

ual

Str

ess

(M

Pa)

Depth in workpiece (mm)

Residual Stressin Radialdirection (y)after relaxing

Residual Stressin Radialdirection (y)before relaxing

62

6.2.3 MESH DISTRIBUTION

Mesh density throughout literature and as stated by simulation software manuals; the

finer a mesh density the more accuracy reached in the obtained results in simulations, but the

more computation time required [50]. Therefore, in order to proceed with the simulations, a

suitable economical mesh density should be determined.

Three mesh densities are tested; coarse, semi-coarse and a fine mesh. Table 6.2 lists the

number of elements and average element size used in each mesh. All 2D meshes are modeled

using quadrilateral elements.

Table 6.2 Mesh Type Description

Mesh Type Number of Elements Average Element Size (mm)

Coarse 2000 0.032

Semi-coarse 4000 0.022

Fine 7500 0.014

As the mesh density is tested from coarse to fine, it is observed that the chip thickness is

decreased from a thickness of 0.431 mm in the coarse mesh, a thickness of 0.41 mm in the semi-

coarse mesh to a thickness of 0.397 mm in the fine mesh. Figure 6.5 shows the simulated mesh

densities.

(a) (b) (c)

Figure 6.5 Simulated mesh densities (a) coarse mesh, (b) semi-coarse mesh

and (c) fine mesh

63

From the three different meshes, circumferential and axial residual stresses are compared

to the experimentally obtained stresses. Figure 6.6 and 6.7 presents the graphs obtained.

Figure 6.6 Circumferential residual stress compared across the mesh distributions

Figure 6.7 Axial residual stress compared across the mesh distributions

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Fine - Circumferential (x)

Semi Coarse - Circumferential(x)

Coarse - Circumferential (x)

Experimental -Circumferential

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Depth in workpiece (mm)

Fine - Axial (z)

Semi Coarse - Axial (z)

Coarse - Axial (z)

Experimental - Axial

64

From the above graphs it is observed that the residual stresses generated from the

different mesh densities follow the same trend generally in circumferential and axial directions

and are close in magnitude and nature.

The Fine and Semi-coarse mesh capture the same trend in the simulation. However, due

to the contact between the chip formed and the work piece in the fine mesh simulation, the

cutting tool stopped at a distance of 1.379 mm. This short distance of where data was collected

has a great influence on the accuracy of the results shown and the difference in magnitude.

Therefore, the author decided to proceed performing the study’s tests with a semi-coarse

mesh, for it has shown accurate results and economical in terms of time.

6.3 FEED RATE ANALYSIS

In this part of the study, the research of feed rate effect on residual stress is presented.

Three feed rates are tested; 0.2 mm/rev, 0.45 mm/ rev and 0.8 mm/rev. The results for each test

are presented and then the tests are compared to each other in order to find a trend in the results

and a conclusion of how the feed rate affects the induced residual stress in a machined

component.

FEED RATE 0.2 mm/rev ANALYSIS

First, the 0.2 mm/rev feed rate is tested. The chip formed is presented in Figure 6.8.

65

Figure 6.8 Feed rate 0.2mm/rev simulation

The residual stress data was collected and graphed. The author thought it would be

interesting to plot the scatter of the 10 selected points of data gathering with the experimental

data. Figure 6.9 presents the graph of the scattered circumferential residual stresses.

Figure 6.9 Scattered Circumferential residual stresses in feed rate 0.2mm/rev test

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Depth in workpiece (mm)

1 - Circumferential

2

3

4

5

6

7

8

9

10

66

Figure 6.10 shows the upper and lower standard deviations from the mean values of the

residual stresses in circumferential direction; showing the range covered by the results along the

depth in the work piece.

Figure 6.10 graph with upper and lower standard deviations from the mean values

of circumferential residual stresses in feed rate 0.2 mm/rev test

It can be observed from the graph in Figure 6.9, that as the data gathering point is further

in the work piece (i.e. as the points goes from point 1 to 10 as explained in the data collection

process in Figure 6.2) the curve changes from being flat to capture the curve of the experimental

data. This might be explained by the machining cutting process going into a steady state phase

and less number of remeshing and smoothing of the results take place further in the work piece.

It is also observed that points 9 and 10 do capture the trend, but have a shift and this could be a

cause of the mesh location as the nodal points being pushed and moved downward by the tool.

Figure 6.11 shows the circumferential residual stress average with the experimental

curve.

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-400

-300

-200

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0

100

0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

Cir

cum

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(MP

a)

Depth in workpiece (mm)

UPPER

LOWER

Mean

67

Figure 6.11 Circumferential residual stresses in feed rate 0.2mm/rev test

From the graph presented in Figure 6.11, it is observed that the trend in the experimental

data is captured by the test performed in this study using DEFORM.

Figure 6.12 presents the graph of the scattered axial residual stresses compared with the

experimental axial residual stress data.

Figure 6.12 Scattered Axial residual stresses in feed rate 0.2mm/rev test

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500

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Residual Stress inCircumferentialdirection (x)

Experimental

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300

400

0 0.05 0.1 0.15 0.2 0.25

Axia

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(MP

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Depth in workpiece (mm)

Experimental - Axial

1

2

3

4

5

6

7

8

9

10

68

Figure 6.13 shows the upper and lower standard deviations from the mean values of the

residual stresses in axial direction; showing the range covered by the results along the depth in

the work piece.

Figure 6.13 graph with upper and lower standard deviations from the mean values

of axial residual stresses in feed rate 0.2 mm/rev test

Figure 6.14 presents the axial residual stresses compared with the experimental.

Figure 6.14 Axial residual stresses in feed rate 0.2 mm/rev test

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-40

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0

20

40

0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

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(M

Pa)

Depth in workpiece (mm)

UPPER

LOWER

Mean

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400

0 0.05 0.1 0.15 0.2 0.25

Axia

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(MP

a)

Depth in workpiece (mm)

Residual stress in Axialdirection (z)

Experimental

69

The same observations seen in the circumferential residual stress graphs are seen in the

axial residual stress graphs. A noticeable difference in the simulation results with the data

measured experimentally is the residual stress at the surface level. Residual stress measured

experimentally is a difficult task, data collected by the X-ray technique should be averaged

especially at peak points. When a peak point is measured, several points should be gathered in

order to confirm the curve’s gradient, strengthening the data collection process and data

reliability. If the surface residual stress measured experimentally is excluded from the results, it

can be stated that the simulations run by DEFORM and the models chosen to represent the

machining process calculate and predict residual stress to an agreeable extent with the

experimental data.

It was interesting to observe the evolving of the residual stress circumferentially and

axially at two fixed points in the work piece at surface level, as shown in Figure 6.15.

Figure 6.15 Two points of residual stress evolution

Point 1 Point 2

70

The residual stresses where gathered every 50 steps passed by the cutting tool. Point 1

was passed by the cutting tool first and after the cutting tool crossed a distance of 3.5 mm, the

machined component is relaxed. The step where the tool passes over the point and the step where

the machined component is relaxed are clearly identified in the following graphs. Figure 6.16

illustrates the circumferential residual stress evolution at the two points.

Figure 6.16 Circumferential residual stress evolution at the two points

Figure 6.17 illustrates the axial residual stress evolution at the two points.

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0 500 1000 1500 2000 2500 3000

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Step Number

RELAXED

TOOL OVER POINT 2

TOOL OVER POINT 1

71

Figure 6.17 Axial residual stress evolution at the two points

It is clearly observed that the residual stress is reached to its maximum compressive value

just before the tool passes over the node itself and then the stresses are relieved till the tool is

removed and the value of the residual stresses are stable around a certain value.

-900

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0 500 1000 1500 2000 2500 3000A

xia

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Step Number

RELAXED

TOOL OVER POINT 2

TOOL OVER POINT 1

72

FEED RATE 0.45 mm/rev ANALYSIS

Next, the feed rate 0.45 mm/rev is tested. The chip formed is presented in figure 6.18.

Figure 6.18 Feed rate 0.45mm/rev simulation

The scattered circumferential residual stresses graph is presented in Figure 6.19.

Figure 6.19 Scattered Circumferential residual stresses in feed rate 0.45mm/rev test

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Depth in workpiece (mm)

Experimental -Circumferential1

2

3

4

5

6

7

8

9

10

73

Figure 6.20 shows the upper and lower standard deviations from the mean values of the

residual stresses in circumferential direction; showing the range covered by the results along the

depth in the work piece.

Figure 6.20 Graph with upper and lower standard deviations from the mean values

of circumferential residual stresses in feed rate 0.45 mm/rev test

The circumferential residual stress average with the experimental curve is presented in

Figure 6.21.

Figure 6.21 Circumferential residual stresses in feed rate 0.45mm/rev test

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UPPER

LOWER

Mean

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(MP

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Depth in workpiece (mm)

Residual Stress inCircumferentialdirection (x)

Experimental

74

Figure 6.22 presents the graph of the scattered axial residual stresses compared with the

experimental axial residual stress data.

Figure 6.22 Scattered Axial residual stresses in feed rate 0.45mm/rev test

Figure 6.23 shows the upper and lower standard deviations from the mean values of the

residual stresses in axial direction; showing the range covered by the results along the depth in

the work piece.

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-200

-100

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25

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(MP

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Depth in workpiece (mm)

Experimental - Axial

1

2

3

4

5

6

7

8

9

10

75

Figure 6.23 Graph with upper and lower standard deviations from the mean values

of axial residual stresses in feed rate 0.45 mm/rev test

Figure 6.24 presents the axial residual stresses compared with the experimental data for

the feed rate 0.45mm/rev test.

Figure 6.24 Axial residual stresses in feed rate 0.45mm/rev test

It is observed that the range of scattered residual stresses obtained by the simulations

capture the values of residual stresses measured experimentally but not the gradient of the curve.

It is noticeable that the data gathering point’s curves are almost flat. This is explained by the use

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UPPER

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Mean

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0 0.05 0.1 0.15 0.2 0.25Axia

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Depth in workpiece (mm)

Residual Stress in Axialdirection (z)

Experimental

76

of the remeshing technique in the updated lagrangian model used by the software DEFORM,

which smooth the obtained results and may lead to loss of accuracy.

FEED RATE 0.8 mm/rev ANALYSIS

Last in the feed rate analysis, the feed rate 0.8 mm/rev is tested. The chip formed is

presented in figure 6.25.

Figure 6.25 Feed rate 0.8 mm/rev simulation

The scattered circumferential residual stresses graph is presented in Figure 6.26.

77

Figure 6.26 Scattered Circumferential residual stresses in feed rate 0.8 mm/rev test

Figure 6.27 shows the upper and lower standard deviations from the mean values of the

residual stresses in circumferential direction; showing the range covered by the results along the

depth in the work piece.

Figure 6.27 Graph of upper and lower standard deviations from the mean values

of circumferential residual stresses in feed rate 0.8 mm/rev test

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700

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Experimental - Circumferential

1

2

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10

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78

The circumferential residual stress average with the experimental curve is presented in

Figure 6.28.

Figure 6.28 Circumferential residual stresses in feed rate 0.8 mm/rev test

Figure 6.29 presents the graph of the scattered axial residual stresses compared with the

experimental axial residual stress data.

Figure 6.29 Scattered Axial residual stresses in feed rate 0.8 mm/rev test

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Residual Stress inCircumferentialdirection (x)

Experimental

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Experimental - Axial

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10

79

Figure 6.30 shows the upper and lower standard deviations from the mean values of the

residual stresses in axial direction; showing the range covered by the results along the depth in

the work piece.

Figure 6.30 Graph with upper and lower standard deviations from the mean values

of axial residual stresses in feed rate 0.8 mm/rev test

Figure 6.31 presents the axial residual stresses compared with the experimental data for

the feed rate 0.8 mm/rev test.

Figure 6.31 Axial residual stresses in feed rate 0.8 mm/rev test

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Residual Stress in Axialdirection (z)

Experimental

80

The same observation observed in the feed rate 0.45 mm/rev simulations is also seen in

the feed rate 0.8 mm/rev simulations. The simulations capture the values and range of residual

stresses measured experimentally but not the gradient of the curve.

The same machining process with the same material model has been simulated by Prasad

[40] using ABAQUS/explicit software with an ALE formulation. Prasad used Johnson – Cook

constitutive material model, the modified Coulomb friction law and a damage initiation criterion

with a critical plastic strain value to fully model the machining process. The results obtained

from Prasad’s model are compared to the results obtained by this study for the different feed

rates simulated.

From the following graphs it is observed that the residual stress data collected by Prasad

using ABAQUS software have a trend of having a high tensile stress at surface level and

decrease with deeper depths to have a zero magnitude at around 0.75 mm of depth. The

difference is clear between the results of the current study and Prasad’s study results and this is

explained by the different friction and fracture criteria model used to present the machining

process. Also, an explicit scheme of integration with an ALE formulation is used in Prasad’s

study.

81

Figure 6.32 presents the circumferential and axial results of Prasad’s model with the

results obtained in this study for feed rate 0.2 mm/rev.

(a) Circumferential residual stress comparison

(b) Axial residual stress comparison

Figure 6.32 Feed rate 0.2 mm/rev comparison with Prasad study

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Prasad study - feedrate 0.2

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Current Study axial -feed rate 0.2

Prasad study axial -feed rate 0.2

82

Figure 6.33 presents the circumferential and axial results of Prasad’s model with the

results obtained in this study for feed rate 0.45 mm/rev.

(a) Circumferential residual stress comparison

(b) Axial residual stress comparison

Figure 6.33 Feed rate 0.45 mm/rev comparison with Prasad study

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Prasad studycircumferential - feedrate 0.45

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Current Study axial -feed rate 0.45

Prasad study axial -feed rate 0.45

83

Figure 6.34 presents the circumferential and axial results of Prasad’s model with the

results obtained in this study for feed rate 0.8 mm/rev.

(a) Circumferential residual stress comparison

(b) Axial residual stress comparison

Figure 6.34 Feed rate 0.8 mm/rev comparison with Prasad study

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Current studycircumferential - feedrate 0.8

Prasad studycircumferential - feedrate 0.8

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Current study axial -feed rate 0.8

Prasad study axial -feed rate 0.8

84

6.3.2 FEED RATE SIMULATION COMPARISON

The influence of the feed rate on the residual stresses induced in a machined component

is analyzed comparing the tests run at feed rates; 0.2 mm/rev, 0.45 mm/rev and 0.8 mm/rev. The

chip formed in the feed rate tests are shown in Figure 6.35.

(a) Feed rate 0.2 (b) Feed rate 0.45 (c) Feed rate 0.8

Figure 6.35 Feed rate simulations

The chip thickness was measured and averaged along the chip in the three simulations,

and it was compared with the chip thickness measured experimentally. Table 6.3 lists the chip

thickness measured for each feed rate simulation.

Table 6.3 chip thickness measured for the feed rate simulations

Feed rate Experimentally measured

chip thickness

Average chip thickness

obtained from simulations

0.2 mm/rev 0.312 mm 0.41 mm

0.45 mm/rev 0.870 mm 0.793 mm

0.8 mm/rev 1.11 mm 1.38 mm

As seen from Table 6.3, chip thickness obtained from simulations varies from the

experimentally measured data and not in a certain manner (i.e. whether overestimate or

underestimate the value). This difference is a result of the remeshing happening throughout the

cutting simulation and the softening percentage of 0.5% used in the fracture criteria. Also, as

85

observed earlier, the chip thickness was affected by the friction coefficient selected in section

6.2.1. The chip generated was not uniform therefore an average was calculated.

Figure 6.36 presents the circumferential residual stress distribution graph of the feed rate

simulations compared to each other.

Figure 6.36 Circumferential residual stresses in feed rate simulations

Figure 6.37 presents the graph of the experimentally measured circumferential residual

stress distributions for the different feed rates tested.

Figure 6.37 Circumferential residual stresses experimentally measured in feed rate tests

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Feed rate 0.45 -Circumferential

Feed rate 0.8 -Circumferential

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Experimental 0.45 -Circumferential

Experimental 0.8 -Circumferential

86

As seen in Figure 6.36 and 6.37, there is a big resemblance between the circumferential

residual stress experimentally measured curves and the data collected curves from the

simulations. It is observed that by increasing the feed rate lower compressive residual stresses in

the circumferential direction (i.e. the cutting direction) are obtained, whether in simulations or

experimentally. An explanation of this observation could be of the higher stresses needed to

remove more material (i.e. more feed) and when the tool is removed a spring back of the stresses

with a greater amount results in the lower compressive stresses.

Figure 6.38 presents the axial residual stress distribution graph of the feed rate

simulations compared to each other.

Figure 6.38 Axial residual stresses in feed rate simulations

Figure 6.39 presents the graph of the experimentally measured axial residual stress

distributions for the different feed rates tested.

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Feed rate 0.2 - Axial

Feed rate 0.45 - Axial

Feed rate 0.8 - Axial

87

Figure 6.39 Axial residual stresses experimentally measured in feed rate tests

Residual Stresses in axial direction simulated and presented in Figure 6.38, do not show

the same trend found in the residual stress in circumferential direction. It is observed that higher

feed rates have higher compressive axial residual stresses. Experimentally this observation is

seen at deeper depths in the machined component (i.e. below 0.1 mm).

Throughout literature there were controversial explanatory views of the influence of feed

rates on the induced residual stress in machining. Outerio et al. [37] concluded that the uncut

chip thickness (i.e. feed rate) seemed to be the parameter having the largest influence on residual

stress and that circumferential residual stress increased when the uncut chip thickness increased

agreeing in point of views with Edoardo Capello [12]. Unlike, M’Saoubi et al. [13] which found

that the influence of the feed rate on the generated surface residual stresses is relatively small.

However, in order to have a firm and reliable saying on the influence of feed rate on the

induced residual stress in machining, more investigations experimentally and by simulations

should be made on a wider range of feed rates.

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Experimental 0.8 -Axial

88

6.4 CUTTING SPEED ANALYSIS

The influence of the cutting speed on the residual stresses induced in a machined

component was analyzed keeping the feed rate constant at 0.2mm/rev. The tests were run at four

different cutting speeds; 400 m/min, 260 m/min, 100 m/min and 40 m/min. The chip formed in

the cutting speed tests are shown in Figure 6.40.

(a) Speed 400 m/min (b) Speed 260 m/min

(c) Speed 100 m/min (d) Speed 40 m/min

Figure 6.40 Cutting Speed simulations

As seen in Figure 6.40, the chip is smoother at higher cutting speed. Ceretti et al [24]

found that the chip curls with higher cutting speeds. The chip thickness was measured and

averaged along the chip, and it was observed that as the cutting speed increases, the chip

thickness as well increases. Table 6.4 lists the chip thickness measured for each cutting speed

simulation.

89

Table 6.4 chip thickness measured for the cutting speed simulations

Cutting Speed Average chip thickness

400 m/min 0.487 mm

260 m/min 0.41 mm

100 m/min 0.4244 mm

40 m/min 0.39 mm

Figure 6.41 presents the circumferential residual stress distribution graph of the cutting

speed simulations compared to each other.

Figure 6.41 Circumferential residual stresses in cutting speed simulations

As seen in Figure 6.41, the circumferential residual stress at the surface has lower

compressive stress as the cutting speed increase and continues to lower depths in the work piece.

This trend is also observed in the axial residual stress distribution graph and the radial

distribution graph; Figure 6.42 and 6.43 respectively.

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Speed 260 -circumferential

Speed 100 -Circumferential

Speed 40 -Circumferential

90

Figure 6.42 Axial residual stresses in cutting speed simulations

Figure 6.43 Radial residual stresses in cutting speed simulations

The predicted results are in agreement concerning the lower compressive stresses and

higher tensile stresses for higher cutting speeds with findings in literature [13, 15 and 27].

Outeiro et al. [37] concluded in their study that residual stress increase with cutting speed. Wang

et al. [38] found that with higher cutting speed, more thermal loads generate higher residual

stress. Also, the residual stress beneath the surface varies with the cutting speeds.

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Speed 260 - Radial

Speed 100 - Radial

Speed 40 - Radial

91

An explanation of this observation could be, due to the higher temperatures reached at

higher speeds as shown in Figure 6.44. At cutting speed 400 m/min a maximum temperature of

2070o degrees is reached, while at 40 m/min a maximum temperature of 975

o degrees is reached.

So as temperature increase because of the cutting speed, the flow stress curve decreases as shown

in Figure 5.2 and modeled by the Johnson – Cook constitutive material model. Therefore, when

the cutting tool is removed a spring back of the stresses results in the lower compressive stresses

for higher cutting speeds.

(a) Temperature distribution at cutting speed 40 m/min

(b) Temperature distribution at cutting speed 400 m/min

Figure 6.44 Temperature distribution in cutting speed simulations

92

6.5 RAKE ANGLE ANALYSIS

To study the influence of tool geometry on residual stresses, the rake angle was selected

for this study of all the cutting geometry parameters, due to its known influence on residual

stresses.

The influence of the tool rake angle on residual stresses was analyzed for three different

rake angles: -6o, 0

o and 6

o. The chip formed in the tool rake angle tests are shown in Figure

6.45.

(a) Rake angle -6o (b) Rake angle 0

o (c) Rake angle 6

o

Figure 6.45 Tool rake angle analysis simulations

Figure 6.46 presents the circumferential residual stress distribution graph of the tool rake

angle simulations compared to each other.

93

Figure 6.46 Circumferential residual stresses in tool rake angle simulations

As seen in Figure 6.46, the circumferential residual stresses slightly decreased when the

rake angle increased from -6o to 0

o and as the rake angle increased to 6

o, the circumferential

residual stress became compressive stresses. The same variations of the residual stresses were

obtained axially, as shown in Figure 6.47.

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Rake angle 0 Circumferential

Rake angle -6 Circumferential

94

Figure 6.47 Axial residual stresses in tool rake angle simulations

The predicted results are in agreement with findings in literature [24, 26 and 37]. The

observation of having lower compressive residual stresses induced in the machined component

when having cutting tools with 0o and -6

o degrees may be explained with higher plastic

deformation work required when using these rake angles and the increase in the contact length

involved between the chip and tool. Both factors lead to high temperatures which as a result of

the lowering of flow stress curves results in lower compressive stresses than positive rake angles.

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Rake angle +6 Axial

Rake angle 0 Axial

Rake angle -6 Axial

95

6.6 TEMPERATURE ANALYSIS

DEFORM software models a complex interaction between deformation, temperature and,

in the case of heat transformation and diffusion. There is a coupling between the entire

phenomenon, as illustrated in Figure 6.48 [7].

Figure 6.48 Relationship between various DEFORM modules

The standard simulation mode; heat transfer, is used in this study where thermal effects

within the simulation, including heat transfer between objects and the environment, and heat

generation due to deformation are applicable.

The temperature distributions in a work piece before and after relaxing of the machined

component are illustrated in Figure 6.49.

96

(a) Machined component before relaxing

(b) Machined component after relaxing

Figure 6.49 Temperature distributions in simulation

From Figure 6.49 it can be observed that the maximum temperature after the machined

component is relaxed have decreased from 1820o degrees to 1150

o degrees.

The author collected the temperature distribution in the work piece at various depths.

Figure 6.50 shows the graph of the temperature distribution in the work piece in the simulation

of cutting speed 400 m/min test, data is collected after machined component is relaxed.

97

Figure 6.50 Temperature distribution in cutting speed 400 m/min test

after component is relaxed

It is observed that temperature decreases at lower surfaces in the machined component.

Temperature is lost to the environment and as seen in Figure 6.49 temperature is mainly centered

in the chip (i.e. material being removed).

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Temperature

98

6.7 3D ANALYSIS

In this part of the study, the research of feed rate effect on residual stress is presented in

3D model.

FEED RATE 0.2 mm/rev ANALYSIS

In the 3D simulations and for the feed rate 0.2 mm/ rev, a work piece of 10 mm long is

used in the simulation as shown in Figure 6.51.

Figure 6.51 Feed rate 0.2 mm/rev in 3D simulation

In DEFORM 3D, to be able to read the data from within the work piece, a tool called

slicing is used, where the work piece is split from where the data is required to be collected, as

shown in Figure 6.52. This technique is used for all feed rate 3D simulations.

99

Figure 6.52 Slicing of work piece in 3D simulations

Afterwards two points are selected (i.e. from surface cut to a depth of 0.21 mm) and a

graph of the state variable selected is calculated as shown in Figure 6.53.

Figure 6.53 State variable graph distribution in 3D simulations

100

Figure 6.54 illustrates the graph of the scattered circumferential residual stresses

collected from the 3D simulation for feed rate 0.2 mm/rev.

Figure 6.54 Scattered circumferential residual stresses in feed rate 0.2 mm/rev 3D test

The circumferential residual stress average with the experimental curve is presented in

Figure 6.55.

Figure 6.55 Circumferential residual stresses in feed rate 0.2 mm/rev 3D test

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Depth in workpiece (mm)

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Residual stress inCircumferentialdirection (y)

Experimental

101

Figure 6.56 illustrates the graph of the scattered axial residual stresses collected from the

3D simulation for feed rate 0.2 mm/rev.

Figure 6.56 Scattered axial residual stresses in feed rate 0.2 mm/rev 3D test

The axial residual stress average with the experimental curve is presented in Figure 6.57.

Figure 6.57 Axial residual stresses in feed rate 0.2 mm/rev 3D test

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Residual Stress in Axialdirection (x)

Experimental

102

It is observed from the residual stresses collected in the simulations that the

circumferential and axial stresses do capture a trend with a very small range of variations in the

stresses. This is also observed in the simulations of feed rate 0.45 and 0.8 mm/rev.

FEED RATE 0.45 mm/rev ANALYSIS

In the 3D simulations and for the feed rate 0.45 mm/ rev and 0.8 mm/rev, a work piece of

5 mm long is used in the simulation as shown in Figure 6.58.

Figure 6.58 Feed rate 0.45 mm/rev in 3D simulation

103

Figure 6.59 illustrates the graph of the scattered circumferential residual stresses

collected from the 3D simulation for feed rate 0.45 mm/rev.

Figure 6.59 Scattered circumferential residual stresses in feed rate 0.45 mm/rev 3D test

The circumferential residual stress average with the experimental curve is presented in

Figure 6.60.

Figure 6.60 Circumferential residual stresses in feed rate 0.45 mm/rev 3D test

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Residual Stress inCircumferentialdirection (y)

Experimental

104

Figure 6.61 illustrates the graph of the scattered axial residual stresses collected from the

3D simulation for feed rate 0.45 mm/rev.

Figure 6.61 Scattered axial residual stresses in feed rate 0.45 mm/rev 3D test

The axial residual stress average with the experimental curve is presented in Figure 6.62.

Figure 6.62 Axial residual stresses in feed rate 0.45 mm/rev 3D test

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Residual Stress in Axialdirection (x)

Experimental

105

FEED RATE 0.8 mm/rev ANALYSIS

The 3D simulations for the feed rate 0.8 mm/rev is shown in Figure 6.63.

Figure 6.63 Feed rate 0.8 mm/rev in 3D simulation

Figure 6.64 illustrates the graph of the scattered circumferential residual stresses

collected from the 3D simulation for feed rate 0.8 mm/rev.

Figure 6.64 Scattered circumferential residual stresses in feed rate 0.8 mm/rev 3D test

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106

The circumferential residual stress average with the experimental curve is presented in

Figure 6.65.

Figure 6.65 Circumferential residual stresses in feed rate 0.8 mm/rev 3D test

Figure 6.66 illustrates the graph of the scattered axial residual stresses collected from the

3D simulation for feed rate 0.8 mm/rev.

Figure 6.66 Scattered axial residual stresses in feed rate 0.8 mm/rev 3D test

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Residual Stress inCircumferentialdirection (y)

Experimental

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1 - Axial

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107

The axial residual stress average with the experimental curve is presented in Figure 6.67.

Figure 6.67 Axial residual stresses in feed rate 0.8 mm/rev 3D test

It could be observed from the 3D simulations, that DEFORM has a weakness and is

unable to predict the residual stresses induced by machining operations. This could be a result of

the inaccurate data collection process used. Due to the inability to collect data at nodes within the

work piece, data might be underestimated or even spread on an area with no precision of value.

Higher mesh density could improve the collected results but on the expense of higher

computation time. However, it should be mentioned that the chip forming animation of the 3D

simulations are good in means of shape and form.

To summarize the results and discussion section, it is observed that throughout the

simulations in the study of feed rates, cutting speeds and rake angles, the results collected were

able to generally capture the magnitude and gradient of the curve of the residual stress

circumferentially and axially measured experimentally at about 0.1 mm and lower depth in the

machined component. DEFORM was not able to capture the measured behavior on the surface

level and up to a depth of 0.1mm. This inability was explained by the remeshing taking place and

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Residual Stress in Axialdirection (x)

Experimental

108

smoothing of the results as the cutting tool cut through the material, causing loss of data and

inaccuracy of results. In addition, improvement in residual stress measurement is needed.

Measuring residual stresses is a laborious task with error ranging from 50 MPa to 200 MPa for a

good measurement [39]. In the experimentally measured results a high gradient of the residual

stress curves is observed with low reliability in the collected data points. Therefore, the

advancement in the measuring capabilities may assist greatly the general modeling capability.

7. FUTURE WORK

The current model provides an accurate method of predicting the induced residual stress

in a machined component to a great extent, by capturing the range of residual stress distribution

across the depth of cut in the work piece and its magnitude. In addition, this study has provided a

clarification of the influence of the cutting process and cutting tool parameters on the induced

residual stress in a machined component. Nonetheless, there are opportunities of further

investigating the rest of the parameters included in the process.

In the study, the influence of the feed rate parameter on the induced residual stress could

not be clearly stated; therefore the author recommends more investigation in this area and

performing tests on a wider range of feed rate experimentally and by simulations in order to

determine a trend. Also, the study could be expanded to test more cutting conditions and cutting

tool geometry, such as; the influence of the cutting tool radius on the induced residual stress. In

addition, this model should be tested on different work piece materials and verified

experimentally in order to confirm the relationships found between the cutting speed and rake

angle in this study.

109

8. CONCLUSION

In this study, a thermo-mechanical numerical simulation model is presented using the

Finite Element Method software DEFORM. The developed model has proved to be able to

predict the induced residual stress in a work piece that undergoes a typical turning machine

operation.

In the first part of this study, effort was made to define the parameters to be used in the

simulations for the fracture criteria; the normalized Cockcroft and Latham model and the friction

Coulomb law. The results of the models were compared with the experimental chip thickness

measured in the labs. It was seen that the critical value of 0.6 for the normalized Cockcroft and

Latham model and a coefficient of friction of 0.3 for the Coulomb law obtained a chip form and

thickness which agreed well with the measured chip experimentally.

In the following part of the study was focused on analyzing the influence of the mesh

distribution, feed rate in 2D and 3D simulations, cutting speed and tool rake angle on the residual

stress state in the machined work piece. The following are concluded from the simulations

performed in this study;

1. The fracture criteria critical value governed the chip form and the coefficient of

friction varies the chip thickness; as the coefficient value decreases, the chip

thickness is as well decreased.

2. The finer the mesh distribution the more accurate results are obtained from the

simulations, but on the expense of the computation time taken to finish the

simulation.

110

3. The feed rate influence on the induced residual stress in machining was not clear in

the simulations compared to the experimentally measured data; therefore more

investigations should be made on a wider range of feed rates.

4. The various cutting speeds effects on the residual stress are visualized from the FEM

simulation; the higher the cutting speed, lower compressive stresses are obtained, and

higher tensile stresses depending on the nature of the stresses whether being tensile or

compressive.

5. The tool rake angle results in higher compressive stresses when the tool rake angle is

increased from -6o to 6

o.

6. The results collected in simulations were able to generally capture the magnitude and

gradient of the curve of the residual stress circumferentially and axially measured

experimentally at about 0.1 mm and lower depth in the machined component to a

high accuracy level.

7. Remeshing is an essential tool in eliminating the element distortion taking place when

the cutting tool cuts through the work piece. However, smoothing of the results and

loss of data and accuracy take place with remeshing and should be taken in

consideration.

8. DEFORM 2D gave accurate residual stress predictions and captured the trends and

magnitude of the experimentally measured results. Also, the data collection from

nodal points was observed to be very efficient and was considered as a strength of the

software.

9. DEFORM 3D gave good chip forming animation in means of shape and form. But,

had a weakness in predicting the residual stress and in data collection.

111

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