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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
9
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
10
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
11
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
12
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].
13
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
-120
-100
-80
-60
-40
-20
0
20
0 0.1 0.2 0.3
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(M
Pa)
Depth in workpiece (mm)
Residual StressinCircumferentialdirection (x)after relaxing
Residual StressinCircumferentialdirection (x)before relaxing
-35
-30
-25
-20
-15
-10
-5
0
5
0 0.1 0.2 0.3
Axia
l R
esid
ual
Str
ess
(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
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(M
Pa)
Depth in workpiece (mm)
Fine - Circumferential (x)
Semi Coarse - Circumferential(x)
Coarse - Circumferential (x)
Experimental -Circumferential
-300
-200
-100
0
100
200
300
400
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(M
Pa)
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
-600
-500
-400
-300
-200
-100
0
100
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
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.
-500
-400
-300
-200
-100
0
100
0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(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
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Residual Stress inCircumferentialdirection (x)
Experimental
-300
-200
-100
0
100
200
300
400
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
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
-140
-120
-100
-80
-60
-40
-20
0
20
40
0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2
Axia
l R
esid
ual
Str
ess
(M
Pa)
Depth in workpiece (mm)
UPPER
LOWER
Mean
-300
-200
-100
0
100
200
300
400
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(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.
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
200
0 500 1000 1500 2000 2500 3000
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
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
-800
-700
-600
-500
-400
-300
-200
-100
0
100
0 500 1000 1500 2000 2500 3000A
xia
l R
esid
ual
Str
ess
(MP
a)
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
-300
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
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
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20
0 0.05 0.1 0.125 0.15 0.175 0.2
Cir
cum
fere
nti
al r
esid
ual
str
ess
(MP
a)
Depth in workpiece (mm)
UPPER
LOWER
Mean
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
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.
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
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
-160
-140
-120
-100
-80
-60
-40
-20
0
0 0.05 0.1 0.125 0.15 0.175 0.2
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
UPPER
LOWER
Mean
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25Axia
l R
esid
ual
Str
ess
(MP
a)
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
-300
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Experimental - Circumferential
1
2
3
4
5
6
7
8
9
10
-250
-200
-150
-100
-50
0
0 0.05 0.075 0.1 0.125 0.175 0.2
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
UPPER
LOWER
Mean
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
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Residual Stress inCircumferentialdirection (x)
Experimental
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Experimental - Axial
1
2
3
4
5
6
7
8
9
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
-160
-140
-120
-100
-80
-60
-40
-20
0
0 0.05 0.1 0.125 0.15 0.175 0.2
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
UPPER
LOWER
Mean
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Current Studycircumferential - feedrate 0.2
Prasad study - feedrate 0.2
-150
-100
-50
0
50
100
150
200
250
300
350
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Current studycircumferential - feedrate 0.45
Prasad studycircumferential - feedrate 0.45
-200
-100
0
100
200
300
400
500
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Current studycircumferential - feedrate 0.8
Prasad studycircumferential - feedrate 0.8
-200
-100
0
100
200
300
400
500
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-300
-250
-200
-150
-100
-50
0
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Feed rate 0.2 -Circumferential
Feed rate 0.45 -Circumferential
Feed rate 0.8 -Circumferential
-300
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Experimental 0.2 -circumferential
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.
-200
-150
-100
-50
0
50
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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.
-400
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Experimental 0.2 -Axial
Experimental 0.45 -Axial
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.
-400
-350
-300
-250
-200
-150
-100
-50
0
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Speed 400 -circumferential
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.
-100
-80
-60
-40
-20
0
20
40
0 0.05 0.1 0.15 0.2 0.25A
xia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Speed 400 - Axial
Speed 260 -Axial
Speed 100 - Axial
Speed 40 - Axial
-20
-15
-10
-5
0
5
0 0.05 0.1 0.15 0.2 0.25
Rad
ial R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Speed 400 - Radial
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.
-140
-120
-100
-80
-60
-40
-20
0
20
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Rake angle +6 circumferential
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.
-40
-30
-20
-10
0
10
20
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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).
0
20
40
60
80
100
120
140
160
0 0.05 0.1 0.15 0.2 0.25
Tem
per
atu
re
Depth in workpiece (mm)
Temperature
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
-25
-20
-15
-10
-5
0
0 0.05 0.1 0.15 0.2 0.25C
ircu
mfe
ren
tial
Res
idu
al S
tres
s (M
Pa)
Depth in workpiece (mm)
1 - Circumferential
2
3
4
5
6
7
8
9
10
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
1 - Axial
2
3
4
5
6
7
8
9
10
-300
-200
-100
0
100
200
300
400
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-2
-1
0
1
2
3
4
5
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
1 - circumferential
2
3
4
5
6
7
8
9
10
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
1 - Axial
2
3
4
5
6
7
8
9
10
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 0.05 0.1 0.15 0.2 0.25
Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
1 - circumferential
2
3
4
5
6
7
8
9
10
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
-200
-100
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25Cir
cum
fere
nti
al R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
Residual Stress inCircumferentialdirection (y)
Experimental
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25
Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
1 - Axial
2
3
4
5
6
7
8
9
10
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
-300
-200
-100
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25Axia
l R
esid
ual
Str
ess
(MP
a)
Depth in workpiece (mm)
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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