INVESTIGATING THE EFFECT OF CP
TITANIUM MICROSTRUCTURE ON THE
MECHANICS OF MICROSCALE
MACHINING
a thesis submitted to
the graduate school of engineering and science
of bilkent university
in partial fulfillment of the requirements for
the degree of
master of science
in
mechanical engineering
By
Alp Aksın
September 2019
INVESTIGATING THE EFFECT OF CP TITANIUM MI-CROSTRUCTURE ON THE MECHANICS OF MICROSCALE MACHINING
By Alp Aksın September 2019
We certify that we have read this thesis and that in our opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.
Yi˘git Karpat(Advisor)
Melih C¸ akmakcı
Orkun ¨Oz¸sahin
Approved for the Graduate School of Engineering and Science:
ABSTRACT
INVESTIGATING THE EFFECT OF CP TITANIUM
MICROSTRUCTURE ON THE MECHANICS OF
MICROSCALE MACHINING
Alp Aksın
M.S. in Mechanical Engineering Advisor: Yi˘git Karpat
September 2019
Metal cutting in microscale brings along many challenges and unanswered ques-tions. Mechanical response of the material to the micro-cutting process is one of them, since feed values and the edge radius of the tool can be in the magnitude of order of the material’s grain size. In addition, the grain morphology of the ma-terial may affect process outputs. This study investigates microstructure effects of the commercially pure titanium (CP Ti) based on analytical and mechanis-tic modeling approaches. A slip line field model was studied considering fracture toughness and edge radius effects. Orthogonal micro-cutting tests were performed on different morphologies at feed levels ranging from 0.25 to 6µm per revolution and cutting force data were collected. Cut chip thickness values were measured by using SEM and used as in-process output in the model. The model outputs were fit to force data and unknown model parameters were identified. Those deter-mined parameters were compared with measurements. The study show that the rake angle and tool edge radius parameters have a consistent disparity between measured and identified values. Evidence of possible wear and material build up at the tool have been observed. Using Bayesian inference, possible range of rake angle values have been further investigated and probability distributions of the rake value were identified for different feed levels. Micromilling of CP titanium has also been considered and a relationship between microscale orthogonal cut-ting and micromilling has been sought. CP titanium was tested by conduccut-ting full immersion micromilling experiments based on mechanistic modeling. Influ-ence of the grain morphology on model coefficients, surface texture and hardness have been discussed.
Keywords: CP titanium, Grain morphology, Microstructure, Micromilling, Micro-cutting, Slip line field theory, Bayesian inference, Mechanistic modeling.
¨
OZET
SAF T˙ITANYUM M˙IKROYAPISININ TALAS
¸
KALDIRMA MEKAN˙I ˘
G˙INE M˙IKRO ¨
OLC
¸ EKTE
ETK˙IS˙IN˙IN ARAS
¸TIRILMASI
Alp Aksın
Makina M¨uhendisli˘gi, Y¨uksek Lisans Tez Danı¸smanı: Yi˘git Karpat
Eyl¨ul 2019
Mikro ¨ol¸cekte metal kesme bir ¸cok zorluk ve cevaplanmamı¸s soruyu beraberinde getirir. Mikro kesme i¸sleminde besleme ve kesme takımı kenar radyus de˘gerleri malzemenin tanecik boyutlarında olabilece˘ginden dolayı, mikro kesme i¸slemine malzemenin mekanik cevabı ¨onemli bu sorulardan biridir. Buna ek olarak malze-menin tanecik morfolojisi kesme i¸slemi sonu¸clarına etki edebilir. Bu ¸calı¸sma tec-imsel arılıkta titanyum (CP Ti) mikroyapısının etkilerini analitik ve mekanis-tik modelleme yakla¸sımına ba˘glı olarak inceler. Kırılma toklu˘gu ve takım ke-nar radyus etkilerini hesaba katarak bir kayma alanı modeli ¸calı¸sılmı¸stır. Or-togonal mikro kesme deneyleri farklı mikroyapılar ¨uzerinde 0.25 ile 6 µm/devir besleme de˘gerleri arasında test edilmi¸stir. Kesme kuvveti bilgisi kaydedilmi¸stir. Olu¸san tala¸s kalınlıkları SEM ile ¨ol¸c¨ulerek modele girdi olarak tanımlanmı¸stır. Model ¸cıktıları kesme kuvveti verisine oturtulmu¸s ve bilinmeyen model parame-treleri belirlenmi¸stir. Belirlenen parametreler ¨ol¸c¨umler ile kar¸sıla¸stırılmı¸stır. Be-lirlenen tala¸s a¸cısı ve takım kenar radyusu parametrelerinin ¨ol¸c¨ulen de˘gerler ile arasında s¨urekli bir fark oldu˘gu g¨ozlemlenmi¸stir. Kesme takımı ¨uzerinde muhtemel a¸sınma ve malzeme birikmesi izleri g¨ozlenmi¸stir. Bayesci sonu¸c ¸cıkarımı yakla¸sımı kullanılarak, muhtemel tala¸s a¸cısı aralı˘gı incelenmi¸stir. Test yapılan besleme de˘gerleri i¸cin tala¸s a¸cısının olasılık da˘gılımı belirlenmi¸stir. Ayrıca, CP Ti i¸cin mikro frezeleme i¸slemi ¸calı¸sılmı¸s, mikro ¨ol¸cekte ortogonal kesme ve frezeleme arasında bir ili¸ski aranmı¸stır. CP Ti ¨uzerinde tam daldırma mikro frezleme deney-leri mekanistik modellemeye ba˘glı olarak yapılmı¸stır. Morfolojinin model kat-sayılarına, y¨uzey dokusuna ve sertlik de˘gerlerine olan tesiri tartı¸sılmı¸stır.
Acknowledgement
I would like to thank my thesis advisor, Assoc. Prof. Yi˘git Karpat, for his patience, guidance and understanding.
I would like to express my gratitude to my manager Dr. Atılgan Toker for his great support. I am also grateful to Roketsan A.S¸. for the financial support received through the research scholarship.
I also would like to thank for his advice and helpfulness, Dr. S¸akir Baytaro˘glu, and for his effort and technical support in the preparation of experimental hard-ware, Lab. Tech. S¸akir Duman.
Finally, I would like to thank my mother S¸¨ukran, grandmother Kadriye for their eternal love and support and the late grand father S¸¨ukr¨u who always be remembered.
Contents
1 Introduction 1
2 Preparation of Test Specimens 4
2.1 Commercially Pure Titanium . . . 4
2.2 Heat Treatment of CP Titanium . . . 6
2.3 Grinding and Electropolishing . . . 9
2.4 Metallographic Examination . . . 16
3 Orthogonal Micro-Cutting of Commercially Pure Titanium on Different Grain Morphologies 21 3.1 Brief Introduction of Atkins’ Metal Cutting Model . . . 22
3.2 Including Edge Radius Effect Using Slip Line Field Theory . . . . 24
3.2.1 Defining Cutting Force Equation . . . 25
3.2.2 Solving for Shear Angle and Tool Tip Friction Angle . . . 28
CONTENTS vii
3.3 Micro Semi-Orthogonal Cutting Experiments . . . 35
3.4 Analysis of the Experimental Data . . . 45
3.4.1 Discussing Cut Chip Thickness Effect . . . 45
3.4.2 Neglecting Nonlinear Region of Cut Chip Thickness . . . . 49
3.4.3 Considering Nonlinear Region of Cut Chip Thickness and Effect of the Rake Angle . . . 53
4 Bayesian Inference of Slip-line Field Parameters Using MCMC Method 66 4.1 Brief Introduction of Markov Chain Monte Carlo and Bayesian Inference . . . 67
4.1.1 Bayesian Inference . . . 67
4.1.2 Markov Chain Monte Carlo (MCMC) Method . . . 68
4.1.3 Application of MCMC to Bayesian Inference . . . 70
4.2 Bayesian Inference for Slip-line Field Model . . . 72
4.2.1 Initialization of Proposal and Prior Distributions . . . 72
4.2.2 Determination and Calculation of Likelihood Functions . . 73
4.2.3 Using Logarithmic Scaling for Prior, Likelihood and Accep-tance Ratio . . . 75
4.2.4 Flowchart of the developed algorithm . . . 76 4.3 Results of the Method for Slip-line Field Rake Angle Parameter . 79
CONTENTS viii
5 Effects of Commercially Pure Titanium Microstructure on the
Mechanistic Model Parameters of Micromilling 89
5.1 Brief Introduction to Mechanistic Models . . . 89
5.2 Mechanistic Modeling of Milling . . . 90
5.2.1 Chip Thickness Calculation . . . 90
5.2.2 Calculation of Tool Engagement Angles . . . 94
5.2.3 Forces Acting on the End Mill . . . 96
5.3 Micro Slot Milling Tests . . . 98
5.4 Analysis of the Experiments . . . 103
6 Conclusion 109
A Tool Edge Images and Measurements 121
List of Figures
2.1 Micro-machining applications (a) fuel injector holes machined by femto-sec laser [18]; (b) features produced by micro-milling [19]; (c) a part produced by micro-milling [20]; (d) a forming tool machined by ultra-precision milling [1]; (e) SEM image of CP titanium dental
implant[17]. . . 5
2.2 Failed cutting trial of CP titanium. . . 6
2.3 Titanium − oxygen binary phase system.[22] . . . 9
2.4 Diagram of the electropolishing aparatus. . . 12
2.5 Electropolishing aparatus. . . 13
2.6 Power supply device used in the study. . . 14
2.7 Example micrographs taken from the study (a) acicular morhology; (b) equiaxed morhology. . . 17
2.8 Micrographs of the semi orthogonal test specimens (a) specimen O1 (as received); (b) specimen O2. . . 19
2.9 Micrographs of a sample before and after micromachining (a) be-fore; (b) after. . . 19
LIST OF FIGURES x
2.10 Micrographs of the slot test specimens (a) specimen S1 (as re-ceived); (b) specimen S2; (c) specimen S3; (d) specimen S4. . . 20
3.1 Sharp tool geometry and force directions. . . 22 3.2 Illustration of slip-line field model [32, 38]. . . 25 3.3 Tool tip friction and ploughing force components under negative
rake angle. . . 26 3.4 Calculation of phi using h and hdwith (a) sharp corner assumption;
(b) considering dead metal zone inclination (λ) and prow angle (ρ) 29 3.5 Flow diagram of the algorithm that developed for the model to
find best matching τy and R. . . 32
3.6 Flow diagram of the algorithm for simulation of force, power and angle values. . . 34 3.7 Illustration of the micro semi-orthogonal cutting test setup. . . 36 3.8 Micro semi-orthogonal cutting test setup. . . 37 3.9 Measurements of cutting tool used in the experiments (a) Rake
and clearance angle; (b) Surface topography scanning profile for edge radius (as received condition). . . 38 3.10 SEM width of cut measurements of as-received CP titanium sample
(O1) . . . 39 3.11 SEM width of cut measurements of heat treated CP titanium
sam-ple (O2) . . . 39 3.12 SEM measurement for uncut chip thickness 0.25µm from
LIST OF FIGURES xi
3.13 SEM cut chip thickness measurements of as-received CP titanium sample (O1) . . . 41 3.14 SEM cut chip thickness measurements of heat treated CP titanium
sample (O2) . . . 41 3.15 Cutting forces and feed forces with respect to uncut chip thickness
of as-received CP titanium sample (O1) . . . 42 3.16 Cutting forces and feed forces with respect to uncut chip thickness
of heat treated CP titanium sample (O2) . . . 42 3.17 Heat treated CP titanium sample O2 tested at h = 6µm unfiltered
and filtered cutting force data comparison. . . 43 3.18 Illustration of the measured angle and radius values on tool geometry. 43 3.19 Sample O1’s (a) chip ratio; (b) plot of hd with respect to h with
linear model1 and model2. . . 46 3.20 Measurement of tool edge T3 at Table 3.2 (a) unused; (b) after test. 46 3.21 Simulation for sample O1; parameters: re = 2.5 µm, α =0.0◦
m =0.94, λ =5.0◦ (a) simulated forces for chip model1, complete linear fit; (b) simulated forces for chip model2, ignoring nonlinear part. . . 48 3.22 Force simulation of (a) sample O1 re=2.50µm, αtool =0◦, m =0.94,
λ =5◦.; (b) sample O2 re =3.30µm, αtool=−5◦, m =0.94, λ =8◦. . 51
3.23 Simulation of angles φ, α, βr for (a) sample O1 re =2.50µm,
αtool =0◦, m =0.94, λ =5◦.; (b) sample O2 re =3.30µm,
LIST OF FIGURES xii
3.24 Proportions of work for (a) sample O1 re =2.50µm, αtool =0◦,
m =0.94, λ =5◦.; (b) sample O2 re =3.30µm, αtool =−5◦,
m =0.94, λ =8◦. . . 53
3.25 Illustration of the tool wear and effect on tool geometry. . . 54 3.26 Illustration of the tool wear with BUE effect. . . 55 3.27 BUE for the T5 (a) LSM image top view (b) SEM image side view. 57 3.28 Comparison of simulated and experimental forces (a) variable rake
angle sample O1; (b) variable rake angle sample O2; (c) constant rake angle sample O1; (d) constant rake angle sample O2. . . 60 3.29 Comparison of simulated slip-line angles (a) variable rake angle
sample O1; (b) variable rake angle sample O2; (c) constant rake angle sample O1; (d) constant rake angle sample O2. . . 61 3.30 Comparison of simulated work proportions (a) variable rake angle
sample O1; (b) variable rake angle sample O2; (c) constant rake angle sample O1; (d) constant rake angle sample O2. . . 63
4.1 Demonstration of single component MCMC method sampling. . . 69 4.2 Cutting Force data at uncut chip thickness 0.25µm (a) normalized
histogram and normal PDF of the data; (b) Randomly sampled data from raw measurement. . . 74 4.3 Flowchart of the Bayesian inference algorithm by using MCMC
method multi parameter sampling. . . 77 4.4 Coeffcient of variation values at various uncut chip values (a)
LIST OF FIGURES xiii
4.5 Sample O1 posterior rake angle distributions (a)h =0.25µm; (b)h =0.50µm; (c)h =1 µm; (d)h =2 µm; (e)h =3 µm; (f)h =4 µm; (g)h =5µm; (h)h =6 µm. . . 83 4.6 Sample O2 posterior rake angle distributions (a)h =0.50µm;
(b)h =1µm; (c)h =2 µm; (d)h =3 µm; (e)h =4 µm; (f)h =5 µm; (g)h =6µm. . . 84 4.7 Change of rake angle posterior distribution mean and 95%
con-fidence interval with respect to uncut chip thickness for sample O1. . . 85 4.8 Change of rake angle posterior distribution mean and 95%
con-fidence interval with respect to uncut chip thickness for sample O2. . . 85 4.9 Force simulations using mean values of posterior rake angle
param-eter distributions for sample O1. . . 86 4.10 Force simulations using mean values of posterior rake angle
param-eter distributions for sample O2. . . 87
5.1 Illustration of geometrical parameters of milling with run-out. . . 91 5.2 Illustration of jth and (j − 1)th tool trajectories. . . 92 5.3 Example plot for uncut chip thickness change with respect to
im-mersion angle. . . 95 5.4 Illustration of entry and exit angle. . . 95 5.5 (a)Vickers micro hardness test results; (b) Measured grain size and
heat treatment wait time; (c) Hardness indent marks taken from a micrograph of S2. . . 99
LIST OF FIGURES xiv
5.6 (a)Micro machining center; (b) Dynamometer, sample and refer-ence coordinate system. . . 101 5.7 (a)Experimental observations of resultant force RMS values with
respect to feed per tooth; (b) Acquisition of force data for feed per toot 8 µm. . . 102 5.8 Specific cutting pressure values with respect to feed per tooth
(cal-culated from mean tangential force and max. chip thickness area). 103 5.9 Roughness values taken from cut slots with respect to feed per
tooth (measurement parameters were λs: 0.25µm and λc: 0.08µm
per ISO4287[73]). . . 103 5.10 (a)Relative true error of model simulation results (RMS) with
re-spect to feed per tooth values; (b) identified run-out distance values from samples. . . 105 5.11 Simulation results of resultant force values (RMS) for different
feeds and experimental data (a) S2; (b) S3. . . 106 5.12 Simulation of forces for S2 in X and Y direction (a) at feed per
tooth 2µm; (b) at feed per tooth 6 µm. . . 106 5.13 (a) Tangential cutting coefficient with respect to Vickers hardness;
(b) Tangential edge force coefficient with respect to Vickers hard-ness. . . 107 5.14 Comparison of specific cutting energy values between micromilling
samples S1, S4 and micro orthogonal cutting samples O1, O2. . . 108
A.1 Sample O1 used tool edge measurements (a) T1; (b) T2; (c) T3. . 122 A.2 Sample O2 used tool edge measurements (a) T4; (b) T5; (c) T6. . 122
LIST OF FIGURES xv
A.3 Sample O1 used tool edge LSM images zoom 50x (a) T1; (b) T2; (c)T3. . . 122 A.4 Sample O2 used tool edge LSM images zoom 50x (a) T4; (b) T5;
(c) T6. . . 123 A.5 End mill tool images after cutting tests (a) Tool used in S1; (b)
Tool used in S2; (c) Tool used in S3 (d) Tool used in S4. . . 123
B.1 Sample O1 cut chip SEM images (a) h =0.25µm; (b) h =0.50 µm; (c) h =1µm; (d) h =2 µm; (e) h =3 µm; (f) h =4 µm; (g) h =5 µm; (h) h =6µm; . . . 125 B.2 Sample O2 cut chip SEM images (a) h = 0.5µm; (b) h =1 µm; (c)
List of Tables
2.1 CP Titanium Grade 2 composition by weight taken from EDAX analysis. . . 7 2.2 Heat reatment plan fot the slot cutting test specimens. . . 7 2.3 Heat reatment plan fot the orthogonal cutting test specimens. . . 8 2.4 Electropolishing parameters for CP Titanium . . . 15 2.5 Grain Size Measurements of the specimens . . . 19
3.1 Micro semi-orthogonal cutting experiment plan for CP titanium . 36 3.2 Tool angle measurements after cutting tests for sample O1. . . 44 3.3 Tool angle measurements after cutting tests for sample O2. . . 44 3.4 Analysis results for samples O1 and O2 . . . 50 3.5 Analysis results for samples O1 and O2 for variable and constant
rake angle considerations . . . 57 3.6 Analysis results for samples O1 and O2 under sticking condition
LIST OF TABLES xvii
3.7 For sample O1; Calculated angles, parameter Z and specific cutting pressure with percentage of contribution from shearing, friction and fraction values . . . 64 3.8 For sample O2; Calculated angles, parameter Z and specific cutting
pressure with percentage of contribution from shearing, friction and fraction values . . . 65
4.1 Normal mean, standard deviation and coefficient of variation val-ues of measured forces for sample O1 and O2 at different uncut chip thickness values . . . 80 4.2 Normal mean, standard deviation and 95% confidence interval
re-sults of posterior rake angle parameter distributions for sample O1 and O2. . . 81
5.1 Micro slot-milling experiment plan for CP titanium . . . 100 5.2 Identified cutting, edge and run-out parameters for all samples . . 105
Chapter 1
Introduction
With the current progress in the technology, the general trend is toward to minia-turization of the devices that have big impact to our lives. Computers and elec-tronics can be given as examples to such devices which consist of a lot of intricate and delicate parts. The manufacturing of such devices also requires miniaturiza-tion of manufacturing process. This endeavor brings other complicaminiaturiza-tions along that need to be overcome. In his work, Masuzawa summarized the state of the art micro manufacturing methods and applications, also concepts that may be promising in the future of technology [1]. Alting et al. addressed some of the problems and solutions about micro-machining and engineering technology [2]. They discussed micro part design, manufacturing and quality control concepts. Other than electronics, there are a lot of research interest in different industries. Production of biomedical products such as implants are discussed by Bartolo et al. [3]. An application in aerospace industry is done on micro drilling of nickel based super alloy by Okasha et al. [4]. Fleischer et al. discussed the high poten-tial of powder injection molding for the production of micro-mechanical parts by means of automation. Meijer et al. gave an overview of new opportunities that state of the art laser technologies providing for the miniaturization trend [5]. All in all, a big change in conventional production methods is in progress.
Metal cutting processes have very old history of development. As the new tech-nologies emerges, the process controlling processors, precision actuators, sensing devices are integrated to conventional machining systems. In current technologies, machining in microscale is possible, where one can produce feeds below microm-eters with a resolution of nanometer positioning accuracy [6]. As mentioned, manufacturing in microscale brings many challenges along. These challenges in micro-cutting may involve positioning accuracy, measurement uncertainty, signif-icant tool deflections, chattering, wear and build up of material. Some of these challenges are also common in macroscale cutting operations, and some are ne-glected due to insignificant effect on the process. In addition to these challenges, material microstructure is another important question that may have important effect in micro-cutting where the material grain size is in the order of tool edge radius and uncut chip thickness values of the process.
Material microstructure effects are on the machining outputs are studied in the literature. Microstructure types of Ti-6Al-4V are observed to be affecting the quality of process by Attanasio et al. They showed that fully lamellar grain morphology yields better tool status and less fluctuated cutting forces [7]. Zhao et al. investigated deformation mechanism of different microstructures of com-mercially pure titanium under ultra precision diamond turning. They conclude that deformation mechanism varies with microstructures, and small grains could reduce crack nucleation [8]. Ahmadi et al. studied micromilling of heat treated Ti-6Al-4V in different microstructures. They used electron backscatter diffrac-tion analysis to investigate machined surfaces, and conclude that post-machined surface’s microstructure is changed after micromilling. Also, lower β-phase frac-tion resulted higher cutting forces [9]. Komatsu et al. experimented on nickel chromium stainless steel X5CrNi18-10 and showed that ultra fine grain structure yield lower shearing force and less burr [10].
In micro-cutting conditions, the well known size-effect phenomenon also gains importance. This effect is commonly defined as an exponential increase in spe-cific cutting energy with decreasing uncut chip thickness. In literature, the size-effect was tried to explain by many researchers using different concepts. Subbiah [11] has categorized these explanations as follow: Material strengthening, Tool
edge radius effect, Sub-surface plastic deformation and Material separation ef-fect. In this work, material separation/fracture effect and tool edge radius effect are studied to explain tool-work material interaction and energy distribution in micro-cutting. Understanding tool-material interaction is important, because sur-face integrity of the machined material is product of this interaction [12]. Sursur-face roughness, cracks and tensile/compressive stress are produced on the surface dur-ing cuttdur-ing process. By usdur-ing correct process parameters, surface integrity can be improved.
In this thesis, microstructure effects of commercially pure titanium (CP tita-nium) is investigated based on manufacturing model parameters by using con-ducted experimental observations. Commercially pure titanium is specifically se-lected as material of interest, as it has less complicated microstructure compared to alloys of titanium. Also, there are not many study considering CP titanium’s microstructure compared to common alloys such as Ti-6Al-4V, although CP ti-tanium is commonly used in medical, chemical and petrochemical industry [13].
In Chapter 2, brief knowledge about CP titanium is given. Heat treatment, characterization and imaging of micrograph procedure also explained in detail. In Chapter 3, orthogonal cutting experiments together with analysis based on a slip line field theory model are addressed. Results are discussed for different grain morphologies in terms of experimental observations and model parameter outputs. In Chapter 4, application of Bayesian inference using MCMC method is discussed for an uncertain parameter. Probability distribution of the parameter is found for different test conditions using the method. In Chapter 5, micro milling experiments of different grain morphologies are given. Results are analyzed by using a mechanistic model. Effect of grain morphology also investigated in terms of mechanistic model parameters such as cutting and edge coefficients. In Chapter 6, conclusions belong to the study is summarized.
Chapter 2
Preparation of Test Specimens
In this chapter, information related with specimen preparations is given. This include practical knowledge about specimen cutting, storing, heat treatment, grinding, etching and metallographic examination methods of commercially pure titanium (CP titanium) for tests.
2.1
Commercially Pure Titanium
Commercially pure (CP) titanium titanium is used in micro cutting tests. It has superior corrosion resistance and service life compared to stainless steel alterna-tives [14]. Specially, its bio-compatibility allowed applications in medical devices, implants, surgical tools/devices [13, 15, 16, 17]. These application areas usually requires very delicate and small features. The size of these features can be in the micro scale range (see Figure 2.1).
Although CP titanium is a robust material in terms of corrosion resistance, it can be degraded under wrong preparation conditions. Mechanical cutting op-eration can cause elevated local temperatures that lead to sudden oxidation of material [21]. For example, mechanical cutting with a precision abrasive disk cutter commonly used for specimen partitioning. This method fails in the case
(a) (b)
(c) (d)
(e)
Figure 2.1: Micro-machining applications (a) fuel injector holes machined by femto-sec laser [18]; (b) features produced by micro-milling [19]; (c) a part pro-duced by micro-milling [20]; (d) a forming tool machined by ultra-precision milling [1]; (e) SEM image of CP titanium dental implant[17].
of CP titanium due to oxidation of material. Mechanical cutting causes rising of temperature of the material in the cutting interface and accelerates oxidation rate. Additionally, high ductility of CP titanium [13] together with heating may cause softening of material and result with high deformation at cutting interface. A failed example of the application can be seen at Figure 2.2. Brown oxidation stain and highly deformed corner can be seen. To avoid such problems, an electri-cal cutting method may be used rather than a mechanielectri-cal method. In the study, specimens are cut by using a wire electric discharge machining (WEDM) device from as-received stock material.
Figure 2.2: Failed cutting trial of CP titanium.
Therefore, correct handling of CP titanium and its preparation is very im-portant to employ successful tests. In next sections, strategies that are used in various processes for CP titanium is shared.
2.2
Heat Treatment of CP Titanium
Heat treatment operation is used to engineer microstructure of titanium. The main goal is to get different micro-structure morphologies. According to lessons learned from the study, heat treatment operation depends not only treatment parameters but also processing history of treated material. Compostional infor-mation about the material used in the studies are given at Table 2.1. CP titanium material used in the study is named “Grade 2” according to American Society for Testing and Materials (ASTM) and it is extruded and cold worked which leaves
deformation in the microstructure. Microstructure of the as-received material can be seen at Subsection 2.4.
Table 2.1: CP Titanium Grade 2 composition by weight taken from EDAX anal-ysis.
Ti Fe Ru Pd O
[%] [%] [%] [%] [%]
98.2 0.339 0.379 0.828 0.25
max.
Different heat treatment plans are applied for the specimens of slot and or-thogonal cutting tests. In some degree, trial and error method is used to get de-sired microstructures, due to temperature controlling difficulties in cooling stages. Thus, heat treatment plans are revised, improved and repeated several times. In this context, final revisions are displayed. Heat treatment plan applied to slot test specimens can be seen at Table 2.2. In line with the same approach used in heat treatment of slot specimens, recipe used for the orthogonal test specimens can be seen at Table 2.3.
Table 2.2: Heat reatment plan fot the slot cutting test specimens.
No. Label Temperature Wait Cooling Method
[◦C] [h]
1 S1 − − as received
2 S2 950 1 furnace cooled
3 S3 950 5 furnace cooled
4 S4 950 10 furnace cooled
Main motivation behind revising these plans are creating microstructures that has different micro morphologies and has grain morphology differences. Thus, getting different morphology response of the polycrystals for the same cutting conditions. Micrographs of these heat treatment plans can be seen in the
Sub-Table 2.3: Heat reatment plan fot the orthogonal cutting test specimens.
No. Label Beta Temp. Beta
Wait
Temperature Wait Cooling Method
[◦C] [h] [◦C] [h]
1 O1 - - - - As received
2 O2 1000 1 850 6 Furnace cooled
of applying vacuum or argon gas atmospheric condition. In this study, argon atmosphere is used in heat treatments.
Atmospheric conditions of heat treatment are as important as temperature levels for the plan. There are different strengthening mechanisms of titanium. The most important one for CP titanium is interstial atoms. Similar to car-bon interstitial atoms in iron lattice, oxygen atoms in titanium lattice makes it stronger [13, 21]. Thus, having these atoms in the heat application environment can change the result of mechanical response of the polycrystal, due to increasing diffusion of interstitials. In the study, this mechanism is inhibited by filling argon environment to heat treatment chamber. In addition, application of noble gas environment decreased oxidation on the surface.
It is significant to give brief information on phase formation of titanium, be-fore continue more on temperature effects on the titanium microstructure. The CP titanium (in some sources called unalloyed titanium), normally has stable al-pha al-phase at room temperature. Alal-pha al-phase represents close packed hexagonal (HCP) lattice configuration for titanium alloys. Two important impurities that usually used to create different grades of CP titanium are iron and oxygen. As it is stated previously, oxygen content of titanium increases its tensile strength [13, 21]. Iron content can’t dissolve in alpha phase and it disperses as stable beta phase. Thus, alpha alloys contain little amount of beta phase at room tempera-ture. Iron content pins grain structure, which is a way of controlling grain size. The lower iron content provides better grain size growth at the same amount of energy [13]. Additionally, oxygen is an alpha stabilizer of titanium. This means
that it increases beta phase transition temperature called “beta transus”. Thus, oxygen content must be taken in consideration when planing heat treatment. As mentioned earlier, oxygen interstitials also one of the main strengthening mech-anism of CP titanium, which leads to strain localization [13]. However, oxygen atoms are not effect modulus of elasticity, in contrast to substitutional elements such as aluminum. A binary phase diagram between oxygen and titanium is given at Figure 2.3 . For the material used in the study, compositional information is given at Table 2.1 and according to this, beta transus is considered as 1000oC. As
it can be seen at Figure 2.3 oxygen content percentage increases beta transition temperature.
Figure 2.3: Titanium − oxygen binary phase system.[22]
2.3
Grinding and Electropolishing
After heat treatment plan is applied to a set of specimen, they are polished for the metallographic examination. The polishing of CP titanium or other alloys
of titanium are not a straight forward procedure. It requires good practical experience, titanium compatible consumables and sufficient tools/devices.
There are a lot of ways to polish titanium alloys [23, 24, 25, 26]. Often polish-ing starts with mechanical grindpolish-ing by uspolish-ing silicon carbide (SiC) papers in wet condition. Subsequently continues with mechanical polishing with cloth and dia-mond suspension/paste. However, conventional polishing methods have a major drawback, that is smearing of ground titanium particles to the polished surface [23]. To prevent smearing of particles, electropolish (EP) is used frequently. In this study, specimens are first ground with proper technique, then electropolished to have highly smooth surface.
Before going into more details about electropolishing, the strategy used in mechanical grinding is given below:
• General tips to consider in all steps: use deionized water (optionally tap water) while grinding, apply circular movement while grinding.
• In first step, use a coarse SiC paper of 240 - 300 grit to remove “alpha-case”, that is surface layer saturated with oxygen. Alpha case forms, if heat treatment chamber of the furnace is open to atmosphere. Due to high effort to remove it, a very thick layer of alpha casing may require different methods of removing such as milling.
• Apply medium 800 grit SiC paper until all stains are removed and opaque color is revealed equally.
• Apply 1200 - 1500 grit SiC paper untill indistinct reflection of an object appears. As an advice tip of a pencil can be used to test.
• Rinse specimen with isopropyl alcohol. Dry it applying air. • Stick a transparent tape on inspection surface to isolate from air.
Note that, a transparent tape is stick on inspection area at the last step of grinding strategy. In this study, important surfaces of test samples are protected
by covering with transparent tape. This method avoids atmosphere gasses to react with test surface. Thus, color and texture changes due to corrosion or oxidation is minimized. After all chemical and mechanical operations, transparent tape method is applied to inspection surfaces to continue protection.
Choosing the correct electrolyte is the most important step of designing an electropolish process. Because electrolyte type affect electrode, holder and cell material of electropolishing apparatus. There are different recipes for the chem-ical composition of electrolyte in the literature. Two commonly used electrolyte mixtures are hydrofluoric acid (HF) based [27, 28] and perchloric acid based [23, 24, 25, 26, 28]. The both mixture have pros and cons. Hydrofluoric acid based mixtures are stable at room temperature and thus cooling of the polishing cell is not important. However, handling of the HF requires plastic hardware made of teflon which is rare and expensive. Cathode material of the HF solution must be graphite, because stainless steel is not compatible. Graphite is very brit-tle and hard to machine, so its cost is high. On the other hand, perchloric acid based electrolyte is not completely stable at working conditions and depending on the application length it requires cooling. But, the main advantage of perchlo-ric acid based electrolyte is low equipment cost. Stainless steel can be used in all conductive parts. Although cooling makes it little complicated, according to practical experience for very short application length it can be neglected. Lastly, perchloric acid mixtures are stated as unstable, but using 72% or more dilute perchloric acid is considered as safe in literature [24]. Therefore, perhcloric acid is chosen as electrolyte mixture.
Preparation of perchloric acid mixture (6% perchloric acid(70%) + 35% bu-toxyethanol + 59% methanol) is described below:
• For 1 litres of mixture: first, pour 590 ml of methanol to pyrex container of at least 1 litres.
• second, pour 350 ml of butoxyethanol.
similar. Use nitrile glove. Note that, order of mixing is important.
Electropolishing (EP) of titanium is performed by using a custom designed apparatus. The apparatus used in EP is illustrated at Figure 2.4 and real device can be seen at Figure 2.6. It has two stainless steel electrode, a pyrex glass chem-ical cell to contain electrolyte. One of the electrodes is the anode. Specimens are connected it by using a holder. Other electrode is the cathode and it is con-nected to negative potential of the power supply. Applying positive potential to the anode starts EP process. Device is heavily modified during the experimental period, because of different specimen geometry requirements.
Figure 2.4: Diagram of the electropolishing aparatus.
Position of the specimen is very crucial for the good result. Only polishing surface must contact with the electrolyte. Unnecessary surfaces must be isolated by covering with an electrical tape. Another crucial point is anode connection. Anode must contact with only specimen. If anode contacts with both specimen and electrolyte, it would short the circuit and bypass specimen. Electrical charge must only pass through the specimen for the correct application. The surface exposing to chemical is where polishing occurs. Lastly, the surface between anode and specimen must be cleaned with SiC paper to remove any stain or oxidation, because it is very important to establish good conductivity. As a rule of thumb, resistance between all connections must be below 10 ohms.
Figure 2.5: Electropolishing aparatus.
Shape of cathode must cover all exposed area of specimen. Cathode position is also important. Cathode material should be evenly spaced from the exposed surface. Uneven positioning may cause uneven current passing on the exposed surface. Current density, which is amount of charge passed in unit time per area, have to be even for all polishing area. Material removal rate is directly proportional with current, current density and charge.
Another very important aspect of electropolish is control of current. Current is time derivative of charge, which takes main role in carrying on chemical reactions between titanium and electrolyte mixture. Thus, controlling current directly af-fect reaction speed, material removal rate on the exposed surface. Control of current is not a simple task, because it depends on many factor such as equip-ment, contact resistance, temperature. Correct equipment for good control of current is “galvanostat”. Galvanostat is capable of keeping current constat in electrolytic cell. However, it is an expensive device. The device used in the study is conventional two channel power supply with rating of 3 A at max. 30 V per channel Figure 2.6 . By serially connecting channels, 3 A at 60 V can be achieved. Contact resistance is kept as low as possible by clearing surface
application time.
Figure 2.6: Power supply device used in the study.
The main idea behind using a conventional power supply is exploiting its con-stant current mode which is normally a safety feature to prevent current exceeding a defined limit. Keeping contact resistance as low as possible (below 10 ohm or lower) and applying high voltage such as 60 Volts produce high currents which can be limited by constant current mode. In real life application, contact resis-tance is not constant and it changes with temperature, contact pressure, surface oxide film etc, electrolyte type. Thus, without actively control current, its almost impossible keep it constant. To give an example, assume a total serial contact resistance of 10 ohms. By using well known V = I × R gives 6 Amps for 60 Volts. Limiting constant current mode to 1.5 Amps actively drops voltage to satisfying level and controls it with the feedback from current value. So any sud-den change in resistance can be compensated with by increasing voltage up to
60 Volts. However, if compensation requires voltage value higher than 60 Volts, a better equipment with higher voltage rating must be used. Finally, according to this usage, important parameters for electropolish of CP titanium is given at Table 2.4.
Table 2.4: Electropolishing parameters for CP Titanium
Parameter Value Comments
Voltage 60−100 V Keep as high as possible.
Con-sider safety limits. Current Density 1.5−2.0 A/cm2 Defines current limit.
Current Limit 1.5−2.0 A for 1 cm2 which is mostly used
area.
Duration 4−8 s
Below, electropolish application is explained step by step:
• Mask and isolate application area with electrical tape (insulation tape). • Calculate exposed area roughly.
• Clean anode to specimen interface by using SiC or handheld electrical grinder.
• Connect specimen to anode by using conductive holder/screw made in stain-less steel.
• Put anode and cathode in to cell.
• Pour sufficient amount electrolyte. Only exposed area must be covered. Cathode must be submerged. Note that electrolyte shouldn’t touch anode directly.
• Adjust parameters given at Table 2.4 on power supply. • Apply current for given time at Table 2.4.
• Rinse specimen with isopropyl alcohol. • Dry it by applying cloth or napkin.
• Stick a transparent tape on exposed surface to isolate from air.
Note that, after electropolishing first specimen in freshly poured electrolyte, transparent color of the mixture turns into dark yellow. This was normal in the case of the study. In preparations, 10-15 electropolish is done successfully without refreshing mixture. Usage of the same mixture for higher number of polishing is not experienced.
2.4
Metallographic Examination
Examination of the microstructure characteristics are done by etching inspec-tion surface and imaging with laser scanning microscope. Examined properties includes morphology of the microstructure, grain size measurement. However, before characterizing CP titanium, some important information related with mi-crostructure properties of unalloyed titanium is addressed.
CP titanium grades belongs to alpha alloy group of titanium alloys. In some sources, it is stated as separately. However, due to its very low alloying impurity concentration, CP titanium is in alpha phase at room temperature. As stated in previous sections, most important alloying contents are oxygen and iron de-fines it grades. CP titanium has two distinct micro structure morphology, these are acicular and equiaxed morphologies [13, 21]. Acicular morphology sometimes called lamellar or “Widmanst¨atten”. Micrographs taken from example samples are given at Figure 2.7. Acicular morphology can be achieved by slowly cooling a specimen from above or close to beta transus temperature. In this case, com-pletely dissolved alpha phase slowly start forming alpha platelets. To slowly cool a specimen, furnace cooling method can be used. To achieve equiaxed morphol-ogy, cooling rate must be increase. According to practical knowledge experienced in the study, air cooling can give equiaxed structure depending on the circulation
of air. However, because of exposing air, specimen will be enriched with oxygen and nitrogen interstitials during cooling. This will cause very brittle and hard “alpha casing” on surface which have to be removed for further processing. In addition, increasing cooling rate in the furnace can give similar results without “alpha casing”.
(a) (b)
Figure 2.7: Example micrographs taken from the study (a) acicular morhology; (b) equiaxed morhology.
Etching of the inspection surface is not always necessary. According to experi-ence, acicular morphology may not require etching and microstructure can easily be inspected merely applying electropolish. On the other hand, equiaxed struc-tures require etching for fully observable results. In this study, Kroll’s Reagent per ASTM E407-07 [29]. Application duration is very subjective parameter. From experience, etching duration is between 10-15 minutes. Sometimes, etching under microscope technique is used to get better results or understand etching duration of the CP titanium. Application of etchant is described step by step below:
• Get specimen on a plastic or glass petri dish.
• Using a pipette, drop couple of droplet of Kroll’s Reagent. Make sure all surface is covered.
• Start timer and observe droplet. Optionally observation can be done under microscope.
• Optionally rinse with isopropyl alcohol. • Dry with napkin or cloth.
• Stick a transparent tape on exposed surface to isolate from air.
To take micrographs, laser scaning microscope (Keyence VKX 110) is used. Result of the slot and orthogonal cutting specimen are given below. As received material morphology of CP Ti Grade 2 can be seen at Figures 2.8(a) and 2.10(a). The as-received material cold worked according to the supplier. Although its structure very complicated and randomized, long stretched lamelar grain bound-aries displays similarities with acicular morphology.
Transformed microstructures after heat treatment procedure can be seen at Figure 2.8(b) and 2.10(b, c, d) for two sample. Polygonal grain boundaries al-most homogeneously dispersed on inspection area. Grain size statistics belong to cutting specimens are given at Table 2.5 according to ASTM E112 – 10 [30]. Here, dmean is the mean grain size diameter, dmax and dmin are the maximum
and minimum measured grain size respectively, also σd is the standard
devia-tion of measurements. It can be seen that specimen O1 is turn into equiaxed grain morphology completely. However, it is observed that grain morphology of the post machined surface actually turns back to acicular-like morphology after micro-cutting tests. An example view taken from one of the equiaxed sample be-fore and after micromachining is shown at Figure 2.9. Post machined surface is neither completely equiaxed nor acicular. Some kind of intermediate microstruc-ture was achieved. This actually means that the changed microstrucmicrostruc-ture did not homogeneously turn to equiaxed morphology. Thus, the changed morphology can not be called equiaxed.
(a) (b)
Figure 2.8: Micrographs of the semi orthogonal test specimens (a) specimen O1 (as received); (b) specimen O2.
(a) (b)
Figure 2.9: Micrographs of a sample before and after micromachining (a) before; (b) after.
Table 2.5: Grain Size Measurements of the specimens
S1 S2 S3 S4 O2 [µm] [µm] [µm] [µm] [µm] dmean 16.45 16.72 17.31 18.27 42.72 dmax 20.56 22.83 20.95 22.56 102.53 dmin 12.14 12.32 10.47 13.58 14.57 σd 3.46 3.38 3.06 4.50 15.25
(a) (b)
(c) (d)
Figure 2.10: Micrographs of the slot test specimens (a) specimen S1 (as received); (b) specimen S2; (c) specimen S3; (d) specimen S4.
Chapter 3
Orthogonal Micro-Cutting of
Commercially Pure Titanium on
Different Grain Morphologies
In micro-cutting processes, the grain size of the work material can be in the order of the edge radius of the tool. In addition, selected uncut chip thickness values of the micro processes are usually lower than mean crystal diameter of the work piece. In this chapter, Atkins’ work on metal cutting modeling [31] which intro-duces the fracture toughness term is briefly explained. Subsequently, Karpat’s study [32] on the implementation of a slip-line field model considering edge ra-dius is explained in detail. A detailed solution methodology is introduced for the model. For the model qualification, micro semi-orthogonal cutting experiments that is done in two different grain morphology of CP titanium is explained. Com-parison of the analysis results and experiments are discussed. Lastly, cutting tool edge condition during tests are addressed. Possible improvements for the edge radius modeling based on observation of the results, evaluation of assumptions and measurements are given.
3.1
Brief Introduction of Atkins’ Metal Cutting
Model
Atkins reported that the work connected with material separation criteria in FEM cutting models are in the range of kJ/m2, contrary to the range of J/m2
[33] which is commonly neglected compared to friction and shearing work. Then, Atkins introduced fracture toughness term (specific work of surface formation) by modifying Merchant’s [34] well known orthogonal model. According to Atkins, the new model is able to explain explain many of the experimental observations by including important surface formation work[31].
The model considers surface specific work in addition to friction and plasticity. Using a single shear plane model with coulomb friction, cutting work can be described as plastic deformation along primary shear plane, friction between chip-tool interface and surface formation work in Equation (3.1) respectively. All these internal work occurs in the existence of externally applied cutting force Fc (in
some references can be shown as Ft tangential force) (Figure 3.1).
Figure 3.1: Sharp tool geometry and force directions.
FcV = τyhwγ V +
Fcsin(β) sec(β − α) sin(φ)V
cos(φ − α) + RwV (3.1)
In Equation (3.1), τy is the shear yield stress, R is the fracture toughness
(specific work of surface formation), γ is the shear strain (Equation (3.2)) [35], h is the uncut chip thickness, w is the width of cut, V is the cutting speed, β is the friction angle at chip-tool interface, α is the tool rake angle, φ is the shear angle of the primary shear plane.
Applying minimum energy principle by taking derivative of Equation (3.1) with respect to φ (dFc/dφ) gives
0 = 1 − sin(β) sin(φ) cos(β − α) cos(φ − α) 1 cos2(φ − α) − 1 sin2(φ) + . . . [cot(φ) + tan(φ − α) + Z] × . . . sin(β) cos(β − α) cos(φ) cos(φ − α) + sin(φ) sin(φ − α) cos2(φ − α) (3.3)
Atkins defines dimensionless parameter Z as
Z = R/(τyh) (3.4)
parameter Z, specifically R/τy ratio constitutes material dependent φ[31].
Equa-tion (3.3) can be solved for φ by numerical methods, such as bisecEqua-tion root finding. A solution methodology is proposed by Subbiah et al. [36].
From Equation (3.3) and (3.4), decreasing uncut chip thickness increases Z and changes φ value, assuming α, β, R/τy are constant. One important characteristics
of this model is that for sufficiently small Z values (about 0.1 and below), solution of Equation (3.3) gives almost constant φ. Also, γ is constant for given rake angle. Lower values of Z is commonly matched with linear region of cutting force vs. uncut chip thickness plots. Thus, material dependency of φ may be answered from this characteristic depending on the ratio of R/τy. As mentioned, φ decreases and
γ increases for higher Z values (above 0.1). Atkins states that widely known size effect occurs at these high values of Z.
Cutting force can be calculated from found φ values as, Fc= τywγ Q h +Rw Q Q = 1 − sin(β) sin(φ) cos(β − α) cos(φ − α) (3.5)
In Equation (3.5) Fc, first term gives slope and second term gives the intercept
value. Slope is a function of τy, γ mainly. Intercept is a function of R. Both terms
are also depend on the term Q, which is function of shear angle, considering rake angle and friction angle is constant. For high values of Z (small h), Q becomes close to unity. Thus, Fc slope and intercept changes. But, for Z < 0.1, Q settles
and linearity achieved.
In the next section, application of slip-line model and integration of edge radius effect to Atkins’ cutting model is addressed.
3.2
Including Edge Radius Effect Using Slip
Line Field Theory
Atkins’ important work on application of fracture toughness property to metal cutting modeling considers only energies required for primary zone shearing, fric-tion at secondary shearing zone and material separafric-tion. Karpat’s [37] work on Atkins’ model to include effect of edge radius. Karpat utilized a slip-line field model with a stagnant metal zone (or dead metal zone) in front of tool edge [32]. As Figure 3.2 indicates, in this model upper boundary of dead metal zone (illus-trated as hatched area) extending from the effective rake angle α for simplicity and inclination angle lower boundary is defined as λ.
Figure 3.2: Illustration of slip-line field model [32, 38].
3.2.1
Defining Cutting Force Equation
Karpat described power distribution of cutting force considering the slip-line model as FcV = τyhw cos(α)V sin(φ) cos(φ − α) + Frsin(φ)V cos(φ − α) + Fpsin(ξ1− λ)V ξ1 + RwV (3.6)
where, some of the new parameters are: Fr that is the tool tip friction force
at secondary shear zone; Fp that is the ploughing force under dead metal zone
(DMZ); ξ1 that is the slip-line angle. In addition, the rake angle α given at
Atkins’ model is not the same here, due to edge radius. Rake angle is assumed to be changing with respect to uncut chip thickness (h). Thus, it is defined as two parameter: alpha that is the effective rake angle which depends on h; αtool
that is the cutting tools actual rake angle which is constant. In Equation (3.6), friction work detailed as two term: tool tip, ploughing. This definition helps to calculate the effect of edge radius.
Slip-line angle ξ1 can be calculated [39] as,
ξ1 = arccos(m)/2 (3.7)
here, m is the friction factor under DMZ (boundary |AD| in Figure 3.2). Friction factor is defined as m = τy/k in which k is the shear flow stress; it is constant in
the assumption of no strain hardening.
Cutting force (Fc) and feed force (Ff) can be written from force balance as
(see Figure 3.3), Fc= Fr cos(βr− α) sin(βr) + Fp sin(βp+ λ) sin(βp) (3.8) Ff = Fr sin(βr− α) sin(βr) + Fp cos(βp+ λ) sin(βp) (3.9)
Figure 3.3: Tool tip friction and ploughing force components under negative rake angle.
where, βr is the friction angle for tool tip friction force (Fr) and βp is the
friction angle for ploughing force (Fp). ploughing force is evaluated under DMZ
as
Tool tip friction force can be calculated as function of Fcby substituting
Equa-tion (3.10) to EquaEqua-tion (3.8), then writing for Fr :
Fr=
Fcsin(βr)
cos(βr− α)
−mτy|AD|w sin(βp+ λ) sin(βr) cos(βr− α) sin(βp)
(3.11)
In Equation (3.11), the length of |AD| is given as [37] |AD| = re[1 + sin(α)]
cos(λ − α) (3.12)
here,re is the edge radius of the cutting tool. In Equations (3.8),(3.9),(3.11); βp
is given as [37] βp = arctan cos(2ξ1) 1 + 0.5π − 2ρ + 2ξ1− 2λ + sin(2ξ1) (3.13) here, ρ is the prow angle and it is calculated from velocity continuity as [40, 37]
ρ = arcsin sin(2λ) √ 2 sin(ξ1)) (3.14)
Substituting Equations (3.11), (3.10) to Equation (3.6) gives [37] Fc 1 − sin(φ) sin(βr) cos(φ − α) cos(βr− α) = τyhw cos(α) sin(φ) cos(φ − α) − . . . mτy|AD|w sin(βp+ λ) sin(βr) sin(φ)
cos(βr− α) cos(φ − α) sin(βp)
+ mτy|AD|w sin(ξ1− λ) sin(ξ1)
+ Rw
(3.15)
which gives the integrated effect of the edge radius and fracture toughness on cutting force. Some arrangements for readability: In Equation (3.15) define Q as
Q = 1 − sin(φ) sin(βr) cos(φ − α) cos(βr− α) (3.16)
Substituting Equation (3.16) to Equation (3.15) and arranging: Fc= τyhw cos(α) sin(φ) cos(φ − α)Q − mτy|AD|w Q N + Rw Q (3.17) here, N is defined as
So far, the unknown parameters are m, λ, τy, R, βr and φ, except measurable
parameters such as re, h etc. Before explaining solution methodology further, it
is important to note that, m and λ is commonly assumed [38, 40]. In Karpat et al. [32], identification of these values were done. Practical knowledge shows that, parameter m is most likely in the range of 0.8 − 0.9. On the other hand, λ as a fraction of ξ1 may get the value of maximum 0.5 arccos(m) which is ξ1 itself.
By defining a ratio fλ = λ/(0.5 arccos(m)), it is seen that for practical results fλ
takes values between 0.8 − 1.0. So, in this study, m and λ are assigned values in practical range. With this in mind, solution of φ and βr among four remained
unknowns is explained in the next subsection.
3.2.2
Solving for Shear Angle and Tool Tip Friction Angle
Finding shear angle (φ) and tool tip friction angle (βr) is originally a starting point
for the solution methodology. To calculate shear angle Atkins used minimum energy principle. Using the same approach, applying minimum work principle to (3.15) by taking derivative with respect to shear angle (dFc/dφ) is calculated
as [37] 0 = sin(βr) cos(βr− α) γ +mre(1 + sin(α)) h cos(λ − α) N + Z − . . . Q cos(2φ − α) sin2(φ) +
mre(1 + sin(α)) sin(βp+ λ) sin(βr)
h cos(λ − α) sin(βp) cos(βr− α)
(3.19)
here, Z is the same as Atkins’ model (Z = R/(hτy)) . In the solution procedure,
Equation (3.19) is used for finding βr rather than φ. Because uncut chip thickness
and cut chip thickness are known in the experimental stage, direct calculation of φ is possible with some assumptions. Thus, finding φ for (h, hd) couples must be
done first.
If we don’t consider DMZ inclination angle λ, deformed chip thickness hd can
be calculated (see Figure 3.4 (a)) as
and here, primary shear zone length |DE| is
|DE| = h/ sin(φ), for λ = 0 (3.21)
So, substituting Equation (3.21) to (3.20) solving for φ gives the answer. Note that, because the experiments in the study have very small uncut chip thickness values (as low as 0.25um), it is assumed that rake angle changes with edge radius (see Figure 3.2). So effective rake angle must also be calculated for the specific h value for each (h, hd).
Effective rake angles can be calculated as
α =
αtool, if h ≥ re(1 + sin(αtool))
arcsin h − re re
, if re(1 + sin(αtool)) > h ≥ 0
(3.22)
here, αtool is cutting tool’s rake angle which is a measurable quantity.
Figure 3.4: Calculation of phi using h and hd with (a) sharp corner assumption;
(b) considering dead metal zone inclination (λ) and prow angle (ρ)
However, because we consider edge radius effect, DMZ is significant. Thus, calculating |DE| by considering λ effect yields (see Figure 3.4 (b))
|DE| = h + J
sin(φ) (3.23)
here |AD| sin(λ) is DMZ inclination angle contribution and |EH| sin(ρ) is prow angle contribution. To find |EH|, the radius of the circular fan field (Rf) must be
known [38]. Rf can be calculated by finding the root of the following equation:
F (Rf) = Rf − . . . sin(ξ1) v u u t " retan π 4 + α 2 + √ 2 sin(ρ)Rf tan(0.5π + α) #2 + 2 (Rfsin(ρ)) 2 (3.25)
There may be different methods to solve Equation (3.25) numerically. “Newton–Raphson”(NR) method is preferred. To use NR, derivative of the Equa-tion (3.25) must be known. Taking derivative of EquaEqua-tion (3.25) with respect to Rf gives dF dRf = 1 − . . . sin(ξ1) " 2√2 sin(ρ) tan(0.5π + α) retan π 4 + α 2 + √ 2 sin(ρ)Rf tan(0.5π + α) ! + 4 sin2(ρ)Rf # 2 v u u t " retan π 4 + α 2 + √ 2 sin(ρ)Rf tan(0.5π + α) #2 + 2 (Rfsin(ρ)) 2 (3.26) After finding Rf, |EH| can be found as [32]
|EH| = Rf/ sin
π 4
(3.27)
So, shear angle assumed to be developed at the minimum energy, can be cal-culated from Equation (3.20) by substituting Equation (3.23), Equation (3.24):
G(φ) = hd−
h + J
sin(φ) sin(0.5π − φ + α) (3.28)
Again Equation (3.28) can be solved by using NR method. To do this, deriva-tive of Equation (3.28) with respect to φ can be find as
dG dφ =
h + J sin(φ)
cos(φ)
sin(φ) sin(0.5π − φ + α) + cos(0.5π − φ + α)
However, according to some numerical experimentation, for practical values of α, ξ1, λ, re, ρ, the value of J approximately equals zero (J ≈ 0). Thus, taking
|DE| the same as (3.21) is sufficient. In this case, G(φ) and dG/d(φ) become G(φ) = hd− h sin(φ) sin(0.5π − φ + α) (3.30) dG dφ = h cos(φ) sin2(φ)sin(0.5π − φ + α) + cos(0.5π − φ + α) sin(φ) (3.31) and φ can be solved from (3.30) by using NR method. After finding φ for corre-sponding (h,hd) couples with α(h), it is possible to solve βr by using “Bisection
Root Finding” method from (3.19).
3.2.3
Solution Methodology
Two types of algorithms are developed for the model: a fitting algorithm that finds best matched τy and R values and a simulation algorithm that calculates
forces, powers and important angles (φ, βretc.) for a range of h values to compare
general trend with experiments.
Former algorithm is useful for finding correct R/τy ratio in the linear region of
the Fc vs. h plots. Capturing the linear region in the experimental stage is vital,
because fitting algorithm uses slope and intercept values. The same approach is used by Atkins in his work [31]. As mentioned in the Subsection 3.1, in small Z values (< 0.1 usually), γ, φ are almost constant; this region is matched with linear region of cutting force plot. For the case of the edge radius effect, because α is function of h, it stabilizes after certain uncut chip thickness (Equation (3.22)). Thus, to fit in the linear region, a chip thickness data point above this threshold (usually two times of re) is required. In Figure 3.5, a detailed flow chart is given.
A data fitting subroutine finds the slope and the intercept of experimental cutting force data by using the linear region. In parallel, the “Select Data” box, selects a data set belong to this linear part (max. uncut chip value set is recommended). For this data set, ρ, βp, α, φ angles are found by using Equations
Figure 3.5: Flow diagram of the algorithm that developed for the model to find best matching τy and R.
the selected data set is created. In the next step, using the calculated angles, the slope and the intercept values; a loop is initiated for each possible Z value. In the loop, tool tip friction angle βr, shear strain γ, parameter Q, N and length |AD|
are calculated for every Z value by using Equations (3.19), (3.2), (3.16), (3.18) and (3.12) . Then, for each Z value, possible τy, R values are calculated by using
Equations (3.32), (3.33). τy = SQ wγ (3.32) RI = IQ w − mτy |AD|N (3.33)
here, S and I are the slope and the intercept of the linear region respectively. Note that, here Q, |AB|, N , γ are different for each possible Z value. Thus, creating possible (τy-RI) pairs. Here, RI indicates the R value calculated from
To find the correct fit, possible τy and RI pairs must satisfy Z = RI/(hτy)
relation for the corresponding Z value. To check this, a secondary R value is calculated as
RZ = hτy Z (3.34)
which is the correct R value for the corresponding Z, τy and the uncut chip
thickness value h selected from linear region.
In the final step, there are two different sets of fracture toughness values (RI
and RZ) which calculated from different relations for possible Z, τy at the selected
h point. Calculating errors of each (RI,RZ) pair and finding the pair that has
the minimum error gives the best match. Error is calculated as
= (RI− RZ)2 (3.35)
The flow diagram of the simulation algorithm is given at Figure 3.6. It sim-ulates force, power and angle values for a given range of h values. It is used as a validation tool to compare experimental forces with simulation results. The simulation algorithm is also useful to observe the general trend of the simulated process outputs.
The simulation diagram has similarities with fitting diagram. However, here the main loop executes for each h value in the specified range. One of the major problem with such simulation is interpolating experimentally measured quanti-ties. Some of these quantities are constant for the whole experiment such as width of cut, rake angle etc.; however, quantities like cut chip thickness hd is
changing for every tested h value. Thus, an approximation model need to be used. In simulation, a linear model with slope and intercept parameter is used for predicting hd values at unknown points. In Subsection 3.4.1, effect of such
approximation will be discussed.
Simulation starts with input values, here, most important parameters τy and
R was found by using fitting algorithm. Constant angles ρ and βp are
Figure 3.6: Flow diagram of the algorithm for simulation of force, power and angle values.
In the next step, calculation loop is executed. Following the order given in diagram: dimensionless parameter Z, effective rake angle α, shear angle φ, tool tip friction angle βr, shear strain γ, parameter Q, N and length |AD| are calculated
for each h value by using equations given in previous subsection. Then, forces Fc, Ff, Fp and Fr are calculated using Equations (3.15), (3.10), (3.10) and (3.11)
respectively. For power calculations, energy distribution in Equation (3.6) is used. Finally, to asses the fitness of the simulation an error calculation subroutine is used. To be able to compare different experimental test errors, normalized root mean squared error (NRMSE) in Equation (3.36) [41] and symetric mean absolute percentage error (SMAPE) in Equation (3.37) [42] are primarily used. For relative comparisons mean squared error (MSE) or mean absolute percentage
error (MAPE) can also be used. N RM SE = s 1 n n X t=1 (Fexpt− Fsimt)2 1 n n X t=1 Fexpt (3.36) SM AP E = 1 n n X t=1 |Fexpt− Fsimt| |Fexpt| + |Fsimt| × 100 (3.37)
In the next section, information about conducted tests and preliminary results will be given.
3.3
Micro Semi-Orthogonal Cutting
Experi-ments
Micro semi-orthogonal cutting test are done with two different microstructure morphology. Micrographs of as-received specimen (O1) and heat treated speci-men (O2) can be seen at Figures 2.8 (a) and (b) respectively. In addition, heat treatment plan can be seen at Table 2.3. Micro semi-orthogonal cutting exper-iment plan is given in Table 3.1. Cutting test illustration at Figure 3.7 shows cutting directions, tool holder position and prepared surface webs. Prepared sur-face webs are cut by ultra precision diamond turning machine (Moore Nanotech). Using such machinery minimizes following errors in the test process and uncer-tainties caused by test equipment.The photograph of the setup can be seen at Figure 3.8.
Table 3.1: Micro semi-orthogonal cutting experiment plan for CP titanium
Parameters Specimen O1 and O2
Cutting speed [m/min] 40
Uncut chip thickness [µm] 0.25, 0.50, 1, 2, 3, 4, 5 and 6
Width of cut [µm] 250
Tool [µm] Tungaloy JXPG06R10F SH725
Tool rake angle [◦] nominal 20 (see Figure 3.9(a)) Tool clearance angle [◦] nominal 7 (see Figure 3.9(a))
Tool edge radius [µm] as-received 2.50±0.50 (see Figure 3.9(b))
Tool width [µm] nominal 1000
Tool usage [-] fresh tool edge used per uncut chip
thick-ness
Cutting forces are recorded by a dynamometer (Kistler mini dynamometer 9256C1 with a charge amplifier) and are saved by a data acquisition card (NI 7854R A/D converter) with a sampling rate of 333 kHz. The cut surface is measured with the scanning laser microscope for width of cut measurements. In addition, width of cut is measured from the cut chips under scanning electron microscope (SEM). Lastly, scanning electron microscope images are collected for cut chip thickness measurements.
(a) (b)
Figure 3.9: Measurements of cutting tool used in the experiments (a) Rake and clearance angle; (b) Surface topography scanning profile for edge radius (as re-ceived condition).
In total, three measured data set is collected per test: forces, width of cuts and cut chip thicknesses. In ideal conditions, width of cut is expected to be constant. However, actual width of the chips are changing due to uncertainty of geometry and machining. Heat generated by friction can cause expansion which may lead to undesired surface deviations. There are other errors sources which is very common in micro cutting conditions. Therefore, width of cut measurement results are used in the normalization of cutting forces by scaling to the target width of cut 250µm. For the as-received specimen (O1) (see Table 2.3), measured width of cut values and 95% confidence interval is given at Figure 3.10. These results are produced by measuring widths of all post-experiment cut chips. An example measurement screen in SEM is shown at Figure 3.12. The same result is also given for the heat treated specimen (O2) at Figure 3.11.
Uncut Chip Thickness [um]
0.25 0.5 1 2 3 4 5 6
Width of Cut [um]
200 220 240 260 280 Mean Values 95% Confidence Interval
Figure 3.10: SEM width of cut measurements of as-received CP titanium sample (O1) .
Uncut Chip Thickness [um]
0.5 1 2 3 4 5 6
Width of Cut [um]
210 220 230 240 250 260 Mean Values 95% Confidence Interval
Figure 3.11: SEM width of cut measurements of heat treated CP titanium sample (O2) .
Figure 3.12: SEM measurement for uncut chip thickness 0.25µm from as-received CP titanium sample (O1) .
In Figure 3.11, there is no measurement result for the uncut chip thickness of 0.25µm, because no chip formation occurred in this point during experiments. Cut chip thickness measurement results for the as-received specimen (O1) and heat treated specimen (O2) are given at Figures 3.13 and Figures 3.14 respectively. These results are produced from over 50 images. From each chip thickness at least three images are captured and digitally measured. Then, mean and confidence interval is calculated. It may be seen that difference between cut chip thickness values are no more than 2µm at specific points for two test set. Also, confidence interval shows that SEM image measurements are in good agreement between different images.
Uncut Chip Thickness [um]
0.25 0.5 1 2 3 4 5 6
Cut Chip Thickness [um] 0 5 10 15
Mean Values
95% Confidence Interval
Figure 3.13: SEM cut chip thickness measurements of as-received CP titanium sample (O1) .
Uncut Chip Thickness [um]
0.5 1 2 3 4 5 6
Cut Chip Thickness [um] 2 4 6 8 10 12 Mean Values 95% Confidence Interval
Figure 3.14: SEM cut chip thickness measurements of heat treated CP titanium sample (O2) .
be seen. Shown force data are mean values of the filtered collected data. Filtering of the data is done by using “NI Diadem” software package’s FFT filtering func-tion. For every experiment point spindle revolution frequency and its 10 adjacent harmonics are filtered by a “Butterworth” low pass digital filter. Thus, higher frequency components are attenuated. By using this method, uncertainty caused by environment is reduced. An example filtered and unfiltered data comparison taken from sample O2 6µm uncut chip thickness test can be seen at Figure 3.17.
Uncut Chip Thickness [um]
0 1 2 3 4 5 6 Force [N] 1 2 3 4 5 Cutting Force (F c) Feed Force(F f)
Figure 3.15: Cutting forces and feed forces with respect to uncut chip thickness of as-received CP titanium sample (O1) .
Uncut Chip Thickness [um]
0 1 2 3 4 5 6 Force [N] 1 2 3 4 5 6 Cutting Force (F c) Feed Force(F f)
Figure 3.16: Cutting forces and feed forces with respect to uncut chip thickness of heat treated CP titanium sample (O2) .
