# Modelling of the machining process of a nickel-titanium based shape memory alloy

Master's Thesis 2013 119 Pages

## Excerpt

ABSTRACT

ACKNOWLEDGEMENT

APPROVAL

DECLERATION

LIST OF TABLES

LIST OF FIGURES

LIST OF ABBREVIATION

LIST OF SYMBOLS

CHAPTER 1: INTRODUCTION
1.1 Background
1.2 Problem Statement
1.3 Research Objectives
1.4 Overview of the Project

CHAPTER 2: LITRATURE REVIEW
2.1 Introduction
2.2 Workpiece Material and Properties
2.2.1 The Applications of Nickel-Titanium
2.2.2 Nickel-Titanium Structure
2.2.3 Mechanical Properties of Nickel-Titanium Alloys
2.3 Material Models
2.3.1 Johnson- Cook Model
2.3.2 Power Law Model
2.3.3 Zerilli and Armstrong Model
2.4 Machining of Nickel-Titanium Alloy
2.4.1 Surface Defect
2.4.2 Orthogonal Machining
2.5 Tool Material and Properties
2.5.1 Titanium Nitride tools

CHAPTER 3: METHODOLOGY
3.1 Introduction
3.2 Finite Element Method (FEM)
3.3 Method of Analysis
3.3.1 The Component of Experiment
3.3.2 What is ANSYS
3.4 Conclusion

Chapter 4: Results and Discussions
4.1 Model Description
4.2 Mesh Condition and Methods
4.2.1 ANSYS LS-DYNA
4.2.2 Solid 164 Element Description
4.3 Boundary Conditions
4.4 Shape Memory Alloy Material Model
4.4.1 Constitute Model for Superelasticity
4.4.2 Material Parameters of SMA Modeling in Superelastic Behavior
4.5 Software
4.5.1 Create the Geometrical Model
4.5.2 Material Properties
4.5.3 Assembling the Parts
4.5.4 Specifying the Solver Parameters
4.5.5 Definition of contact
4.5.6 Apply Boundary Conditions
4.6 Discussion and Comparison
4.6.1 Experimental Study
4.6.2 Simulation Variables and Results
4.6.3 Final Diagrams Obtained in the Modeling
4.7 Conclusion

Chapter 5: Conclusion and Recommendations
5.1 Conclusion
5.2 Recommendation

REFERENCES

APPENDIX A: Solid 164 Specification

APPENDIX B: Shape Memory Alloy (SMA)

APPENDIX C: The Complete Results of The Simulation

## ABSTRACT

One of the aims of this study is to optimize machining of nickel based shape memory alloys. Nickel-titanium (Nitinol) is one the famous shape memory material which applied in wide range of products especially in aerospace, medical, and biomedical. The main issue in this project is related to the materials which cannot be machine easily, high tool wear, high cutting force, huge hardness and surface defects are made many problems into their machining. Experimental studies were compared with simulations in this report and the main section of that is the optimum cutting speed of nickel-titanium machining would be obtained. Experimental studies show that the cutting speed of machining of nickel-titanium alloy might be around 100 m/min, because the tool wear and cutting force are in minimum condition. In this study, by applying ANSYS software based on the finite element method, the optimum speed of machining process could be guessed around 100 m/min. Cutting speed-Stress diagram in the modeling results have confirmed the same cutting speed in machining process of NiTi in compare with experimental results.

## ACKNOWLEDGEMENT

All praise and gratitude will be to God the almighty for his mercy and support during course of our life and moments of truth.

First and foremost, I would like to acknowledge my deep gratitude and appreciation to my dear supervisor Dr. Mohd Roshdi Hassan for his continual support and endless encouragement and patience, without all nothing would have been accomplished. My special thanks go to my examiner Ir. Razali Samin for his guidance and working.

Special thanks to my dear friend Sarmad D. S. Dawood who his friendship and assistance has meant more to me than I could ever express. I could not complete my work without invaluable friendly assistance of him. I hereby would like to thank all people who somehow helped me to achieve these results.

I am deeply grateful to my family’s support, without which I could have never been where I am today. Their unconditional love has always shown me the right path. Their love provided my inspiration and was my driving force. I owe them everything and wish I could show them just how much I love and appreciate them.

## LIST OF TABLES

Table 1-1: A List of Alloys That Exhibit SMA Along With Their Ranges

Table 2-1: Mechanical Properties of NiTi in Austenite and Martensite

Table 2-2: Mechanical Properties of NiTi in Detail

Table 4-1: Superelastic Option Constants

## LIST OF FIGURES

Figure 2-1: Cross Section of a Jet Engine

Figure 2-2: Nickel-Titanium Application in Medical Equipments a) Eyeglass Frames, b) Orthodontic Therapy Tooth, c) Medical Guide Wires, d) Stent

Figure 2-3: Artificial Sphincter (AS) and its Energy Transmission System That is Made of Shape Memory Alloy (SMA)

Figure 2-4: Scanning Electron Micrograph of The TWSME Micro-Gripper

Figure 2-5: (a) Austenite (b) Martensite Lattice Structures

Figure 2-6: Austenite and Martensite Microstructure Shapes

Figure 2-7: Relationship between Phase Transformation Temperatures and Applied Stress

Figure 2-8: DSC Thermogram of A NiTi Alloys

Figure 2-9: Superelastic Effect (SE) in Shape Memory Alloys

Figure 2-10: Superelastic Behavior in Shape Memory Alloy

Figure 2-11: Simulation of Self Healing Composite

Figure 2-12: Shape Memory Effect (SME) in Shape Memory Alloys (SMA)

Figure 2-13: Two Way Shape Memory Effect

Figure 2-14: Shape Memory Effect (SME)

Figure 2-15: Some Problems in the Machining of NiTi: a) High Tool Wear, b) Adverse Chip Form, c) Burrs Formation After Turning, d) Grinding.

Figure 2-16: Surface Damages in Machining of Nickel-Titanium Alloys: (a) Metallographic Microstructure after Turning Process (b) Lay Pattern after Dry Milling Process (c) Metal Debris after Turning Process, and (d) Smeared Material and Feed Marks after Turning Process.

Figure 2-17: Surface Tearing Mechanism in Machining Process

Figure 2-18: (a) Oblique Machining (b) Orthogonal Machining

Figure 2-19: The Circle of Merchant Method

Figure 2-20: Various Material of Cutting Tool after NiTi Machining, Cubic Boron Nitride (CBN), Polycrystalline Diamond (PCD), Composite Ceramics (CC) and Oxide Ceramics (OC)

Figure 2-21: Titanium Nitride Coated for a Drilling Tool

Figure 2-22: The Application of TiAlN and TiCN in Various Tools

Figure 3-1: Flow Chart of The Project Procedure

Figure 3-2: Number of Technical Publication on Modeling between 1970 and 1999 44

Figure 3-3: Schematic of Tool and Workpiece Position That Designed by AutoCAD Software

Figure 3-4: Tool and Workpiece Geometrical Dimension in This Study

Figure 3-5: Cutting Angle and Force Components (Woodson and Koch 1970)

Figure 3-6: The Modular Structure of ANSYS

Figure 4-1: Motion of Mesh and Material with Various Methods

Figure 4-2: SOLID 164 Structural Solid Geometry

Figure 4-3: FE Simulation Model for Boundary Conditions of ALE Method

Figure 4-4: The Mesh Condition Design for Tool and Workpiece in The ANSYS Software

Figure 4-5: Idealized Stress-Strain Diagram of Superelastic Behavior

Figure 4-7: Autodesk Inventor 3D Model

Figure 4-8: Define the Material properties in the ANSYS Software

Figure 4-9: Define Material Model Behavior

Figure 4-10: The Assemble Parts in the Software

Figure 4-11: Specifying the Solver Parameters

Figure 4-12: The Definition of Contact Parameters

Figure 4-13: Boundary Condition Included Tool and Workpiece

Figure 4-14: Cutting Force-Cutting Speed Diagram Due to Weinert et al. Experimental Results

Figure 4-15: Displacement Summation Due to Cutting Speed 20 m/min

Figure 4-16: Shear Stress in XY Direction Due to Cutting Speed 20 m/min

Figure 4-17: Von Mises Stress Due to Cutting Speed 20 m/min

Figure 4-18: Displacement Summation Due to Cutting Speed 100 m/min

Figure 4-19: Shear Stress in XY Direction Due to Cutting Speed 100 m/min

Figure 4-20: Von Mises Stress Due to Cutting Speed 100 m/min

Figure 4-21: Displacement Summation Due to Cutting Speed 130 m/min

Figure 4-22: Shear Stress in XY Direction Due to Cutting Speed 130 m/min

Figure 4-23: Von Mises Stress Due to Cutting Speed 130 m/min

Figure 4-24: Von Mises Stress -Velocity Diagram for the Machining of Nickel Titanium alloy in Various Cutting Speeds

Figure 4-25: Shear Stress-Velocity Diagram for the Machining of Nickel Titanium alloy in Various Cutting Speeds

## LIST OF ABBREVIATIONS

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## 1. CHAPTER 1: INTRODUCTION

### 1.1 Background

Au-Cd alloys were the first SMA that is discovered in 1951. After that Buehler and his colleagues at the USA Naval Ordinance Laboratory (NOL) that was in White Oak, Maryland, introduced Nickel-Titanium alloys as Nitinol (for nickel, titanium, and NOL) in 1960. They found out the Nitinol wire straightened at higher temperature when be cooled and it was deformed into a coil, it has capacity to become straight upon reheating, again. Fighter aircraft (F-14 Tomcat) in the USA Navy was the first project that shape memory alloys are applied for the couplings of titanium hydraulic tubing. According to that, Collars were machined from a Ni-Ti alloy with inside diameters at room temperature slightly smaller than the outside diameter of the tubing. They were mechanically expanded by about eight percent and slipped over the tubing when collars were cooled to cryogenic temperatures and collars revert to their original diameter after heating and by the way, it will be very tight shrink-fit coupling (Wilkes and Liaw, 2000).

Different scientist in various years found out special materials that call them Shape Memory Alloys (SMA). These materials have the unusual property of being able to sustain and recover large strains (about 10%) without inducing irreversible plastic deformation and to ‘remember” a previous configuration and return to their original shape with the temperature changing. (Delaey et al., 1974; Perkins et al., 1976; Funakubo, 1987; Wayman and Duerig, 1990; Brinson and Lammering, 1993). Nakanishi in 1983 believed that SMA has a special thermo mechanical behavior in

temperature and stress induced martensite transformation. Schroeder and Way in

1977, Saburi and Way in 1979 were the other scientists that have the same opinions about the shape memory materials (Tokuda, Ye et al., 1999).

There is a list of some alloys with SMA properties in Table 1.1 that is mentioned to their transformation composition and temperature range (Wilkes and Liaw, 2000):

Table 1-1: A List of Alloys That Exhibit SMA Along With Their Ranges (Wilkes and Liaw, 2000)

Nickel-Titanium alloy is one of the most famous shape memory alloys that its

applications and properties are explained in detail in literature review. But, this considerable alloy has a problem in the industries that is related to its machining. Because conventional methods in machining such as; turning, milling or drilling face difficulties in considerable tool wear in these alloys. Also, this matter needs high experienced operators that it increases the costs. Moreover, the conventional techniques have high thermal condition clearly and this phenomenon cause to change in mechanical effects in shape memory materials (Falvo, 2007).

There are not any systematic and comprehensive methods what help to industrial processes for physical and applicable operation. Physical prediction models need for future modeling studies with reliable experiment how consider all effects on a lot of parameters for machining of nickel-titanium alloys, therefore finite element modeling (FEM) and its related analytical result is closed to empirical and experimental method. By this way, simulation by FEM method is suggested to realize machining process induced surface integrity simply.

1.2 Problem Statement

Researchers have been trying to find solutions to increase the machinability of Nickel- Titanium alloy through FEM modeling and experimental methods. There are a lot of parameters that have influence on the workpiece’s surface quality. Feed rate, cutting speed, tool wear, tool geometry and properties, cutting depth and workpiece materials and properties are some of these considerable elements which worth to be investigated. Many surface defects can be detected in machining process especially in

micron precision investigations. Grain deformation, feed marks and chip redeposition

are the famous surface defects. Furthermore, plucking of bits from the surface can make two various defects how tearing and dragging can be resulted of this matter. Literature review section verifies surface defects in detail. Overall, cutting parameters adjusting for eliminating these defects is really difficult, and they cannot remove completely, but by this method, they can reduce them significantly (Falvo, 2007).

Therefore, cutting parameters should be adjusted, for example; changing and optimizing the feed rate can altered feed marks problem in machining. Moreover, the optimization of cutting speed can be effected on microchip debris rate on the surface or depth of cutting value can be modified in some parameters such as; tearing, dragging, plucking and smearing. These surface defects are the main problem in the machining of nickel-titanium alloys, therefore this is necessary that cutting condition should be optimized.

1.3 Research Objectives

1. To apply ANSYS software based on finite element method for the machining of nickel-titanium alloy.

2. To analyst of material model to represent stress variations in different velocities under machining condition.

3. To generate structural analysis environment and obtain the related results such as Stress-Velocity diagram.

4. To obtain optimized cutting speed (velocity) in the machining operation of nickel-titanium (NiTi) workpiece by comparing the results.

1.4 Overview of the Project

This study concentrates on the machining process of nickel based shape memory alloy how finite element method is chosen in simulating machining operation of nickel- titanium. ANSYS software verifies the influence of various cutting speeds by comparison between velocity-temperature and velocity-stress diagrams to obtain optimized cutting speed.

Chapter 1 presents a background about studying with the problem statements and research objectives.

Chapter 2 explains nickel Titanium application and its mechanical properties such as SE and SME. Material modeling by particular formulation and machining process are the other subjects that are discussed in this chapter. Various material models for the simulation of machining are discussed in literature review in Chapter 2. Section 2.3 is related to machining process with surface defects and explanation of orthogonal machining with influence of parameters. Tool properties and material is the last part which is verified in this chapter.

Chapter 3 shows the suit methodology that is introduced an appropriate finite element theory for analysis of machining. ANSYS software and its application are explained in this chapter.

Chapter 4 reports the discussion and result of applied method to obtain optimized cutting speed in machining process. In this chapter, the obtained result from software analysis is discussed and velocity-stress diagram are compared with experiment study.

Chapter 5 is related to conclusion and the suggestions for further studies. There is a

brief comment about the project and obtained results and it has proposed to follow this subject in the other processes.

2. CHAPTER 2: LITRATURE REVIEW

2.1 Introduction

This chapter verifies material properties and their application in both workpieces and tools. Also, the witting about materials and experimental machining processes has investigated, while finite element method has the capacity of prediction by material modeling in the various FEM softwares. NiTi characteristics will be assayed in the workpiece part and properties. Next part will be about the material flow models and their related formulations. Machining operation is the further subject that it consists of differential machining process, too. Finally last parts inquire about suit tools that can resist tool wear problem and improve cutting process.

2.2 Workpiece Material and Properties

As Figure 2.1, shape memory alloys based on Nickel-Titanium or Nitinol indicate a principal metal portion of the aircraft structural and engine parts. These critical components use in aerospace industry and these manufactured parts have high reliability levels with good surface integrity that are relevant parameters used for measuring the quality of finish machined surfaces (Ulutan and Ozel, 2011).

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Figure 2-1: Cross Section of a Jet Engine (Ulutan and Ozel, 2011)

Also, shape memory property of Nitinol cause to use it greatly. These alloys machining was discovered to be very hard, and this matter related to their high ductility and work hardening behavior. There were a suggestion for these materials that the tool wear is high then the feed rate and cutting speed will be high or low, so rising the material removal rate while taking care of the surface quality by rapid tool changing was recommended (Weinert and Petzoldt, 2004).

#### 2.2.1 The Applications of Nickel-Titanium

Nowadays, nickel titanium alloy is applied in many various equipments because of its particular characteristics. Shape memory alloys use mostly in medical and biomedical devices, however the other application can mention to Connectors for hydraulic tubing in aircraft, critical roles in a large array of applications including active vibration control of structures, heat engines and automatic switches in household appliances and etc (Banks and Weres, 1976; Funakubo, 1987; Rogers eb al., 1989; Falcioni, 1992 ;Brinson and Lammering, 1993). There are some considerable applications that have been mentioned in following explanations.

There are some advantages of shape memory alloys in the biomedical field, something like the execution of less invasive surgeries cause to use them instead of conventional implantable alloys. Nitinol or NiTi as the famous SMA alloy exploit remarkable properties and temperature is just parameter that effect on material deformation and return to original shape (Descamps 1991; Tarnita et al., 2009).

There are some common medical applications in various equipments such as; Medical Guide Wires that are thin and long NiTi metal wire with superelastic effect. This effect causes to use in the body in two reasons. First this guide wire reduces complication and it is removed from body without any injuries and second it has an ability to transmit a twist from one side in wire to the other side. Moreover, Orthodontic Therapy Tooth movement needs constant stress what can create with SMA effect because coil springs using superelastic materials have been designed. By using superelasticity effect in SMA material, deformation eliminate completely and this matter cause to create Eyeglass Frames as medical equipment. Shape memory effect cause these frames come back to their original shape after any deformation. Figure 2.2 presents some of these equipment that are designed according to shape memory affects (Auricchio, Taylor et al., 1997; Stirling, Yu et al., 2011).

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Figure 2-2: Nickel-Titanium Application in Medical Equipments a) Eyeglass Frames, b) Orthodontic Therapy Tooth, c) Medical Guide Wires, d) Stent (Auricchio, Taylor et al., 1997; Stirling, Yu et al., 2011)

As shown in Figure 2.2, Stent is one of the most applicable production and life-saving achievements. In 1983, Dotter’s group made the first Nitinol Stent like a simple coiled Nitinol wire and was delivered into a dog’s femoral artery by guide catheter. Before that Palmaz and Schatz in 1987 had made stainless steel stent but the concept of Nitinol stent covered with fabric graft was first introduced in 1993 and the in-vivo study in human of drug-eluting stent was published in 2001 which marked the stent has evolved into an enabling technology as drug delivery device rather than a pure mechanical scaffold (Song, 2010).

Medical application of SMA is really current in this decade because of its high ratio of the recovery force to weight and large recoverable strains. It may repeatable with 50,000 cycles of heating and cooling. The artificial anal sphincter is deformable and durability part with simple structure and it has really low mechanical failure rate. Also the duration of this artificial anal sphincter is between 30 to 90 days. In fact artificial sphincter (AS) consists of two Nitinol actuators sandwiching the intestine. As seen in Figure 2.3, the dimension is (70 × 18.5 × 0.73 ) jointed and foil type heater considered for them. Each SMA plate has meander winding to control in the opening and closing of the anal canal. Changing in SMA plates happens with heating and reverse transformation. DC/AC external power provides power to heat between two plates, It means the transcutaneous energy transmission system (TETS) supply it (Liu, Luo et al., 2007).

Figure 2-3: Artificial Sphincter (AS) and its Energy Transmission System That is Made of Shape Memory Alloy (SMA) (Liu, Luo et al., 2007)

Shape Memory Alloys like NiTi are used in actuators as a basic material for fabrication and their simply design including functional stability, a suitable structural fatigue life, smart control systems, higher phase transformation temperatures, and cost reduction. Also, other markets like consumer products or the automotive industry are really interested to use of Shape Memory Alloys for large-scale production. For example, thermostat valve with a NiTi actuator spring for automotive is really applicable. Conventional preheating systems operated in stable time about 50 min or longer for vehicles with large, heavy engines but in new systems with SMA material, this time decrease to 10 min (Frotscher and Eggeler, 2011).

Microsystems apply widely because of some advantages like; higher resolution enhanced Portability, reduction of consumables, faster response time, higher efficiency, less-volume, etc. The emphasis is put on material issues as seen from an actuator design perspective or in the other example the micro gripper jaw opens and closes up by heating. These grippers want to operate like the reversible finger motion, but thermal cycling causes that they can not to recover its original shape. After hundred thermal cycles between martensite and austenite phases, stress rise up and change to a big defect. Overall, micro grippers have a fantastic fatigue properties (>200,000 cycles). Figure 2.4 shows scanning electron micrograph of the TWSME micro-gripper and thermo mechanically cycles for working (Pelton, Stöckel et al., 2000).

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Figure 2-4: Scanning Electron Micrograph of The TWSME Micro-Gripper (Pelton, Stöckel et al., 2000)

There are many applications of shape-memory alloys in nuclear power. These equipments use in nuclear power include packing, passive safety systems, connecting, sealing elements (thermo-couplings) for pipes and electric drives, applicable devices in repair and assembly equipments, thermo-mechanical drives and motors, dampers, thermo-detectors, flow rate regulators, direct-action (self-operating) emergency systems, electric contact devices, units and elements (compensators) in electrical transmission lines, and others. These equipments with SMA materials work in the temperatures between 100℃ to above 600° . Moreover this temperature can change in actuates from 5 െ 10℃ to 40 െ 50℃ (Ionaitis, Kotov et al., 1995).

#### 2.2.2 Nickel-Titanium Structure

NiTi or nitinol can be two disparate crystal structures or phases according to various temperatures; martensite (Lower temperature) and austenite (higher temperature) (Al- Haidary and Al-Khatiab 2006). There are many properties of NiTi phases such as; Yong modulus, damping behavior, electrical resistance and etc. NiTi behavior in various temperatures and martensite or austenite phase transformation can verify in atomic scale and it is called Thermoelastic Martensitic Transformation (TMT). By this method crystal lattice structure provides minimum energy state in related temperature. Austenite structure is Body Centered Cubic (BCC) that the nickel atom is in center of the crystallographic cube and titanium atoms are in the cube’s eight corners (Otsuka and Ren, 2005).

Figure 2.5 shows that the austenitic phase has homolographic micro-structure and in the other hand, martensite has less homolographic, it means, its lattice structure include a rhombus balancing with an atom in the corners. According to SMA effect, martensite transforms into austenite when temperature is increased or applied stress is removed.

Therefore this matter present that the thermal loading and mechanical loading have opposite effect on nitinol (Adiguzel, 2007; Falvo, 2007). Some researchers (Delaey, Krishnan et al., 1974; Perkins, Edward, et al., 1976; Funakubo, 1987) demonstrated that when stress is applied to this material, thermodynamic considerations indicate that there is a critical stress at which the crystal phase transformation from austenite to martensite can be induced.

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Figure 2-5: (a) Austenite (b) Martensite Lattice Structures (Otsuka and Ren, 2005)

In Nitinol, high temperature phase has bcc crystal structure and low-temperature phase has monoclinic phase and there is another phase known as the R phase which has the rhombohedra crystal structure, appearing in some special cases. In fact R phase considers between higher temperature (A) and lower temperature (M) and the recoverable strain in R phase is really small because it is just 0.5 % in comparison with the martensitic transformation with 6.5-8.5 %. However, the R phase has some attractive properties (Uchil 2002; Waitz, 2008).

The phase transformation from austenite to martensite consist of four transition temperatures, named as martensite finish (Mf), martensite start (Ms), Austenite finish

(Af), and Austenite start (As). According to these tempratures, Mf < Ms < As < Af. So, there is no phase change Ms < T < As and both martensite and austenite may coexist within Mf < T< Af (Rahman, 2008).

The various martensite phase collocate themselves in a self accommodation behavior when NiTi materials is cooled below temperature Ms in the lack of applied stress and it happen without macroscopic shape change. These single martensites variants are created from the cooling of austenite called twinning. martensite variants rearrange into a signal variant when mechanical loading apply on the marten site structure and this mechanism is called detwinning that is the cause of shape memory behavior. Figure 2.6 shows phase transformation in various temperatures, applied stress and crystalline structure of NiTi alloys (Otsuka and Ren, 2005).

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Figure 2-6: Austenite and Martensite Microstructure Shapes

Austenite (b) Twinned Martensite (c) Detwinned Martensite (Otsuka and Ren, 2005)

If T ≥ Af, during unloading of the material a reverse transformation to austenite occurs because of the instability of martensite at these temperatures in the absence of stress. This recovery of high strain values upon unloading yields a characteristic hysteresis loop, which is known as pseudoelasticity. If As < T < Af, upon unloading is a partial pseudoelastic recovery; the remaining residual strain can be fully recovered after heating the material above Af.

If T < As, then there is no pseudoelastic recovery and the result is a different manifestation of the shape memory effect (Brinson, 1993). Four phase transformation temperatures grow by increasing the applied stress, it is shown in Figure 2.7 (Otsuka and Ren, 2005). Austenite and martensite phases in different temperatures and also plastic transformation are clear in the picture (Ortın and Delaey, 2002).

Figure 2-7: Relationship between Phase Transformation Temperatures and Applied Stress (Brinson, 1993)

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Differential Scanning Calorimeter (DSC) thermogram is a technique to identify the transformation of NiTi alloys. Martensite to austenite transformation in the heating temperature range represents in Figure 2.8 and it shows the reverse transformation upon cooling (Bellouard, 2008; Falvo, 2007).

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Figure 2-8: DSC Thermogram of A NiTi Alloys (Bellouard, 2008)

#### 2.2.3 Mechanical Properties of Nickel-Titanium Alloys

Mechanical properties for NiTi are shown in Tables 2.1 and 2.2 which are assigned from different references (Schwartz, 2002) (Baumann, 2004). Table 2 shows the mechanical properties of NiTi in Austenite and Martensite states and Table 3 follows this information in more detail. There are various factors that have affected on the mechanical properties, such as; manufacturing process, alloy composition, cyclic loading and the rate of strain (Fugazza, 2003).

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Table 2-1: Mechanical Properties of NiTi in Austenite and Martensite (Schwartz, 2002) (Baumann, 2004)

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Table 2-2: Mechanical Properties of NiTi in Detail (Schwartz, 2002) (Baumann, 2004)

SMA can recover strain in two ways (Rahman 2008):

- Pseudoelasticity or Superelasticity (SE)
- Shape Memory Effect (SME)

##### 2.2.3.1 Superelastic Effect (SE)

Superelastic behavior as a potential is a clear reason for the growing interest in SMA based devices. This phenomenon is occurred during loading and unloading above Austenite Finished (Af) during stress induced martensite transformation and return to austenite upon unloading. As Figure 2.9 shown, the alloy is stressed at above Austenite Finished (Af) temperature externally how it transform to detwinned martensite and it is unstable in the high temperature, so SMA alloy come back to the original shape in unloading.

Figure 2-9: Superelastic Effect (SE) in Shape Memory Alloys (Fugazza, 2003)

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In fact the transformation returns to austenite and primary shape is recovered. The schematic of Superelastic Effect (SE) is shown in the Figure 2.10. (Fugazza, 2003; Falvo, 2007). Overall, superelasticity based application have two advantages:

- It make to recover large deformation up to strain of 8%
- Transforming Stress guarantees constant stress over non negligible strain intervals (Auricchio, Taylor et al., 1997).

Figure 2-10: Superelastic Behavior in Shape Memory Alloy (Auricchio, Taylor et al., 1997)

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SMA materials can be applied for recent self healing designs such as composites because of their special effect in SME and SE. In 1997, Files and Forbell found out that some cracks expand on the specimen during loading and unloading and they discovered martensitic phase transformation cause to create these cracks. Also, these cracks can eliminate by simple heating and reverse transformation. Figure 2.11 shows the simulations of self healing composite by ABAQUS that propagate crack heal after simple heating (Burton, Gao et al., 2006) (Hassan M.R., 2013).

Figure 2-11: Simulation of Self-Healing Composite (Hassan M.R., 2013)

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##### 2.2.3.2 Shape Memory Effect (SME)

Nickel-Titanium alloys represent the shape memory effect in martensite phase when it is deformed and after unloaded, the temperature stay at below Mf. As Figure 2.12 shown, in one-way Shape Memory Effect (SME), material return to its original shape by simply increasing the temperature above Af. The shape recovery is obtained during heating, and then this phenomenon is called one way shape memory effect (OWSME) (Mantovani, 2000).

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Figure 2-12: Shape Memory Effect (SME) in Shape Memory Alloys (SMA) (Mantovani, 2000)

Nagasawa and Sabouri in 1974 discovered the remembering effect of shape memory alloys can occur in the martensite phase. So, they called them “the reversible shape memory effect” but now they are famous in Two-Way Shape Memory Effect (TWSME). It is possible to modify SMA materials by this property, without applied stress, just by shifting temperature between Austenite Finished (Af) and Martensite Finished (Mf). First of all Wang and Buehler reported two way shape memory effect for Nickel-Titanium alloy, but Nagasawa et al. explained that this effect has happened for Ni-Ti, Ni-Al and Cu-Zn alloys, too. Therefore, when the specimen’s temperature is below Ms, the reversible shape memory effect was observed. Figure 2.13 represents two way shape memory effect in below (Scherngell and Kneissl, 1998).

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Figure 2-13: Two Way Shape Memory Effect (Scherngell and Kneissl, 1998)

Also, the other diagram as Figure 2.14 shows the thermal cycle recover the material after loading and unloading to the original shape (Fugazza, 2003).

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Figure 2-14: Shape Memory Effect (SME) (Fugazza, 2003)

This last effect must be memorized by the material through a learning process that consists of it storing the energy (for example, under internal shape constraints) that will be freed through cooling the required thermodynamic. One of interesting effects of SMA related to the high-damping effect which is the ability of a material to transform mechanical energy (for example; provided by an applied force) into thermal energy (in the form of heat dissipation). By this way, this material has ability to resist shocks and absorb vibrations (Mantovani, 2000).

### 2.3 Material Models

Manufacturing processes like machining consist of various deformations with different stress, stain and temperature that they create complex deformation states. Many parameters affect on the machining of NiTi and the modeling of material strengthening mechanism can help to analyze the material application and machining process easily. There are numerous material models in these years; however there is not any particular model in the process of manufacturing that has ability to predict formation completely. Therefore, there is a review of material models in below part to introduce some of them.

#### 2.3.1 Johnson- Cook Model

This model is the most applicable model as a phenomenological material model with the based on finite element model (FEM). This modeling presents the material’s behavior and its dependence of flow stress on temperature and strain rate (Johnson and Cook, 1983). The mathematical model of J-C model is shown in below:

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According to this equation is the rate of strain 0 is the rate of reference strain and some constants in this formulation are: A=yield stress, B, n= the hardness of strain, C= a constant rate of strain. Also in second relation, is the melting temperature and is the temperature in the room (Johnson and Cook, 1983).

#### 2.3.2 Power Law Model

The below mathematical formulation represents power law model:

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As it shown, this simple model is applied for ordinary deformation models of any material. Usually, the power law method use to determined constant K and n in this formulation and it is not related to catch strain and temperature in flow stress (Guo, Wen et al., 2005).

#### 2.3.3 Zerilli and Armstrong Model

This model shows new formulation based on dislocation mechanics in the material deformation model. According to this method, the formulations are different in FCC and BCC crystal lattice structures, because dislocation phenomenon cannot occur in BCC lattice according to stress or temperature while it happens in the FCC crystal lattice structures (Zerilli and Armstrong, 1987).

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There is extra component of stress as ∆ which is obtained from the effect of dislocation density on the yield stress. , are in order the strain and the rte of strain, is the stress, is intensity of micro structural stress and finally the constants are defined as 1, 2, 3, 4, 5.

Material model in this study is based on Johnson-Cook model but shape memory alloys have particular affects so that ANSYS software has defined a complete model for this type of materials. Chapter 4 has been investigated the special material model in details.

### 2.4 Machining of Nickel-Titanium Alloy

Machining has a main characteristic in a wide complex of manufacturing processes how it is designed for removing material from workpiece. The basic machining operation can be categorized to milling, drilling, turning, sawing, shaping, broaching and abrasive machining (Hassan, 2013).

Milling process is to remove surface by predetermined value of material from a workpiece how movement activity is between rotational cutting tool and workpiece. Drilling is another process that wants to create round holes in the material of workpiece. Turning is a cutting process that removes material by generating external and cylindrical forms and if the cutting process focuses on the internal turning, it is called Boring for internal shapes. Sawing cutting process works with the power of saw to make differential geometries.

Shaping is a cutting process by removing material from surfaces how it uses a single point tool that support with a ram. The tool reciprocates in a linear motion despite the workpiece. Broaching process applies a cutting tool with particular cutting edge. In this operation, multiple transverse cutting with push-pull motion that remove material with axial cutting. Finally, Abrasive machining process can be defined in grinding how the small chips of material are removed from the workpiece (Mackerle 1998; Mackerle, 2003).

NiTi alloys are famous for their tensile deforming in a ductile manner (about 50% strain) before fracturing but some difficulties such as tool wear, high ductility, work hardening, high toughness and viscosity in the cutting processes have caused machining characteristics of NiTi to be high complicated. So, these problems can incur low workpiece quality with inferior chip breaking and burrs formation that

Figure 2.15 presents some of these influences that the behavior of unconventional stress-strain creates them during cutting processes of shape memory alloys (Weinert and Petzoldt, 2004).

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Figure 2-15: Some Problems in the Machining of NiTi: a) High Tool Wear, b) Adverse Chip Form, c) Burrs Formation After Turning, d) Grinding (Weinert and Petzoldt, 2004)

Some particular techniques have been used to machine nickel-titanium to overcome their difficulties such as Electric Discharge Machine (EDM), Laser cutting, wire cut machine, electrochemical machining and chemical milling but there are limited. Therefore it is better to solve these problems by some approaches how understanding of conventional machining be considerable. In this project, mechanical cutting parameters want to be invested for obtaining the optimal machining parameters (Wu, Lin et al., 1999; Lin et al., 2000). The next part has mentioned to the surface defects in machining processes of nickel-titanium.

#### 2.4.1 Surface Defect

There are many surface defects in Ni-Ti (Nitinol) machining process and the main forms such as feed marks, surface drag, debris of microchips, surface plucking, tearing surface, material cracking, surface cavities, adhered material particles, chip layer formation, deformed grains, slip zones, laps (material folded onto the surface), and lay patterns that some of them shown in Figure 2.16 (Ulutan and Ozel, 2011).

These defects can be affected by the cutting parameters. For example feed marks are really considerable parameter in machining but its severity can be changed by modifying and optimizing the feed rate. In the other case, cutting speed have affect on the amount of surface’s microchip debris. Also, depth of cut can be affect on some surface defects such as tearing, smearing, dragging or material plucking.

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Figure 2-16: Surface Damages in Machining of Nickel-Titanium Alloys: (a)

Metallographic Microstructure after Turning Process (b) Lay Pattern after Dry Milling Process (c) Metal Debris after Turning Process, and (d) Smeared Material and Feed Marks after Turning Process (Ulutan and Ozel, 2011)

They are common problem is the machining of nickel-titanium alloys and the cutting parameters should be optimized. Investigation in micron precision shows plenty surface defects in machining process. Chip redeposition to the surface and deformed grain are the other surface defect in this verification, because the plucking of bits and its related redeposition on the surfaces cause to different defect. First, these particles can cause tearing and dragging on the surface and second it is difficult to adjust the cutting parameters according to these surface defects. Figure 2.17 has shown the tearing mechanism in machining process (Ulutan and Ozel, 2011).

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Figure 2-17: Surface Tearing Mechanism in Machining Process (Ulutan and Ozel, 2011)

Residual stresses create after machining processes when the workpiece material abandoned thermo-mechanical load and this energy cannot be retrieved completely. In the other hand, residual stress is the remained stresses in material when the loading is removed. Cutting parameters and tool conditions cause to create tensile plastic deformation and this matter effect on morkpiece material, because residual stress is a potential to create in term of propagation, crack initiation and fatigue failure. Therefore they should remove or prevent to happening during machining processes (Kim and Daly, 2011). Plastic deformation is the main threat of surface integrity that comes from the plastic deformation of the workpiece in the machining process.

This surface defect affects on the workpiece deformation directly and a lot of parameters can create or prevent them, something like; workpiece parameters (material, grain size), tool parameters (rake angle, edge radius, shape, coating, wear) and cutting parameters (cutting speed, feed and depth of cut) (Ulutan and Ozel, 2011; Mackerle, 2003; Sun and Feng, 2006).

#### 2.4.2 Orthogonal Machining

This part wants to figure out the process of cutting force generation. Normally, the value of cutting parameters in designed experiment are really considerable to obtain optimize workpiece and tool interaction. Generally, cutting parameters such as; cutting speed, feed rate, depth of cut and tool geometry like; rank angle, clearance angle and finally material properties determine the influence of workpiece and tool adjustment for machining operation. Also, these parameters can affect on tool wear, surface quality and cutting forces.

One of the widely applied machining in industries is turning with fundamental metal forming. There are various metal forming processes milling, drilling, deep-hole drilling, slotting and etc, but turning operation modeling is the base model process to figure out the other machining processes. In fact, there are two main processes for removal material in the machining. Orthogonal machining is the basic process and the other is oblique that the both of them have been shown in Figure 2.18.

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Figure 2-18: (a) Oblique Machining (b) Orthogonal Machining (Merchant, 1944)

Mechanic of chip formation in this type of machining should be investigated. A simple definition of metal cutting is the operation of removing a layer of metal as chips to obtain designed dimension and shape with a good surface quality. Figure 15 presented two orthogonal and oblique cutting method processes how according to the picture, cutting edge is in the direction of tool motion in the orthogonal method while oblique cutting has an angle other than 90 degree. So, orthogonal cutting is simpler to investigating and understanding and simulation or experimental machining will be done in good condition.

It needs to consider directions and force values in any metal cutting process; therefore the prediction is really important to any act. So, this matter needs to figure out cutting forces in basic model after that it can be developed reliable models. Workpiece material flow, tool properties and condition, and cutting parameters are the considerable elements to have influence on the mechanism of chip formation. If the cutting speed be low, the chip formation will be disconnected (Juneja and Sekhon, 1987). Also the chip formation will be unstable the shearing process, if the cutting speed grow (Shaw, 1984; Trent and Wright, 2000).

In 1944, Merchant discovered the first quantitative analysis for cutting forces. In his idea, the shear plane should locate upon the shear stress how it be maximum rate. This theory tried to make some assumptions and reductions. According to this method, the ratio of cutting width to unformed chip thickness is a large value, so cutting parameters should be considered in two dimensional. Moreover, cutting tool simplify to sharp tool with continues chip formation except built up edge and the shear zone is assumed a plane. Then these considerations are applied in orthogonal cutting parameters with related forces as shown in Figure 2.19 (Merchant, 1944).

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Figure 2-19: The Circle of Merchant Method (Merchant, 1944)

According to this figure, is the shear plane, , are due to the basic cutting force () and finally is thrust force. So, there are the formulations about these parameters (Merchant 1944):

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### 2.5 Tool Material and Properties

NiTi is a shape memory alloy with particular properties and effects. In this decade, many scientists discover various tools to resist its tool wear, work hardening, high ductility and etc. These cutting tool materials cause to create applicability to machining NiTi. For example, high tool wear cause to not choose uncoated cemented carbide as a NiTi tool because it make a cratering on the tool in rake face. Therefore, tungsten carbide usually applied as a tool material and TiN family (especially TiCN and TiAlN) can be applied as a cover to decrease tool wear (Weinert, Petzoldt et al. 2004). For example, TiN can be suit material for coating the high speed steel drill, because the research exhibits it has a better ability in drilling in compare with high speed drill with steel material for machining of NiTi. It causes to increase the hardness of tool and resistance of tool wearing. In another sample, tungsten and carbide has a same property how they can raise the ability of drilling and resist in front of 5000 N of drilling force. Moreover, they have more toughness, viscosity and perfect pseudoelasticity of nickel-titanium as shape memory alloy ( Lin et al., 2000).

Cubic boron nitride or CBN is one of the most applicable tools with the high potential, hardness and economic. Also, polycrystalline diamond or PCD has a same affect with the high resistance to wearing and it uses for machining of light metal most of the time. Although these materials are suit for the machining of NiTi, but Figure 2.20 has a comparison between them in upper pictures. Also, there are two more pictures in lower parts that present the machining affect on composite ceramic (CC) and oxide ceramics (OC). As it clear, they are not capable of machining process nitinol except of their cutting parameters (Weinert, Petzoldt et al., 2004; Zou, Chen et al., 2009).

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Figure 2-20: Various Material of Cutting Tool after NiTi Machining, Cubic Boron Nitride (CBN), Polycrystalline Diamond (PCD), Composite Ceramics (CC) and Oxide Ceramics (OC) (Weinert, Petzoldt et al., 2004)

#### 2.5.1 Titanium Nitride tools

Titanium Nitride is a highly hard ceramic tool (famoused as TiNite or TiN) that applied in the experimental part of this study. This material always used as a covering on steel, Titanium tools, aluminum and carbide components to increase the quality of surface properties. TiN cause to make a hard tool and it protect the surfaces or it can apply in decorative purpose (it is like a golden metal). Corrosion resistance and edge retention are the other famous application of Titanium Nitride on machine tooling. By this material, machining like milling cutters and drill bits can be improved in the time of their life. Figure 2.21 shows a milling tool that covered by TiN material (Binter, 2013).

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Figure 2-21: Titanium Nitride Coated for a Drilling Tool (Binter, 2013)

Titanium Nitride was developed to titanium aluminum nitride (TiAlN or AlTiN) and titanium carbon nitride (TiCN) which be made of TiN with similar effect, But they are enhanced in hardness and corrosion resistance with a ranging of colors from light gray to closing black such as Figure 2.22. Also, they have a lower friction coefficient in numerous applications and improved abrasive wear resistance. Smooth operation, inferior high temperature tolerance, keeping sharp corners and edges are the other advantages of these new materials as a tool in machining process (BryCoat, 2013).

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Figure 2-22: The Application of TiAlN and TiCN in Various Tools (BryCoat, 2013)

## 3. CHAPTER 3: METHODOLOGY

### 3.1 Introduction

Experimental method for machining is always expensive and time consuming. Also, experimental approach sometimes includes many parameters such as cutting condition, tool geometry, workpiece material properties and etc that make it more difficult. Finite element method (FEM) is another approach that applies mathematic simulation during numerical procedure. Machining research is a complex task with some difficult elements like; elasticity and plasticity, metallurgy, heat transfer, contact problem, lubrication, fracture machines and so on that computational model can predict the deformations, strain, stress, temperature in the workpiece or tool under particular cutting parameters (Mackerle, 1998).

This chapter describes the methodology procedure and considered method of machining simulation by finite element method. First, the appropriate software for this computational simulation will introduced as ANSYS and the capability of this software will be explained completely. Second, the dimensions of nickel-titanium workpiece and cutting tool will be discussed in this modeling. Their mechanical and material properties have described in the literature review part.

According to this simulation, this project is a quantitative research method with numerical data such as statistics and percentages. It means a quantitative research is the relationship between variables and these variables are measured according to the particular instrument; so, this data can be analyzed. Research procedure will be according to the aforementioned objectives. It means, first of all, achieved data from literature review will be investigated and input data will be obtained. After that, the cutting condition in the orthogonal machining process will be simulated in different velocities. In the last part stress condition will be assessed in machining process of nickel titanium alloy how final result compare together to obtain optimize velocity in machining process. Overall, Figure 3.1 shows the flowchart of the project procedure.

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Figure 3-1: Flow Chart of The Project Procedure (Author’s own work)

### 3.2 Finite Element Method (FEM)

Metal cutting is a widely nonlinear with thermo mechanical process. Friction between tool and workpiece create a heat zone and it may make a plastic deformation. There are differential mechanical forces in tool and workpiece. Finite element method (FEM) is the most frequently applied to prevent experimental process. This simulation is a good technique to predict some tests without doing experiments. By this way, some surface defects like; residual stresses, plastic deformation and others can be predictable and the capability of this method is able to change parameters in machining processes and do the analysis again for measuring the sensitivity of obtained result (Han and Lu, 2006).

Also, simulation according to FEM method can optimize the time and its prediction usually is close to experimental results. It generally occurs for residual stress measurement in material constitutive model. Sometimes, elasto-viscoplastic and material constitutive models combine in FEM method to obtain a good solution for various fields and get detail for the chip formation processes. During machining process, the computational software can show physical phenomenon according to continuum mechanics maxims. So, according to this techniques, machine condition can be changed and reduce the machining time and this matter is technologic capabilities in modern computational software. The operation analysis is common in the most of industrial machining processes and they have spatial computation that obtain many parameters like; stress, strain and temperature in their 2D or 3D models. In these models, chip formation can be calculate fairly with high accuracy to predict realistic fields in something like; damage zones on the cutting tool, residual stress, chip formation, possible wear tool, hardness on the machined workpiece. Finite element models for machining improve by advanced computer models and numerical methods in this decade. Therefore, computational challenges in 2D and 3D analysis are stayed unsolved (Han and Lu, 2006).

It is really difficult to create removal chips from workpiece by FEM simulation and this suffering depends on artificial chip separation methods. FEM formulations have a capability to remesh simulation of material plastic flow in the workpiece and tool area (Ulutan and Ozel, 2011). Therefore, simulation can predict chip flow and breaking phenomenon so that the controlling of chip movement during the contact part of tool is really considerable factor for tool wear models. Workpiece deformation, large plastic stress, hardening of strain, thermal effect, contact properties and its friction play main obligation in the mechanism of chip formation. The optimize design in simulation provide practical solutions for machine tools and its geometry and by this way, machining process will be improved the result.

The most researcher applied in-house finite element code till the mid of 1990, but currently there are many modeling of machining process in finite element method, such as; LS DAYNA, ABAQUS (STANDARD/EXPLICT), ALGOR, MARC, FLUENT and so on. The majority of these FEM softwares are applicable for continuous chip, however AdvantEdge, FORGE and DEFORM are the other software which have a capability in the simulation of discontinuous chip formation. Figure 3.2 shows, number of publication of metal modeling from 1970 to 1999 that the cutting processes were simulated by handful paper about chip formation (Ng and Aspinwall, 2002).

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Figure 3-2: Number of Technical Publication on Modeling between 1970 and 1999 (Ng and Aspinwall, 2002)

### 3.3 Method of Analysis

It should be noted that the method of analysis which will be done with the help of ANSYS software so that it would be examined in short steps and changes.

#### 3.3.1 The Component of Experiment

There are four standard forms for experimental method according to the creswell research methodology. Participates, materials, procedure and measures are organized this standard method. There is complete detail and definition of experimental method for this report which be mentioned in following (Creswell, 1994).

The basic information and related data for this study are divided into the following subjects:

- Elastic parameters should be obtained by material properties of nickel- titanium. Young’s modulus () and Poisson’s ratio () are some of this essential parameters.
- Plastic parameters should be applied to obtained variable. There is a stress- strain curve which can give these criteria for Nickel-Titanium alloy.
- Following relations use in the simulation definition. Because NiTi is particular material and it should be simulated according to superelasticity effect.
- Machining parameters such as various velocities, constant feed rate, temperature, chip thickness and so on, are obtained from the experimental paper.
- Tool material properties, dimension, coefficient friction between tool and material should be applied. This main information should be extract form experimental machining that is mentioned in the following.

ANSYS software needs to use these data which experiment the variables. So, this study wants to simulate the machining of NiTi in differential cases by this software. Technical engineering support and system support are the perfect capability of this software. All kind of materials such as linear, nonlinear, isotopic and anisotropic behavior can be investigated by ANSYS software. This software provides a simple consistent interface for generating, submitting, monitoring and evaluating result from ANSYS software. In the next section this software and its capabilities will be explained in detail.

The material properties of workpiece and tool are mentioned in the literature review, however their size and geometries which is applied in this project, assigned in following. Figure 3.3 shows the schematic of tool and workpiece in this project that the basic geometries are designed in AutoCAD Software.

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Figure 3-3: Schematic of Tool and Workpiece Position That Designed by AutoCAD Software (Author’s own work)

The size of workpiece and tool to doing simulation in this study are available in Figure 3.4 how chip thickness () will be 0.2 mm in each pluse of machining.

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Figure 3-4: Tool and Workpiece Geometrical Dimension in This Study (Author’s own work)

Meanwhile, in the tool geometry that illustrated in Figure 3.5, the angles are specified to relief angle () 6 degree and rank angle () 7 degree (Woodson and Koch, 1970; Weinert and Petzoldt, 2004).

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Figure 3-5: Cutting Angle and Force Components (Woodson and Koch 1970)

#### 3.3.2 What is ANSYS

ANSYS software is designed for a general purpose to apply for simulating interactions of whole discipline of physics, structural mechanics, fluid dynamics, electromagnetic, heat transfer, vibration and etc for technical engineers. This software has a capacity to create a working condition or tests how any test can be done in the virtual environment before manufacturing prototypes of final products. Moreover, ANSYS software is able to improve in the weak points of products, calculate the life of tool or even it can predict the future problems by Three Dimension (3D) simulation. Figure 3.5 presents the modular structure of ANSYS software how it can work integrated with the other engineering software by collecting Finite Element Analysis (FEA) and Computer Aided Design (CAD) connection modules (FIGES, 2013).

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Figure 3-6: The Modular Structure of ANSYS (FIGES, 2013)

ANSYS software has a capacity to import Computer Aided Design (CAD) data and make geometry with preprocessing capability. At this level, finite element model (meshing) is occurred to generate the required computation as defining loading. Therefore, Numerical analysis and graphs are the results of simulation. The interesting point about ANSYS software is the quickly calculation for advance engineering analysis. It has a perfect ability to do simulations safety with variety of contact algorithms. Linear or nonlinear material models or time based loading are the other capacities of ANSYS software (FIGES, 2013).

ANSYS workbench is defined as a platform that integrates simulation technologies and complete CAD system with incomparable performance and automation. It is powerful software to solve the complex algorithms and improve the final products in virtual environments. Furthermore, ANSYS workbench is written for high rate compatibility of particular job or analysis, and it is not limited for anybody who has a license in it.

### 3.4 Conclusion

This study tries to find the optimum speed of machining by applying finite element model and ANSYS software has a good capability for this matter. So, the research procedure is described in this section step by step to obtain final result which introduced as optimum speed of machining. Also, the dimensions and material specifications for both tool and workpiece is mentioned in this chapter in detail.

## 4. Chapter 4: Results and Discussions

### 4.1 Model Description

Finite element method (FEM) reviews and analysis the machining of nickel-titanium by applying ANSYS software. This approach wants to improve the machining process by optimizing the parameters and Arbitrary-Lagrangian-Eulerian (ALE) framework will be employed with appropriate meshing to consider elastic-plastic deformations. There is many models that using various types of element for analyzing. The simulation of this study should cover the connection between workpiece and tool.

Therefore, three dimensional modeling (3D) can predict better result for this respect when they compared to the experimental results. ANSYS software has a good finite element model that is called solid 164. This FE model contains of eight nodes and each node has three degrees of freedom. The capabilities of this model are huge deflection, large strain behavior, model plasticity and reduce in the applying of integration method (Thimmapuram, 2011).

### 4.2 Mesh Condition and Methods

The chip removing from workpiece material is always considerable issue for scientists. Researchers have applied effective strain, crack generation, propagation and geometric distortion for chip analyzing in the past. According to that, the finite element code consisted of Differential algorithms such as node/element, sideline and remeshing for chip parting. Moreover, the selection method for algorithm was depending on the sharpness of cutting edge. In this section, mesh conditions related to this study will be explained. There are big deformations in nonlinear simulations, because these deformations finite element would distort; so, it is essential to apply adaptive meshing tools to reduce distortion in the mesh.

Mesh condition is attached to the tool and workpiece in Lagrangian formulation and it is defined according to displacement increments and FE solution. In this method, displacement increment is a function of time step. So, explicit solution can be applied for material removing during the cutting process. Although the implicit formulation is depend on the time step, but the solution does not depend on the time step value, because time step is not physical significance. Moreover, the lagrangian material model can be elastic-plastic, viscoplastic or only plastic and these matter causes to researchers apply the both multiplicative and additive decomposition of plastic and elastic strains (Athavale and Strenkowski, 1998).

ALE method is applied in this study because it is combines of lagrangian and eulerian analysis. Thus, mesh motion at free boundaries is constrained to the material motion and also material and mesh motions are independents. It means that 8 nodes has been used with radius integration, but for better results it is need to calculate deployment of mesh that will analyzed after drawing the diagram. Figure 4.1 shows the motion of mesh and material in various methods (Emamian, 2013).

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Figure 4-1: Motion of Mesh and Material with Various Methods (Emamian, 2013)

#### 4.2.1 ANSYS LS-DYNA

As it was introduced in the methodology section, ANSYS software is applied in this study. This software has an particular part that is called ANSYS LS-DYNA. It combines the LS-DYNA explicit finite element program with the powerful processing capabilities of the ANSYS program. This explicit method of solution applied by LSDYNA provides huge deformation dynamics, fast solution in the short time, quasistatic programs with large deformations and multiple nonlinearities, complex contact and impact problems. By applying this integrated software, LY-DYNA can find an explicit dynamic solution and also, review the results that they applied standard ANSYS post-processing tools (ANSYS, 2009).

#### 4.2.2 Solid 164 Element Description

Solid 164 is applied for three dimension modeling (3D) of solid structures in ANSYS software. This model has eight nodes for each element and every node has three degrees freedom in x, y and z directions as shown in Figure 4.2 (ANSYS, 2009).

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Figure 4-2: SOLID 164 Structural Solid Geometry (ANSYS, 2009)

Solid 164 element has many capabilities such as; plasticity, creep, stress stiffening, large deflection and strain. Also, there is a mix formulation for simulating of deformation how it is close to fully incompressible hyperelastic materials and incompressible elastoplastic materials. Hence, solid 164 can be assorted general modeling in 3D solid structures, because it allocates for pyramid degenerations, tetrahedral and prism when applied in irregular regions. There are many differential elements that supported the solid 164; some element technologies like; B-bar, uniformly decreased integration and increased strains. Solid 164 is used any of the following material models for solid elements:

- Isotropic Elastic
- Orthotropic Elastic
- Anisotropic Elastic
- Bilinear Kinematic
- Plastic Kinematic
- Viscoelastic
- Power Law Plasticity
- Johnson-Cook Plasticity
- Zerilli-Armestrong
- Composite Damage
- Concrete Damage
- Honeycomb
- Elastic Plastic Hydrodynamic
- Elastic Fluid

The more information about SOLID 164 and its relations are mentioned in the Appendix A in the end of project (ANSYS, 2009).

### 4.3 Boundary Conditions

The boundary condition applied by the majority of the past models show stable conditions. The TiN tool is considered rigidly with the particular properties and nickel-titanium workpiece permitted to move in the velocity’s direction. Also, the chip avoided from penetrating the coated tool, but it is complete free otherwise. Figure 4.3 shows the boundary conditions in below (Arrazola and Özel, 2010).

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Figure 4-3: FE Simulation Model for Boundary Conditions of ALE Method (Arrazola and Özel, 2010)

According to this method; the mesh condition modeling is presented in Figure 4.4 for both tool and workpiece in ANSYS software.

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Figure 4-4: The Mesh Condition Design for Tool and Workpiece in The ANSYS Software (Author’s own work)

### 4.4 Shape Memory Alloy Material Model

Some material models are discussed in the literature review. There was mentioned that john-cook model is the most applicable material model in machining process. But shape memory alloy are different material and it needs particular model that can be able define its special effect such as superelasticity. ANSYS software has a separate definition for shape memory material that is mentioned in its material modeling procedure.

#### 4.4.1 Constitute Model for Superelasticity

Superelasticity effect and its related diagrams explained in literature review, but phase transformation mechanisms in microscopic status are explained in this section in details. Superelastic behavior is involved:

1. Austenite to martensite (A->S)
2. Martensite to austenite (S->A)
3. Martensite reorientation (S->S)

Martensite and austenite are two considerable phases that have main rule in superelasticity effect. Martensite fraction (ξS) and austenite fraction (ξA) are two internal variables with the below relation:

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The material behavior is considered isotropic and the relations will be extended by Drucker-Prager loading function to obtain material parameters. Appendix B has defined these formulations to prove the internal variables in details and obtained material parameters are presented in Figure 4.5.

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Figure 4-5: Idealized Stress-Strain Diagram of Superelastic Behavior (ANSYS, 2009)

The final stress-strain relations in this model are shown in below where the elastic stiffness tensor is D, tension is , transformation strain tensor is , and finally material parameter like strain is .

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#### 4.4.2 Material Parameters of SMA Modeling in Superelastic Behavior

ANSYS software applies some constants to model the superelastic behavior of SMA material. These six constants are defined the stress-strain behavior in the machining process as loading and unloading that used in the unaxial stress state. Table 4.1 presents them which applied in superelastic state to modeling by ANSYS software. Also, the numerical values of these constants have defined in the literature review before (in material properties section).

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Table 4-1: Superelastic Option Constants

### 4.5 Software

All the steps of the analysis are investigated in this section and finally outputs and results would be considered. To obtain the results, it is better to present the software steps as follows.

#### 4.5.1 Create the Geometrical Model

Modeling was done in 2 parts: First, as Figure 4.6 shown, the outlines of the 3 parts was drawn in AutoCAD in the X-Y plan, according to the required dimensions, and saved as a DXF transfer file.

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Figure 4-6: AutoCAD 2D Model (Author’s own work)

And in the second part, the DXF file was then read into Autodesk Inventor, where the outlines were extruded in the Z direction to create solid parts ready for transfer to ANSYS. Figure 4.7 presents the 3D geometrical model in Autodesk Inventor software.

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Figure 4-7: Autodesk Inventor 3D Model (Author’s own work)

After the second, modeling part was finished; the solid parts were exported from Inventor in the Initial Graphics Exchange Specification (IGES) file format, to be read into ANSYS Software for meshing.

#### 4.5.2 Material Properties

In this step, material properties would be defined. It is obvious that the workpiece and tool materials which used in this study has elastic-plastic characteristic that would be entered in the software. The material models were defined as LS-DYNA Elastic materials using the isotropic model, and values for the density, Young's modulus, and Poisson's Ratio were entered. So, two materials were defined as follow;

- Material 1 was defined as Tungsten Carbide, and was used to model the tool.
- Material 2 was defined as Nitinol (NiTi), and was used to model the chip and workpiece.

Figure 4.8 and 4.9 show the method to enter the input properties into software. The material properties were defined in the literature review in details.

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Figure 4-8: Define the Material properties in the ANSYS Software (Author’s own work)

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Figure 4-9: Define Material Model Behavior (Author’s own work)

#### 4.5.3 Assembling the Parts

In this step, tool and workpiece are assembled together as shown in Figure 4.10. LS- DYNA requires that all components be sorted into parts, so the solver can know which part interacts with the other parts. To define the parts for LS-DYNA, two stages were done:

- The nodes and elements were grouped into ANSYS components
- These components were entered into LS-DYNA (using the EDPART command), and also used to specify the parts that would be given loads (i.e. velocity for the part and constraints for the workpiece)

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Figure 4-10: The Assemble Parts in the Software (Author’s own work)

#### 4.5.4 Specifying the Solver Parameters

The different parameters which LS-DYNA needs for its solving were entered as two dimensional arrays, and two arrays were defined, one for time and the other for velocity of the tool. Figure 4.11 presents the solver parameters in the software.

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Figure 4-11: Specifying the Solver Parameters (Author’s own work)

#### 4.5.5 Definition of contact

The fifth step, the interaction properties as illustrated in Figure 4.12 between objects how the LS-DYNA contact definition commands were used to define two nodal surfaces that were given contact parameters:

- The contact area between the tool and chip, using the LS-DYNA general contact option, and including the friction coefficients between Tungsten Carbide and Nitinol (NiTi).
- The contact area between the chip and the workpiece, using the LS-DYNA tiebreak option, and included specify the ultimate tension and shear stress values for Nitinol (since the separation of the chip from the workpiece represents a material failure state, and the tiebreak option takes into account that any computed stresses exceed the ultimate values means that the tie has broken i.e. the material has failed).

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Figure 4-12: The Definition of Contact Parameters (Author’s own work)

#### 4.5.6 Apply Boundary Conditions

The boundary conditions included giving the tool a velocity BC and giving the nodes of the workpiece on the bottom and far side (away from the tool) faces a fixed BC in all axes as it shown in Figure 4.13.

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Figure 4-13: Boundary Condition Included Tool and Workpiece (Author’s own work)

### 4.6 Discussion and Comparison

For conducting this study, after investigations of affective conditions in the solution processes and selecting the proper data regards to the type of workpiece that mentioned before in the literature review, the following issues was considered that would discussed the results and conclusions.

The aim of this study is to investigate the effect of speeds and find the optimum of cutting speed. For this purpose, three different speeds were chosen to find the relationship between stress condition in various velocities. To obtain optimal condition of NiTi machining process, investigating the optimum speed are significant and this is clear that travelling speeds is a main factor in stress issues. The relation between differential speeds and heat input is complex during machining process. High stress creates a big problem in the machining and makes to increase hardness of nickel-titanium workpiece. Generally, lower cutting force and in direct relation, lower stress in the machining process cause improve the mechanical properties as well as decrease hardness, distortion and residual stress (Weinert and Petzoldt, 2004).

#### 4.6.1 Experimental Study

In comparison with Weinert et al. (Weinert and Petzoldt, 2004) cutting forces changes with different cutting speeds. He considered three different velocities in the experimental machinability of nickel-titanium and compared the influence of cutting speed on it. There were high cutting forces at low cutting speed ( = 20 m/min) while tool wear was high too. But tool wear started to reduce when the cutting speed increased. They found out the cutting speed between 60 and 130 m/min (60 < < 130 m/min) in the best range, because the cutting forces and tool wear are in lowest values. Moreover, cutting forces increased again in above 130 m/min ( ൐ 130) and also this growing make the temperature high and it cause to create hardness in chip formation zone. Also the friction between tool and workpiece causes to burn chip due to higher working temperature in above cutting speed 140 m/min. Figure 4.14 presents the cutting force-cutting speed diagram due to Weinert et al. experimental results (Weinert and Petzoldt, 2004)

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Figure 4-14: Cutting Force-Cutting Speed Diagram Due to Weinert et al. Experimental Results (Weinert and Petzoldt, 2004)

Also, according to Weinert et al. study, 100 m/min can be suit cuttings speed because it has more advantage compare with the other velocities in the range. As it was defined in the literature review, continuous chip formation is a significant surface defect in machining, but in the experimental machining, chip breaking has better condition in the velocity of 100 m/min. moreover, they concluded this cutting speed has a minimum tool wear and cutting forces ( Weinert, Petzoldt et al., 2004).

#### 4.6.2 Simulation Variables and Results

This study shows the stress condition of different cutting speeds with constant conditions such as same feed rate (f=0.05 mm), chip thickness (= 0.2 mm), relief angle (=6 degree) and rank angle (=7 degree) that these parameters were mentioned in methodology section. Cutting force has a direct relation with stress according to the material models that are defined in literature review. Therefore, it is reasonable to have same results for different velocities and obtained stress such as cutting force experimental results. By the way, this study wants to investigate the effect of different cutting speeds on the machining stress to obtain optimum cutting speed for machining of nickel-titanium alloys. According to the Weinert et al. (Weinert and Petzoldt, 2004) experimental study, three cutting speeds are considered in this project; 20 m/min, 100 m/min and 130 m/min.

##### 4.6.2.1 Cutting Speed 20 m/min

In this section, the displacement summation due to cutting speed 20 m/min is presented in Figure 4.15. Also, the shear stress simulation in XY direction and von mises stress are shown in Figure 4.16 and 4.17 how the stress value is observable in any simulation figure. The complete figures about all three cutting speeds such as; deformed shape, displacement summation, displacement in (X,Y,Z) directions, shear stress in (XY, XZ, YZ) plane, Stress in (X,Y,Z) directions, velocity summation, velocity in (X,Y,Z) directions and von mises stress are available in Appendix C in details.

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Figure 4-15: Displacement Summation Due to Cutting Speed 20 m/min (Author’s own work)

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Figure 4-16: Shear Stress in XY Direction Due to Cutting Speed 20 m/min (Author’s own work)

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Figure 4-17: Von Mises Stress Due to Cutting Speed 20 m/min (Author’s own work)

##### 4.6.2.2 Cutting Speed 100 m/min

There is the displacement summation of cutting speed 100 m/min in the Figure 4.18. Moreover, shear stress in XY direction and von mises stress are presented in Figures 4.19 and 4.20.

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Figure 4-18: Displacement Summation Due to Cutting Speed 100 m/min (Author’s own work)

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Figure 4-19: Shear Stress in XY Direction Due to Cutting Speed 100 m/min (Author’s own work)

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Figure 4-20: Von Mises Stress Due to Cutting Speed 100 m/min (Author’s own work)

##### 4.6.2.3 Cutting Speed 130 m/min

Also, the displacement summation of cutting speed 100 m/min is mentioned in the Figure 4.21. Moreover, shear stress in XY direction and von mises stress are presented consecutively in Figures 4.22 and 4.23.

Figure 4-21: Displacement Summation Due to Cutting Speed 130 m/min (Author’s own work)

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Figure 4-22: Shear Stress in XY Direction Due to Cutting Speed 130 m/min (Author’s own work)

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Figure 4-23: Von Mises Stress Due to Cutting Speed 130 m/min (Author’s own work)

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#### 4.6.3 Final Diagrams Obtained in the Modeling

Figure 4.24 shows the von mises stress-velocity diagram that obtained from the simulation of machining nickel titanium alloy. It is obvious, cutting speed 100 m/min has the lowest stress value in this diagram and this cutting speed value would be considered the best compare with 20 and 130 m/min such as the experimental study.

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Figure 4-24: Von Mises Stress -Velocity Diagram for the Machining of Nickel Titanium alloy in Various Cutting Speeds (Author’s own work)

Also shear stress-velocity diagram has been confirmed the pervious obtained result as shown in Figure 4.25. Obviously, the velocity 100 m/min is the optimal cutting speed according to this diagram, again. Therefore, this graph has complying with the experimental study and it is acceptable.

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Figure 4-25: Shear Stress-Velocity Diagram for the Machining of Nickel Titanium alloy in Various Cutting Speeds (Author’s own work)

### 4.7 Conclusion

In general, this section will summarize all the steps of this study with overall comparison from two aspects. First is about the comparison study with experimental and the other is about comparison between objectives and achieved information in this project. Due to limitation, simulation approach was chosen. Nevertheless, this approach has many benefits such as investigating many strength and weaknesses before actual job. Select the tool material and shape and also the workpiece and find the experimental data which have both of them analysis was difficulties of this study, although tool material was solid in this study.

Workpiece materials extracted from Schwartz and Baumann studies (Schwartz 2002) (Baumann 2004) and also, tool properties and machining parameters like; cutting speeds, feed rate, chip thickness, relief angle, rank angle and so on were selected from Weinert et al. (Weinert and Petzoldt 2004; Weinert, Petzoldt et al. 2004; Weinert, Petzoldt et al. 2004) in various research studies. The effect of differential cutting speeds regards to stress investigated and compared with the experimental. Weinert et al. discovered 100 m/min is the best cutting speed in the machining of nickel-titanium because the cutting forces and tool wear are in minimum values while the chip formation is in good condition. After that, the simulation of machining in Figures 4.24 and 4.25 present Stress would be reduce when cutting speed increased and also it would be increased in the high cutting speed like 130 m/min. Moreover, the obtained simulation result is complying with experimental output.

## 5. Chapter 5: Conclusion and Recommendations

### 5.1 Conclusion

One of the aims of this study is to optimize machining of nickel based shape memory alloys. Nickel-titanium (Nitinol) is one the famous shape memory material which applied in wide range of products especially in aero-space, medical, biomedical and the others. Shape memory effect is created due to various temperatures, loading and unloading how these materials can return to their original shape. Shape memory effect (SME) and superelasticity (SE) are two considerable factors which are made SMA as a special materials with different behaviors. Austenite and martensite are two main phases which have influence on these materials to create SME in different temperatures.

These materials cannot be machined easily how high tool wear, high cutting force, huge hardness due to machining temperature, surface defects are made them so critical. This study obtained the objectives into four consecutive sections. According to the survey that was done in the previous chapters, characteristic of nickel-titanium shape memory alloy have been considered. These materials are really hard, therefore; their applied tools and machining situation are more particular than the other materials. Moreover, in this study, the machining tool geometry and design investigated. Strength and weaknesses of the process considered and this study by ANSYS software have been simulated that its results are in Chapter 4.

Experimental studies were compared with simulations in this report and the main section of this study which is the optimum cutting speed of nickel-titanium alloy machining is defined as 100 m/min according to the objectives. Stress would be decreased due to the increasing the cutting speed in the NiTi machining and after a period of cutting speeds range (around 100 m/min), it be increased. Also, the experimental study show same the velocity can be acceptable for the machining of NiTi, because tool wear and cutting forces are in minimum values.

### 5.2 Recommendation

1. Temperature investigation would be important factor that can help to improve in the machining process, because high temperature cause create hard working and this matter is current in the machining of shape memory alloys.
2. Experimental analysis for machining process of nickel-titanium alloy is recommended to obtained accurate data and documented results separately.
3. The other machining process can be investigated in details, for example, drilling, milling, deep hole milling, turning, grinding are particular machining processes which can be simulated one by one to improve in their processes individually.

By this method, shape memory alloys can be investigated in various machining processes to obtain optimum parameters for better results in comparison with their experimental results.

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APPENDIX A: Solid 164 Specification

Appendix A was removed for publication due to copyright. It can be read at http://www.ansys.stuba.sk/html/elem_55/chapter4/ES4-164.htm

APPENDIX B: Shape Memory Alloy (SMA)

Appendix B was removed for publication due to copyright. It can be read at https://www.sharcnet.ca/Software/Ansys/15.0.7/en-us/help/ans_mat/smas.html 9. APPENDIX C: The Complete Results of the Simulation 10. (Author’s own work)

These are the post processing results for the 20, 100 and 130 m/min cases. It is obvious the maximum and minimum values of each item from the image itself, since anything with MX is the maximum (SMX, VMX,...etc), and anything with MN is the minimum. The time of the analysis is given as TIME in all images (i.e. the time at which the analysis was stopped, which in general is about .01 seconds from the start of the movement of the tool towards the chip). The maximum deflection is given as DMX in all images Units are: Meters for length, Newton/meter squared for stress, Meters / second for velocity, Seconds for time.

C.1 The Cutting Speed 20 m/min

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Figure C1: Deformed shape due to velocity 20 m/min

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Figure C2: Displacement Summation of XYZ Contours 20

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Figure C3: Shear Stress in XY Direction for Contours 20

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Figure C4: Shear Stress in XZ Direction for Contours 20

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Figure C5: Shear Stress in YZ Direction for Contours 20

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Figure C6: Velocity Summation of XYZ Contours 20

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Figure C7: Von Mises Stress 20

C.2 The Cutting Speed 100 m/min

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Figure C8: Deformed shape due to velocity 100 m/min

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Figure C9: Displacement Summation of XYZ Contours 100

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Figure C10: Shear Stress in XY Direction for Contours 100

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Figure 11: Shear Stress in XZ Direction for Contours 100

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Figure C12: Shear Stress in YZ Direction for Contours 100

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Figure C13: Velocity Summation of XYZ Contours 100

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Figure C14: Von Mises Stress 100

C.3 The Cutting Speed 130m/min

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Figure C15: Deformed shape due to velocity 130 m/min 102

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Figure C16: Displacement Summation of XYZ Contours 130

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Figure C17: Shear Stress in XY Direction for Contours 130

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Figure C18: Shear Stress in XZ Direction for Contours 130

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Figure C19: Shear Stress in YZ Direction for Contours 130

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Figure C20: Velocity Summation of XYZ Contours 130

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Figure C21: Von Mises Stress 130

## Details

Pages
119
Year
2013
ISBN (Book)
9783668364776
File size
6.4 MB
Language
English
Catalog Number
v346768
Institution / College
Universiti Putra Malaysia – University Putra Malaysia (UPM)