Titanium SMAs utilizing GRA-based AHP and RSM

Electrochemical arc micro-drilling of Nickel-Titanium SMAs utilizing GRA-based AHP and RSMNITISH KUMAR  ( [email protected] )

National Institute of Technology Jamshedpur https://orcid.org/0000-0001-7602-4883Amaresh Kumar 

Research Article

Keywords: Nickel-Titanium, Shape Memory Alloys (SMAs); drilling, GRA, electrochemical, RSM, AHP

Posted Date: June 29th, 2022

DOI: https://doi.org/10.21203/rs.3.rs-1770408/v1

License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

Electrochemical arc micro-drilling of Nickel-

Titanium SMAs utilizing GRA-based AHP and RSM

Nitish Kumar1,*, and Amaresh Kumar1

1Department of Production & Industrial Engineering, National Institute of Technology Jamshedpur, Jharkhand-

831014, India

*Corresponding author: [email protected]

ABSTRACT

Electrochemical arc machining (ECAM) is a hybrid technique which is discovered by the further development of

ECDM. As Nickel-Titanium is a hard-to-cut shape memory alloy, therefore ECAM has been utilized. For any

manufacturing industry, the machining characteristics are an essential component of the process for the production

of NiTi-based things, therefore in this study, MRR, TWR, over cut, and delamination have been chosen as

performance parameters whereas voltage, electrolyte concentration (ethanol with ethylene glycol and NaCl), and

tool rotation has been selected as variable parameters. The molybdenum has a low tendency to react chemically,

therefore it was chosen as a tool for drilling NiTi. The optimum drilling condition has been detected as 20 v/v% of

electrolyte concentration, 0 rpm of tool rotation, and 80V of voltage with help of the GRA-based AHP technique,

and further, the GRG was optimized by RSM. The optimum value of the performance parameter has been

observed as 101.19 mg/min, 0.006 mg/min, 0.111, and 1.16 for MRR, TWR, OC, and delamination respectively.

The SEM analysis revealed HAZ, a white layer, melted droplet, number of cavities, craters, and microvoids near

the drilled hole. Furthermore, EDX analysis proved that the work surface can be free of Mo after machining

Nitinol by electrochemical arc machining. Also, the XRD analysis revealed the development of carbides like TiC

in the melting zone of a drilled hole, where that carbide can vanish the shape memory properties in HAZ. As the

electrolyte used is a water-free electrolyte, therefore no formation of oxides was observed.

Keywords: Nickel-Titanium, Shape Memory Alloys (SMAs); drilling, GRA, electrochemical, RSM, AHP

Nomenclatures:

DH, d: Diameter of hole

DT: Diameter of tool

D: Maximum diameter

MRR: Material removal rate

SV: Servo voltage

WLT: White layer thickness

WL: White layer

SI: Surface integrity

NiTi: Nickel-titanium

MS: Machined surface

DE: Discharge energy

TWR: Tool wear rate

NCM: NCM

SMAs: Shape memory alloys

TW: Tool wear

SME: Shape memory effect

MS: Machined surface

RSM: Response surface methodology

AHP: Analytic hierarchy process

GRA: Grey relational analysis

TR: Tool rotation

DoE: Design of experiments

GRC: Grey relational coefficient

1 Introduction

The NiTi SMAs or Nitinol became popular because of their many applications in various fields like

telecommunication, automotive industries, medical and aerospace, etc. [1] including civil industry [2]. The NiTi

SMAs have broad application in electromechanical system (MEMS) devices [3], a thermomechanical system for

actuators and sensors [4], stent delivery [5], neurology implants [6,7], self-expandable stents [8], orthopedics and

cardiology [9], drug delivery systems and implantable devices [10], and eyeglass frames [11] including

compatibility for MRI [12]. The NiTi has unique properties like corrosion resistance [13] and shape memory

effect including high ductility and strong adhesion property [14] which provide difficulty for conventional

machining. Furthermore, the NiTi SMAs have poor thermal conductivity leading to the concentration of heat on

the tooltip exhibiting higher toughness, providing higher TW and extreme strain hardening promotes difficulty in

conventional machining [15] and [16]. Therefore, unconventional machining processes are preferable for the

machining of SMAs [17].

The drilling of micro-holes in NiTi alloy can be done by EDM, ECM, and ECAM. The drilling of a 5

mm blind square hole in NiTi alloy has been done with the help of the EDM process with a copper tool. The

variable parameters were considered as gap current, POFF, gap current, and the electrical conductivity of the

workpiece and PON. The author found that the MRR was inversely proportional to gap voltage i.e. higher MRR

was achieved at lower gap voltage. Also, the TWR increased with an increase in gap current [18]. Abidi et al. also

performed drilling of micro-holes in NiTi SMA by micro-electrical discharge machining. The various parameters

were voltage, capacitance, and tool electrode material whereas the performance parameters were TWR, overcut,

circularity, MRR, taper angle, and SR. It has been concluded that the quality of micro-holes was good at lower

voltage whereas the overcut was mostly affected by the material of the electrode [19]. Also, the performance

parameters like SR, taper angle, and overcut were strongly affected by the electrode material followed by voltage

during drilling of NiTi alloy by micro-electrical discharge machining [20]. Furthermore, the drilling of NiTi SMA

by micro-EDM described the migration of tool electrodes to the MS including the development of NiTiO3 and

TiO3 which might act as protecting layers for NiTi. A stable oxide layer has also been generated on the MS which

may well provide the utilization of conventional TiO2 coating for biomedical implants [21].

The previous works of literature mainly deal the machining like cutting, grooving, etc. by NCM process

including drilling by EDM process. In EDM, the metallurgical damage to the MS due to the drawbacks of using a

liquid dielectric medium for sparking provided a lesser surface quality finish while maintaining a reasonable

machining rate. Furthermore, in ECM, several limitations like cavitation, spark damage, and electrolyte boiling

has been reported. The MRR can be as much as five and forty times greater than respectively EDM and ECM

when thermal electrical discharges in the machining gap aid the ECM process and this process has been termed

electrochemical arc machining (ECAM) [22]. Furthermore, the supervision of radial overcut and delamination are

tiring assignments in ECM [23]. A hybrid NCM process like ECAM can be utilized for machining NiTi SMAs

because more work should be done on the ECAM.

The micro-holes have been drilled on electrically conductive material by utilizing ECAM or SAEM

(Sparc-assisted electrochemical machining). Using the SAEM process, drilling and electrochemically finishing a

micro-hole can be done with the same machining equipment with the same parameters [24,25]. For

electrochemical micromachining of NiTi alloy, 20 vol. % of ethanol electrolyte solutions are preferable. The

electrolyte solution of 40 g/L has been prepared by mixing Ethanol with Ethylene glycol at different

concentrations with the further addition of NaCl to improve surface quality. Ethanol is capable of dissolving TiCl4

into the workpiece and can diminish the development of oxide films [26].

For the current research work, electrochemical arc machining (ECAM) has been utilized to drill micro

blind holes on Ni55.7Ti SMA because no study has been published exploring the machinability of NiTi SMAs by

ECAM to the author’s knowledge. The process parameters such as tool rotation, voltage, and electrolyte

concentration including performance parameters such as MRR, OC, delamination, and SR have been considered

for drilling micro blind holes after reviewing past works of literature. Multiple objective optimization techniques,

GRA-based AHP, and further, the GRG optimized by RSM have been implemented in the current study. That

technique was employed to attain the optimum settings for supporting the applications of NiTi SMAs. Most of the

studies have distributed equal weight to the variable parameters during optimization but few studies based on

conventional machining like turning of Ti6Al4V alloy [27] utilized different weights according to the relative

importance of variables. As, the AHP technique promised improved outcomes compared to equal weights,

therefore, in this non-conventional machining study, GRA-based AHP and RSM provided truthful tactics to

enhance the performance parameters.

2 Research motivation

The center of attention of the current research is multiple responses for optimization of the performance

parameters during drilling of Ni55.7Ti SMA. The performance parameters were enhanced by utilizing RSM

together with GRA-based AHP. The utilized AHP showed the capability of productivity enhancement

(maximizing MRR and minimizing TWR, OC, and delamination). The input parameters (electrolyte

concentration, voltage, and tool rotation on TW) affect the productivity level of the drilled hole, therefore, the

insertion of MRR in the factorial analysis is essential to integrate the productivity level. Otherwise, the necessity

for the enhancement in productivity of drilled holes can not be noticed due to the outcome of varying MRR with

the varying input parameters.

3 Electrochemical arc machining (ECAM)

An upgraded hybrid non-conventional machining process has been discovered by the further development of

ECDM. ECDM is developed by combining ECM and EDM. In the ECM process, the workpiece acts as an anode

and the tool electrode acts as a cathode and also an electrolyte has been used as a conductive medium to prepare

electrolyte cells together with the tool electrode and workpiece. In the EDM process, the material is removed

utilizing electrical sparks (discharges) when a rapidly recurring current is utilized between the workpiece and tool

electrode which are separated by dielectric fluid. In ECDM, both cathode and anode, where the tool electrode has

been connected to the cathode and inert material used as an anode, have been immersed into an electrolyte to

develop an electrolyte cell-like ECM.

The connections of cathode and anode differentiate ECDM and ECAM processes. The anode acts as a non-

machining electrode in ECDM and if this anode is removed for further connection with the workpiece, then

machining of electrically conductive materials is achievable and its terms as ECAM process. The discharges

developed between electrolytes and tools in ECDM but in ECAM discharges developed between workpiece and

tool. ECAM is an amendment of EDM because the electrolyte is used instead of a dielectric medium. As it has

been known that EDM is used to machine micro holes, but there are limited works of literature where machining

of micro-holes has been done on electrically conductive materials by using ECAM. ECAM can be employed by

constant or pulse voltage. The machining of metallic materials like hole drilling, wire cutting, turning, and

smoothing surfaces can be done by ECAM [28].

Fig. 1 Experimental setup of micro-drilling with ECAM

In the ECAM process, the electrolyte has been filled between the workpiece (anode) and tool electrode to

form an electrolyte cell where the workpiece (anode) has been almost covered with electrolyte and is separated

from the tool electrode as shown in Fig.1. Electrolysis has been occurred after applying a voltage across the

electrolyte cell and due to this, hydrogen gas is produced across the cathode, and oxygen gas is formed across the

anode. More gas is formed due to an increase in voltage. It has been known that the shape of the tool electrode is

smaller than the workpiece; therefore, gas covers the tool electrode at a faster rate than the workpiece. Due to the

development of the gas layer, resistance has been developed between the boundary of the electrolyte and the tool

electrode. After covering the tool electrode with gas with adequate voltage, gas has been ionized because of the

Townsend mechanism [29] and by this, an ohmnic region developed which represents ohmnic behavior limited to

a voltage (Ulim). When more Ulim has been applied, the limiting current region developed according to the

development of united gas bubbles on the electrode surfaces and this limiting current region ends after reaching

the critical voltage (Ucrit). If the applied voltage increases to Ucrit, a transition region has been formed with

compact gas films around the electrode. It has been stated that electrochemical discharge takes place only if the

potential drop across the gas layer is higher than a critical value. Therefore, by increasing the applied voltage

higher than Ucrit, an arc region has been developed where the spark takes place.

The setup of ECDM has been developed in the Department of Production & Industrial Engineering, National

Institute of Technology, Jamshedpur by the research scholar Dr. Pravin Pawar under the guidance of Prof.

Amaresh Kumar. This setup of ECDM has been modified to ECAM.

4 Experiment details

A rectangular Ni55.7Ti SMA workpiece of 150mm×120mm×1.5mm was considered for machining by

ECAM. The mechanical properties and chemical compositions of the same material have been described in Table

1 and Table 2 respectively. The three levels of parameters (electrolyte concentration, tool rotation, and voltage)

were chosen based on previous studies and the same is presented in Table 3.

Table 1. The chemical compositions of Ni55.7Ti SMA

Element Ti Ni Co Cu Cr Fe Nb C H O N

Wt.% Remainder 55.7 0.005 0.005 0.003 0.015 0.005 0.04 <0.001 0.036 0.001

Table 2. The mechanical properties of Ni55.7Ti SMA

Tensile Strength (MPa) Yield Strength (MPa) Elongation (%) Bend Test (α>130) 645 190 18 qualified

Table 3: The machining variables with levels

Factors Levels Values

Electrolyte concentration (v/v %) 3 0, 10, 20

Tool rotation (rpm) 3 0, 50, 100

Voltage (V) 3 60, 70, 80

4.1 Machining process

This work consists of four performance parameters overcut, TWR, delamination factor, and MRR of the

workpiece material. A molybdenum tool electrode of 3mm diameter has been utilized as a cathode. The anodic

workpiece and the tip of the tool electrode have been maintained at a small distance and this distance is filled by

the ethylene glycol electrolyte solution where a thin layer of electrolyte slightly covered the surface of the

workpiece. The ethylene glycol has been mixed with NaCl to prepare a 1M solution and the same has been

considered as zero concentration of electrolyte. The electrolyte concentration of 10 v/v % and 20 v/v % has been

prepared by further addition of ethanol in that 1 M solution.

The MRR has been calculated by using the following equation:

MRR �mgmin� =Weight of workpiece before machining−Weight of workpiece after machiningMachining time (1)

The TWR has been calculated by using the following equation:

TWR �mgmin� =Weight of tool before machining−Weight of tool after machiningMachining time (2)

The subtraction of the diameter of a tool with the diameter of drilled micro-hole provided the Overcut

(OC) of the drilled micro-hole as given in Eqs (3).

OC = DH-DT (3)

An essential parameter like delamination factor (Fd) is needed to scrutinize the condition of the drilled

hole and that can be evaluated as follows [30]:

Fd =D𝑑𝑑 (4)

Fig. 2 (a) Delamination of hole [23,31], hole diameter and maximum diameter for (b) exp. run 1 (electrolyte

concentration as 0, tool rotation as 0 and voltage as 60V), (c) exp. run 4 (electrolyte concentration as 0, tool

rotation as 50 and voltage as 60V) and (d) exp. run 12 (electrolyte concentration as 10 v/v %, tool rotation as 0

and voltage as 60V)

The structural integrity and quality of machining can be altered due to the existence of a delamination

zone (Fig. 2a) and that delamination is usually detected during drilling. The enhancement in the quality of drilled

micro-hole can be traced by observing the value of the delamination factor as unity [31]. The delamination and

overcut were measured by optical microscope. The diameter of the delamination zone and the micro-hole were

evaluated by ImageJ software (Fig. 2b–d). Figure 2 (b), 2 (c) and 2 (d) shows hole diameter as d and maximum

diameter as D for an experiment runs 1, 4, and 12, and similarly, the diameters for all experiment runs have been

calculated.

4.2 Design of experiments

The machining experiments were executed by utilizing a multilevel factorial design as shown in Table 4.

The main effect plots were used to examine individual performance parameters. AHP weight method has been

used to derive the grey relational function. Furthermore, the maximum GRG predicted the optimized variable

parameters. Again, a regression model was established for GRG by optimizing the GRG with the help of RSM.

Finally, the authentification of the model has been completed by analyzing the optimized condition.

Table 4: DoE using multilevel factorial design

Run

Electrolyte

concentration

(v/v%)

Tool

rotation

(rpm)

Voltage

(V)

MRR

(mg/min)

Tool wear rate

(mg/min) OC Delamination

1 0 0 60 30.15 0.1 0.0855 1.731

2 0 0 70 50 0.03 0.498 1.442

3 0 0 80 70.24 0.12 0.658 1.285

4 0 50 60 40.33 0 0.411 1.958

5 0 50 70 60 0.25 0.371 1.509

6 0 50 80 80.46 0 0.436 1.165

7 0 100 60 41 0.1133 0.446 1.651

8 0 100 70 61.86 0.1233 0.429 1.163

9 0 100 80 85.33 0.24 0.474 1.272

10 10 0 60 40.01 0.00136 0.146 1.743

11 10 0 70 60.35 0.003 0.499 1.191

12 10 0 80 80.87 0.0067 0.117 1.596

13 10 50 60 52.62 0.105 0.54 1.646

14 10 50 70 73 0.467 0.61 1.309

15 10 50 80 95.38 0.536 0.418 1.344

16 10 100 60 50.5 0.1333 0.418 1.346

17 10 100 70 61.33 0.3 0.511 1.188

18 10 100 80 71.33 0.5 0.529 1.416

19 20 0 60 60 0 0.618 1.234

20 20 0 70 81.96 0.0025 0.35 1.627

21 20 0 80 101.19 0.006 0.111 1.16

22 20 50 60 71.41 0.0133 0.644 1.195

23 20 50 70 91 0.014 0.566 1.266

24 20 50 80 99.47 0.01533 0.409 1.821

25 20 100 60 51.61 0.36 0.547 1.299

26 20 100 70 79.23 0.57 0.598 1.272

27 20 100 80 93.33 0.933 0.455 1.187

4.3 Experimental data analysis

The effect of micro-drilling conditions (electrolyte concentration, tool rotation, and voltage) on the

performance parameters (OC, TWR, delamination, and MRR) was analyzed by the obtained data of response

parameters. The main effect plot revealed the tendency of each performance parameter in Fig. 3 (a–d), where it

can be spotted that MRR increases with the rise in voltage and electrolyte concentration whereas MRR first

increases and then decreases in the case of tool rotation. The enhancement in MRR with voltage is due to an

increase in arc generation. Similar behavior of voltage on MRR was reported by Magabe et al. [32] during

WEDM of Ni55.8Ti and by Antil et al. [31] during ECDM of hybrid polymer matrix composites. Furthermore, the

TWR and OC were increased with the increase of tool rotation but delamination decreased. Again, the growth of

voltage provided enhancement in TWR whereas OC first increased and then decreased. The overcut surged with a

surge in the concentration of electrolytic but at the intermediate level, decrement in over cut spotted [31].

Therefore, from figure 3, it can be concluded that higher MRR can be achieved by applying higher electrolyte

concentration and higher voltage. Furthermore, lower TWR can be achieved by applying lower voltage and tool

rotation whereas lower OC and delamination can be achieved by applying lower tool rotation and higher tool

rotation respectively.

Fig. 3 Main effect plots of performance parameters (a) MRR, (b) TWR, (c) OC, and (d) Delamination

The top response for MRR was attained at higher voltage including at higher electrolyte concentration

whereas, for TWR and delamination, the best responses were attained at higher electrolyte concentration, lower

tool rotation, and lower voltage. Furthermore, the best value of OC was attained at a lower value of all input

parameters. The higher voltage provided higher MRR, TWR, and OC. The highest and lowest responses for all the

experimental runs are shown in Table 5. It has been clear that decision-making utilizing multi-objective

optimization is required for these responses because the best responses have been constructed by dissimilar

settings.

Table 5 The highest and lowest responses attained from micro-drilling settings

Responses

Micro-drilling settings and their levels

Attained

value

Electrolyte

concentration

(v/v%)

Tool

rotation

(rpm)

Voltage

(V)

MRR (mg/min) Highest 101.19 20 0 80

Lowest 30.15 0 0 60

Tool wear rate

(mg/min)

Highest 0 20 0 60

Lowest 0.933 20 100 80

OC Highest 0.0855 0 0 60

Lowest 0.658 0 0 80

Delamination Highest 1.16 20 0 60

Lowest 1.958 0 50 60

4.4 GRA for multi-objective optimization

It is very difficult to get an enhancement of a specific response without allaying the other in NCM. This

research intends to set up the optimal variables corresponding to GRA. The normalization of each response of

performance parameters of all experimental runs has been completed by using Eqs. (5) and (6), respectively

within the 0-1 range and also, the same equations provided the higher, the better, and smaller the better feature

[33]. The methodology of multi-objective optimization for the performance parameters during drilling of NiTi

alloy has been similar to the earlier research [27,34]. The optimization of performance parameters utilizing GRA

together with AHP based on multilevel factorial design converts a multiple response challenge into a single

function [35]. The several procedures required for the accomplishment of GRA are stated as follows:

4.4.1 Data preprocessing

The first step of GRA is Normalization which is done by transforming each response of performance

parameters of all experimental runs to a common scale (0–1). The specific objective like minimization of TWR,

overcut, delamination, and maximization of MRR was maintained for the normalization of responses. Hence, the

output value of all tests for four performance parameters (TWR, MRR, overcut, and delamination) were

normalized for the target value revealed in Table 6. The values for TWR, overcut, and delamination are evaluated

as “smaller the better” using Eq. 5, but for MRR, the motive was “larger the better” and the arrangement is

normalized using Eq. 6 and which is revealed in Table 6.

For the larger-the-better feature 𝑥𝑥𝑡𝑡∗(𝑘𝑘) = 𝑥𝑥𝑡𝑡0(𝑘𝑘)−𝑚𝑚𝑚𝑚𝑛𝑛.𝑥𝑥𝑡𝑡0(𝑘𝑘)𝑚𝑚𝑚𝑚𝑥𝑥.𝑥𝑥𝑡𝑡0(𝑘𝑘)−𝑚𝑚𝑚𝑚𝑛𝑛.𝑥𝑥𝑡𝑡0(𝑘𝑘)

(5)

Where 𝑥𝑥𝑡𝑡°(𝑘𝑘) is the existing pattern, 𝑥𝑥𝑡𝑡∗(𝑘𝑘) the pattern after the data pre-processing, 𝑚𝑚𝑚𝑚𝑥𝑥 𝑥𝑥𝑡𝑡°(𝑘𝑘) the biggest value

of 𝑥𝑥𝑡𝑡°(𝑘𝑘) and 𝑚𝑚𝑚𝑚𝑚𝑚 𝑥𝑥𝑡𝑡°(𝑘𝑘) imply the lowest value of 𝑥𝑥𝑡𝑡°(𝑘𝑘) .

For lower the better feature 𝑥𝑥𝑡𝑡∗(𝑘𝑘) = 𝑚𝑚𝑚𝑚𝑥𝑥 𝑥𝑥0(𝑘𝑘)−𝑥𝑥0(𝑘𝑘)𝑚𝑚𝑚𝑚𝑥𝑥 𝑥𝑥𝑡𝑡0(𝑘𝑘)−𝑚𝑚𝑚𝑚𝑛𝑛 𝑥𝑥𝑡𝑡0(𝑘𝑘)

(6)

Table 6 Normalizing sequence and deviation sequence

Normalizing the sequence of data preprocessing Deviation sequence

MRR TWR OC Delamination MRR TWR OC Delamination

0 0.8928189 1 0.2844612 1 0.1071811 0 0.7155388

0.27942 0.9678457 0.279476 0.6466165 0.72058 0.0321543 0.720524 0.3533835

0.56433 0.8713826 0 0.8433584 0.43567 0.1286174 1 0.1566416

0.1432995 1 0.431441 0 0.8567005 0 0.568559 1

0.4201858 0.7320472 0.50131 0.5626566 0.5798142 0.2679528 0.49869 0.4373434

0.7081926 1 0.3877729 0.9937343 0.2918074 0 0.6122271 0.0062657

0.1527309 0.8785638 0.3703057 0.3847118 0.8472691 0.1214362 0.6296943 0.6152882

0.4463682 0.8678457 0.4 0.9962406 0.5536318 0.1321543 0.6 0.0037594

0.7767455 0.7427653 0.3213974 0.8596491 0.2232545 0.2572347 0.6786026 0.1403509

0.138795 0.9985423 0.8943231 0.2694236 0.861205 0.0014577 0.1056769 0.7305764

0.4251126 0.9967846 0.2777293 0.9611529 0.5748874 0.0032154 0.7222707 0.0388471

0.713964 0.9928189 0.9449782 0.4536341 0.286036 0.0071811 0.0550218 0.5463659

0.3163007 0.8874598 0.2061135 0.3909774 0.6836993 0.1125402 0.7938865 0.6090226

0.6031813 0.4994641 0.0838428 0.8132832 0.3968187 0.5005359 0.9161572 0.1867168

0.9182151 0.4255091 0.419214 0.7694236 0.0817849 0.5744909 0.580786 0.2305764

0.2864583 0.8571275 0.419214 0.7669173 0.7135417 0.1428725 0.580786 0.2330827

0.4389077 0.6784566 0.2567686 0.9649123 0.5610923 0.3215434 0.7432314 0.0350877

0.5796734 0.4640943 0.2253275 0.679198 0.4203266 0.5359057 0.7746725 0.320802

0.4201858 1 0.069869 0.9072682 0.5798142 0 0.930131 0.0927318

0.7293074 0.9973205 0.5379913 0.414787 0.2706926 0.0026795 0.4620087 0.585213

1 0.9935691 0.9554585 1 0 0.0064309 0.0445415 0

0.5807995 0.9857449 0.0244541 0.9561404 0.4192005 0.0142551 0.9755459 0.0438596

0.8565597 0.9849946 0.1606987 0.8671679 0.1434403 0.0150054 0.8393013 0.1328321

0.9757883 0.9835691 0.4349345 0.1716792 0.0242117 0.0164309 0.5650655 0.8283208

0.3020833 0.6141479 0.1938865 0.8258145 0.6979167 0.3858521 0.8061135 0.1741855

0.6908784 0.3890675 0.1048035 0.8596491 0.3091216 0.6109325 0.8951965 0.1403509

0.8893581 0 0.3545852 0.9661654 0.1106419 1 0.6454148 0.0338346

4.4.2 Computation of GRC

The calculation of GRC has been completed by utilizing the normalized values with the help of Eq. 7.

The ideal value of the response is related to the experimental values by GRC.

Following pre-processing of the data, the correlation between the ideal and real normalized test results is

determined to be denoted by a GRC or €𝑡𝑡(𝑘𝑘).

The GRC can therefore be denoted as,

€𝑡𝑡(𝑘𝑘) =∆𝑚𝑚𝑚𝑚𝑚𝑚−€∆𝑚𝑚𝑚𝑚𝑚𝑚∆0𝑚𝑚(𝑘𝑘)−€∆𝑚𝑚𝑚𝑚𝑚𝑚 (7)

The highest and lowest value of the deviation sequence is Δmax and Δmin respectively. The deviation sequence, ∆0𝑚𝑚(𝑘𝑘) in the above equation can be assessed by Eq. 8. ∆0𝑚𝑚(𝑘𝑘) =) = ⃦ 𝑥𝑥0(𝑘𝑘) − 𝑥𝑥𝑚𝑚(𝑘𝑘) ⃦ (8) ∆𝑚𝑚𝑚𝑚𝑥𝑥= 𝑚𝑚𝑚𝑚𝑥𝑥∀𝑗𝑗𝑗𝑗𝑚𝑚𝑚𝑚𝑚𝑚𝑥𝑥∀𝑘𝑘 ⃦𝑥𝑥0(𝑘𝑘) − 𝑥𝑥𝑚𝑚(𝑘𝑘) ∣ (9)

∆𝑚𝑚𝑚𝑚𝑛𝑛= 𝑚𝑚𝑚𝑚𝑥𝑥∀𝑗𝑗𝑗𝑗𝑚𝑚𝑚𝑚𝑚𝑚𝑥𝑥∀𝑘𝑘 ⃦𝑥𝑥0(𝑘𝑘) − 𝑥𝑥𝑚𝑚(𝑘𝑘) ⃦ (10)

Where the reference and comparability sequence has been denoted by 𝑥𝑥0(𝑘𝑘) and 𝑥𝑥𝑚𝑚(𝑘𝑘) respectively. In the current

research, the value of € (distinguishing coefficient) is considered 0.5, which can range between 0–1. The values of

GRC assessed for the four performance parameters are revealed in Table 7.

Table 7 GRC and GRG calculated from the responses

Exp.

run

Electrolyte

concentration

(v/v%)

Tool

rotation

(rpm)

Voltage

(V)

GRC

GRG

MRR TWR OC Delamination

1 0 0 60 0.3333333 0.8234775 1 0.4113402 0.13905645

2 0 0 70 0.4096413 0.939577 0.4096601 0.5859031 0.145871509

3 0 0 80 0.5343764 0.7953964 0.3333333 0.7614504 0.151707492

4 0 50 60 0.3685412 1 0.4679199 0.3333333 0.143418326

5 0 50 70 0.4630426 0.6510816 0.5006559 0.5334225 0.132210945

6 0 50 80 0.6314667 1 0.4495485 0.9876238 0.186403173

7 0 100 60 0.3711211 0.8045878 0.4425976 0.4483146 0.129292807

8 0 100 70 0.4745491 0.7909461 0.4545455 0.9925373 0.14909019

9 0 100 80 0.6913196 0.6602972 0.4242312 0.7808219 0.164862263

10 10 0 60 0.3673216 0.9970931 0.8255227 0.4063136 0.152791987

11 10 0 70 0.465165 0.9936102 0.4090747 0.927907 0.161714266

12 10 0 80 0.6361032 0.9858411 0.9008655 0.4778443 0.190955909

13 10 50 60 0.4224046 0.816273 0.3864327 0.4508475 0.135766625

14 10 50 70 0.5575263 0.4997322 0.3530681 0.7281022 0.131864074

15 10 50 80 0.8594241 0.4653367 0.4626263 0.6843911 0.1721494

16 10 100 60 0.4120172 0.7777593 0.4626263 0.6820513 0.136054155

17 10 100 70 0.4712125 0.6086106 0.4021777 0.9344262 0.132416148

18 10 100 80 0.5432854 0.4826694 0.3922576 0.6091603 0.128141953

19 20 0 60 0.4630426 1 0.3496183 0.8435518 0.15942715

20 20 0 70 0.6487671 0.9946695 0.5197458 0.460739 0.18368284

21 20 0 80 1 0.9873016 0.9182037 1 0.246978185

22 20 50 60 0.543951 0.9722801 0.3388577 0.9193548 0.168844908

23 20 50 70 0.7770729 0.9708637 0.373329 0.790099 0.199511294

24 20 50 80 0.9538131 0.9681838 0.4694547 0.3764151 0.220548357

25 20 100 60 0.4173913 0.5644283 0.3828151 0.7416357 0.118884262

26 20 100 70 0.6179541 0.4500724 0.3583725 0.7808219 0.136923922

27 20 100 80 0.8188105 0.3333333 0.4365231 0.9366197 0.158778283

4.4.3 Calculation of GRG

The assigned weight value of each response has been utilized during the conversion of the multiple GRC

into a combined factor by GRG. The weighted GRG was evaluated by Eq. 11. Furthermore, the weight

assignment for four responses was developed by the AHP method.

(𝛾𝛾𝑚𝑚) = ∑ 𝜔𝜔𝑘𝑘𝑛𝑛𝑘𝑘=1 €𝑡𝑡(𝑘𝑘) (11) ∑ 𝜔𝜔𝑘𝑘𝑛𝑛𝑘𝑘=1 = 1 (12)

4.5 Weight factors using the AHP

The several steps required for assigning the weights to the responses by AHP are represented below.

a) The weight of each response is evaluated by the decision-maker utilizing the AHP method. The

establishment of a pairwise matrix (Am×m) [27] with m attributes is completed in the first step as revealed

in Eq. 13, where the comparative rank of each attribute concerning the target is established by using

Saaty’s 9-point scale (Table 8). According to the relative importance, the respective standing of each

attribute relevant to the goal is determined and then arranged in the pairwise matrix as revealed in Table

9. During the determination of the respective standing, the values of attributes in the row are compared

with the values of attributes in the column. If an attribute is compared with the other, then a reciprocal

value of the corresponding attribute is allotted (A12 = 1/A21) and if compared with itself (Aij = 1 for i=j),

then a value of 1 is allotted.

Table 8 Nine-point Saaty’s scale

Scale Definition Explanation

1 Equally important Indifferent

3 Weakly important Slightly better

5 Strongly important Better

7 Very strongly important Much better

9 Extremely important Much better

2,4,6,8 Intermediate value When compromise needed

𝐴𝐴𝑚𝑚×𝑚𝑚 =

𝐴𝐴1𝐴𝐴2𝐴𝐴3−𝐴𝐴𝑗𝑗−𝐴𝐴𝑚𝑚 ⎣⎢⎢⎢⎢⎢⎢ 1 𝐴𝐴12 𝐴𝐴13𝐴𝐴21 1 𝐴𝐴23𝐴𝐴31 𝐴𝐴32 1

−−− 𝐴𝐴1𝑗𝑗 − 𝐴𝐴1𝑚𝑚𝐴𝐴2𝑗𝑗 − 𝐴𝐴2𝑚𝑚𝐴𝐴3𝑗𝑗 − 𝐴𝐴3𝑚𝑚− − − − − − −𝐴𝐴𝑚𝑚 𝐴𝐴𝑚𝑚2 𝐴𝐴𝑚𝑚3− − −𝐴𝐴𝑚𝑚1 𝐴𝐴𝑚𝑚2 𝐴𝐴𝑚𝑚3 −−− 1 − 𝐴𝐴𝑚𝑚𝑚𝑚− − −𝐴𝐴𝑚𝑚𝑗𝑗 − 1 ⎦⎥⎥⎥⎥⎥⎥ (13)

Table 9 The Pairwise matrix comparing attributes

MRR TWR OC Delamination

MRR 1 3 5 7

TWR 1/3 1 5 7

OC 1/5 1/5 1 3

Delamination 1/7 1/7 1/3 1

The enhancement in productivity, as well as quality of drilled hole of NiTi alloy without

deterioration of tool, was the objective of this research because the immigration of elements from the tool

to the drilled hole may affect the quality of drilled hole. The expansion of productivity is important

because NiTi alloys are difficult to machine. Hence, MRR was allocated a higher weight followed by

TWR, OC, and delamination. Table 9 displays the ranking of these attributes in a pairwise matrix.

b) The evaluation of the normalized weight of the attributes is completed by using the geometric mean

method. Table 10 displays the geometric mean and normalized weight evaluated from the pairwise

matrix by Eqs. 14 and 15.

GM=�∏ 𝑚𝑚𝑚𝑚𝑗𝑗𝑚𝑚𝑗𝑗=1 �1/𝑚𝑚 (14) 𝑤𝑤𝑗𝑗 = 𝐺𝐺𝐺𝐺𝑚𝑚/∑ 𝐺𝐺𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚=1 (15)

c) The consistency index (CI) is calculated by utilizing Eq. 16 for the pairwise matrix. The value of λmax

was evaluated by the addition of the relative score column-wise, and then multiplication with

corresponding normalized weights of the attributes and summing the resultants. In this study, the value of

λmax emerged to be 4.22780 and CI equal to 0.07593. 𝐶𝐶𝐶𝐶 =λ𝑚𝑚𝑚𝑚𝑚𝑚−𝑚𝑚𝑚𝑚−1 (16)

d) At last, the consistency ratio (CR) of the matrix was evaluated by Eq. 17. Table. 11 was utilized to select

the random index (RI) for four attributes which are 0.89 for N = 4. Thus, the CR value in the present

research was estimated to be 0.085319. The consistency of the judgment is based on the value of CR

attained from the pairwise matrix and a value of 0.1 or less is usually acceptable testifying a good

investigation being made about the case at hand.

𝐶𝐶𝐶𝐶 =𝐶𝐶𝐶𝐶𝑅𝑅𝐶𝐶 (17)

Table 10 The geometric mean and normalized weights of the attributes

Responses Geometric mean Normalized weights (Wj)

MRR 3.201086 0.540268

TWR 1.848148 0.311924

OC 0.588566 0.099336

Delamination 0.287191 0.048471

Table 11 Attributes and their random consistency index (RI) [36]

N 1 2 3 4 5 6 7 8 9 10

RI 0 0 0.52 0.89 1.11 1.25 1.35 1.4 1.45 1.49

4.5.1 GRG result

The normalized weights (Table 10) utilizing AHP were used to evaluate grey relational function (Eq. 18).

The GRG of each experimental run was discovered by utilizing these weights which are revealed in Table 12

where the best run was found to be experiment run #21.

GRG= ¼ [0.540268 GRCMRR + 0.311924 GRCTWR +0.099336 GRCOC+0.048471 GRCDelamination] (18)

Table 12 Grey Relational Grade

Experiment

run GRG Rank

1 0.13905645 18

2 0.145871509 16

3 0.151707492 14

4 0.143418326 17

5 0.132210945 23

6 0.186403173 5

7 0.129292807 25

8 0.14909019 15

9 0.164862263 9

10 0.152791987 13

11 0.161714266 10

12 0.190955909 4

13 0.135766625 21

14 0.131864074 24

15 0.1721494 7

16 0.136054155 20

17 0.132416148 22

18 0.128141953 26

19 0.15942715 11

20 0.18368284 6

21 0.246978185 1

22 0.168844908 8

23 0.199511294 3

24 0.220548357 2

25 0.118884262 27

26 0.136923922 19

27 0.158778283 12

5 Results and discussions

The appropriate value of GRG attained for all the drilling settings was detected for experiment #21

corresponding to parameters (electrolyte concentration = 20, TR = 0 rpm, and V = 80) followed by experiment

#24 (20 v/v %, 50 rpm and 80V) and experiment #23 (20 v/v %, 50 rpm and 70V. Fig. 4 revealed the main effects

plot for GRG attained from the response table of GRG.

Fig. 4 shows the main effects plot of GRG

Fig. 4 Main effects plot for GRG

5.1 Regression model for GRG function

A full quadratic model of RSM was utilized to establish multiple objective functions for GRG, which is

completely suitable for the GRG attained from the experimental outcomes. The model equation is revealed in Eq.

(19). 𝐺𝐺𝐶𝐶𝐺𝐺 = 0.00660 − 0.00501 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 + 0.000428 𝑇𝑇𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 +

0.001139 𝑉𝑉𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝑙𝑙𝐸𝐸 + 0.000140 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 × 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 −0.000004 𝑇𝑇𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 × 𝑇𝑇𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 − 0.000030 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 × 𝑇𝑇𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 +

0.000073 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚𝐸𝐸𝑚𝑚 × 𝑉𝑉𝐸𝐸𝐸𝐸𝐸𝐸𝑚𝑚𝑙𝑙𝐸𝐸 ……... (19)

The suitability of the established model is only inadequate for drilling Ni55.7Ti SMA; using the

molybdenum tool, within the settings (60V ≤ Voltage ≤ 80V), (50 rpm ≤ tool rotation ≤ 100 rpm), and (0 v/v % ≤ electrolyte concentration ≤ 20 v/v %).

The surface and contour plots of GRG are revealed in Fig. 5. The interaction of the drilling settings for

the attained value of GRG is revealed by surface plots. The attained value of GRG is maximum at higher

electrolyte concentration and higher voltage.

Figure 6 displays the calculation of the GRG attained from experiments and evaluated from the

regression model. The maximum value of GRG for experiment #21 is because of the higher electrolyte

concentration at a higher voltage that helped to improve MRR.

Fig. 5 Surface and contour plots for GRG

Fig. 6 Calculation of the GRG attained from experiments and evaluated from the regression model

From figure 7, it can be concluded that the GRG has been mostly affected by voltage. The combined

effect of electrolyte concentration and tool rotation followed by electrolyte concentration and voltage can also be

observed.

Fig. 7 Pareto chart for GRG

5.2 ANOVA for GRG

The MINITAB® software was utilized to perform statistical analysis, where ANOVA was conducted at a

95% confidence level to elect the variable parameters which significantly influence the performance parameters to

study the effects of each variable on the responses. The ANOVA results have been shown in Table 13. A

quadratic model with the precision of R2 = 80.78% signaled the best fit. Furthermore, the ANOVA table signaled

that the voltage is the utmost significant factor with an impact of 26.27% followed by tool rotation and electrolyte

concentration on the performance parameters and GRG.

Table 13 ANOVA results for GRG

Source DF Adj SS Adj MS F-Value Contribution

Model 7 0.019398 0.002771 11.40 80.77%

Linear 3 0.014113 0.004704 19.36 58.76%

Electrolyte concentration 1 0.003519 0.003519 14.48 14.65%

Tool rotation 1 0.004286 0.004286 17.64 17.84%

Voltage 1 0.006309 0.006309 25.96 26.27%

Square 2 0.001877 0.000938 3.86 7.81%

Electrolyte concentration*Electrolyte

concentration

1 0.001174 0.001174 4.83 4.88%

Tool rotation*Tool rotation 1 0.000703 0.000703 2.89 2.92%

2-Way Interaction 2 0.003408 0.001704 7.01 14.19%

Electrolyte concentration*Tool rotation 1 0.002764 0.002764 11.37 11.5%

Electrolyte concentration*Voltage 1 0.000644 0.000644 2.65 2.68%

Error 19 0.004617 0.000243 - 19.22%

Total 26 0.024015 - - 100%

5.3 Optimization of the GRG

Table 14 revealed the optimal drilling conditions which were achieved by response surface optimization by

developing a model shown in Eq. 19. The optimized value of GRG was attained at the machine settings of

electrolyte concentration 20 v/v %, tool rotation 0 rpm, and voltage 80V with composite desirability of 0.868340

which is revealed in Fig. 8.

Table 14 Multiple Response Prediction

Variable Setting

Electrolyte concentration 20

Tool rotation 0

Voltage 80

Fig. 8 Responses optimized at maximum GRG

5.4 Authentication of optimum parameter

The input parameters were first optimized by GRA with AHP where the best-optimized run was found to

be experiment run #21, refer to Table 12. The parametric settings for the same run were 20 v/v % of electrolyte

concentration, 0 rpm of tool rotation, and 80V of voltage. Further, the GRA was also optimized by using RSM

which again found the experiment run #21 as optimized parametric settings. Therefore, it can be concluded that

the optimized parametric settings for the optimization of MRR, TWR, OC, and delamination should be 20 v/v %

of electrolyte concentration, 0 rpm of tool rotation, and 80V of voltage. The optimized value of MRR, TWR, OC,

and delamination was measured as 101.19 mg/min, 0.006 mg/min, 0.111, and 1.16 respectively for drilling of

Ni55.7Ti SMA by electrochemical arc machining process.

6 Surface analysis of drilled hole at optimum parameter

The effect of optimum parameters on micro-hole formed during micro-ECAM can be observed from the

SEM micrographs (figure 9). The attained SEM images are revealed in Figs. 9-10 which illustrate HAZ, white

layer, melted droplet, craters, and, number of cavities and also explain the end surface as well as boundary surface

of a blind hole where the development of ridge-rich surface and microvoids were spotted. The melting and

ejecting of molten metal during drilling causes the development of the ridge-rich surface. The development of

microvoids was due to the outflow of entrapped gases [37]. The white layer has been observed near the boundary

of the hole which is formed due to higher voltage [38]. It has also been found craters in the white layer [39]. The

discontinuous machining provided electrochemical debris and uneven disintegration of the surface around the hole

[23]. The wide craters on the MS were also spotted due to high DE [40]. The higher DE provided more globules,

micropores, and microcracks on the MS [41]. Therefore, it can be said that the increasing DE led to the

resolidification and melting of materials on the MS [32,42–45]. Also, the development of a WL on the MS

because of thermal effects might depreciate the standard of SME of the material [46].

Fig. 9 SEM analysis of blind hole at optimum parameter

Fig. 10 Large number of microvoids

Fig. 11 EDX analysis of NiTi (a) outer surface without drilling showed actual composition and (b) drilled surface

showed without deposition of Mo

The deposition of the electrode to the MS changes the surface properties of Nitinol and also may change the

behavior from a perspective of the application [38,47], therefore the deposition of material should be reduced. The

tool electrode should provide a low wear rate and should have higher electrical conductivity [48]. Figure 11

proved that the work surface can be free of Mo after machining Nitinol by NCM [41,43]. The melting point of

Mo is quite high, and it has a low tendency to react chemically, hence it is work-free [49] and therefore it

diminishes the probability of deposition of material molybdenum electrode to the workpiece during machining

[50]. Thus, the molybdenum electrode is suitable for NCM of NiTi SMAs.

Furthermore, the XRD analysis (figure 11) revealed the development of carbides like TiC in the melting

zone of the drilled hole, where that carbide can vanish the shape memory properties in HAZ [51]. As the

electrolyte used in this current research is a water-free electrolyte, therefore no formation of oxides was observed.

The previous researcher also revealed that the addition of ethanol in the electrolyte can reduce the development of

oxides [52].

Fig. 11 XRD analysis of drilled hole found TiC

7 Conclusion

The experimental exploration was reflected for drilling NiTi SMAs utilizing ECAM. The optimum

parameter was accomplished with the help of multi-objective optimization. The following involvement can be

attained from the analysis:

1 AHP weight method was utilized in GRG to obtain the optimal solution for analyzing multiple

objectives. Again, RSM has been applied for obtaining optimum GRG. The same optimum input

parameter as 20 v/v % of electrolyte concentration, 0 rpm of tool rotation, and 80V of voltage was

obtained by optimization of the response parameters only by GRG and optimization of GRG by

RSM. The optimized value of MRR, TWR, OC, and delamination was measured as 101.19 mg/min,

0.006 mg/min, 0.111, and 1.16 respectively for drilling of Ni55.7Ti SMA by electrochemical arc

machining process.

2 ANOVA results discovered that the individual parameter (voltage followed by electrolyte

concentration) as well as 2- the way interaction parameter (electrolyte concentration × tool rotation)

affected the drilling conditions for hard-to-cut NiTi alloy.

3 The SEM photographs of the blind hole observed equal hole radius all over the periphery including

HAZ, white layer, melted droplet, craters, and, number of cavities and also the development of

ridge-rich surface and microvoids around the end surface as well as boundary surface of a blind hole.

The white layer has been observed near the boundary of the hole which is formed due to higher

voltage. EDX analysis proved that the work surface can be free of Mo after machining Nitinol by

electrochemical arc machining.

4 The XRD analysis revealed the development of carbide like TiC in the melting zone of the drilled

hole, where that carbide can vanish the shape memory properties in HAZ. As the electrolyte used is

a water-free electrolyte, therefore no formation of oxides was observed.

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Statements & Declarations

Funding: The authors declare that no funds, grants, or other support were received during the preparation of this

manuscript.

Competing Interests: The authors have no relevant financial or non-financial interests to disclose.

Author Contributions: All authors contributed to the study conception and design. Material preparation, data

collection and analysis were performed by Nitish Kumar and Prof. Amaresh Kumar. The first draft of the manuscript

was written by Nitish Kumar and all authors commented on previous versions of the manuscript. All authors read

and approved the final manuscript.