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Study on Laser Hardening Parameters of ASTM Grade3 Pure Titanium on an Angle of Entry of Hardened Bead Profile and Power density

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Study on laser hardening parameters of ASTM Grade 3 pure titanium on an angle of entry of hardened bead profile and power density

Duradundi Sawant Badkar Department of Mechanical Engineering, Shri Balasaheb Mane Shikshan Prasarak Mandal Ambap's, Ashokrao Mane

Group of Institutions, Vathar Tarf Vadgaon, Dist: Kolhapur -416112, Maharashtra State, India. *Corresponding Author Email: [email protected]

This research paper includes the laser transformation hardening of commercially pure titanium sheet of 1.6mm thickness is investigated using CW Nd:YAG laser. Commercially

pure titanium has prevalent application in various fields of industries including the medical, nuclear, thermal, marine, defense, automobile aerospace and pharmaceutical

industries. A FFD with RSM is employed to establish, optimize and to investigate the relationships of three laser transformation hardening process parameters: laser power, scanning speed, and focused position on laser hardened bead profile parameters such as

angle of entry of hardened bead profile and power density. RSM is used to develop pseudo-closed-form models from the computational parametric studies. Adequacies of

developed models were analyzed by ANOVA. Effects of laser process parameters on an angle of entry of hardened bead profile and power density were also carried out using

RSM. The laser power and scanning speed consecutively have a positive and significant effect on angle of entry of hardened bead profile and power density respectively as compared to the focal point position among all laser hardening process parameters. The

optimum laser hardening conditions are identified sequentially to minimize an angle of entry of hardened profile, power density. The validation results demonstrate that the

developed models are accurate with low percentages of error.

Keywords: Laser transformation hardening, response surface methodology, full factorial design, analysis of variance,

bead geometry

INTRODUCTION

Laser surface hardening by inducing phase transformations through the heating effect of a laser

beam was one of the first laser based fabrication methods to be commercialized, in the early 1970s. From

last five years, advanced developments have been taken place in the technology of laser sources, optics, and

software, which are enabling the process to be viewed more favourably against the competing processes. More suitable laser sources presently available, such as

multikilowatt Nd:YAG, CO2 and diode lasers, and beam

delivery optics have been developed. The basic principle of laser phase transformation hardening of titanium and

its alloys involves two major steps: 1. Beta phase formation, in which the material is heated to/above the

beta transus temperature, that is, β-transus (888OC or

1621OF), in order to form the material with 100% beta

phase (but below the melting point) and 2. “Self-quenching” or cooling down, where, the β-phase is transformed into harder acicular (plate-like) α martensite

(transformed β) or maintain β phase (beta) to

International Research Journal of Materials Science and Engineering Vol. 3(1), pp. 019-034, April, 2017. © www.premierpublishers.org. ISSN: 1539-7897

Research Article


Badkar et al. 020

room temperature. The β-transus is defined as the lowest

equilibrium temperature at which the material is 100% beta or alpha, which does not exist. It has been

confirmed that the β-transus is critical in deformation processing and in heat treatment processes. A accurate heat treatment process involves the heating stage to be

long enough for the β-phase formation to complete and permit the alloying elements such as manganese,

carbon, oxygen and nitrogen to stabilize it and dissolve iron, molybdenum, copper, nickel, vanadium and silicon

into the matrix. Self-quenching should be quick enough so as to control the normal breaking down of β-phase into the initial α or α+ β phases and produce martensite

instead [1]. The literature survey predicts that several authors have

published their research work only on various types of laser welding process modeling and parameters optimization of different steel materials as base metal and

conducted the experimental based on full factorial design, Box–Behnken design matrix, Plackett-Burman design

matrix, and central composite design matrix and Taguchi‟s orthogaonal arrays by using response surface

methodology (RSM) as an optimization tool. D.S.Badkar et al. investigated the effects of laser transformation hardening variables on the heat input and hardened-bead

geometry parameters such heat input, hardened bead width and hardened depth of commercially pure titanium

using Box–Behnken design with response surface methodology [1]. In this research work

the authors specifically focused on development of mathematical models, analyzing the developed models adequacy by an analysis of variance (ANOVA) and

studied the effects of laser transformation hardening parameters: laser power, scanning speed and focal point

position on an angle of entry of hardened bead profile and power density of hardened bead profile of commercially pure titanium of nearly ASTM Grade3 using

full factorial design matrix to conduct the experiments and optimized by response surface methodology.

Yangyang Zhao et al, response surface methodology (RSM) was used to develop models to predict the

relationship between the processing parameters: laser power, welding speed, gap and focal position and the laser weld bead profile: weld depth, weld width and

surface concave and identify the correct and optimal combination of the laser welding input variables to obtain

superior weld joint [2]. Shuang Liu et al. carried out a systemic study on the HPDDL (high-power direct-diode

laser) cladding process by depositing Fe-based powder on ASTM A36 steel base material. The influences of input process parameters: laser power, powder feeding

rate, carrier-gas flow rate, and stand-off distance on the output responses such as powder catchment efficiency,

height of clad and width of clad were analyzed. The experiments were conducted by central composite design matrix and a quadratic regression models were

developed using a RSM and tested by the ANOVA

method, the relationship between the output responses and the processing parameters were analyzed and

discussed [3]. Ruifeng Li, et al, investigated the laser surface hardening in the AISI 1045 steel using two kinds of industrial lasers such as high-power diode laser

(HPDL) and a CO2 laser, respectively and studied the effect of process parameters such as beam power, travel

speed on structure and case depth of hardened steel [4]. Chen et al. used ANOVA methodology to find the optimal

laser process parameters and to evaluate quantitatively the quality characteristics of laser transformation hardening of SNCM 439 steel by a long-pulsed Nd-YAG

laser beam. They obtained a significant improvement in the quality of laser transformation hardening by Nd-YAG

laser [5]. Ali Alidoosti et al. based on full factorial design the Electrical discharge machining characteristics of nickel–titanium shape memory alloy has been

investigated [6]. K.Y. Benyounis, developed an empirical relationship between the welding process parameters

and the output variables of the welded joint so as to establish the welding parameters that lead to the desired

weld quality using the design of experiment (DoE) [7]. A.Vairis and M. Petousiset et al. applied the parametric design of the experiments the fractional factorial method

to assess the effect of a number of factors on the impact strength of linear friction welding of Ti6Al4V joints [8]. S

Rajakumar et al. developed an empirical relationship between the friction-stir-welding process and tool input

variables to achieve a maximum tensile strength of AA7075–T6 aluminium alloy using response surface methodology [9]. Ali Khorram et al. employed RSM to

establish the design of experiments and to optimize the bead geometry of CO2 Laser Welding of Ti 6Al 4V[10]. R.

Palanivel et al. established a systematic approach to develop the mathematical model for predicting the ultimate tensile strength, yield strength and percentage of

elongation of AA6351 aluminum alloy which is extensively used in automobile industries, aircraft

engines and defense industries by integrating friction stir welding process parameters such as tool rotational

speed, welding speed, and axial force [11]. Xiao Yun Zhang et al. used the response surface methodology (RSM) to study the influence of laser welding parameters

on weld seam quality [12]. Sanjay Kumar et al. conducted the experiments on square butt joint plate of 5083 H111

aluminium alloy using full the factorial design of experiments and established the mathematical models

for depth of penetration and convexity formation were established by using multiple nonlinear regression analytical models and are checked for their

adequacy [13]. Padmanaban et al. developed an empirical relationship to between the tensile strength and

pulsed current gas tungsten arc welded AZ31B magnesium alloy welding process parameters [14]. Kamal Pal et al. in their article developed the

http://portal.acm.org/author_page.cfm?id=81350581982&coll=DL&dl=ACM&trk=0&cfid=34558590&cftoken=72759484

http://www.scientific.net/author/Xiao_Yun_Zhang_4



http://www.tandfonline.com/action/doSearch?action=runSearch&type=advanced&result=true&prevSearch=%2Bauthorsfield%3A%28Pal%2C+Kamal%29


Int. Res. J. Mat. Sci. Engin. 021

modelling and optimization of deposition efficiency in highly non-linear pulsed metal inert gas welding. They

performed the design of experiments using central composite design matrix and developed the model by

response surface methodology [15]. U. Reisgen et al. in their research work, numerical and graphical optimization techniques of the CO2 laser beam welding of dual phase

(DP600)/transformation induced plasticity (TRIP700) steel sheets were carried out using response surface

methodology (RSM) based on Box–Behnken design [16]. Since high power density offers many advantages such

as deep penetration, high welding speed and improved quality of welding joints. But in case of laser transformation hardening , materials to be hardened

instead of melting as in case of welding, therefore it is must and necessarily required to have the desirable,

feasible and optimum power density in order to establish proper laser heating effect. The main objective of this research study is to develop an empirical relationship,

modelling, optimization and to analyze the influence of laser process parameters: laser power, scanning speed

and focused position on an angle of hardened bead geometry and power density of the commercially pure

titanium has been investigated. Statistical tools such as the design of experiments, analysis of variance, and regression analysis are used to develop the relationships.

The developed empirical relationship can be effectively used to predict the laser transformation hardening of

commercially pure titanium at the 95% confidence level. Finally, the Response surface methodology is used to

model the laser transformation hardening process. Experimental Design

The design of experiments (DoE) is a methodology which

encompasses the application of various types of experimental designs, generation of polynomial equations, and mapping of the response over the

experimental domain to determine the optimum formulation(s). A full factorial

design allows the identification of the formulation components that have a significant effect on stability and

all the interactions among the formulation components. DOE techniques allow the engineer to change multiple factors simultaneously; such an approach considerably

reduces the number of experiments required and also allows the engineer to investigate interactions and

higher order effects. If the engineer chooses a model where factor settings are chosen such that all possible

combinations are tested, then the model is called the full-factorial design. A full-factorial design allows the analysis of effects of main factors, interactions, and, depending on

the factor levels, higher order effects. An interaction can be thought of as a new factor which is a combination

of two or more factors. Interactions are not intuitive and their effects are hard to predict. Even if a DOE is more efficient than a one-factor-at-a-time approach, the matrix

can still be very large and may not be suitable for a variety of reasons including lack of necessary materials,

lack of time available on the machine, lack of man-hours, or all of the above. For example, a process with 5 factors

evaluated at 2 levels will require 25 = 32 experiments for

a full-factorial [17-20]. Response Surface Methodology (RSM) is a tool that was

introduced in the early 50's by Box and Wilson (1951) [21]. It is a collection of mathematical and statistical

techniques useful for the approximation and optimization of stochastic models. Applications of

RSM can be found in e.g. chemical, engineering and clinical sciences. Response Surface Methodology (RSM) is an empirical, technique involving the use of Design

Expert software to derive a predictive model similar to regression analysis [22]. Response

surface methodology (RSM) is a statistical, mathematical and experimental process optimization technique to determine and represent the cause and effect

relationship between true mean responses and input control variables influencing the responses as a

two or three-dimensional hyper mesh surface. A response surface model with the full factorial design with

3 independent formulation variables (factors) at 3 different levels was used to study the effects on dependent variables. Full factorial Design statistical

screening design was used to optimize and evaluate main effects, interaction effects and

quadratic effects of the formulation laser hardening process parameters on the performance of laser

hardened bead geometry of laser transformation hardened commercially pure titanium sheet. A 3-factor, the 3-level design used is suitable for exploring quadratic

response surfaces and constructing second-order polynomial models. This quadratic design model is given

by a set of points at the midpoint of each edge of a multidimensional cube and a centre point replicate. The nonlinear computer-generated

(Statgraphics, Manugistics Inc, Rockville, MD) quadratic model is given as

,2

333

2

22212113223311321123322110 xbxbxbxxbxxbxxbxbxbxbbY (1)

Where, Y is the measured response associated with each factor level combination; b0 is an intercept; b1 to b33 are the regression coefficients; and X1, X2, and X3 are the

independent variables [23]. The dependent and independent variables selected are shown in Table 2.

These high, medium, and low levels were selected from the preliminary experimentation.

Experimental Methodology

Table 1 shows the chemical composition of commercially pure Titanium used as base material for the experimental

work. The experiments are conducted based on the full factorial design with three factors, three levels. [24]. As per this design matrix, total numbers of experiments


Badkar et al. 022

Table 1. Chemical composition of commercially pure Titanium

Table 2. Process variables and experimental design levels used

Figure 1. Solid state Nd:YAG Laser source at WRI used for experimental work

Figure 2. Experimental set-up showing the laser beam head and shielding arrangements in the working chamber.

considered for conducting the experiments are 3

3=27 as

there are three input process parameters each at three levels. Therefore, a total of 27 experiments were carried

out for each configuration. The selected values of the process parameters along with their units and notations

are given in Table 2.

Experiments are carried out using A CW, 2 kW, with

radiation wavelength λ=1.06 μm Nd:YAG laser source from GSI Lumonics as shown in Fig.1. Fig. 2 shows a

photograph of the corresponding experimental setup. The experiment was carried out as per the full factorial design

matrix in a random order to avoid any methodical error.

Element Ti C Fe Mo V Zr Cu O N Al

% by Weight Bal. 0.011 0.15 0.003 0.029 0.0039 0.14 0.1 0.003 1.1

Variables -1 0 1

Laser power, (Watts) LP X1 750 1000 1250

Scanning speed, (mm/min) SS X2 1000 2000 3000

Focused position, (mm) FP X3 -30 -20 -10



Heat Input SSLP cmJ / and Power

4. 2HBW

LPDensity

2/ mWatts

Where, LP= Laser Power, Watts SS=Scanning Speed, mm/min HBW=Hardened Bead Width, mm Figure 3. The schematic diagram of laser hardened-bead profile geometry with experimental measurable responses.

A Gaussian continuous wave spherical beam configuration was used throughout the experimental

work. A 120 mm focal optic was used with varying beam spot size depending on a defocusing distance to obtain a wide scan area. Pure argon gas is used as shielding

medium and is supplied at the constant flow rate of 10 litres/min. Transverse section specimens were cut from

laser hardened-bead on trials of commercially pure titanium sheet and mounted using Araldite. Standard metallographic was made for each transverse sectioned

specimens. For metallic specimen preparation, sequential grinding with silicon carbide (SiC) abrasive papers such

as 120 or 240 grit for rough ground followed by decreasing the size of the SiC papers: 320, 400, 600, up

to finer papers 800 and 1200 grit. The bead profile parameters „responses‟ were measured using an optical microscope. An optical microscope used for

measurement was a portable video microscope, LM525 having image processing computer controlled software

based on LINUX OS 9.3 with digital micrometres attached to it with an accuracy of 0.001 mm, which

allowed to measure directional movement in x-axes and y-axes. Figure 3 shows the schematic diagram of laser hardened-

bead profile geometry with experimental measurable responses, which presents the measured parameters,

such as hardened bead width, hardened depth, an angle of entry of hardened bead profile and power density for CW spherical beam. The measured laser hardened bead

profile parameters „responses‟ were recorded. Table 3 demonstrates the 3

3 full factorial design layout matrix with

code independent variables.

RESULTS AND DISCUSSIONS

The results of the laser hardened-bead profile were measured according to the design matrix with coded independent process variables as shown in Table 3 of the

transverse sectioned specimens using the optical microscope mentioned earlier, the measured

responses are listed in Table 4. Initially, analyzing the measured responses for model adequacy by using the Design expert software package, the fit summary output

indicates that the linear model is significantly significant for Angle of Entry of Hardened Bead profile (AEHB)

response, therefore it will be used for further analysis, while for the other response power density the quadratic

model are statistically recommended for the further analysis.

Analysis of Variance (ANOVA) for Response Surface Full Model

The adequacy of the developed models was tested using

the Analysis of Variance (ANOVA) technique and the results of the linear and quadratic order response surface models fitting in the form of analysis of variance (ANOVA)

are given in Tables 4-5.

The same Tables show also the other adequacy measures R

2, adjusted R

2 and predicted R

2.From the

same table it has been observed that all the values of

coefficient of determination “R2” are nearly equal to 1 and

clearly, we must have 0 ≤ R2 ≤ 1, with larger values being

more desirable. The entire adequacy measures are


Badkar et al. 024

Table 3. 33 Full Factorial Design Layout Matrix with code independent variables.

Exp. No X1 X2 X3 X1

2 X2

2 X3

2 X1X2 X2X3 X1X3 X1X2X3

LP SS FP LP2 SS

2 FP

2 LPxSS SSxFP LPxFP LPxSSxFP

1 -1 -1 -1 1 1 1 1 1 1 -1

2 0 -1 -1 0 1 1 0 1 0 0

3 1 -1 -1 1 1 1 -1 1 -1 1

4 -1 0 -1 1 0 1 0 0 1 0

5 0 0 -1 0 0 1 0 0 0 0

6 1 0 -1 1 0 1 0 0 -1 0

7 -1 1 -1 1 1 1 -1 -1 1 1

8 0 1 -1 0 1 1 0 -1 0 0

9 1 1 -1 1 1 1 1 -1 -1 -1

10 -1 -1 0 1 1 0 1 0 0 0

11 0 -1 0 0 1 0 0 0 0 0

12 1 -1 0 1 1 0 -1 0 0 0

13 -1 0 0 1 0 0 0 0 0 0

14 0 0 0 0 0 0 0 0 0 0

15 1 0 0 1 0 0 0 0 0 0

16 -1 1 0 1 1 0 -1 0 0 0

17 0 1 0 0 1 0 0 0 0 0

18 1 1 0 1 1 0 1 0 0 0

19 -1 -1 1 1 1 1 1 -1 -1 1

20 0 -1 1 0 1 1 0 -1 0 0

21 1 -1 1 1 1 1 -1 -1 1 -1

22 -1 0 1 1 0 1 0 0 -1 0

23 0 0 1 0 0 1 0 0 0 0

24 1 0 1 1 0 1 0 0 1 0

25 -1 1 1 1 1 1 -1 1 -1 -1

26 0 1 1 0 1 1 0 1 0 0

27 1 1 1 1 1 1 1 1 1 1

Table 4. ANOVA table for angle of entry of hardened bead profile (Reduced Linear Model).

Source Sum of

df Mean F p-value

Squares Square Value Prob > F

Model 4496.9 3 1498.95 84.995 < 0.0001 significant

LP 2454.2 1 2454.2 139.16 < 0.0001

SS 1520.6 1 1520.58 86.221 < 0.0001

FP 522.08 1 522.076 29.603 < 0.0001

Residual 405.62 23 17.6358

Corrected Total 4902.5 26

Std. Dev. 4.1995 R-Squared 0.9173

Mean 54.449 Adjusted R-Squared 0.9065

C.V. % 7.7127 Predicted R-Squared 0.88

PRESS 588.08 Adequate Precision 32.484

closer to 1, which is in reasonable agreement and indicate adequate models. The adequate precision is

greater than 4 in all cases and is desirable. An adequate precision ratio above 4 indicates adequate model

discrimination. The ANOVA Tables 4-5 also shows the

model terms Std. Dev, Mean, C.V and PRESS. At the same time, relatively lower values of the coefficient

of variation, C.V., from the Tables 4-5 indicates improved precision and reliability of the conducted experiments.

Small values of PRESS are desirable. In all the cases the



Table 5. ANOVA table for power density (Reduced Quadratic Model).

Source Sum of

df Mean F p-value

Squares Square Value Prob > F

Model 70668.7 5 14133.7 42.7601 < 0.0001 significant

LP 17.2897 1 17.2897 0.05231 0.8213

SS 52754.8 1 52754.8 159.604 < 0.0001

FP 11203.7 1 11203.7 33.8955 < 0.0001

LP x SS 5667.18 1 5667.18 17.1454 0.0005

SS2 1025.77 1 1025.77 3.10335 0.0927

Residual 6941.25 21 330.536

Corrected Total 77610 26

Std. Dev. 18.1806 R-Squared 0.9106

Mean 261.962 Adjusted R-Squared 0.8893

C.V. % 6.94018 Predicted R-Squared 0.8462

PRESS 11938.1 Adequate Precision 23.527

Predicted (reduced) vs Actual

R2 = 0.9173

25

30

35

40

45

50

55

60

65

70

75

80

85

25 30 35 40 45 50 55 60 65 70 75 80 85 90

Actual values of AEHB, Degrees

Pre

dic

ted

(re

du

ce

d)

va

lue

s o

f A

EH

B, D

eg

ree

s

Figure 4. Scatter diagram of angle of entry of hardened bead profile (AEHB).

values of PRESS are considerably small [24]. The values of “Probability > F” in Tables 4-5 for all models are less

than 0.0500 indicate that all models are significant. In all cases, the “Residuals” values are very small related to

the sum of squares of models which implies the R-Squared value nearer to 1. Very small values of

“Residuals” are desired and it is good. Initially, Table 4 shows ANOVA linear model for the angle of entry of hardened-bead profile (AEHB). It ensured that

there is a linear relationship between the main effects of the three process parameters. It is evident from the Table

that the main effect of LP, SS, and FP are significant model terms. In this case, the main effect of LP, SS, and

FP are all the most important factors those influence the AEHB profile. It is important to note that fit summary

output indicates that the linear model is statistically significant for the AEHB model. Since AEHB totally

depends on HBW and HD, it is also conferred that HBW and HD models are statistically significant Similarly, Table 5 shows ANOVA for power density (PD),

which indicates that SS, FP, interaction effect of laser power with focused position (LP×FP), and second order


Badkar et al. 026

Predicted (reduced) vs Actual

R2 = 0.9106

125

150

175

200

225

250

275

300

325

350

375

400

125 150 175 200 225 250 275 300 325 350 375 400 425

Actual values of power density, W/mm2

pre

dic

ted

(re

du

ce

d)

va

lue

s o

f p

ow

er

de

ns

ity

, W

/mm

2

Figure.5. Scatter diagram of power density (PD).

Table 6. Confirmation experimental parameters under various conditions.

Exp No

Process parameters

Responses Actual Value

Predicted value

Error Error %

1

LP=750Watts AEHB(degrees) 33.07 33.58 -0.51 -1.542

SS=3000mm/min FP= -20mm

PD(W/mm2) 293.1 299.7 -6.6 -2.252

2



PD(W/mm2) 305.84 324.65 -18.8 -6.147

3



PD(W/mm2) 281.14 274.76 6.38 2.269

4

LP=750Watts AEHB(degrees) 38.77 37.38 1.39 3.585


PD(W/mm2) 233.1 229.28 3.82 1.639

5

LP=750Watts AEHB(degrees) 49.51 48.16 1.35 2.727


PD(W/mm2) 288.92 279.17 9.75 3.375

6

LP=750Watts,


AEHB(degrees) 42.06 42.77 -0.71 -1.688

PD(W/mm2) 258.77 254.22 4.55 1.758

effect of scanning effect (SS

2) are the most significant

terms associated with PD model. It is important to note that though, the main effect of laser power (LP) is not

having the significant effect but interaction effect of laser

power with scanning speed (LP×SS) has a significant

effect on power density model. However, the main effect of SS and FP are the most important factors those

influencing the PD sequentially.



Design-Expert® Software

AEHBDesign points above predicted valueDesign points below predicted value77.67

33.08

X1 = B: SSX2 = A: LP

Actual FactorC: FP = -20

1000

1500

2000

2500

3000

750

875

1000

1125

1250

33

44.3

55.5

66.8

78

A

EH

B,

De

gre

es

Scanning speed, mm/min Laser power, Watts

Figure 6. 3D graph shows the effect of LP and SS on AEHB.


AEHBDesign Points77.67

33.08



1000 1500 2000 2500 3000

750

875

1000

1125

1250AEHB, Degrees

Scanning speed, mm/min

La

se

r p

ow

er,

Wa

tts

35.57

37.56

39.54

41.53

43.52

45.5147.49

49.48

51.47

53.46

55.44

57.43

59.42

61.4063.39

65.38

67.3769.35

71.34

73.33

Figure 7. Contours graph shows the effect of LP and SS on AEHB.

It has been observed from all models that except for the

model, angle of entry of hardened-bead profile (AEHB), the main effect FP has less influence, as compared to LP

and SS. Since the laser transformation hardening process itself is of heat treatment of surface layers with

the desired optimum depth of penetration. Means that in

the case of laser transformation hardening process the

laser beam is a defocused beam with a negative focal position with minimum energy loss is merely

preferable instead of focused one. All above consideration indicates an excellent adequacy of the

response surface multiple regression models. Each


Badkar et al. 028



33.08

X1 = C: FPX2 = A: LP

Actual FactorB: SS = 2000

-30

-25

-20

-15

-10

750

875

1000

1125

1250

35

44.3

53.5

62.8

72

A

EH

B,

De

gre

es

Focused position, mm Laser power, Watts

Figure 8. 3D graph shows the effect of LP and FP on AEHB.



33.08



-30 -25 -20 -15 -10

750

875

1000

1125

1250AEHB, Degrees

Focused position, mm

La

ser

po

we

r, W

att

s

39.0140.64

42.26

43.89

45.5147.14

48.76

50.39

52.01

53.64

55.26

56.89

58.51

60.14

61.76

63.3965.01

66.64

68.26 69.89

Figure 9. Contours graph shows the effect of LP and FP on AEHB.

observed value is compared with the predicted value for all the models are shown by the scatter diagrams from

the Figures 4-5 respectively. The final mathematical models in terms of coded factors

as determined by design expert software are given below:

Angle of Entry of Hardened Bead profile (AEHB) =54.4489+11.6767LP - 9.1911SS+5.3856FP (2)

Power Density (PD) = 253.2450 - 0.9801LP - 54.1371SS + 24.9485FP + 21.7317LP x SS + 13.0752SS

2 (3)

While the following final empirical models in terms of actual factors:

Angle of Entry of Hardened Bead profile (AEHB) = 36.896+ 0.0467LP -0.0092SS + 0.5386FP (4)

Power Density (PD) = 424.94 -0.1778LP-0.0851SS+2.4948FP+ (9E-05) LP x SS + (1E-05) SS

2

(5)





33.08

X1 = C: FPX2 = B: SS

Actual FactorA: LP = 1000

-30

-25

-20

-15

-10

1000

1500

2000

2500

3000

36

44.8

53.5

62.3

71

AE

HB

, D

eg

re

es

Focused position, mm Scanning speed, mm/min

Figure 10. 3D graph shows the effect of SS and FP on AEHB.

Validation of the models

Figures 4-5 show the relationship between the actual and predicted values of the heat input, hardened bead width,

hardened depth, the angle of entry of hardened bead profile and power density respectively. These Figures 4-

5 indicate that the developed models are adequate because the residuals in a prediction of each response are minimum since the residuals tend to be close to the

diagonal line. Furthermore, to verify the adequacy of the developed models, six confirmation experiments were

carried out using new test conditions, but are within the experimental range defined early. Using the point

prediction option in the software, the HI, AEHB and PD of the validation experiments were predicted using the previously developed models. Table 6

summarizes the experiments condition, the actual experimental values, the predicted values,

error and the percentages of error.

EFFECT OF PROCESS FACTORS ON HARDENED BEAD PROFILE PARAMETERS

Angle of Entry of Hardened Bead Profile (AEHB)

The most significant factor influencing the AEHB is the SS as the results indicated. This is due to the fact that at

low SS the HI will be greater. This large amount of heat

will be conducted from the fusion zone to a greater depth

of hardness, which in turn ensures the increase in the AEHB profile with the surface. The results show also that LP contributes secondary effect on AEHB. An increase in

LP results in the increase in AEHB, because of increase in PD increases the hardened depth. Moreover,

defocused beam i.e. decreases in the focused position, which means wider laser beam spot results in spreading the laser power onto a wide area. Therefore, the wide

area of the base metal will be heated leading to an increase in hardened bead width, and decrease in the

hardened depth, thereby decreasing the AEHB. The results also indicate that interaction effects

of LP´FP and SS´FP, second order effects of LP2 and

FP2 are contributing remarkable effect on AEHB. From

the Figures 6 and 7, it is evident that AEHB increases

with increase in LP and decrease in SS. Figures 8 and 9, it is seen that AEHB goes on increases as the LP

increases and FP increases i.e. from -30mm to -10mm. From the Figures 10 and 11, it is also observed that the

AEHB increases with a decrease in SS and increase in FP, i.e. from -30mm to -10mm .

Power Density (PD)

Power density is directly related to the LP and FP which in turn related to the HBW. As the focused position decreases i.e. from -10mm to -30mm (or defocusing

increases), the hardened bead width increases


Badkar et al. 030



33.08



-30 -25 -20 -15 -10

1000

1500

2000

2500

3000AEHB, Degrees


Sc

an

nin

g s

pe

ed

, m

m/m

in

41.2642.65

44.04

45.43

46.8148.20

49.59

50.98

52.37

53.75

55.14

56.53

57.92

59.3160.70

62.08

63.47

64.8666.25

67.64

Figure 11. Contours graph shows the effect of SS and FP on AEHB

Design-Expert® SoftwareFactor Coding: ActualPD

Design points above predicted valueDesign points below predicted value369.644

171.763



750

875

1000

1125

1250

1000

1500

2000

2500

3000

150

200

250

300

350

P

ow

er

de

nsity,

W/m

m2

Scanning speed, mm/min Laser power, Watts

Figure 12. 3D graph shows the effect of LP and SS on power density

simultaneously. It can be calculated as Power density

=2

LPPD

HBW , Watts/mm

2. From Figures 12 and 13, it is

evident that as SS increases power density goes on

increases which in turn decrease the HBW thereby fulfilling the above equation mentioned. Power density is

directly related to laser power but variation in power

density depends on scanning speed and focused position for predicting the output parameters or „responses‟. Figures 14 and 15 show the effects of LP and FP on

power density. From the Figures, it has been observed that as FP increases i.e. from -30 mm to -10mm, power

density linearly increases. Therefore, power density has a linear relationship with the focused position. LP alone has

no significant effect on power density since power density




Design Points369.644

171.763



1000 1500 2000 2500 3000

750

850

950

1050

1150

1250Power density, W/mm2

Scanning speed, mm/min

La

se

r p

ow

er,

Wa

tts

197.853

202.999

210.232

215.002

223.245

229.89240.688

247.937

257.519

266.883

278.255

289.083

300

310.717

319.422

327.614

235.116

Figure 13. Contours graph shows the effect of LP and SS on power density.



171.763



750

850

950

1050

1150

1250

-30

-25

-20

-15

-10

150

200

250

300

350

P

ow

er

de

nsity,

W/m

m2

Focused position, mm Laser power, Watts

Figure 14. 3D graph shows the effect of LP and FP on power density.

is the distribution of power on a substrate which depends

on focused position. The most influencing factors those

affecting the power density are SS and FP. From the

Figures 16 and 17, it is true that as the SS and FP


Badkar et al. 032



171.763



-30 -25 -20 -15 -10

750

850

950

1050

1150



La

se

r p

ow

er,

Wa

tts

233.21

240.055250.341

258.261

269.299

236.868

243.583

254.302

266.233

272.695

276.061

262.446

247.128

230.468

Figure 15. Contours graph shows the effect of LP and FP on power density.



171.763



1000

1500

2000

2500

3000

-30

-25

-20

-15

-10

150

202.5

255

307.5

360

P

ow

er

de

nsi

ty,

W/m

m2

Focused position, mm Scanning speed, mm/min

Figure 16. 3D graph shows the effect of SS and FP on power density.

increase the power density increases. This ensures that

power density has a linear relationship with scanning speed and focused position. From the above results, it is

known that as SS increases hardened bead width decreases. As hardened bead width decreases obviously power density thereby increases.

CONCLUSIONS

The presented research work has portrayed the

application of design of experiments (DOE) for conducting the experiments. Three models were developed for predicting the angle of entry of hardened





171.763



-30 -25 -20 -15 -10

1000

1500

2000

2500



Sca

nn

ing

sp

ee

d,

mm

/min

201.696

209.833

218.126

226.778

236.663

246.549

256.435

266.32

276.206

286.092

295.978

305.863 315.749

325.635 332.866

194.965

Figure 17. Contours graph shows the effect of SS and FP on power density

bead profile (AEHB) and power density (PD) of the laser transformation hardened commercially pure titanium by

using multiple regression analysis using 33 Full Factorial

Design (FFD). The following conclusions were drawn

from this investigation within the factors limits considered.

Full Factorial Design (FFD) can be employed to develop mathematical models for predicting

laser hardened- bead geometry.

The laser power density linearly increases with

increasing laser power and decreasing scanning speed.

It is evident that angle of entry of hardened bead profile increases with increase in laser power and

decrease in scanning speed. It has been also concluded that angle of entry of hardened bead profile increases

with increase in laser power, a decrease in scanning speed and increase in focused position i.e. from -30mm to -10mm.

It has been concluded that as the scanning speed and focused position increases power density

increases. It results that power density has the linear relationship with scanning speed and focused position.

From the results it has been derived that power density is inversely proportional to the hardened bead

width. As scanning speed increases hardened bead width decreases. As scanning speed increases hardened bead width decreases, thereby power density increases.

ACKNOWLEDGEMENTS

The authors are grateful to the management of the Welding Research Institute (WRI), BHEL, Tiruchirappalli-

620014, Tamil Nadu, India for extending the facilities of Laser Materials Processing Laboratory to carry out the research work. The authors also wish to express their

sincere thanks for the constant encouragement received from the faculties of MANIT Bhopal during the course of

the work.

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Accepted 11 April, 2017

Citation: Badkar DS (2017). Study on Laser Hardening

Parameters of ASTM Grade3 Pure Titanium on an Angle

of Entry of Hardened Bead Profile and Power density. International Research Journal of Materials Science and

Engineering, 3(1): 019-034.

Copyright: © 2017 Badkar DS. This is an open-access

article distributed under the terms of the Creative

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.



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