Materials & Design Materials and Design 29 (2008) 92–97 www.elsevier.com/locate/matdes

Developing mathematical models to predict tensile properties of pulsed current gas tungsten arc welded Ti–6Al–4V alloy M. Balasubramanian a

a,*

, V. Jayabalan b, V. Balasubramanian

c

Department of Production Engineering, Sathyabama University, Old Mamallapuram Road, Chennai 600 119, India b Department of Manufacturing Engineering, Anna University, Guindy, Chennai 600 025, India c Department of Manufacturing Engineering, Annamalai University, Annamalai Nagar 608 002, India Received 4 April 2006; accepted 1 December 2006 Available online 21 December 2006

Abstract Titanium (Ti–6Al–4V) alloy has gathered wide acceptance in the fabrication of light weight structures requiring a high strength-toweight ratio, such as transportable bridge girders, military vehicles, road tankers and railway transport systems. The preferred welding process of titanium alloy is frequently gas tungsten arc (GTA) welding due to its comparatively easier applicability and better economy. In the case of single pass GTA welding of thinner section of this alloy, the pulsed current has been found beneficial due to its advantages over the conventional continuous current process. Many considerations come into the picture and one need to carefully balance various pulse current parameters to arrive at an optimum combination. Hence, in this investigation an attempt has been made to develop mathematical models to predict tensile properties of pulsed current GTA welded titanium alloy weldments. Four factors, five level, central composite, rotatable design matrix is used to optimise the required number of experiments. The mathematical models have been developed by response surface method (RSM). The adequacy of the models has been checked by ANOVA technique. By using the developed mathematical models, the tensile properties of the joints can be predicted with 99% confidence level. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Pulsed current; Gas tungsten arc welding; Design of experiments

1. Introduction Titanium and its alloys have been considered as one of the best engineering metals for industrial applications [1]. Ti–6Al–4V have excellent specific tensile and fatigue strengths and corrosion resistance, mainly used for aircraft structural and engine parts, material for petrochemical plants and surgical implants [2]. This is due to the excellent combination of properties such as elevated strength-toweight ratio, toughness and excellent resistance to corrosion make them attractive for many industrial applications. However, welding of titanium alloy leads to grain coarsen*

Corresponding author. Tel.: +91 44 25026503; fax: +91 44 24819579. E-mail addresses: manianmb@rediffmail.com (M. Balasubramanian), [email protected] (V. Jayabalan), [email protected] (V. Balasubramanian). 0261-3069/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2006.12.001

ing at the fusion zone and heat affected zone (HAZ) [3]. Weld fusion zones typically exhibit coarse columnar grains because of the prevailing thermal conditions during weld metal solidification. This often results in inferior weld mechanical properties and poor resistance to hot cracking. It is thus highly desirable to control solidification structure in welds and such control is often very difficult because of higher temperatures and higher thermal gradients in welds in relation to castings and the epitaxial nature of the growth process. Nevertheless, several methods for refining weld fusion zones have been tried with some success in the past: inoculation with heterogeneous nucleants [4], microcooler additions, and surface nucleation induced by gas impingement and introduction of physical disturbance through techniques such as torch vibration [5]. In this process, two relatively new techniques namely, magnetic arc oscillation and current pulsing, have gained

M. Balasubramanian et al. / Materials and Design 29 (2008) 92–97

wide popularity because of their striking promise and the relative ease with which these techniques can be applied to actual industrial situations with only minor modifications of the existing welding equipment [6,7]. Pulsed current gas tungsten arc (PCGTA) welding, developed in 1950s, is a variation of GTA welding which involves cycling of the welding current from a high level to a low level at a selected regular frequency. The high level of the peak current is generally selected to give adequate penetration and bead contour, while the low level of the background current is set at a level sufficient to maintain a stable arc. This permits arc energy to be used efficiently to fuse a spot of controlled dimensions in a short time producing the weld as a series of overlapping nuggets and limits the wastage of heat by conduction into the adjacent parent material as in normal constant current welding. In contrast to constant current welding, the fact that heat energy required to melt the base material is supplied only during peak current pulses for brief intervals of time allows the heat to dissipate into the base material leading to a narrower heat affected zone (HAZ). The technique has secured a niche for itself in specific applications such as in welding of root passes of tubes, and in welding thin sheets, where precise control over penetration and heat input are required to avoid burn through [7]. Extensive research has been performed in this process and reported advantages include improved bead contour, greater tolerance to heat sink variations, lower heat input requirements, reduced residual stresses and distortion. All these factors will help in improving mechanical properties. Current pulsing has been used by several investigators to obtain grain refinement in weld fusion zones and improvement in weld mechanical properties [8]. However, reported research work on relating the pulsed current parameters and mechanical properties are very scanty. Moreover, no systematic study has been reported so far to correlate the pulsed current parameters and mechanical properties. Metallurgical advantages of pulsed current welding frequently reported in the literature include refinement of fusion zone grain size and substructure, reduced width of HAZ, control of segregation, etc., [5]. Statistical tools have been used by many investigators [9–11], which has gained wide acceptance. Hence, in this investigation an attempt has been made to develop mathematical models to predict the tensile properties of pulsed current GTA welded titanium alloy using statistical tools such as design of experiments, analysis of variance and regression analysis. 2. Scheme of investigation In order to achieve the desired aim, the present investigation has been planned in the following sequence: (i) Identifying the important pulsed current GTA welding parameters that which are having influence on fusion zone grain refinement and tensile properties.

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(ii) Finding the upper and lower limits of the identified parameters. (iii) Developing the experimental design matrix. (iv) Conducting the experiments as per the design matrix. (v) Recording the responses. (vi) Identifying the significant factors. (vii) Developing the mathematical models. (viii) Checking the adequacy of the developed models.

2.1. Identifying the important parameters From the literatures [5–8] and the previous work [9–11] done in our laboratory, the predominant factors which are having greater influence on fusion zone grain refinement of pulsed current GTA welding process have been identified. They are (i) peak current, (ii) background current, (iii) pulse frequency and (iv) pulse on time. 2.2. Finding the working limits of the parameters A large number of trial runs have been carried out using 1.6 mm thick sheets of titanium (Ti–6Al–4V) alloy to find out the feasible working limits of pulsed current GTA welding parameters under the welding conditions specified in Table 1. Different combinations of pulsed current parameters have been used to carryout the trial runs. The bead contour, bead appearance and weld quality have been inspected to identify the working limits of the welding parameters. From the above analysis following observations have been made: (i) If the peak current is less than 60 A, then incomplete penetration and lack of fusion was observed. At the same time, if the peak current is greater than 100 A, spatter was observed on the weld bead surface. (ii) If the background current is lower than 20 A, the arc length is found to be very short. On the other hand, if the background current is greater than 60 A, then arc becomes unstable and arc wandering is observed due to increased arc length.

Table 1 Welding conditions Power source

Lincoln, USA

Polarity Welding current Arc voltage Electrode Electrode diameter Shielding gas Gas flow rate Torch position Operation Welding speed

AC 60–100 A pulsed current 22 V W + 2% thoriated (alloy) 2.5 mm Argon 10 l/min Vertical Automatic 300 mm/min

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Table 2 Important factors and their levels S. no.

Factor

Notation

Unit

Levels coded (2)

(1)

(0)

(+1)

(+2)

1 2 3 4

Peak current Base current Frequency Time

P B F T

A A Hz s

60 20 0 35%

70 30 3 40%

80 40 6 45%

90 50 9 50%

100 60 12 55%

(iii) If the pulse frequency is 0 Hz, then the bead appearance and bead contour appears to be similar to that of constant current weld beads. Further, if the pulse frequency is greater than 12 Hz, then more arc glare and arc spatter was experienced. (iv) If the pulse on time is lower than 35%, then weld nugget formation is not so smooth on the contrary, if the pulse on time is greater than 55%, then overmelting of base metal and overheating of tungsten electrode was noticed.

2.3. Developing the experimental design matrix By considering all the above conditions, the feasible limits of the parameters have been chosen in such a way that the Ti–6Al–4V alloy should be welded without any weld

defects. Due to wide ranges of factors, it has been decided to use four factors, five levels, rotatable central composite design matrix to optimise the experimental conditions. Table 2 presents the ranges of factors considered and Table 3 shows the 31 set of coded conditions used to form the design matrix. The first 16 experiments have been formulated as per 24 (two levels and four factors) factorial design. The 16 experimental conditions (rows) have been formed for main effects by using the formula 2nc1 for the low (1) and high (+1) values; where ‘nc’ refers to the column number. For example, in Table 3, the first four rows are coded as 1 and next four rows are coded as +1, alternatively, in the third column [because nc = 3 and therefore 231 = 4]. The next eight experimental conditions are called as corner points, i.e., keeping one factor at the lowest/highest level and the remaining factors at middle level. The last seven experimental conditions are known as corner points,

Table 3 Design matrix and experimental results Expt no.

P (X1)

B (X2)

F (X3)

T (X4)

Tensile strength (MPa)

Yield strength (MPa)

Notch tensile strength (MPa)

Notch strength ratio

Elongation (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0

1020 1060 1000 1040 1030 1075 1015 1060 1005 1045 990 1025 1010 1060 995 1040 1100 1070 1120 1090 975 1000 1110 1080 1140 1120 1150 1135 1160 1115 1155

958 1001 952 995 992 1041 978 1014 957 987 931 969 961 1014 959 1008 1065 1030 1070 1035 923 940 1046 1026 1080 1100 1075 1060 1110 1090 1085

1142 1293 1080 1185 1185 1333 1126 1230 1045 1130 1020 1035 1111 1200 1055 1135 1390 1295 1425 1340 985 1040 1390 1300 1475 1425 1450 1400 1325 1390 1350

1.12 1.22 1.08 1.14 1.15 1.24 1.11 1.16 1.04 1.08 1.03 1.01 1.1 1.13 1.06 1.09 1.26 1.21 1.27 1.23 1.01 1.04 1.25 1.2 1.28 1.27 1.26 1.23 1.21 1.25 1.19

3.7 4.6 3 4.25 4 4.85 3.5 4.6 3.2 4.4 2.5 3.85 3.4 4.65 2.75 4.3 5.15 4.85 5.4 5 2.4 2.8 5.3 5 5.8 5.1 5.6 5.9 5.8 5.3 5.1

M. Balasubramanian et al. / Materials and Design 29 (2008) 92–97

i.e., keeping all the factors at the middle level and it is normally done to know the repeatability of the experimental procedures. The method of designing such matrix is dealt elsewhere [12,13]. For the convenience of recording and processing the experimental data, the upper and lower levels of the factors are coded as +2 and 2, respectively, and the coded values of any intermediate levels can be calculated by using the expression [13]. Xi ¼

½2X  ðX max þ X min Þ ðX max  X min Þ=2

ð1Þ

Y ¼ f ðP ; B; F ; T Þ

95

ð2Þ

The second order polynomial (regression) equation used to represent the response surface ‘Y’ is given by X X X Y ¼ b0 þ bi x i þ bii x2i þ bij xi xj ð3Þ and for four factors, the selected polynomial could be expressed as Y ¼ b0 þ b1 ðP Þ þ b2 ðBÞ þ b3 ðF Þ þ b4 ðT Þ þ b11 ðP 2 Þ þ b22 ðB2 Þ þ b33 ðF 2 Þ þ b44 ðT 2 Þ þ b12 ðPBÞ þ b13 ðPF Þ

where Xi is the required coded value of a parameter of any value X from Xmin to Xmax; Xmin is the lower level of the parameter and Xmax is the upper level of the parameter. 2.4. Conducting the experiments and recording the responses The base metal used in this investigation is a high strength titanium alloy of Ti–6Al–4V grade. The chemical composition of the base metal was obtained using a vacuum spectrometer (ARL-Model: 3460). Sparks were ignited at various locations of the base metal sample and their spectrum was analysed for the estimation of alloying elements. The chemical composition of the base metal in weight percent and mechanical properties is given in Tables 4 and 5 respectively. Tensile specimens were prepared as per the ASTM E8M-90a (ASTM, 1991a) guidelines as shown in Fig. 1. Tensile tests were carried out in 100 kN, electromechanical controlled Universal Testing Machine (Make: FIE-BLUE STAR). The specimen was loaded at the rate of 1.5 kN/min as per ASTM specifications, so that tensile specimen undergoes deformation. The specimen finally fails after necking and the load versus displacement was recorded. The 0.2% offset yield strength was derived from the diagram. At each experimental condition, three specimens were tested and average values are presented in Table 3.

Y ¼ f ðPeak current; base current; pulse frequency; pulse on timeÞ Table 4 Chemical composition (wt%) of the base metal Al

V

C

Fe

O

N

H

Ti

% By weight

6.3

4

0.006

0.17

0.166

0.006

0.002

Balance

Table 5 Mechanical properties of base metal

998

1146

910

Elongation (%)

10

X  XX Y  0:035714 ðX ii Y Þ X bi ¼ 0:041667 ðX i Y Þ X XX bii ¼ 0:03125 ðX ii Y Þ þ 0:00372 ðX ii Y Þ X   0:035714 Y X bij ¼ 0:0625 ðX ij Y Þ b0 ¼ 0:142857

ð5Þ ð6Þ

ð7Þ ð8Þ

All the co-efficients have been tested for their significance at 90% confidence level applying student’s t-test using SPSS statistical software package. After determining the significant co-efficients, the final models were developed using only these coefficients and the final mathematical models to estimate tensile properties, developed by the above procedure are given below: (i) Yield strength

ð9Þ (ii) Tensile strength TS ¼ 1139:31 þ 11:67P  8:33B þ 6:25F  7:91T  20:03P 2  15:04B2  44:41F 2  17:53T 2 þ 1:88PF  1:25FT ð10Þ (iii) Percentage of elongation

Elements

Yield strength (MPa)

where b0 is the average of responses and b1 ; b2 ; . . . ; b23 are the co-efficients that depend on respective main and interaction effects of the parameters. The value of the co-efficients has been calculated using the following expressions [15] and the calculated values are presented in Table 6:

 14:07B2  44:32F 2  18:19T 2 þ 2:06PF  1:31FT

Representing the tensile properties, say yield strength of the joint by Y, the response function can be expressed as [14,15]

Notch tensile strength (MPa)

ð4Þ

YS ¼ 1085:73 þ 11:29P  7:29B þ 10:46F  7:7T  15:3P 2

3. Developing mathematical models

Ultimate tensile strength (MPa)

þ b14 ðPT Þ þ b23 ðBF Þ þ b24 ðBT Þ þ b34 ðFT Þ

Vicker’s hardness (0.5 kg) 320

Charpy impact test (J) 18

E% ¼ 5:5 þ 0:35P  0:21B þ 0:16F  0:18T  0:23P 2  0:18B2  0:82F 2  0:19T 2 þ 0:07PB þ 0:08PT þ 0:034BF  0:02BT ð11Þ (iv) Notch tensile strength NTS ¼ 1402:17 þ 19:96P  22:45B þ 16:7F  30:04T  41:4P 2  32:6B2  102:4F 2  40:02T 2  6:93PB  9:68PT

ð12Þ

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M. Balasubramanian et al. / Materials and Design 29 (2008) 92–97

Fig. 1. Dimensions of tensile specimen: (a) un-notched flat specimen; (b) notched flat specimen.

(v) Notch strength ratio NSR ¼ 1:24 þ 0:0117P  0:02B þ 0:016F  0:03T

Table 6 Calculated values of the co-efficients for all the models Coefficient

Yield strength

Tensile strength

Elongation

Notch tensile strength

Notch strength ratio

b0 b1 b2 b3 b4 b11 b22 b33 b44 b34 b12 b13 b14 b23 b24

1085.737 11.291 7.291 10.458 7.708 15.327 14.077 44.327 18.202 1.312 0.562 2.062 0.0625 0.4375 0.0625

1139.31 11.66676 8.3334 6.25005 7.91673 20.0442 15.0442 44.4192 17.5442 1.25 0.625 1.875 0 0.625 0

5.5 0.352 0.214 0.164 0.185 0.234 0.178 0.822 0.197 0.015 0.065 0.003 0.078 0.034 0.028

1402.17 24.458 30.958 23.125 12.625 36.020 26.020 118.521 35.395 6.062 10.562 4.062 14.937 0.4375 5.687

1.241 0.0116 0.02 0.0158 0.0325 0.0139 0.010 0.066 0.016 0.0075 0.0087 0.0012 0.0137 1.39E–17 0.005

 0:013P 2  0:01B2  0:06F 2  0:016T 2  0:013PT ð13Þ 3.1. Checking the adequacy of the developed mathematical models The adequacy of the developed models has been tested using the analysis of variance technique (ANOVA) [15]. As per this technique, if the calculated value of the Fratio of the developed model is less than the standard Fratio (from F-table) value at a desired level of confidence (say 99%), then the model is said to be adequate within the confidence limit. Similarly, calculated value of the Rratio of the developed model exceeds the standard tabulated value of the Rratio for a desired level of confidence (say 99%), then

Table 7 ANOVA test results for all the models Terms

TS

YS

NTS

NSR

E

First order terms Sum of squares (SS) Degrees of freedom (dof) Mean square (MS)

7375.059 4 1843.765

8387.234 4 2096.808

93,799.58 4 23,449.9

0.0442 4 0.0110

5.394 4 1.3486

Second order terms Sum of squares (SS) Degrees of freedom (dof) Mean square (MS)

68,159.56 10 6815.956

64,984.14 10 6498.414

438,201.1 10 43,820.11

0.1345 10 0.0134

21.1925 10 2.11925

Error terms Sum of squares (SS) Degrees of freedom (dof) Mean square (MS)

1771.429 6 295.2381

1621.429 6 270.2381

16,942.86 6 2823.81

0.0064 6 0.0010

0.7085 6 0.1180

Lack of fit Sum of squares (SS) Degrees of freedom (dof) Mean square (MS)

13,098.79 10 1309.879

12,758.75 10 1275.875

121,980.5 10 12,198.05

0.0443 10 0.0044

4.827 10 0.4827

Fratio (calculated) Fratio (from table) (10, 6, 0.01)

4.436 7.87

4.72 7.87

4.319 7.87

4.1 7.87

4.088 7.87

Rratio (calculated) Rratio (from table) (14, 6, 0.01)

18.274 4.66

19.393 4.66

13.457 4.66

11.81 4.66

16.08 4.66

Whether the model is adequate?

Yes

Yes

Yes

Yes

Yes

M. Balasubramanian et al. / Materials and Design 29 (2008) 92–97 Table 8 Values of co-efficient of determination for all the models S. no.

Model

Co-efficient of determination (r2)

1 2 3 4 5

Yield strength Tensile strength Percentage elongation Notch tensile strength Notch strength ratio

0.91 0.91 0.89 0.89 0.89

97

welded Ti–6Al–4V alloy within the range of parameters considered for investigation. Acknowledgements The authors would like to thank the Head of the Department and faculty members of Manufacturing Engineering Department, Annamalai University, Annamalai Nagar, Tamil Nadu, for rendering their support and for making all the facilities available in the Metal joining laboratory and Material testing laboratory to carryout this investigation. The authors are also grateful to Mr. K. Anbazhagan, Chennai, for making necessary arrangements to procure the base metal for investigation. The authors wish to thank Mr. Babu, DRDO Project Associate, Annamalai University, for rendering helping hand to carryout the statistical analysis.

References

Fig. 2. Correlation graph for the response tensile strength.

the model may be considered to be adequate within the confidence limit. ANOVA test results for all the responses are presented in Table 7. From the table, it can be understood that all the developed models are adequate to predict the tensile properties of pulsed current GTA welded titanium alloy at 99% confidence level. Coefficient of determination ‘r2’ is used to find how close the predicted and experimental values lie and it is calculated using the following expression r2 ¼ Explained variation=Total variation The value of ‘r2’ is found to be falling between 0.89 and 0.91 for all the developed models as presented in Table 8, which indicates high correlation between experimental values and predicted values and this is further supported by correlation graph of tensile strength shown in Fig. 2. 4. Conclusions (a) Mathematical models have been developed to predict the tensile properties of pulsed current GTA welded Ti–6Al–4V alloy incorporating pulsed current parameters. (b) The developed models can be effectively used to predict the tensile properties of pulsed current GTA

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