Austenitic stainless steel sheets have gathered wide acceptance in the fabrication of components, which require high temperature resistance and corrosion resistance, such as metal bellows used in expansion joints in aircraft, aerospace, and petroleum industry. In case of single pass welding of thinner sections of this alloy, Pulsed Current Microplasma Arc Welding (PCMPAW) was found beneficial due to its advantages over the conventional continuous current process. The quality of welded joint depends on the grain size, hardness, and ultimate tensile strength, which have to be properly controlled and optimized to ensure better economy and desirable mechanical characteristics of the weld. This paper highlights the development of empirical mathematical equations using multiple regression analysis, correlating various process parameters to grain size, and ultimate tensile strength in PCMPAW of AISI 304L sheets. The experiments were conducted based on a fivefactor, fivelevel central composite rotatable design matrix. A genetic algorithm (GA) was developed to optimize the process parameters for achieving the desired grain size, hardness, and ultimate tensile strength.
AISI 304L is an austenitic stainless steel with excellent strength and good ductility at high temperature. Typical applications include aeroengine hot section components, miscellaneous hardware, tooling, and liquid rocket components involving cryogenic temperature. AISI 304L can be joined using a variety of welding methods, including Gas Tungsten Arc Welding (GTAW), Plasma Arc Welding (PAW), Laser Beam Welding (LBW), and Electron Beam Welding (EBW). Of these methods, low current PAW (MicroPAW) has attracted particular attention and has been used extensively for the fabrication of metal bellows, diaphragms which require high strength and toughness. PAW is conveniently carried out using one of two different current modes, namely, a continuous current (CC) mode or a pulsed current (PC) mode.
Pulsed current MPAW involves cycling the welding current at selected regular frequency. The maximum current is selected to give adequate penetration and bead contour, while the minimum is set at a level sufficient to maintain a stable arc [
In this investigation, experiments conducted using the design of experiments concept were used for developing mathematical models to predict such variables. Many works were reported in the past for predicting bead geometry, heat affected zone, bead volume, and so forth, using mathematical models for various welding processes [
Kim et al. reviewed that optimization using regression modeling, neural network, and Taguchi methods could be effective only when the welding process was set near the optimal conditions or at a stable operating range [
In the present study, a sequential genetic algorithm has been used to optimize the process parameters and achieve minimum fusion zone grain size, maximum hardness, and ultimate tensile strength of PCMPAW AISI 304L sheets.
Austenitic stainless steel (AISI 304L) sheets of
Chemical composition of AISI 304L (weight%).
C  Si  Mn  P  S  Cr  Ni  Mo  Ti  N 

0.021  0.35  1.27  0.030  0.001  18.10  8.02  —  —  0.053 
Welding conditions.
Power source  Secheron Microplasma Arc Machine (Model: PLASMAFIX 50E) 
Polarity  DCEN 
Mode of operation  Pulse mode 
Electrode  2% thoriated tungsten electrode 
Electrode diameter  1 mm 
Plasma gas  Argon and hydrogen 
Plasma gas flow rate  6 Lpm 
Shielding gas  Argon 
Shielding gas flow rate  0.4 Lpm 
Purging gas  Argon 
Purging gas flow rate  0.4 Lpm 
Copper nozzle diameter  1 mm 
Nozzle to plate distance  1 mm 
Welding speed  260 mm/min 
Torch position  Vertical 
Operation type  Automatic 
Important factors and their levels.
Levels  

Serial number  Input factor  Units  −2  −1  0  +1  +2 
1  Peak current  Amperes  6  6.5  7  7.5  8 
2  Back current  Amperes  3  3.5  4  4.5  5 
3  Pulse rate  Pulses/second  20  30  40  50  60 
4  Pulse width  %  30  40  50  60  70 
Design matrix and experimental results.
Serial number  Peak current (Amperes)  Back current (Amperes)  Pulse rate (pulses/second)  Pulse width (%)  Grain size (Microns)  Hardness (VHN)  Ultimate tensile strength (UTS) (Mpa) 

1  −1  −1  −1  −1  20.812  198  713 
2  1  −1  −1  −1  30.226  190  705 
3  −1  1  −1  −1  21.508  199  718 
4  1  1  −1  −1  27.536  193  706 
5  −1  −1  1  −1  27.323  193  706 
6  1  −1  1  −1  25.206  195  710 
7  −1  1  1  −1  25.994  195  705 
8  1  1  1  −1  23.491  197  706 
9  −1  −1  −1  1  26.290  194  705 
10  1  −1  −1  1  29.835  190  700 
11  −1  1  −1  1  20.605  200  715 
12  1  1  −1  1  27.764  193  708 
13  −1  −1  1  1  30.095  190  698 
14  1  −1  1  1  26.109  194  706 
15  −1  1  1  1  27.385  193  704 
16  1  1  1  1  25.013  195  710 
17  −2  0  0  0  20.788  196  710 
18  2  0  0  0  25.830  195  706 
19  0  −2  0  0  31.663  188  701 
20  0  2  0  0  27.263  193  708 
21  0  0  −2  0  25.270  195  712 
22  0  0  2  0  26.030  194  705 
23  0  0  0  −2  24.626  195  711 
24  0  0  0  2  26.626  194  705 
25  0  0  0  0  24.845  196  710 
26  0  0  0  0  24.845  196  710 
27  0  0  0  0  20.145  200  720 
28  0  0  0  0  24.845  195  710 
29  0  0  0  0  20.045  201  718 
30  0  0  0  0  24.845  195  710 
31  0  0  0  0  20.445  198  712 
Three metallurgical samples are cut from each joint, with the first sample being located at 25 mm behind the trailing edge of the crater at the end of the weld and mounted using Bakelite. Sample preparation and mounting are done as per ASTM E 31 standard. The samples are surface grounded using 120 grit size belt with the help of belt grinder and polished using grade 1/0 (245 mesh size), grade 2/0 (425 mesh size), and grade 3/0 (515 mesh size) sand paper. The specimens are further polished by using aluminum oxide initially and by utilizing diamond paste and velvet cloth in a polishing machine. The polished specimens are etched by using 10% Oxalic acid solution to reveal the microstructure as per ASTM E407. Micrographs are taken using metallurgical microscope (Make: Carl Zeiss, Model: Axiovert 40MAT) at 100x magnification. The micrographs of parent metal zone and weld fusion zone are shown in Figures
Microstructure of parent metal zone.
Microstructure of weld fusion zone.
Grain size of parent metal and weld joint is measured by using Scanning Electron Microscope (Make: INCA Penta FETx3, Model: 7573). Figures
Grain size of parent metal.
Grain size of weld fusion zone.
Vickers’s microhardness testing machine (Make: METSUZAWA CO., LTD, JAPAN, Model: MMTX7) was used to measure the hardness at the weld fusion zone by applying a load of 0.5 Kg as per ASTM E384. Average values of three samples of each test case are presented in Table
Three transverse tensile specimens are prepared as per ASTM E8 M04 guidelines and the specimens after wire cut Electro Discharge Machining are shown in Figure
The output response of the weld joint (
Using MINITAB 14 statistical software package, the significant coefficients were determined and final model is developed using significant coefficients to estimate grain size, hardness, and ultimate tensile strength values of weld joint.
The final mathematical models are given by grain size (
The adequacy of the developed models was tested using the analysis of variance technique (ANOVA). As per this technique, if the calculated value of the
ANOVA table.
Source  DF  Seq SS  Adj SS  Adj MS 



Grain size  
Regression  14  249.023  249.023  17.7873  6.10  0.000 
Linear  4  65.207  65.207  16.3018  5.59  0.005 
Square  4  91.443  91.443  22.8608  7.84  0.001 
Interaction  6  92.372  92.372  15.3954  5.28  0.004 
Residual error  16  46.639  46.639  2.9149  
Lack of fit  10  9.750  9.750  0.9750  0.16  0.994 
Pure error  6  36.889  36.889  6.1481  
Total 





Hardness  
Regression  14  228.18  228.18  16.299  5.67  0.001 
Linear  4  61.17  61.17  15.292  5.32  0.006 
Square  4  83.64  83.64  20.910  7.27  0.002 
Interaction  6  83.38  83.38  13.896  4.83  0.005 
Residual error  16  46.01  46.01  2.876  
Lack of fit  10  10.58  10.58  1.058  0.18  0.991 
Pure Error  6  35.43  35.43  5.905  
Total 





Ultimate tensile strength  
Regression  14  676.218  676.218  48.3013  6.87  0.000 
Linear  4  205.667  205.667  51.4167  7.31  0.002 
Square  4  210.551  210.551  52.6379  7.48  0.001 
Interaction  6  260.000  260.000  43.3333  6.16  0.002 
Residual error  16  112.524  112.524  7.0327  
Lack of fit  10  1.667  1.667  0.1667  0.01  1.000 
Pure error  6  110.857  110.857  18.4762  
Total 


DF: degrees of freedom, SS: sum of squares, MS: mean squares, and
From Table
The purpose of optimization is to minimize grain size and maximize hardness and ultimate tensile strength. The tool used for optimization is GA. GA is an adaptive search and optimization algorithm that mimics principles of natural genetics. Due to their simplicity, ease of operation, minimum requirements, and global perspective they have been successfully used in a wide variety of problem domains [
GA simulates the survival of the fittest among individuals over consecutive generations for solving a problem. Each generation consists of a population of characters. Each individual represents a point in a search space and a possible solution. The individuals in the population are then made to go through a process of evolution. The basic concept of GA is to encode a potential solution to a problem as a series of parameters. A single set of parameter value is termed as the genome of an individual solution. An initial population of individuals is generated randomly. In every generation the individuals in the current population are decoded according to a fitness function. The chromosomes with the highest population fitness are selected for mating. The genes of the parameters are allowed to exchange to produce new ones. These new ones then replace the earlier ones in the next generation. Thus the old population is discarded and the new population becomes the current population. The current population is checked for acceptability or solution. The iteration is stopped after the completion of maximum number of generations or on the attainment of the best results [
The GA algorithm for the optimization problem is given below.
Step 1: choose a coding to represent problem parameters, a selection operator, a crossover operator, and a mutation operator.
Step 2: choose population size (
Step 3: initialize a random population of strings of size
Step 4: if
Step 5: perform crossover on random pair of strings.
Step 6: perform mutation on every string.
Step 7: evaluate strings in the new population; set
Parameters used in GA.
Grain size  Hardness  Ultimate tensile strength  

1  Sample size  30  40  40 
2  Crossover probability  0.7  0.96  0.2 
3  Mutation probability  0.1  0.7  0.01 
4  Number of generations  100  100  100 
5  Type of crossover  Single  Single  Single 
The optimization of grain size, hardness, and ultimate tensile strength was carried with the help of its mathematical equation. The mathematical equation is considered as objective function. The source code was developed using Turbo C. It is desirable to maximize hardness and ultimate tensile strength and minimize grain size. The objective function for minimizing grain size, as in (
Figure
Variation of grain size with number of generations.
Figure
Variation of hardness with number of generations.
Figure
Variation of ultimate tensile strength with number of generations.
Based on the results obtained in GA, the optimum values of PCMPAW input parameters and output responses like grain size, hardness, and ultimate tensile strength are computed and presented in Table
Comparison of GA and experimental values.
Welding parameters  Experimental values  GA values 

Grain size  
Peak current (Amperes)  7  6.634 
Back current (Amperes)  4  3.851 
Pulse rate (pulses/second)  40  36.386 
Pulse width (%)  50  55.011 
Grain size (Microns)  20.045  22.13219 


Hardness  
Peak current (Amperes)  7  6.517 
Back current (Amperes)  4  4.117 
Pulse rate (pulses/second)  40  30.276 
Pulse width (%)  50  40.4843 
Hardness (VHN)  201  201.033981 


Ultimate tensile strength  
Peak current (Amperes)  7  6.514 
Back current (Amperes)  4  3.912 
Pulse rate (pulses/second)  40  30.098 
Pulse width (%)  50  40.004 
Ultimate tensile strength (Mpa)  720  718.7376 
Empirical models are developed for grain size, hardness, and ultimate tensile strength for PCMPAW AISI 304L austenitic steel sheets using RSM CCD design matrix. The weld quality parameters like grain size, hardness, and ultimate tensile strength are optimized using GA. The objective is to minimize grain size and maximize hardness and ultimate tensile strength. The optimum values obtained using GA are 22.13219 Microns grain size, 201.033981 VHN hardness, and 718.7376 MPa ultimate tensile strength. The optimum values obtained using GA are in good agreement with experimental values
The authors declare that there is no conflict of interests regarding the publishing of this paper.
The authors would like to thank Shri. R. Gopla Krishnan, Director, M/s Metallic Bellows (I) Pvt Ltd, Chennai, India, and Mr. P. V. Vinay, Associate Professor, GVP College for PG courses (Technical Campus), Visakhapatnam, for their support to prepare this paper.