# Improvement in the Design of Welded Joints of EN 235JR Low Carbon Steel by Multiple Response Surface Methodology

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{a}) of 3–4 µm can be achieved on high-quality weld cords, but values of 7–8 µm are more likely on industry standard welds cords [8]. Micro-hardness and hardness are usually used to quantify the strength of each constituent in the weld joint by determining the average hardness of each phase [9]. Some researchers [10,11] have investigated the relationship between hardness and tensile strength and used it to assess the strength of the welded joint. High values of hardness in the welded zone may be attributed to a fine grain size [12,13]. Lower values of hardness in the HAZ may be related to grain growth and a ferrite phase in this region [14,15]. In this sense, it is necessary for the difference between the hardness levels of parent material, weld cord and HAZ to be as low as possible so that the strength of the weld is as homogeneous as possible [16]. Moreover, the power consumed during the manufacture of welded joints affects greatly the yield, tensile strength, residual stresses and hardness. Similarly, the inputs or process parameters have a considerable influence on the weld area and power that is consumed, which can provide an idea of the amount of material that is provided to the welded joint. For example, the power that is consumed, the speed and the amount of filled material that is provided for the weld cord also should be considered, since they markedly affect the total manufacturing cost of welded products. The most desirable welded joint is the one that has the lowest possible values of residual stresses, surface roughness (R

_{a}), hardness and manufacturing cost, but with its yield stress, tensile strength and speed maximized. The process of achieving the optimal welded joint solely on the basis of trial-and-error when the design requirements of cost, strength and surface finish are considered is a difficult task that should result in an unacceptable cost. In this context, some researchers have used the response surface methodology (RSM) in order to reduce the number of experiments that are necessary to obtain the optimal combination of inputs or process parameters. RSM is a statistical method that is used widely to model and optimize processes. It uses the input variables of the process and their responses or outputs to identify the combined effect of the input variables and obtain the best response [17]. RSM attempts to replace the implicit functions of the original design optimization problem with an approximation model that is traditionally a polynomial function (regression models) and, therefore, less expensive to evaluate. When there is more than one output, several response surfaces should be optimized using MRS. In this paper, a group of regression models that are based on the RSM was used to determine the relationship between the welding process parameters (inputs) and the welded joints parameters (outputs). Then, while considering design requirements based on manufacturing cost, manufacturing speed, strength and surface finish, the optimal welded joints were achieved by the MRS with the desirability functions. The weld cord area is the welded joint parameter that is used when the design requirements are based on the cost, whereas yield stress, tensile strength, residual stresses and hardness are the parameters used when the design requirements are based on the welded joint strength. Finally, roughness (R

_{a}) is the parameter that is used when the design requirements are based on the surface finish. This paper concentrates on a study of the butt joint with complete penetration (X-groove) of EN 235JR low carbon steel for a range of speeds, currents and voltages for inputs or process parameters of 120–180 amps, 3–10 mm/s and 20–30 volts. The remaining inputs or process parameters (flow rate of the shielding gas, orientation of the electrode and the distance between the nozzle and plate) were assumed to be constants with values of 20.0 L/min, 80° and 4.0 mm, respectively.

## 2. Modelling Using the RSM

_{1}, x

_{2}, x

_{3}, …, x

_{k}) are the vectors of inputs, e is an error and f is a function that consists of cross-products of the terms that form the polynomial. The quadratic model (second-order) is one of the most widely-used polynomial functions and is expressed in Equation (2):

_{0}, b

_{i}, b

_{ii}and b

_{ij}are calculated by using regression analysis. Nevertheless, these functions sometimes do not give good results for complex problems with many nonlinearities and a high number of inputs. This is because they are continuous functions that are defined by polynomials and cannot be adjusted when the data are sparse. The p-value (or Prob. > F) is defined as the probability of obtaining a result that is equal to or greater than what was actually observed, assuming that the model is accurate. It can be computed by the analysis of variance (ANOVA). If the Prob. > F of the model and no term in the model exceeds the level of significance (say α = 0.05), the model may be considered to be adequate within a confidence interval of (1 − α). Some researchers have used ANOVA with the aim of analysing the influence of the inputs or process parameters on the outputs of the process [21,22]. When a problem has more than one output, it is called MRS and implicates conflict between outputs because an optimal configuration for one output may differ greatly from the optimal for another output. Harrington [23] presented a compromise between outputs. It consisted of desirability functions for each output, Equations (3) and (4), and an overall desirability that is defined as the geometric mean of the desirability D for each output (Equation (5)).

_{r}is the model that is used for prediction. A second higher degree polynomial should be used to optimize one or several responses [24]. The desirability approach involves transforming each estimated response into a unitless utility that is bounded by 0 < d

_{r}< 1, where a higher value of d

_{r}indicates that the response value is more desirable. The optimization part of the R package v.1.6, [25] searches for a combination of importance factors (or weights from 1–3) that simultaneously satisfy the optimization criteria of each of the responses and inputs.

## 3. Welded Joint Parameters that Were Studied Using RSM

## 4. Experimental Setup and Results Obtained

_{2}) (see Figure 1c). Each of the specimens was machined in order to obtain sufficient samples for the different welded joint characterization tests (see Figure 1d).

#### 4.1. Residual Stresses

#### 4.2. Hardness

#### 4.3. Yield Stress and Tensile Strength

#### 4.4. Surface Roughness

_{a}) appears on the left side of each figure, as well as the path that the portable roughness tester probe followed to determine the roughness (right side). The face of the weld bead shown in Figure 6b has higher values of waves than those that appear in Figure 6a, which generate higher values of roughness. The profile of the roughness shown in Figure 6a has a lower roughness value (R

_{a}= 1.63 μm) than the value that appears in Figure 6b (R

_{a}= 9.16 μm).

#### 4.5. Weld Cord Area Surface Roughness

## 5. Design of Experiments

_{a}), hardness (H), yield stress (YS), tensile strength (TS) and the maximum residual stress (RS). The range in which the different levels of current, speed and voltage were adjusted was based on the experience of the laboratory personnel, as well as on the manufacturing of a group of preliminary welded samples in order to ensure that the welded specimens had no defects and imperfections. Thus, for example, Figure 8 shows some preliminary tests in which the specimens that were manufactured present defects and imperfections. Figure 8a shows a weld bead in which the flow rate of the shielding gas and the orientation of the electrode are incorrect (in this case, 10.0 L/min and 65°, respectively, when the correct values are 20.0 L/min and 80°, respectively (see Section 4)). In this figure, the pores in the weld cord are visible. They have been caused by a poor melting of the filler material cord. Furthermore, Figure 8b shows a weld joint that was manufactured with the following input parameters: a current of 260 amp, a voltage of 30 volts and a speed of 3 mm/s. In this case, the heat supplied during the welding process was excessive and caused the metal base, which had a thickness of 6 mm, to melt.

## 6. Results and Discussion

#### 6.1. Modelling the Area, Yield Stress, Tensile Strength, Roughness and Residual Stress Using RSM

^{2}, p-value, MAE and RMSE) were used to select the most accurate model. These equations show the second degree polynomial functions that were obtained to model area (A), roughness (R

_{a}), hardness (H), yield stress (YS), tensile strength (TS) and residual stresses (RS). These equations show how each of the outputs is obtained by a combination of second-order polynomials that are formed by a combination of input variables.

^{2}− 1.337 × V + 0.0142 × C × V

_{a}= 30.084 − 0.284 × C + 0.001094 × C

^{2}+ 7.566 × S − 0.0285 × C × S + 0.1416 × S

^{2}− 2.455 × V + 0.0054 × C × V − 0.201 × S × V + 0.059 × V

^{2}

^{2}− 46.377 × V + 0.261 × C × V

^{2}− 167.101 × S + 0.882 × C × S − 2.888 × S

^{2}+ 48.827 × V − 0.355 × C × V + 2.351 × S × V

^{2}− 135.596 × S + 0.699 × C × S − 2.539 × S

^{2}+ 80.884 × V − 0.559 × C × V + 2.012 × S × V

^{2}+ 0.214 × C × S + 3.620 × S

^{2}+ 86.219 × V − 0.202 × C × V − 2.382 × S × V − 0.622 × V

^{2}

^{2}) was calculated as the measure of the amount of variation around the mean that was obtained by the regression model. The results showed that all values of R

^{2}are close to one. This indicates that these models possess good predictive capacity.

_{k}

_{Experiment}are the responses that were obtained experimentally, and Y

_{kModel}are those that were obtained from the quadratic models that were developed with RSM and m specimens. Table 9 shows the prediction errors, where the maximum error corresponds to YS (MAE equal to 6.826 and RMSE equal to 7.345), and the minimum error corresponds to RS (MAE equal to 2.993 and RMSE equal to 3.504).

_{a}(Figure 9b), H (Figure 9c), TS (Figure 9d), YS (Figure 9e) and RS (Figure 9f). The figures show that these models are adequate for the prediction of these values because the residuals that were obtained are small and the correlations between actual and predicted values are high.

#### 6.2. Multi-Response Optimization

_{a})). The overall desirability obtained in these design requirements was 0.789. From the results that appear in Table 10, Table 11, Table 12 and Table 13, it can be seen that the process parameters obtained are very similar for all different design requirements studied. Thus, for example, the range in which the current reaches its value for the different design requirements that were studied extends from 140.593 amps–150.372 amps, whereas the ranges for speed and voltage were, respectively, 7.139 mm/s–9.261 mm/s and 28.541 volts–29.999 volts. In addition, the optimal value of the voltage when the first three design requirements criteria were considered is 29.999 volts. From these results, it follows that the optimal process parameters that are obtained for different design requirements are found in a relatively narrow range.

_{k}

_{,norm}are the normalized outputs that were obtained from the outputs or welded joint parameters from the models that were developed with RSM and the outputs or welded joint parameters that were obtained experimentally. The error shown in the last two columns represents the MAE and RMSE, which have been normalized for each of the variables in each of the five design requirements that were studied. However, the normalized MAE and RMSE that appear in the last two rows correspond to the errors in each of the outputs or welded joint parameters studied. For example, when strength is considered to be a design requirement for welded joints, the errors obtained are the smallest (MAE = 0.15 and RMSE = 0.16), but when all variables are considered equally important, the error is the largest (MAE = 0.27 and RMSE = 0.28). The reason for this difference in the errors could be that, when all variables are considered equally important, the models must have a more general behaviour. In contrast, the maximum errors obtained for each of the outputs are lower when predicting hardness (MAE = 0.15 and RMSE = 0.16) and greater when predicting residual stresses (MAE = 0.28 and RMSE = 0.28). This difference may be due largely to the difficulty of obtaining the residual stress according to the hole-drilling strain-gage method [38] used in this case. It requires a significant number of operations for its development. In addition, the values of MAE and RMSE that were obtained for each of the different outputs or welded joint parameters are all in acceptable agreement.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) ABB 1500 IRB robot with the ESAB 180 welding machine used to manufacture all welded joints with gas metal arc welding (GMAW). (

**b**) The welding process employed in the manufacture of the butt joint with complete penetration (X-groove). (

**c**) Common welding parameters used in GMAW and considered in this case. (

**d**) Butt joint with complete penetration (X-groove) manufactured: details of the specimens to be machined for the different welded joint characterization tests.

**Figure 2.**(

**a**) X-ray radiograph that shows a weld bead that was analysed. (

**b**) Analysis using ultrasonic testing.

**Figure 3.**(

**a**) RS-200 milling guide machine. (

**b**) Detail of the strain gauge rosette type CEA-06-062UM-120.

**Figure 4.**(

**a**) Lines in which the hardness values in both the weld and the base metal were measured. (

**b**) Micrograph that shows the hardness HV values obtained every 0.2 mm. (

**c**) Varying hardness values obtained in both lines (centre line and parallel line).

**Figure 5.**(

**a**) Yield stress and tensile strength according to the ISO 5178 Standard Test Method. (

**b**) Specimens after they were tested according to ISO 5178.

**Figure 6.**Roughness profile obtained and paths that the portable roughness tester probes followed to determine the roughness. (

**a**) Low values of roughness obtained and (

**b**) high values of roughness obtained.

**Figure 8.**(

**a**) Pores in the weld cord due to incorrect values of flow rate of the shielding gas and the orientation of the electrode. (

**b**) Melting of the base metal due to excessive heat supplied to the welding process.

**Figure 9.**Scatter diagram of: (

**a**) area (A), (

**b**) roughness (R

_{a}), (

**c**) residual stress (RS), (

**d**) hardness (H), (

**e**) yield stress (YS) and (

**f**) tensile strength (TS).

**Table 1.**Independent variables and experimental design levels used with the Box–Behnken design (BBD) method.

Input | Notation | Magnitude | Levels | ||
---|---|---|---|---|---|

−1 | 0 | 1 | |||

Current | C | amps | 120 | 150 | 180 |

Speed | S | mm/s | 3 | 6.5 | 10 |

Voltage | V | volts | 20 | 25 | 30 |

**Table 2.**Design matrix and specimens obtained by BBD. A, area of the weld cord; H, hardness; YS, yield strength; TS, tensile strength; RS, residual stress.

Inputs | Outputs | ||||||||
---|---|---|---|---|---|---|---|---|---|

Exp. No. | C | S | V | A | R_{a} | H | YS | TS | RS |

(amps) | (mm/s) | (volts) | (mm^{2}) | (µm) | (MPa) | (MPa) | (MPa) | (MPa) | |

14 | 150 | 6.5 | 25 | 26.7219 | 2.3 | 179 | 339.229 | 396.45 | 79.3 |

1 | 120 | 3 | 25 | 42.342 | 1.967 | 185 | 355.449 | 404.63 | 172.991 |

3 | 120 | 10 | 25 | 12.3578 | 8.269 | 244 | 67.526 | 158.3 | 267.577 |

6 | 180 | 6.5 | 20 | 29.642 | 3.608 | 172 | 311.631 | 414.11 | 128.07 |

10 | 150 | 10 | 25 | 18.9386 | 5.091 | 251 | 298.46 | 341.85 | 180.314 |

12 | 150 | 10 | 30 | 22.5676 | 2.57 | 220 | 339.883 | 382.85 | 195.392 |

13 | 150 | 6.5 | 25 | 26.5941 | 2.82 | 205 | 337.921 | 359.05 | 89.451 |

4 | 180 | 10 | 25 | 22.454 | 2.508 | 286 | 294.12 | 334.79 | 323.307 |

16 | 150 | 6.5 | 25 | 28.5 | 2.58 | 205 | 356.43 | 416.5 | 83.774 |

8 | 180 | 6.5 | 30 | 42.934 | 5.411 | 182 | 332.603 | 364.37 | 155.425 |

15 | 150 | 6.5 | 25 | 24.1788 | 2.59 | 210 | 349.236 | 411.63 | 89.5 |

5 | 120 | 6.5 | 20 | 17.608 | 6.299 | 289 | 106.12 | 126.52 | 101.618 |

2 | 180 | 3 | 25 | 58.75 | 8.196 | 160 | 211.282 | 287.42 | 130.536 |

17 | 150 | 6.5 | 25 | 25.3 | 2.32 | 177 | 344.069 | 382.7 | 81.7 |

11 | 150 | 3 | 30 | 55.858 | 8.95 | 130 | 351.865 | 406.37 | 132.678 |

7 | 120 | 6.5 | 30 | 21.274 | 4.852 | 142 | 340.472 | 412.67 | 250.234 |

9 | 150 | 3 | 25 | 60.648 | 3.716 | 160 | 376.18 | 424.71 | 62.902 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

S | 1 | 2495 | 2495 | 285 | 3.29 × 10^{−9} | *** |

C × S | 1 | 352.21 | 352.21 | 40 | 5.54 × 10^{−5} | *** |

S^{2} | 1 | 404.02 | 404.02 | 46 | 3.00 × 10^{−5} | *** |

V | 1 | 87.24 | 87.24 | 10 | 9.17 × 10^{−3} | ** |

C × V | 1 | 133.55 | 133.55 | 15 | 2.465× 10^{−3} | ** |

Residuals | 11 | 96.44 | 8.77 | |||

R^{2} | 0.984 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

C | 1 | 0.346 | 0.346 | 2 | 2.394057 × 10^{−1} | |

C^{2} | 1 | 9 | 9 | 44 | 2888 × 10^{−4} | *** |

S | 1 | 2 | 2 | 12 | 1.15299 × 10^{−2} | * |

C × S | 1 | 36 | 36 | 172 | 3.51 × 10^{−6} | *** |

S^{2} | 1 | 9 | 9 | 42 | 3.458 × 10^{−4} | *** |

V | 1 | 2 | 2 | 8 | 2.58224 × 10^{−2} | * |

C × V | 1 | 3 | 3 | 13 | 9.3021 × 10^{−3} | ** |

S × V | 1 | 19 | 19 | 89 | 3.14 × 10^{−5} | *** |

V^{2} | 1 | 6 | 6 | 29 | 1.0289 × 10^{−3} | ** |

Residuals | 7 | 1 | 0.209 | |||

R^{2} | 0.991 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

C | 1 | 450 | 450 | 2 | 1.988151 × 10^{−1} | |

S | 1 | 16,744.5 | 16,744.5 | 70 | 7.71 × 10^{−6} | *** |

C × S | 1 | 1122.3 | 1122.3 | 5 | 5.48739 × 10^{−2} | . |

S^{2} | 1 | 330.5 | 330.5 | 1 | 2.655811 × 10^{−1} | |

V | 1 | 6984.7 | 6984.7 | 29 | 2.923 × 10^{−4} | *** |

C × V | 1 | 6162.3 | 6162.3 | 26 | 4.692 × 10^{−4} | *** |

Residuals | 10 | 2376.3 | 237.6 | |||

R^{2} | 0.964 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

C | 1 | 9805 | 9805 | 17 | 3.4049 × 10^{−3} | ** |

C^{2} | 1 | 35,302 | 35,302 | 61 | 5.27 × 10^{−5} | *** |

S | 1 | 10,862 | 10,862 | 19 | 2.5365 × 10^{−3} | ** |

C × S | 1 | 34,366 | 34,366 | 59 | 5.80 × 10^{−5} | *** |

S^{2} | 1 | 1902 | 1902 | 3 | 1.080436 × 10^{−1} | |

V | 1 | 15,245 | 15,245 | 26 | 9.059 × 10^{−4} | *** |

C × V | 1 | 11,383 | 11,383 | 20 | 2.2114 × 10^{−3} | ** |

S × V | 1 | 2539 | 2539 | 4 | 7.00186 × 10^{−2} | . |

Residuals | 8 | 4650 | 581 | |||

R^{2} | 0.981 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

C | 1 | 11143 | 11143 | 11 | 1.07556 × 10^{−2} | * |

C^{2} | 1 | 26,095.2 | 26,095.2 | 26 | 9.773 × 10^{−4} | *** |

S | 1 | 11,654.1 | 11,654.1 | 11 | 9.622 × 10^{−3} | ** |

C × S | 1 | 21,564.9 | 21,564.9 | 21 | 1.7561 × 10^{−3} | ** |

S^{2} | 1 | 1363.2 | 1363.2 | 1 | 2.80849 × 10^{−1} | |

V | 1 | 13,132.5 | 13,132.5 | 13 | 7.09 × 10^{−3} | ** |

C × V | 1 | 28,205.5 | 28,205.5 | 28 | 7.641 × 10^{−4} | *** |

S × V | 1 | 1859.6 | 1859.6 | 2 | 2.137441 × 10^{−1} | * |

Residuals | 8 | 8154.2 | 1019.3 | |||

R^{2} | 0.966 |

Var. | Df | Sum of Sq. | Mean Square | F-Value | p-Value | Sig. Code |
---|---|---|---|---|---|---|

C | 1 | 379.2 | 379.2 | 2 | 1.821709 × 10^{−1} | |

C^{2} | 1 | 27,557 | 27,557 | 155 | 1.62 × 10^{−6} | *** |

C × S | 1 | 29,079 | 29,079 | 164 | 1.32 × 10^{−6} | *** |

S^{2} | 1 | 7656.8 | 7656.8 | 43 | 0.0001758 | *** |

V | 1 | 11,144.2 | 11,144.2 | 63 | 4.70 × 10^{−5} | *** |

C × V | 1 | 3676 | 3676 | 21 | 1.8783 × 10^{−3} | ** |

S × V | 1 | 8275.1 | 8275.1 | 47 | 1345 × 10^{−4} | *** |

V^{2} | 1 | 679.7 | 679.7 | 4 | 8.6221 × 10^{−2} | . |

Residuals | 8 | 1421.5 | 177.7 | |||

R^{2} | 0.992 |

**Table 9.**Results of the predicted error criteria for area (A), roughness (Ra), hardness (H), yield stress (YS), tensile strength (TS) and residual stresses (RS).

A (mm^{2}) | R_{a} (µm) | H (kp/mm^{2}) | TS (MPa) | YS (MPa) | RS (MPa) | |
---|---|---|---|---|---|---|

MAE | 4.223 | 3.513 | 6.597 | 4.529 | 6.826 | 2.993 |

RMSE | 5.311 | 4.221 | 7.484 | 5.359 | 7.345 | 3.504 |

Goal | Importance | Value | Desirability | |
---|---|---|---|---|

Current (C) | In range → 120.0 | 1.0 | 143.788 | 1.0 |

Speed (S) | Maximize → 10.0 | 1.0 | 8.218 | 0.745 |

Voltage (V) | In range → 20.0 | 1.0 | 29.999 | 1.0 |

Area (mm^{2}) | Minimize → 12.357 | 1.0 | 23.819 | 0.762 |

R_{a} (µm) | Minimize → 1.967 | 1.0 | 3.159 | 0.829 |

H (kp/mm^{2}) | Minimize → 130.0 | 1.0 | 174.803 | 0.718 |

YS (MPa) | Maximize → 376.18 | 1.0 | 376.186 | 1.0 |

TS (MPa) | Maximize → 424.71 | 1.0 | 424.976 | 1.0 |

RS (MPa) | Minimize → 62.92 | 1.0 | 149.859 | 0.666 |

Overall Desirability | 0.808 |

Goal | Importance | Value | Desirability | |
---|---|---|---|---|

Current (C) | In range → 120.0 | 1.0 | 140.593 | 1.000 |

Speed (S) | Maximize → 10.0 | 1.0 | 8.192 | 0.741 |

Voltage (V) | In range → 20.0 | 1.0 | 29.999 | 1.0 |

Area (mm^{2}) | Minimize → 12.357 | 3.0 | 22.819 | 0.480 |

R_{a} (µm) | Minimize → 1.967 | 1.0 | 3.310 | 0.807 |

H (kp/mm^{2}) | Minimize → 130.0 | 1.0 | 170.551 | 0.744 |

YS (MPa) | Maximize → 376.18 | 1.0 | 369.756 | 0.979 |

TS (MPa) | Maximize → 424.71 | 1.0 | 423.210 | 0.994 |

RS (MPa) | Minimize → 62.9 | 1.0 | 157.145 | 0.638 |

Overall Desirability | 0.749 |

Goal | Importance | Value | Desirability | |
---|---|---|---|---|

Current (C) | In range → 120.0 | 1.0 | 149.88 | 1.0 |

Speed (S) | Maximize → 10.0 | 3.0 | 9.261 | 0.715 |

Voltage (V) | In range → 20.0 | 1.0 | 29.999 | 1.0 |

Area (mm^{2}) | Minimize → 12.357 | 1.0 | 24.318 | 0.752 |

R_{a} (µm) | Minimize → 1.967 | 1.0 | 2.656 | 0.901 |

H (kp/mm^{2}) | Minimize → 130.0 | 1.0 | 202.029 | 0.546 |

YS (MPa) | Maximize → 376.18 | 1.0 | 368.234 | 0.974 |

TS (MPa) | Maximize → 424.71 | 1.0 | 408.647 | 0.946 |

RS (MPa) | Minimize → 62.9 | 1.0 | 167.653 | 0.597 |

Overall Desirability | 0.759 |

**Table 13.**The fourth criterion considered: welded joint strength based on tensile strength, yield stress and residual stress.

Goal | Importance | Value | Desirability | |
---|---|---|---|---|

Current (C) | In range → 120 | 1.0 | 149.086 | 1.0 |

Speed (S) | Maximize → 10 | 1.0 | 7.139 | 0.591 |

Voltage (V) | In range → 20 | 1.0 | 28.541 | 1.0 |

Area (mm^{2}) | Minimize → 12.357 | 1.0 | 26.964 | 0.697 |

R_{a} (µm) | Minimize → 1.967 | 1.0 | 3.000 | 0.852 |

H (kp/mm^{2}) | Minimize → 130 | 1.0 | 176.750 | 0.705 |

YS (MPa) | Maximize → 376.18 | 3.0 | 380.721 | 1.0 |

TS (MPa) | Maximize → 424.71 | 3.0 | 424.712 | 1.0 |

RS (MPa) | Minimize → 62.9 | 3.0 | 118.240 | 0.488 |

Overall Desirability | 0.739 |

Goal | Importance | Value | Desirability | |
---|---|---|---|---|

Current (C) | In range → 120 | 1.0 | 150.372 | 1.0 |

Speed (S) | Maximize → 10 | 1.0 | 8.561 | 0.794 |

Voltage (V) | In range → 20 | 1.0 | 29.877 | 1.0 |

Area (mm^{2}) | Minimize → 12.357 | 1.0 | 25.067 | 0.736 |

R_{a} (µm) | Minimize → 1.967 | 3.0 | 2.472 | 0.798 |

H (kp/mm^{2}) | Minimize → 130 | 1.0 | 190.386 | 0.620 |

YS (MPa) | Maximize → 376.18 | 1.0 | 379.262 | 1.0 |

TS (MPa) | Maximize → 424.71 | 1.0 | 419.307 | 0.981 |

RS (MPa) | Minimize → 62.9 | 1.0 | 148.494 | 0.671 |

Overall Desirability | 0.789 |

**Table 15.**Outputs or welded joint parameters that were obtained according to the five design requirements studied

Des. Crit. | Experimental Values Obtained | |||||||
---|---|---|---|---|---|---|---|---|

A (mm^{2}) | R_{a} (µm) | H (kp/mm^{2}) | YS (MPa) | TS (MPa) | RS (MPa) | MAE | RMSE | |

1st Crit. | 22.23 | 2.85 | 169.23 | 368.29 | 418.76 | 164.95 | 0.27 | 0.28 |

2nd Crit. | 21.43 | 3.12 | 168.32 | 358.66 | 419.32 | 136.45 | 0.25 | 0.27 |

3rd Crit. | 25.28 | 2.46 | 192.95 | 371.34 | 412.65 | 149.75 | 0.21 | 0.22 |

4th Crit. | 25.86 | 3.11 | 181.23 | 383.68 | 427.22 | 105.23 | 0.15 | 0.16 |

5th Crit. | 24.87 | 2.31 | 193.50 | 384.62 | 421.37 | 128.54 | 0.15 | 0.18 |

MAE | 0.19 | 0.19 | 0.15 | 0.23 | 0.20 | 0.28 | 0.21 | 0.21 |

RMSE | 0.21 | 0.20 | 0.16 | 0.26 | 0.22 | 0.28 | 0.22 | 0.23 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lostado Lorza, R.; Escribano García, R.; Martínez Calvo, M.Á.; Múgica Vidal, R. Improvement in the Design of Welded Joints of EN 235JR Low Carbon Steel by Multiple Response Surface Methodology. *Metals* **2016**, *6*, 205.
https://doi.org/10.3390/met6090205

**AMA Style**

Lostado Lorza R, Escribano García R, Martínez Calvo MÁ, Múgica Vidal R. Improvement in the Design of Welded Joints of EN 235JR Low Carbon Steel by Multiple Response Surface Methodology. *Metals*. 2016; 6(9):205.
https://doi.org/10.3390/met6090205

**Chicago/Turabian Style**

Lostado Lorza, Ruben, Ruben Escribano García, María Ángeles Martínez Calvo, and Rodolfo Múgica Vidal. 2016. "Improvement in the Design of Welded Joints of EN 235JR Low Carbon Steel by Multiple Response Surface Methodology" *Metals* 6, no. 9: 205.
https://doi.org/10.3390/met6090205