TRIP steel sheets

TRIP steel sheets

Optics & Laser Technology 44 (2012) 92–101 Contents lists available at ScienceDirect Optics & Laser Technology journal homepage: www.elsevier.com/lo...

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Optics & Laser Technology 44 (2012) 92–101

Contents lists available at ScienceDirect

Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec

Statistical modeling of laser welding of DP/TRIP steel sheets U. Reisgen, M. Schleser, O. Mokrov, E. Ahmed n RWTH Aachen University, Welding and Joining Institute, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 January 2011 Received in revised form 28 April 2011 Accepted 19 May 2011 Available online 23 June 2011

In this research work, a statistical analysis of the CO2 laser beam welding of dual phase (DP600)/ transformation induced plasticity (TRIP700) steel sheets was done using response surface methodology. The analysis considered the effect of laser power (2–2.2 kW), welding speed (40–50 mm/s) and focus position (  1 to 0 mm) on the heat input, the weld bead geometry, uniaxial tensile strength, formability limited dome height and welding operation cost. The experimental design was based on Box–Behnken design using linear and quadratic polynomial equations for predicting the mathematical models. The results indicate that the proposed models predict the responses adequately within the limits of welding parameters being used and the welding speed is the most significant parameter during the welding process. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Laser welding Design of experiment Statistical modeling

1. Introduction Tailor welded blanks (TWBs) of advanced high strength steels (AHSS), e.g. DP and TRIP steels, are rapidly gaining popularity in the automotive industry as they allow materials that may be different in thickness or material properties or both to be combined in a single pressed and stamped part in order to improve product performance. They are the result of a neverending quest for a material that allows increased fuel efficiency while allowing for ease of manufacturability, performance and styling. According to the press release of a material supplier, about 15% of the body structure of a car is made of TWBs parts, which will increase to 25–30% in the next 5–10 years [1]. Welding of AHSS is a challenge since the characteristics of high strength with good formability cannot be sustained under the extensive heating, melting and solidification during welding process. Welding input parameters play a very significant role in determining the quality of a weld joint. The joint quality can be defined in terms of properties such as weld bead geometry, mechanical properties and distortion. Generally, the quality of a weld joint is directly influenced by the welding input parameters during the welding process; therefore, welding can be considered as a multi-input multi-output process. Unfortunately, a common problem that has faced the manufacturer is the control of the process input parameters to obtain a good welded joint with the

n

Corresponding author. Tel.: þ492418093870/71; fax: þ492418092170. E-mail addresses: [email protected], [email protected] (E. Ahmed). 0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.05.025

required bead geometry and weld quality with minimal detrimental residual stresses and distortion [2]. Traditionally, a time-consuming trial and error development effort, with weld input parameters chosen by the skill of the engineer or machine operator should be used to determine the weld input parameters for every new welded product to obtain a welded joint with the required specifications. Then welds are examined to determine whether they meet the specification or not. Finally the weld parameters can be chosen to produce a welded joint that closely meets the joint requirements [3]. Nowadays, application of design of experiment (DoE), evolutionary algorithms and computational network are widely used to develop mathematical relationships between the welding process input parameters and the output variables of the weld joint in order to determine the welding input parameters that lead to the desired weld quality. Koleva [4] studied the influence of electron beam welding parameters, namely electron beam power, welding velocity, distance from the main surface of the magnetic lens to the focus point and the distance between the magnetic lens and the sample surface on the welding depth and width. The experiment was performed with samples of 1H18NT austenitic steel. The author has suggested the use of the developed models for online control of the process. This allows the selection of the optimal levels eliminates the time required for testing and prevents losses of components. The relationship between electron beam welding parameters (beam power, welding velocity and focus position) and weld depth and weld width using response surface methodology (RSM) in order to improve the quality of the process in mass production has been established by Koleva [5]. The author reported that the optimal process parameter values when welding stainless steel are power of 6.5–8 kW, welding

U. Reisgen et al. / Optics & Laser Technology 44 (2012) 92–101

velocity of 11.667–1.333 mm/s and focus position of 78 mm below the sample surface. Benyounis et al. [6] applied the RSM to investigate the effect of laser beam welding (LBW) parameters (laser power, welding speed and focal point position) based on four responses (heat input, penetration, bead width and width of heat affected zone) in CO2 laser butt welding of medium carbon steel plates of 5 mm thick. The authors found that the heat input plays an imported role in the weld bead parameters and welding speed has a negative effect while laser power has a positive effect on all the responses. Sathavornvichit et al. [7] studied the optimal factors of flux cored arc welding process for steel ST37. The process variables current (250–300 A), voltage (25–30 V), stick out (45–55 mm) and angle (451–751) of welding are used in the study of optimization of tensile of weldment by RSM follow a central composite design. The authors indicated that the optimum conditions are 300 A of current, 30 V of voltage, 45 mm of stick out and 601 of angle. The effect of the laser welding parameters on the bead geometry of 2.5 mm thick AISI 304 stainless steel has been evaluated by Manonmani et al. [8]. In this study the relationships between the process parameters (beam power, welding speed and beam incidence angle) and the weld bead parameters (penetration, bead width and area of penetration) have been developed using RSM. To verify the developed models a conformity test run was carried out using intermediate values of the process parameters. It was confirmed that the models developed were accurate since the error percentages were between 4.317% and 3.914%. It was demonstrated that the depth of penetration and penetration area increase as the beam power and the beam angle increase. Also, as the welding speed increases, the width decreases, whereas the penetration depth and area increase to an optimum value and then decrease with further increases in welding speed. This is due to the fact that the effect of key holing is predominant at lower speed and as the welding speed is increased the mode of heat transfer changes from key holing to conduction type of welding. It was reported that the variation in the bead width is slightly affected by the process parameters. Benyounis and Olabi [9] introduced a comprehensive literature review of the application of statistical techniques in the area of welding evaluation and optimization. This review was classified according to the output features of the weld, i.e. bead geometry and mechanical properties of the welds. The authors also gave a comparison between the most common statistical approaches used in the evaluation of welding processes. The authors concluded that the evaluation methods covered in this survey are appropriate for modeling, control and optimizing the different welding process. The survey reveals the high level of interest in the adaptation of RSM and artificial neural networks (ANNs) to predict responses and optimize the welding process. Genetic algorithm (GA) and RSM would reveal good results for finding out the optimal welding conditions. Kishore et al. [10] analyzed the effect of welding process parameters in qualitative manner for welding of AISI1040 steel using processes of shielded metal gas welding. Taguchi method is used to formulate the experimental layout. Exhaustive survey suggest that 5–7 control factors viz., arc voltage, arc current, welding speed, nozzle to work distance and gas pressure predominantly influence weld quality, even plate thickness and backing plate too have their own effect. Design of experiments based on orthogonal array is employed to develop the weldments. The authors showed that the weld speed should be less than 0.45 m/min for 3 mm plate and 0.35 m/min for 5 mm in metal inert gas welding, Taguchi method proved to be robust in design of experiments for evaluation of the quality and the cost of experiments can be reduced by selecting proper orthogonal array. The evaluation of laser welding of DP/TRIP steel sheets are considered one of the essential objectives in transportation industry because there is no sufficient data found in the literature.

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Padmanaban and Balasubramanian [11] developed an empirical relationship to predict tensile strength of the laser beam welded AZ31B magnesium alloy by incorporating process parameters such as laser power, welding speed and focal position. The experiments were conducted based on a three factor, three level, central composite face centered design matrix with full replications technique. The authors indicated that the welding speed has the greatest influence on tensile strength, followed by laser power and focal position. A maximum tensile strength of 212 MPa is obtained under the welding conditions in which the laser power is 2.5 kW, welding speed of 5.0 m/min and focal position of  1.5 mm. Welding speed is the factor which has the greater influence on tensile strength, followed by laser power and focal position. Ruggiero et al. [12] optimized the weld-bead profile and costs of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316. The effect of laser power (1.1–1.43 kW), welding speed (25–75 cm/min) and focal point position (0.8 to 0.2 mm) on the weld-bead geometry (i.e. weld-bead area, upper width, lower width, and middle width) and on the operating cost was investigated using RSM. The authors found that a laser power of 1.1 kW is an optimum input to obtain excellent welded joints produced from austenitic stainless steel AISI316 and low carbon steel. The welding speed is the parameter that most significantly influences the main weld bead dimensions, the middle width and the area, and so it has to be set between 72.6 and 75 cm/min, with the focused position being around  0.44 mm. The welding operating cost achieved with these optimization conditions is cheaper than the expected cost. From literature survey, there are no previous works to show the characterization of laser welding of DP/TRIP steel sheet by statistical approach so it is important to statistically investigate this subject. However there is no information available in the open literature on the characterization of laser welding of DP/TRIP steel sheet by statistical approach. Hence, this research work aims to develop mathematical models using RSM to predict the heat input and to describe the laser weld bead profile (i.e. weld penetration and welded zone width) for continuous wave CO2 laser butt welding of DP/TRIP steel sheets and to evaluate the variation in their mechanical properties due to the welding process. 2. Methodology A three-factor-three-level Box–Behnken statistical design with full replication was used to optimize and evaluate main effects (linear, quadratic and interaction effects) of the CO2 LBW. Laser beam power, welding speed and focus position are the laser independent input variables of the welding process while the depth of penetration, bead width, tensile strength, limited dome height and welding operation cost are the dependent output variables. The predicting of heat input and welding cost using a DoE approach, is to develop process optimization mathematical models, inside the statistical software Design-Expert which will be carried out in the next work. In order to find the limitation of the process input parameters, trial simulation runs were carried out by varying one of the process parameters at a time using BEAMSIM software [13]. Statistical software Design-Expert V.8.0.4.1 (Stat-Ease, Minneapolis, MN, USA) was used to code the variables and to establish the design matrix. The independent process variables, the goals of experimental measured responses and design matrix are shown in Tables 1, 2 and 3 respectively. All the regression model building methods and tools for checking the adequacy of the model are therefore appropriate in the RSM. Assume y to be the observed value of a response variable which depends upon the levels x1, x2 ,y, xk of some k quantitative factors. The response function is then written as Y ¼ f ðx1 ,x2 , . . ., xk Þ þ e

ð1Þ

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Table 1 Independent process variables and experimental design levels. Variable

Unit

Laser power (P) Welding speed (S) Focus position (F)

Goal

kW mm/s mm

Code

Minimize Maximize In range

Low 1

Medium 0

High þ1

2 40 1

2.1 45  0.5

2.2 50 0

Table 2 Goals of experimental measured responses. Response

Unit

Goal

Heat input (HI) Weld penetration (WP) Weld width (WW) Tensile strength (TS) Limited dome height (LDH) Welding operation cost (Cost)

kJ/mm mm mm MPa mm h/m

Minimize Maximize (or target) Minimize Maximize Maximize Minimize

Table 3 Design matrix with code independent process variables. Std

Run

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

3.2. Characterization

Value

01 08 13 14 04 16 10 03 05 07 09 06 11 17 02 15 12

P (kW)

S (mm/s)

F (mm)

2.0 2.2 2.0 2.2 2.0 2.2 2.0 2.2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1

40 40 50 50 45 45 45 45 40 50 40 50 45 45 45 45 45

 0.5  0.5  0.5  0.5  1.0  1.0 0 0  1.0  1.0 0 0  0.5  0.5  0.5  0.5  0.5

n X

bi xi þ e

At least two transverse specimens were cut from each weldment. The average values of weld profile parameters, tensile strength and limited dome height were recorded for each response. 3.2.1. Weld bead geometry The bead profile parameters (weld penetration and width) were measured using an optical microscope where thin sections were cut from the representative laser welded specimens, mounted and polished as per the standard metallographic procedures as shown in Fig. 1. 3.2.2. Mechanical properties Room temperature uniaxial tensile testing was used to evaluate the tensile properties of the base metals using DIN EN 100021:2001 while the standard ultimate tensile strength of the welds was determined using transverse samples cut from representative

where e is the noise or error term in observing the response. For a graphical display of the estimated response surface, contour plotting is often employed. The linear response surface model can be expressed as Y ¼ b0 þ

requirements for weight reduction and safety. DP600 steel was received in a hot-rolled, galvanized condition and with a thickness of 2.5 mm while TRIP700 steel was received in a cold-rolled, galvanized condition and with a thickness of 1.25 mm. The phase constituents of the investigated steels are 17% martensite and 83% ferrite in DP600 steel while are 16% bainite, 11% retained austenite and 73% ferrite in TRIP steel. The chemical compositions of the investigated steels are summarized in Table 4. Bead on plate butt joints of 2.5 mm DP600 and 1.25 mm TRIP700 steel sheets were performed using CO2 LBW. The size of each plate was 160 mm  70 mm. The plate’s edges were prepared to ensure full contact along the weld line during laser welding. Absence of visible welding defects and approximately full penetration of TRIP steel sheet were the criteria of choosing the working ranges. The experiments were carried out according to the design matrix in a random order to avoid any systematic error using a continuous wave 6 kW CO2 laser. Butt joint configurations with the weld line oriented parallel to the rolling direction were obtained in all welds. Helium was employed as a shielding gas from the top surface at a flow rate of 20 l/min (0.00033 m3/s). The shielding gas nozzle was inclined the 451 and positioned in front of the laser beam source.

ð2Þ

Table 4 Chemical composition of investigated DP600 and TRIP700 steels.

DP TRIP

C

Mn

Al

Si

P

S

0.06 0.18

0.86 1.56

0.03 1.04

0.10 0.37

0.03 0.07

o0.001 o0.001

i¼1

where b0 and bi are the unknown parameters. The quadratic response model consists of all the linear terms, square terms and linear interactions and can be expressed as Y ¼ b0 þ

n X i¼1

bi xi þ

n X

bii x2ii þ

i¼1

n X n X

bij xi xj þ e

ð3Þ

i¼1j¼1

3. Experimentation 3.1. Materials and process Two commercially available types of steels, DP and TRIP, were used in this work. These steels are ideal for meeting auto industry

Fig. 1. Experimental weld bead geometry.

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Table 5 Experimental measured responses. Std Responses HI (kJ/mm) Weld profile geometry Mechanical properties

Fig. 2. Erichsen test set-up (DIN EN ISO 20482).

welds of TWB according to DIN EN 895: 1995. The crosshead speed was constant in all tensile testing and equal to 10 mm/min. The formability of both base metals and TWB was evaluated using the Erichsen test according to DIN EN ISO 20482. The experimental set-up is shown in Fig. 2. The base materials and TWB were carefully placed to locate the weld line at the center of the dome punch. A 20 mm diameter hemispherical punch was used with a velocity of 10 mm/min. Draw-in of the specimens was resisted by 200 kN as sheet holder force to assure a pure stretching condition. To minimize friction between the punch and sheet, specimens were cleaned and lightly coated with graphitized grease.

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

40.000 44.000 32.000 35.200 35.556 39.111 35.556 39.111 42.000 33.600 42.000 33.600 37.333 37.333 37.333 37.333 37.333

Cost ¼

18:00 þ1:47P 3:6S

h=h, ðaccording to Germany’s prices, October 2010Þ

ð4Þ where P is the laser power in kW and S is the welding speed in mm/s.

4. Development of statistical models The experimental results of the weld bead profile, tensile strength and limited dome height are listed in Table 5. The measured responses were analyzed by the design expert software Design-Expert V.8.0.4.1. 4.1. Heat input

WW (mm)

TS (MPa)

LDH (mm)

Cost (h/m)

1.62 2.41 0.98 1.83 1.12 2.32 1.22 2.43 2.26 1.35 2.33 1.31 1.72 1.69 1.78 1.81 1.65

1.08 1.36 1.04 1.09 1.30 1.52 1.07 1.23 1.54 1.16 1.26 1.02 1.13 1.16 1.09 1.17 1.03

789 801 763 768 766 781 769 785 793 762 797 766 770 772 777 773 775

5.22 5.68 7.01 8.17 4.85 6.81 5.11 6.97 5.91 7.33 6.01 7.25 6.76 6.19 6.31 6.57 5.28

0.145 0.147 0.116 0.118 0.129 0.131 0.129 0.131 0.146 0.117 0.146 0.117 0.130 0.130 0.130 0.130 0.130

Table 6 ANOVA for heat input (HI) reduced quadratic model. Source

3.2.3. Welding cost analysis For evaluation the LBW process, the operation cost has to be carefully analyzed and calculated. For the LBW machine system used in this study, the operating cost included laser electric power, chiller control power, gas bottle rental, laser gas, shielding gas, maintenance labor, etc. and it can be summarized according to [14]:

WP (mm)

Sum of squares df

Model 167.8 P (power) 25.6 S (speed) 141.12 PS 0.16 S2 0.92 Residual 0.001.01 Lack of fit 0.001.01 Pure error 0 Cor total 167.8

Mean square F-value

4 41.95 1 25.6 1.0 141.120 1.0 0.160 1.0 0.920 12.0 0.000 8.0 0.000 4.0 0.000 16.0

496911 3.03Eþ 05 1.67E þ06 1895.26 10930.8

Prob 4F o0.0001 Sign. o0.0001 o0.0001 o0.0001 o0.0001

R2 ¼ 1, adj R2 ¼1, pred R2 ¼ 1 and adeq precision¼ 2403.696.

The analysis of variance indicates that for the heat input model, the main effect of the laser power (P), welding speed (S), the second order effect of welding speed (S2) and the two level interaction of laser power and welding speed (PS) are the most significant model terms associated with heat input. The final mathematical models in terms of coded factors as determined by design expert software are HI ¼ 37:33 þ 1:79P4:20S0:20PS þ0:47S2 ð5Þ While the following final empirical models in terms of actual factors are: HI ¼ 37:57847 þ35:8875P1:6804S0:4PS þ 0:018671S2

The test for significance of the regression models, the test for significance on individual model coefficients and the lack of-fit test were performed using the same statistical package. By selecting the step-wise regression method, which eliminates the insignificant model terms automatically, the resulting ANOVA Table 6 for the reduced quadratic model summarizes the analysis of variance of HI and shows the significant model terms. The value of adequate precision is dramatically greater than 4. The adequate precision ratio above 4 indicates adequate model discrimination [15,16]. Table 6 also shows that the model F-value of 496911 implies the model is significant. There is only a 0.01% ( o0.0001) chance that a ‘‘Model F-Value’’ this large could occur due to noise. Values of ’’Prob 4F’’ less than 0.05 indicate model terms are significant. In this case P, S, PS, S2 are significant model terms.

ð6Þ

4.2. Weld bead geometry By selecting the step-wise regression method, which eliminates the insignificant model terms automatically, the resulting ANOVA Tables 7 and 8 for the reduced linear and quadratic models summarize the analysis of variance of each response and show the significant model terms. In all cases the value of adequate precision are dramatically greater than 4. The adequate precision ratio above 4 indicates adequate model discrimination. The model F-value of 118.13, as shown in Table 7, implies the model is significant. In this case P and S are significant model terms. Table 8 shows the model F-value of 21.62 implies the model is significant. In this case P, S, F and F2 are significant model terms.

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Table 7 ANOVA for penetration (WP) reduced linear model.

Table 9 ANOVA for TS reduced quadratic model.

Source

Sum of squares

df

Mean square

F-value

Prob 4F

Model P (power) S (speed) Residual Lack of fit Pure error Cor total

3.29 2.05 1.24 0.19 0.18 0.017 3.49

2.0 1.0 1 14 10 4 16

1.650 2.050 1.24 0.014 0.018 4250

118.13 147.20 89.05

o0.0001 o0.0001 o0.0001

4.19

Source Sign.

0.09

Sum of squares df

Model 2243.03 P (power) 288 S (speed) 1830.12 2 S 124.9 Residual 110.97 Lack of fit 72.17 Pure error 38.8 Cor total 2350

Mean square F-value Prob4F

3 747.68 1 288 1 1830.12 1.0 124.900 13.0 8.540 9.0 8.020 4.0 9.700 16.0

87.59 33.7 214 14.6 0.83

o 0.0001 Sign. o 0.0001 o 0.0001 0.00210 0.63

Not sig.

R2 ¼0.9441, aAdj R2 ¼ 0.9361, pred R2 ¼ 0.905 and adeq precision ¼36.307. R2 ¼ 0.9529, adj R2 ¼ 0.940, pred R2 ¼0.9173 and adeq precision ¼29.812. Table 8 ANOVA for weld width (WZ) width reduced quadratic model. Source

Sum of

Model P (power) S (speed) F (focal position) F2 Residual Lack of fit Pure error Cor total

0.36 0.063 0.11 0.11 0.077 0.05 0.037 0.013 0.41

squares

df

Mean square

F-value

Prob4F

4 1 1 1.0

0.09 0.063 0.11 0.110

21.62 15.2 26.1 26.7

o0.0001 0.0021 0.0003 0.0002

Sign.

1.0 12.0 8.0 4.0 16.0

0.077 0.004 0.005 0.003

18.55

0.0010

1.4

0.40

Not sign.

Table 10 ANOVA for LDH reduced quadratic model. Source

Sum of squares

df

Mean square

F-value

Prob 4F

Model P (power) S (speed) S2 Residual Lack of fit Pure error Cor total

10.69 3.70 6.02 0.97 2.62 1.32 1.31 13.31

3 1 1 1 13 9 4 16

3.56 3.70 6.02 0.97 0.20 0.15 0.33

17.66 18.34 29.85 4.8

o 0.0001 0.0009 0.0001 0.0473

0.45

Sign.

0.8545

R2 ¼ 0.80, adj R2 ¼0.76, pred R2 ¼ 0.67 and adeq precision ¼14.207.

R2 ¼0.878, adj R2 ¼ 0.8376, pred R2 ¼ 0.7374 and adeq precision 16.426.

The predicted R2 of 1.00 or close to 1.00 is in reasonable agreement with the adjusted R2 of 1.00 or close to 1.00. The adequate precision measures the signal to noise ratio. The ratio is greater than 4 and indicates an adequate signal. For the penetration model, the analysis indicated that there is a linear relationship between the main effects of the parameters. Also, in case of welded zone width model the main effect of laser power (P), welding speed (S), focused position (F) and the second order effect of the focused position (F2) are significant model terms. However, the main effect of welding speed (S) and the main effect of focused position (F) are the most significant factors associated with the welded zone width. The final mathematical models in terms of coded factors as determined by design expert software are

The adequate precision is 29.812, indicating adequate model discrimination. The developed reduced quadratic mathematical model in terms of coded factors and actual values are exhibited as follows. Final tensile strength equation in terms of coded factors is

WP ¼ 1:75 þ0:51P0:39S

ð7Þ

4.4. Limited dome height

WW ¼ 1:13 þ 0:089P0:12S0:12F þ 0:13F 2

ð8Þ

The analysis results for the reduced quadratic model, which is suggested by the software for the calculated tensile values are shown in Table 10. High F-value for a parameter means that the parameter effect on the joints characteristics is large. The results show that the highest value F at a laser power of about 18.34 but that at the welding speed is equal to 29.85, which means that power has less effect on the process. Other model adequacy measures R2, adjusted R2 and predicted R2 are presented in the same table. All the adequacy measures indicate an adequate linear model. The adequate precision is 14.207, indicating adequate model discrimination. The developed reduced quadratic mathematical model in terms of coded factors and actual values is exhibited as follows. Final equation in terms of coded factors is

While the following final empirical models in terms of actual factors are: WP ¼ 5:33279þ 5:06250P0:078750S

ð9Þ

WW ¼ 0:3275þ 0:8875P0:02325S þ0:30389F þ 0:53889F 2 ð10Þ 4.3. Tensile strength The analysis results for the reduced quadratic model which is suggested by the software for the calculated tensile values are shown in Table 9. High F-value for a parameter means that the parameter effect on the joints characteristics is large. The results show that the highest value is at a welding speed of about 214, but that at the laser power is equal to 33.7, which means that power has less effect on the process. Other model adequacy measures R2, adjusted R2 and predicted R2 are also presented. All the adequacy measures indicate an adequate quadratic model.

TS ¼ 774:44 þ6P15:12S þ 5:43S2

ð11Þ

Final tensile strength equation in terms of actual factors is TS ¼ 1224:44444þ 60P22:575S þ 0:21722S2

ð12Þ

For the tensile strength the developed quadratic model, the analysis of variance indicates that welding speed ‘S’ is the stronger welding parameter affecting the responses.

LDH ¼ 6:09 þ 0:68P þ 0:87S þ0:48S2

ð13Þ

Final equation in terms of actual factors is LDH ¼ 22:72944þ 6:8P21:5475S þ 0:019122S2

ð14Þ

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Table 11 ANOVA for cost reduced linear model. Source

Sum of squares

df

Mean square

F-value

Prob 4F

Model P S Residual Lack of fit Pure error Cor total

1.69E  03 8.00E  06 1.68E  03 9.53E  06 9.53E  06 0 1.70E  03

2 1 1 14 10 4 16

8.45E  04 8.00E  06 1.68E  03 6.81E  07 9.53E  07 0

1241.42 11.75 2471.09

o0.0001 0.0041 o0.0001

Sign.

R2 ¼0.9944, adj R2 ¼0.9936, pred R2 ¼ 0.9912 and adeq precision¼ 89.445.

Fig. 4. Scatter diagram of WP.

Fig. 3. Scatter diagram of HI.

4.5. Welding operation cost The operating costs for joining the above DP/TRIP steel sheets were calculated using Eq. (4). The mathematical model was developed to minimize the operating costs. Same procedure was followed to check the model adequacy. The analysis results are shown in Table 11 for the reduced linear model which is suggested by software for the received result of the welding operating costs. The same table shows the other adequacy measures R2, adjusted R2 and predicted R2. All the adequacy measures indicate an adequate quadratic model. The adequate precision of 89.445 indicates adequate model discrimination. The developed linear mathematical model in terms of coded factors and actual values are exhibited as follows. Final operating welding cost equation in terms of coded factors is Cost ¼ 0:13 þ 1:00E03P0:015S

Fig. 5. Scatter diagram of WW.

ð15Þ

Final operating welding cost equation in terms of actual factors is Cost ¼ 0:24021 þ 1:00E02P2:90E03S

ð16Þ

5. Validation of the models Fig. 6. Scatter diagram of TS.

Figs. 3–5 show the relationship between the actual and predicted values of HI, WP and WW, respectively. While Figs. 6–8 show the actual measured tensile strength versus predicted tensile strength values, the actual measured LDH versus predicted LDH values and the actual measured costs versus predicted cost values, respectively. These figures indicate that the developed models are adequate because the residuals in prediction of each response are minimum,

since the residuals tend to be close to the diagonal line indicating that the model can adequately describe the response within the limits of the factors being investigated herein. Furthermore, to verify the adequacy of the developed models, three confirmation experiments were carried out using new test conditions, but are within the experiment range defined early.

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predicted values and the percentages of error. As shown in Tables 12 and 13, all error values are in the range of engineering errors and accepted in the industry.

6. Effects of welding process parameters 6.1. Heat input The heat input is directly related to the laser power, the welding speed and welding efficiency. It can be calculated directly from heat input¼ (P/S)  Z, where Z is the welding efficiency and equal to 0.8 [6]. From Figs. 9 and 10 it is evident that as the P increases and the S decreases the heat input increases. 6.2. Weld bead profile 6.2.1. Weld penetration From the results it is clear that the P and S parameters are significantly affecting the penetration (WP). These effects are due to the following: the increase in P leads to an increase in the heat input, therefore, more molten metal and consequently more WP will be achieved. However, the idea is reversed in the case of welding speed (S) effect, because the welding speed (S) matches

Fig. 7. Scatter diagram of LDH.

Fig. 8. Scatter diagram of costs.

Table 12 Confirmation experiments of the HI, WP and WW responses. Exp. no.

1 2 3

P, kW

2.05 2.10 2.15

S, mm/s

40 43 50

F, mm

 1.2  1.0  1.2

WP, mm Act.

Pred

1.85 2.02 1.77

1.90 1.91 1.61

9E9, %

WW, mm Act.

Pred

2.45 5.34 8.81

1.07 0.87 0.91

0.97 0.77 0.83

9E9, %

LDH, mm

9E9, % Fig. 9. Graph of effects of P and S on HI.

9.05 11.32 8.85

Table 13 Confirmation experiments of the TS response. Exp. no.

1 2 3

P, kW

2.05 2.10 2.15

S, mm/s

40 43 50

F, mm

 1.2  1.0  1.2

TS, MPa Act.

Pred

804 795 781

792 781 768

1.49 1.72 1.66

Act.

Pred

5.02 6.13 7.53

5.36 5.82 7.78

9E9, %

6.87 5.00 3.31

Using the point prediction option in the software, the HI, WP, WW, TS, and LDH of the validation experiments were predicted using the previous developed models. Tables 12 and 13 summarize the experiments condition, the actual experimental values, the

Fig. 10. Contour graph of effects of P and S on HI.

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an opposite with the heat input. To achieve maximum WP the laser power has to be maximum while S has to be minimum. Figs. 11 and 12 show the effect of process parameters on the weld penetration. 6.2.2. Welded zone width The results indicate that the welding speed (S) and focused position (F) are the most important factors affecting the welded zone width (WW). An increase in welding speed (S) leads to a decrease in WW. This is due to the laser beam traveling at high speed over the welding line when S is increased. Therefore the heat input decreases leading to less volume of the base metal being melted, consequently the width of the welded zone decreases. Therefore, wide area of the base metal will melt leading to an increase in WW or vice versa. The results also show that laser power (P) contributes the secondary effect in the WZ width dimensions. An increase in P results in slight increase in the WW because of the increase in the heat input. Figs. 13–15 show the effect of process parameters on the weld width (WW).

Fig. 13. 3D graph of effects of P and S on WW.

6.3. Tensile strength Laser power: High power density at the workpiece is crucial to achieve keyhole welding and to control the formation of welds. It can be seen that the laser power also has a strong effect on the

Fig. 14. Contour graph of effects of P and S on WW.

Fig. 11. 3D graph of effects of P and S on WP.

Fig. 15. Contour graph of effects of F and S on WW.

Fig. 12. Contour graph of effects of P and S on WP.

tensile strength of the laser-welded joint. In fact, the higher laser power resulted in a higher response value, due to the fact that using high laser power would increase the power density. This leads to more penetration resulting in an improved response.

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The LDH is directly proportional to the welding speed as shown in Fig. 19. Finally, Fig. 20 shows the effect of laser power and welding speed on the laser operation costs.

Fig. 16. 3D graph of effects of P and S on TS.

Fig. 18. 3D graph of effects of P and S on LDH.

Fig. 17. Contour graph of effects of P and S on TS.

Fig. 16 shows a 3D graph of the effect of P and S on the tensile strength at F¼ 0.0 mm. Welding speed: It is evident from the results that the welding speed is the most significant factor associated with the response. The highest tensile strength value was observed to be at a speed of 40 mm/s. It is evident that by increasing welding speed the response would decrease. The tensile strength is inversely proportional to the welding speed as shown in Fig. 17.

Fig. 19. Contour graph of effects of P and S on LDH.

6.4. Limited dome height Laser power: High power density at the workpiece is crucial to achieve keyhole welding and to control the formation of welds. It can be seen that the laser power also has a strong effect on LDH of the laser-welded joint. In fact, the higher laser power resulted in a higher response value, due to the fact that using high laser power would increase the power density. This leads to more penetration resulting in an improved response. Fig. 18 shows a 3D graph of the effect of P and S on the tensile strength at F ¼0.0 mm. Welding speed: Formability was higher for higher welding speed, as an increase in welding speed led to reduce specific energy input and faster cooling after passage of the laser beam.

Fig. 20. 3D graph of effects of P and S on cost.

U. Reisgen et al. / Optics & Laser Technology 44 (2012) 92–101

7. Conclusions The CO2 LBW of DP600/TRIP700 steel sheets has been experimentally studied and statistically analyzed. The following points are generally concluded. The mathematical models developed can adequately predict the responses within the factors domain. The welding speed is the most significant parameter during CO2 LBW of DP/TRIP steel sheets. The developed models could be used for mass production for computerized welding process by programming them into a computer numerical controlled (CNC) laser welding machine. In such a way the quality of the product and process will go to the desired higher level and at the same time will make savings from testing and losses.

Acknowledgments This article was conducted within the framework of the Ph.D. program ‘Integration simulation, modeling and experimental investigation of the laser beam welding of the advanced high strength steels’. The financial support of Welding and Joining Institute of the RWTH Aachen (Germany) and the Higher Education Ministry (Egypt) is gratefully acknowledged. References [1] Monaco A, Sinke J, Benedictus R. Experimental and numerical analysis of a beam made of adhesively bonded tailor-made blanks. International Journal of Advanced Manufacturing Technology 2009;44:766–80. [2] Kolahan F, Heidari M. A new approach for predicting and optimizing weld bead geometry in GMAW. International Journal of Aerospace and Mechanical Engineering 2011;5(2):138–42.

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