Residual Stresses Prediction for CO 2 Laser Butt-Welding of 304- Stainless Steel K. Y. Benyounis, A. G. Olabi and M. S. J. Hashmi

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1 Applied Mechanics and Materials Vols. 3-4 (2005) pp Online: (2005) Trans Tech Publications, Switzerland doi: / Residual Stresses Prediction for CO 2 Laser Butt-Welding of 304- Stainless Steel K. Y. Benyounis, A. G. Olabi and M. S. J. Hashmi Material Processing Research Centre, Dublin City University, Dublin 9, Ireland. khaled.benyounis2@mail.dcu.ie, abdul.olabi@dcu.ie and saleem.hashmi@dcu.ie Keywords: Residual stress, hole drilling, laser welding, stainless steel 304, RSM Abstract. Residual stresses are an integral part of the total stress acting on any component in service. It is important to determine and/or predict the magnitude, nature and direction of the residual stress to estimate the life of important engineering parts, particularly welded components. This work aims to introduce experimental models to predict residual stresses in the heat-affected zone (HAZ). These models specify the effect of laser welding input parameters on maximum residual stress and its direction. The process input variables considered in this study are laser power ( kw), travel speed ( cm/min) and focal point position (- 1 to 0 mm). Laser butt-welding of 304 stainless steel plates of 3 mm thick were investigated using a 1.5 kw CW CO 2 Rofin laser as a welding source. Hole-drilling method was employed to measure the magnitude, and direction of the maximum principal stress in and around the HAZ, using a CEA UM-120 strain gauge rosette, which allows measurement of the residual stresses close to the weld bead. The experiment was designed based on Response Surface Methodology (RSM). Fifteen different welding conditions plus 5 repeat tests were carried out based on the design matrix. Maximum principal residual stresses and their directions were calculated for the twenty samples. The stepwise regression method was selected using Design-expert software to fit the experimental responses to a second order polynomial. Sequential F test and other adequacy measures were then used to check the models adequacy. The experimental results indicate that the proposed mathematical models could adequately describe the residual stress within the limits of the factors being studied. Using the models developed, the main and interaction effect of the process input variables on the two responses were determined quantitatively and presented graphically. It is observed that the travel speed and laser power are the main factors affecting the behavior of the residual stress. It is recommended to use the models to find the optimal combination of welding conditions that lead to minimum distortion. Introduction Response surface methodology (RSM) is a set of mathematical and statistical techniques that are useful for modeling and predicting the response of interest affected by several input variables and the aim is to optimize this response [1]. RSM also specifies the relationships among one or more measured responses and the essential input factors [2]. The use of laser welding, as a high quality low distortion-welding process is well known. However, as a fusion welding process some distortion is still introduced, which can cause problems for high precision welding of critical components [3,4]. Residual stresses also play an important rule in determining the life of the welded components in service. It is well known that compressive residual stresses have a beneficial effect on the fatigue life and crack propagation of materials whereas tensile residual stresses reduce their performance. In service and in some cases it is better to have a mechanical part free of residual stress. In other cases, compressive residual stress needs to be introduced to the surface of the part in order to improve such mechanical behavior [5]. Among the other factors like materials type and thickness the welding process input parameters are also affecting residual stresses magnitude and nature [6]. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-09/10/15,15:40:09)

2 126 Advances in Experimental Mechanics IV Accordingly, during the nature of the design and manufacturing stage of a welded part it is necessary to have information related to residual stresses (magnitude and direction), and it is important to establish the relationship between process input parameters and principal residual stresses magnitude and direction. This paper introduces experimental models to predict the maximum residual stress and its direction in terms of the welding process input parameters namely, laser power, travel speed and focused position. Experimental Design The experiment was designed based on three factors five levels central composite rotatable design with full replication [2]. Laser power ( kw), travel speed ( cm/min) and focused position (- 1 to 0 mm) being the laser welding input variables. Table 1 shows the process variables, their standardized limits and coded values. Statistical software Design-Expert V6 was used to code the variables and to establish the design matrix shown in Table 2. RSM was applied to the experimental data using the same statistical software, polynomial equation was fitted to the experimental data to obtain regression equations for the two responses. The statistical significance of the terms in each regression equation was examined using the sequential F-test, lack-of-fit test and other adequacy measures using the same software to select the best models. Experimental Work Laser welding. Stainless steel grade AISI 304 in plate form with dimension of 180 mm x 120 mm x 3 mm were butt-welded using a 1.5 kw CW CO 2 Rofin laser. Argon gas was used as shielding gas at constant flow rate of 5 l/min. During laser welding operation the plates were clamped rigidly Fig. 1to avoid any deformation caused by the thermal loading, which may affect the results. No special heat treatments were carried out either before or after the laser welding. However, the plates edges were prepared to ensure the full contact of the two plates along the weld line during the buttwelding. Samples were prepared by changing one variable to identify the working ranges of the variables under investigation. Absence of obvious welding defects and reasonable depth of penetration were the criteria for choosing the working ranges. The welding operation was accomplished according to the design matrix Table 2 in the DCU workshop, in a random order to avoid any systematic error in the experiment. Residual stress measurements. Hole drilling method was used to measure the principal stresses and their direction. This technique is one of the stress-relaxing methods [7], which analyze the stress-relaxation produced in a metal part when material is removed. By measuring the deformation caused by the relaxation, the values of the residual stress present in the part before the metal was removed can be determined by analyzing the successive state of equilibrium [5]. The basic test procedure described in Measurement Group TN was followed [8]. A CEA UM-120 strain gauge rosette was used, which allows measurement of the residual stresses close to the weldbead, to ensure the hole in the HAZ. This type of rosette is designed in such way to make an angle between ε 1 and the weld-center line of -45º if installed as in Fig. 2. A commercially available milling guide equipment model RS-200 with an ultra-high speed air turbine and a carbide cutter of diameter 1.6 mm were used to drill a full depth hole (i.e mm) in the center of the strain gauge rosette as recommended in the guide [8,9]. Calibration coefficients a and b for full depth of and respectively and the measured micro-strains Table 3 were used to calculate the principal stresses and their direction. The calculated responses for the twenty samples are presented in Table 4.

3 Applied Mechanics and Materials Vols Table 1. Independent variable and experimental design levels used. Variable Notation Unit Standardised levels Laser power P [kw] Travel speed Focused position F [mm] Table 2. Design matrix. No Run Run P S F No order order P S F Table 3. Measured micro-strains. Samples E E E Fig. 1: Clamping the specimen during laser welding. Fig. 2: Strain gauge rosette installation, photo enlarged. Results and Discussion Analysis of Variance. The test for significance of the model, test for significance on each model term and lack of fit were conducted. The resulting ANOVA Table 5 and Table 6 for the reduced quadratic models summarize the analysis of variance of each response and show the significant model terms. The values of Prob. > F in both Table 5 and 6 for the two models are less than 0.05 which indicate that the models are significant also indicate that the terms in the two models have a significant effect on the responses being investigated. Despite the lack of fit in the second model is significant Table 6 the model is adequate and can be used to predict the directing of σ Max. The same tables also show adequacy measure R 2. The two values of R 2 indicate reasonable agreement and adequate models. In the two cases the value of Adequate precision are greater than 4. Adequate precision ratio above 4 indicates adequate model discrimination.

4 128 Advances in Experimental Mechanics IV For the first response σ Max the analysis of variance indicates that the main effect and second order effect of laser power (P & P 2 ), welding speed (S & S 2 ), focused position (F & F 2 ) as well as the two level of interaction of laser power and welding speed (PS) are significance model terms. However, the welding speed is the most important factor affecting σ Max. Fig. 3 shows the contours and 3D graph of the effect of laser power and welding speed on σ Max. Eq. 1 is the final equation in terms of actual factors. For the second response α, the analysis of variance shows that the main effect welding speed (S), and the two level of interaction of welding speed and focused position (SF) are significance model terms. However the main effect of laser power (P), focused position (F) and second order effect of welding speed (S 2 ) were added to support hierarchy. Fig. 4 shows the contours and 3D plot of the effect of welding speed and focused position on the direction of the maximum principal stress. Eq. 2 is the final equation in terms of actual factors. Table 4 shows the predicted values and the percentage of error in prediction of the two responses for the twenty samples. Effect of process factors on σ Max and α. The results indicate that the three factors are significantly affecting the σ Max and α. However the welding speed is the main factor associated with σ Max, this affect is due to the fact that an increasing in (S) leads to a decreasing in the heat input and consequently less thermal loading due to the relatively low temperature of the weld-pool and the area around it. But the idea is reversed with the laser power effect; because as the (P) increases the heat input increases resulting in raising the temperature in and around the fusion zone, therefore more distortion occurs. Using a focused beam leads to an increase in the power density, which raises the temperature of the weld-pool and the area surrounding it resulting in more distortion. Table 4: Actual, predicted responses and % of errors in prediction. Sample Max. Principal stress [MPa] σ Max Direction [Degree] α No. Actual Predicted Residual % Error Actual* Predicted Residual* % Error * The model developed and residuals calculated using the actual response without rounding.

5 Applied Mechanics and Materials Vols Table 5. ANOVA for response surface reduced quadratic model of σ Max. Source Sum of Mean F Squares DF Square Value Prob > F Model < Significant P < S < F P S F < P*S Residual Lack of Fit Not significant Pure Error Cor Total R 2 = Adeq. Precision = Table 6. ANOVA for response surface reduced quadratic model of α. Sum of Mean F Source Squares DF Square Value Prob > F Model Significant P S F S S*F Residual Lack of Fit Significant Pure Error Cor Total R 2 = Adeq. Precision = σ Max = P 3.034S F P S F PS. (1) α = P S F S SF. (2) 1.30 Max. principal stress [MPa] P [kw] Max. principal stress [MPa] P [kw] Fig. 3: Contours and 3D plots show the effect of P and S on the σ Max at F = mm.

6 130 Advances in Experimental Mechanics IV Alpha [degree] F [mm] Alpha [degree] F [mm] Fig. 4: Contours and 3D plots show the effect of F and S on α, the direction of σ Max at P = 1.2 kw. Conclusion The following can be concluded among the limits of the factors being investigated. 1. The models developed can adequately describe the responses under investigation. 2. Welding speed is the most important factor affecting the maximum principal stress and its direction. 3. It is possible to use the developed models to find optimal process factors combinations that would minimize the distortion. References [1] D. C. Montgomery: Design and Analysis of Experiments, (2 nd Ed, John Wiley & Sons, New York, (1984). [2] A. I. Khuri and J. A. Cornell: Response Surfaces Design and Analysis (2 nd ed, Marcel Dekker, New York 1996). [3] C. Dawes: Laser Welding (Abington Publishing, New York, NY, 1992). [4] J. Gabzdyl, A. Johnson, S. Williams and D. Price: Laser Weld Distortion Control by Cryogenic cooling (Proceedings of SPIE- The Inter. Society for optical Eng. Vol. 4831(2002), p [5] J. Lu: Handbook of Measurement of Residual stresses (Society of Experimental Mechanics Inc, the Fairmont press, 1996). [6] L. P. Connor: Welding Handbook (AWS, Miami 1991). [7] A. G. Olabi and M. S. J. Hashmi: Review of Methods for measuring Residual Stresses in Components (Proceedings of 9 th Conf. on Manufacturing Research Sep. 1993). [8] Technical Note TN-503: Measurement of Residual Stresses By the Hole Drilling Strain Gauge Method ( on ). [9] P. V. Grant, J. D. Lord and P. S. Whitehead: The Measurement Of Residual Stresses By the Incremental Hole Drilling Technique (National Physical Laboratory 2002).

7 Advances in Experimental Mechanics IV / Residual Stresses Prediction for CO 2 Laser Butt-Welding of 304-Stainless Steel / DOI References [7] A. G. Olabi and M. S. J. Hashmi: Review of Methods for measuring Residual Stresses in Components (Proceedings of 9th Conf. on Manufacturing Research Sep. 1993). doi: / (93)90211-n [7] A. G. Olabi and M. S. J. Hashmi: Review of Methods for measuring Residual Stresses in Components Proceedings of 9th Conf. on Manufacturing Research Sep. 1993). doi: / (93)90211-n