Prediction of steel plate deformation due to triangle heating using the inherent strain method

Transcription

1 J Mar Sci Tecnol (005) 10:11 16 DOI /s Prediction of steel plate deformation due to triangle eating using te inerent strain metod Cang Doo Jang 1, Tae Hoon Kim, Dae Eun Ko 3, Tomas Lamb 4, and Yun Sok Ha 5 1 Department of Naval Arcitecture and Ocean Engineering, Seoul National University, San 56-1, Sillim dong, Kwanak-gu, Seoul , Korea LG EDS, Korea 3 Samsung Heavy Industries, Korea 4 University of Micigan, USA 5 Seoul National University, RIMSE, Korea Abstract In a sipyard, line eating and triangle eating are two major processes carried out by skilled workers to form curved plates in various sapes under various eating conditions. Tere ave been many studies on line eating, but triangle eating as rarely been studied owing to its complicated eating process wit irregular multieating pats and igly concentrated eat input. Triangle eating is te most labor-intensive job. Hence, it is essential for most sipyards to study te automation, as well as te improvement, of te triangle eating process in order to increase ull-forming productivity. In tis study, a pioneering attempt to simulate triangle eating was made. A circular disk-spring model is proposed as an analysis model for te elastoplastic procedure of triangle eating, and te inerent strain metod is also used to analyze te deformation of plates. Te results of te simulation were compared wit tose of experiments and sowed good agreement. It is sown tat te present approac and te model used in tis study are effective and efficient for simulating triangle eating for te steel plate forming process in sipbuilding. Key words Triangle eating Termal elastoplastic analysis Inerent strain region List of symbols b breadt of te inerent strain region for te elliptical type b ze breadt of te inerent strain region according to z for te elliptical type b zt breadt of te inerent strain region according to z for te trapezoid type b 1 te longer breadt of te inerent strain region for te trapezoid type b te sorter breadt of te inerent strain region for te trapezoid type d maximum dept of te inerent strain region for te elliptical type Address correspondence to: C.D. Jang (cdjang@snu.ac.kr) Received: September 10, 004 / Accepted: June 17, 005 dept of te inerent strain region for te trapezoid type e* inerent strain Introduction In a sipyard, line eating and triangle eating are two major processes carried out by skilled workers to form curved plates in various sapes under various eating conditions. Te eating process is selected according to te sape of te curved plate required. Te line eating process is used to form plates of te saddle type or te twisted type, wereas te triangle eating process is mainly applied to te concave type. Many studies ave been carried out on line eating, but triangle eating as rarely been studied owing to its complicated eating process, wit irregular multieating patways and igly concentrated eat input. Triangle eating as mainly been used to form te bow and stern plates of sips ulls, wic is te most labor-consuming job (Fig. 1). Hence, it is essential for sipyards to develop a more efficient fabrication system for te automation, as well as te improvement, of triangle eating processes in order to increase productivity. In tis study, a pioneering attempt to simulate triangle eating was made. An analysis model of triangle eating using te inerent strain metod 1 is proposed, and te computation procedure for te size and sape of te inerent strain distribution is described. Te inerent strain is te sum of elastically irrecoverable strains wic induce permanent deformation of te plate. For example, plastic strain, termal strain, and pase transformation strain are typical inerent strains. To induce inerent strain, a circular-disk spring model (Fig. ) was proposed for D termal elastoplastic analysis. Te spring model is a simulation of te elastic restraint from te surrounding area outside te disk

2 1 C.D. Jang et al.: Predicting steel plate deformation against expansion or srinkage of te disk due to temperature canges. Te results of te analysis were compared wit te experimental results to validate te usefulness and effectiveness of te proposed metod. Simplified analysis model for triangle eating In tis study, a simplified analysis model of triangle eating is proposed, as sown in Fig. 3. Wen triangle eating is carried out, te breadt and dept of te inerent strain region are raised from te starting point (C) to te end point (C ) of te eating process. In tis model, it is assumed tat te inerent strain region consists of line-eating elements, eac of wic ave increased breadt and dept in te x-direction. Because te breadt and dept of eac element increases linearly, tey are taken as increasing linearly from te first element to te last one in order to simplify te computations. Based on te results of eat transfer analysis and experiments, it was found tat te inerent strain region goes troug te tickness of te plate at te end edge, as sown in Fig. 3d. In tis case, te sape of te inerent strain region is a trapezoid. Determination of te inerent strain region Te inerent strain region is assumed to be a region were te maximum temperature exceeds Ac1 (ª700 C). 3 From te experimental results, it was found tat te section pertaining to te inerent strain region is as sown in Fig. 3c and d. In te section at A A, te sape of te inerent strain region is elliptical, and te equation for te breadt dept relation is as given in Eq. 1. In te section at B B, te sape of te inerent strain region is a trapezoid, and te equation for te breadt dept relation is as given in Eq.. Tese two sapes are determined by weter te dept of eat penetration is more tan te tickness of te plate or not. From te experimental results, te reason wy te isotemperature line canges from a curve to a straigt line after full penetration is tat te conduction speed along te back surface is muc faster tan te eat convection speed to te air. b = b - 1 Ê ze Á z d Ë - ˆ 1 b zt = b - b z b + + b 1 1 (1) () Computation of equivalent loads for finite-element analysis Equivalent loads can be calculated by integrating te inerent strains in te cross section. After applying tese equivalent loads to te plate, te final termal deformation due to triangle eating can be obtained troug elastic structural analysis. By integrating te inerent strains, te srinkage force per unit lengt and te bending moment per unit lengt can be calculated, as in Eqs. 3 and 4. 1,4 Fig. 1. Triangle eating in a sipyard f = - d b z b E z e*d (3) Ú K r K 1 Fig.. Circular-disk spring model

3 C.D. Jang et al.: Predicting steel plate deformation 13 Z Y c a Z Y b d Fig. 3. Analysis model for triangle eating. a plan view. b C C section. c A A section. d B B section Fig. 4. Equivalent loads in te analysis model Fig. 5. Specifications of plate specimen (mm) m = - d b z b E z z e* d (4) Ú Te distribution of te srinkage forces and bending moments is illustrated in Fig. 4. Te test models are supported in a suitable way to prevent deflections due to te weigt of te steel plates. Fig. 6. Longitudinal deflection of a 30-mm plate at y = 0mm Deformation of a flat plate Figure 5 sows te specifications of te specimen plate, and Table 1 gives te conditions cosen for te triangle eating experiment. 5 Te triangle eating was performed on a flat plate 0 30mm tick, as sown in Fig. 5. Experimental results on te longitudinal deflection and transverse srinkage were obtained and were compared wit te analysis results. 6 Figures 6 and 7 sow te longitudinal deflections of te 30-mm plate at y = 0 mm, and at y = 50mm. In Fig. 6, te analysis results are almost te same as te experimental results at x = 0 100, but a difference appears in

4 14 C.D. Jang et al.: Predicting steel plate deformation Table 1. Conditions for te triangle eating experiment for a flat plate Tickness Heating velocity Heating conditions Material 0 mm 130 mm/min Oxygen pressure 700 KPa A-grade mild steel 5 mm 100 mm/min Propane pressure 70KPa 30 mm 80 mm/min Water cooling Table. Conditions for te triangle eating experiment for a cylindrical plate Tickness Heating velocity Radius of curvature Heating conditions Material 30 mm 10 mm/min 1000mm Oxygen pressure 700Kpa A-grade mild steel Propane pressure 70 KPa Water cooling Fig. 7. Longitudinal deflection of a 30-mm plate at y = 50 mm Fig. 8. Transverse srinkage of a 30-mm plate te latter part of te eating process. In te analysis, te FEM commercial code (ANSYS 9.0) was used. Te elements of te model were selected by sell type, and te mes size was almost square (1cm 1cm). Comparison of analysis results and experimental results Wen te plate is eated te eated surface becomes lumpy. Te deformations caused by tis penomenon cannot be calculated numerically. Terefore, te difference observed in te latter part of te eating process (x = 400 mm) is caused by tis pysical penomenon and te pase-transformation effect. Te inerent strain in tis metod does not contain pase transformation strain because te water-cooling temperature is assumed to be sufficiently low. However, te value and tendency of te deflections in te analysis results are in good agreement wit tose in te experimental results, as sown in Figs. 6 and 7. Figure 8 sows te analysis and experimental results for transverse srinkages, wen triangle eating is performed on a flat plate 30 mm tick. Te analysis results sow a fairly good agreement wit te experimental Fig. 9. Specifications of a cylindrical plate results. Tus, te proposed simplified analysis model for triangle eating is validated. Deformation of a cylindrical plate In tis section, te proposed and validated triangleeating model is used for an analysis of te deformations of a cylindrical plate used for manufacturing concave curved plates, and te analysis results are compared wit experimental results. Table sows te experimental conditions, and Fig. 9 sows te specifications of a cylindrical plate. A quarter-cylinder plate model was used in te analysis. Figure 10 sows te deformation of a quarter-cylinder plate. As sown in

5 C.D. Jang et al.: Predicting steel plate deformation 15 tendency. Tus, te approac and model used in tis study are verified to be an effective and efficient to simulate triangle eating for te steel plate forming process in sipbuilding. Conclusions Fig. 10. Deformation of a cylindrical plate Fig. 11. Longitudinal deflection of a cylindrical plate Fig. 1. Transverse deflection of a cylindrical plate Fig. 10, point A is deflected downward from te origin, and points B and C are deflected upward from te origin. Te tree-dimensional deformations can be observed, but in tis analysis only longitudinal deflections (O A, B C) and transverse deflections (O B, A C) were considered. In oter words, te original value and te deflection of points A, B, and C were compared in te z-direction. Figure 11 sows te longitudinal deflections in te analysis result, and te experimental result at y = 0 (O A in Fig. 10). Figure 1 sows te transverse deflections in te analysis result, and te experimental result at x = 0 (O B in Fig. 10). Te results of tis simulation were compared wit tose from experiments and sowed good agreement. Te analysis results for te cylindrical plate using te analysis model of triangle eating proposed well correspond to te experimental results in terms of value and Te main conclusions from tis study are summarized below. 1. A pioneering attempt to simulate te steel plate forming process by triangle eating was successfully accomplised.. From te results of te eat transfer analysis and te cutting test, it was confirmed tat te sape of te zone affected by eat exceeding Ac1 (ª700 C) is elliptical or trapezoidal according to te plate tickness and te eating conditions. 3. Te circular disk-spring model is acceptable as an analysis model for te elasto-plastic procedure of triangle eating. 4. A simplified approac to predicting deformations of a steel plate due to triangle eating was proposed based on inerent strain analysis, and te results of tis simulation sowed good agreement wit tose of experiments wit flat and cylindrical plates. 5. Tis approac and te model used in tis study were sown to be an effective and efficient to simulate triangle eating for te steel plate forming process in sipbuilding 6. Te complicate termal elasto-plastic problem of triangle eating was formulated into a simple elastic analysis wit ig computation efficiency. Terefore, tis approac can be applied to real-time control of te triangle eating process. 7. Tis approac based on inerent strain analysis provided a basis for developing an improved and automated plate-forming system by triangle eating. Acknowledgments. Tis work was supported by a Korea Researc Foundation grant (KRF E0008). Te autors express sincere gratitude for te support. Te autors also tank and Hyun Soo Ryu, Seoul National University, for is elp in preparing tis manuscript. References 1. Jang CD, Seo SI, Ko DE (1997) A study on te prediction of deformations of plates due to line eating using a simplified termal elasto-plastic analysis. J Sip Prod 13:1. Sin JG, Mosaiov A (1991) Modified strip model for analyzing te line eating metod. Part 1. Elastic plates. J Sip Res 35:

6 16 C.D. Jang et al.: Predicting steel plate deformation 3. Jang CD, Ha YS, Ko DE, et al (00) Determination of inerent strain region for plate bending analysis due to line eating. J Soc Nav Arcit Korea 39:1 4. Nomoto T, Omori T, Sato T, et al (1990) Development of simulator for plate bending by line eating. J Soc Nav Arcit Jpn Watanabe M, Sato K (1961) Effect of welding conditions on te srinkage distortion in welded structures. Welding J Seo SI, Jang CD (1999) A study on te prediction of deformations of welded sip structures. J Sip Prod 15: 7. Jang CD, Seo SI, Yang YH (001) Development of a new finite element analysis of deformation of plate due to line eating. J Sip Prod 17:1 8. Ueda Y, Yamakawa T (1973) Analysis of termal elastic-plastic beavior of metals during welding by finite element metod. J Jpn Welding Soc 4:6