ABSTRACT In this study, the proposed linearized inherent strain method for predicting straightening of welded structures is investigated. Thermal elastic-plastic analysis is used to compute inherent strain of a thin flat plate caused by line heating. An accurate gas heat source model is employed in simulating the heating process. Transversal inherent strain is linearized from the computed distortion of the flat plate and applied in the elastic analysis, using higher order Gauss-Legendre (4-nodes shell elements). The accuracy of the proposed method is demonstrated by comparing the angular distortion of both analyses. Furthermore, different plate orientations are taken into account. INTRODUCTION Welding process is one of the most popular assembly method used by many industries such as ships and bridges. However, welding produces many unavoidable problems such as welding residual stress, crack propagation, and welding distortion especially for thin plates and large structures. The welding should be straightened, or the quality of the structure will decrease and the maintenance cost will increase. Welding distortion is caused due to shrinkage during the thermal cycle. It can be separated into the longitudinal shrinkage, transverse shrinkage, and angular distortion, see Fig. 1. In the last decades, ship designers have improved ship performance using thinner and lighter steel plates to reduce the ship weight. However, several problems with welding distortion have appeared as a result of thin plates welding for large structure fabrication. Mechanical and thermal straightening techniques are used to solve this problem. But mechanical techniques are difficult to apply to 3-D structures as ship blocks. Therefore, thermal processes are preferred because it is more economical and more flexible. These techniques create irreversible strain (inherent strain). As discussed by Ueda (1991, 1993), heat straightening consists of applying specific controlled heat patterns to the plastically deformed regions of welded structures in a single or repetitive heating phase and in-plane contraction during the cooling phase. Unfortunately, this method depends most of the cases on the experience of the skilled workers.

ABSTRACT Plates with double curvature are widely used in shipbuilding, and induction heating for plate bending is usually employed in shipyards due to its advantages such as high precision, high efficiency and so on. In this study, induction heating equipment with high frequency and 25KW in power was used to conduct experiments for different heating pattern, and typical bending plates with saddle shape and sail shape were obtained. Meanwhile, Three-coordinate Measuring Machine (TMM) was applied to measure the distribution and magnitude of out-of-plane bending deformation of the considered plates. Then, Thermo-Elasto-Plastic (TEP) FE analysis was carried out to predict the out-ofplane bending deformation generated by induction heating, which has a good agreement with it by measuring. With the integration of computed plastic strains caused by induction heating, elastic FE analysis with heating bending moment was implemented for effective prediction of out-of-plane bending deformation. Computed result of elastic FE analysis agrees well with the result from measurement and TEP FE analysis, while elastic FE analysis consumes less computer resource and computing time. INTRODUCTION The ship hull is made up of a large number of plates with complex curvatures, especially at the bow and stern where there are many double curvature plates such as saddle or sail shape. Thus, plate forming is an essential procedure for shipbuilding, which will be related to the production efficiency and precision of ship structure, as well as fabrication cost and schedule of shipyards (Zhou et al. 2014). Hot forming is an important method of plate bending forming in shipyards. The temperature distribution in the thickness direction is uneven because of local heating the plate, so that the bending moment would be generated to make the plate produce out-of-plane displacement. There are three main ways of hot forming according to heating source forms, including line heating with flame (oxygen-acetylene flame), laser heating and high frequency induction heating. At present, the fore two hot bending forming ways are more common than plate forming by high frequency induction heating, which is still on the early stage in shipyards. However, due to its unique advantages, it has attracted more and more attention. Compared with plate forming by line heating with oxygen-acetylene flame, high frequency induction heating is easier to accurately control the heating region and achieve automation, as well as high efficiency and few pollution (Heo et al. 2010); for plate forming by laser heating, it has low cost, simple equipment, and large heating power. As a result, plate forming by high frequency induction heating has a broad prospect in the efficient and automatic plate bending forming of shipyards.

ABSTRACT This paper mainly proposes simplified prediction procedure of temperature and deformation behavior for ship hull plate by moving thermal process. Maximum temperature Tum , dimensions (breadth b and depth h ) of inherent strain zone (ISZ) are firstly introduced to evaluate thermal forming behavior. Then non-dimensional technological parameters for Tum , b and h are derived based on dimensional analysis, which are subsequently utilized to analyze critical factors through parametric correlation analysis, respectively. Finally, non-dimensional predictions for Tum , b and h are carried out by multi-variable regression, respectively, and utilized to calculate bending angular deformation θ x Inhs based on inherent strain method. Therefore, we can prevent material mechanical degradation from overheating in advance, and improve dimensions of ISZ through adjusting technological parameters. It can be concluded that the proposed procedure can excellently predict Tum , b and h within maximum deviations of 6.95%, 6.63% and 9.70%, respectively, and calculate bending angular deformation θ x with less time to achieve automatic forming. INTRODUCTION Thermal forming process is an effective and economical method for fabricating flat metal plates into three-dimensional complicated shapes (Yu et al., 2001), which are typically utilized for bodies of ocean platform, ship hull and airplane, and rapid prototyping of complex curved surfaces to meet hydrodynamic performance. They cannot be formed at one time by mechanical roll or bending and require much more labor cost. Generally, the dimensions can arrive at more than 10m and the shapes are also mutually different, therefore they cannot be fabricated by batch-type production. They are incrementally fabricated by experienced technicians through adopting oxyacetylene torch as heat source along designed paths to generate non-uniform temperature distribution. Then surrounding cooling regions would prevent the expanding of heated zones to obtain non-uniform shrinkage strain distribution along thickness direction, and thus generate membrane shrinkage and bending angular deformation (Park et al., 2016). But this manual trial-and-error method is largely dependent on experience of each craftsmen resulting in low repeatability and efficiency.

Abstract It is generally experienced by engineers in shipyards that it is difficult to predict and control distortions of curved 3D blocks during assembly. Even in case of bilge blocks in the parallel part, twisting of the block is often observed. So far, there is no theoretical explanation why it happens. According to the Authors' understanding, the distortion of the welded structure is produced by two causes. One is the local shrinkage introduced by welding, such as transverse shrinkage and angular distortion. The other is the gap and misalignment introduced during sequential welding process. In this study, the mechanism of the twisting deformation is investigated from these points of views. For this, elastic shell FEM developed by authors based on the concept of inherent deformation and interface element is employed. Further, the method to straighten the twisting distortion by line heating is proposed based on the numerical study.

ABSTRACT: Welding is one of the essential processes for assembling steel structures such as ships and bridges. However, it is impossible to avoid residual stress and distortion. To prevent or minimize these problems, quantitative prediction and effective control of welding residual stress and deformation are necessary. To compute welding deformation, two methods are often used. One is the thermal elastic plastic finite element method (FEM) and the other is elastic FEM using inherent deformation. Thermal elastic plastic FEM is effective for accurate evaluation of welding deformation but requires large computational time. Elastic FEM using inherent deformation requires very short computational time, but the inherent deformations of all welding joints composing the structure must be known beforehand. However, these two methods can be combined to take advantage of both. The inherent deformations of welding joints are computed using thermal elastic plastic FEM and stored in a database, which is used to compute the welding deformations of large structures using elastic FEM. Nevertheless, these methods for welding analysis can require very long computational time and memory, even if the model is a simple weld joint. Therefore, for faster calculations and analyzing large structures, we developed the iterative substructure method (ISM) and idealized explicit FEM for welding simulation. In this study, a thermal elastic plastic analysis using ISM is applied to a weld joint model. The plastic strain distribution obtained by ISM is used for inherent strain analysis using idealized explicit FEM to analyze a block model of a large ship. The block model is 8.5 m × 8.5 m × 4.4 m with more than 300 welding lines. The simulated results agree well with the measured distortion. In addition, the influence of the welding direction on the welding deformation of the targeted ship block is investigated.

In plate forming by line heating the usage of water as a cooling source is common. However, the relationship between water-cooling and plate deformation is not well established. This reduces the possibility of automating the process. In order to solve this problem, the influence of the rate of cooling on inherent deformation is first examined. Then, the inherent deformation produced by line heating is studied in detail. Finally, the relationship between inherent deformation and heating condition is recorded into an inherent deformation database. This database can be used to directly predict inherent deformation due to line heating and therefore enable the automation of the process. INTRODUCTION In plate forming by line heating, water-cooling is usually used due to its effectiveness in increasing plate deformation. However, the mechanism of forced cooling such as water cooling is highly complex and it is not fully understood. Therefore, it is necessary to create a method to predict the influence of water-cooling on plate deformation and therefore, enable the usage of automatic machines. Although there have been many papers reporting the line heating method, very few papers are dealing with the effect of water cooling on deformation of plates due to line heating, [e.g. Satoh, Matsui, Terai and Iwamura (1970), Jamg, Kim, Ha and Lee (2005), Ji, Yujun, Zhuoshang, Yanping and Jun (2006), Ha and Jang (2007)]. Not a clear relationship between water-cooling and deformation of plates due to line heating has been found yet. Various attempts have been made to understand the mechanism of heat transfer in pool boiling (the key to explain the influence of water-cooling on line heating process), [e.g. Davidson and Schueler (1960), Han and Griffith (1965), Mikic and Rohsenow (1969), Judd and Hwang (1976), Haramura and Katto (1983), Liu and Wang (2001), Wu, Yang and Yuan (2002), etc.]. However, the calculation of the convection coefficient is a difficult problem and cannot be described by using a single relationship.

A 3-D thermal-elastic-plastic finite element analysis is performed to investigate the influence of temperature dependent material properties on prediction of inherent deformation due to line heating when numerical analysis by FEM is used. First, the temperature dependent material properties are defined. Variation with different degree was introduced and the resulting inherent deformation is then compared. Meanwhile, the other properties and process parameters are kept unchanged. Accordingly, the influence of various material properties on inherent deformation is revealed and discussed. It is found that the temperature dependent material properties play a key role on prediction of inherent deformation. Finally, conclusions of this numerical study are outlined. INTRODUCTION The plate forming using gas torch, induction heating or more recently laser heating is one of the most important forming processes actually used in shipyards. However, the line heating process is far to be fully automated, causing delays in the production line. The main reason of this is due to the fact that the relation between applied heat and final plate deformation, the key to automate the process, is too complicated to analyze by using simple mechanical models. In order to find a relation between these two parameters, it is necessary to consider other influential factors affecting the process such as the geometry of the plate, the cooling condition, the location of the heating line, multiheating lines, heat-induced curvature, residual stresses and inter-heating temperature [Vega et al. (2007), Vega et al. (2008), Vega (2009)]. The authors aim to propose a practical and accurate method to predict deformation of actual size plates such as those used in shipbuilding. As a fundamental component of this method, a line heating inherent deformation database is necessary. This inherent deformation database besides being mainly dependent on primary factors such as the plate thickness, the speed of heat source and the heat input, it also takes into account secondary factors such as the geometry of the plate, the cooling condition, the location of the heating line, multi-heating lines, heat-induced curvature, residual stresses, and inter-heating temperature.

ABSTRACT Experimental observation have shown that the heat induced deformation produced by crossed heating lines is significantly affected by the crossing especially at the cross area. Aiming to clarify this effect, through the inherent deformation theory, we numerically clarify and quantify the influence of crossed heating lines on heat induced deformation. First, it is demonstrated that the heat induced deformation of single heating lines may not be super-imposed upon one another to approximate the inherent deformation of the resultant curved surface. Then, a method to accurately predict the heat induced deformation produced by crossed heating lines is proposed. INTRODUCTION Line heating is an effective method to form curved shell plates with complex three-dimensional geometry. However, line heating process is mostly dependent on the skill of hard-to-find experienced workers. Therefore, automation is highly required. At present, no automatic system that can accurately form a plate without significant human help has been developed. The main reason of this is that the mechanism of plate forming using the line heating method is highly complicated for analysis with simple analytical models. The difficulty comes from the material and the geometrical nonlinearities as well as the variation of temperature in the spatial and time domains. The study of thermal-elastic-plastic behavior of the line heating process has received attention of many researchers for about the past 40 years. The first attempt to use an analytical approach to simulate the line heating process was by Suhara (1958) and Iwasaki, Hirabe, Taure, Hujikura and Shiota (1975). They modeled the problem using the beam theory and the solution was obtained analytically. Due to these restrictions, their model can deal only with ideal situations. Iwamura and Rybicki (1973) also analyzed the process using a beam model normal to the heating line, employing the finite-difference approach to solve the problem.

ABSTRACT The temperature of the gas adjacent to the plate TG and local heat transfer coefficient α can be considered to remain nearly unchanged with time during spot and line heating. A generic algorithms (GA)- based direct identification technique for TG and α is proposed. TG and α during a spot heating test is identified by the proposed technique, and TG for this spot heating test is measured by laser induced fluorescence technique. The validity of the proposed GA-based technique is investigated by comparing the identified and measured TG, and comparing the measured TB and that calculated by giving the identified TG and α as thermal boundary conditions. As results, the followings are found. Distributions of TG and α during a spot heating test can be directly identified by proposed GA-based technique. The identified TG is close to the one measured by a LIF system. The plate back surface temperature during the spot heating test calculated from the identified TG and α is comparable to the one measured. The results obtained demonstrate the accuracy of the identified heat input parameters and the validity of the proposed GAbased identification technique. The proposed GA-based identification technique is valid for the high power heating case for which the conventional IHC-based techniques are not applicable. INTRODUCTION Flame line heating is an effective method for forming flat steel plates into three-dimensional shapes for ships and other structures. However, this technique requires skilled workers who are now in short supply. Hence the urgent need to automate this process. The problem of flame forming of metal plate can be separated into two sub-problems: the heat transmission problem and the elasto-plastic deformation problem. In fact, the solution of the first problem is a prerequisite to approaching the second one.

In order to clarify the mechanism of thick plates forming by complex line heating, the distribution characteristics of inherent deformation produced by overlap, parallel and cross heating lines is studied. From this study it is found that the final inherent deformation is not a simple addition of that produced by individual heating. It is also found that the heating sequence has an important role in the production of deformation. Finally, correction factors are proposed to improve the accuracy of the prediction method. When these factors are obtained for a range of cases, deformation can be estimated by elastic analysis using the inherent deformation theory even with complex heating sequences. INTRODUCTION Line heating is an effective method to form curved shell plates with complex three-dimensional geometry. However, line heating process is mostly dependent on the skill of hard-to-find experienced workers. Therefore, automation is highly required. At present, no automatic system that can form a plate without significant human help has been developed. This is because the heat-induced deformation has many complex and uncertain factors, which are obstacles to the accurate prediction required by automatic systems. In forming of thin plates, applying line heating in simple patterns is usually enough to achieve the required deformation of the plate. However, in forming thick plates, it is necessary to apply large amounts of heat. Therefore, a combination of overlap, parallel and cross heating lines on both surfaces of the plate is required. On the other hand, when multiple heating lines are applied, residual stresses caused by a previous heating line affect the inherent deformation of the current heating line making it difficult to predict the deformation by simply superimposing inherent deformations of single heating lines in an elastic analysis. In this paper, the behavior of a thick plate formed by line heating is studied.

ABSTRACT In case of actual line heating process in the shipyard, the various weaving motions of gas torch moving along the target heating line have been adopted. By adopting weaving motions, it is possible to keep the maximum temperature under melting point and also to maintain the constant heating velocity through rhythmical motion of workers. In this study, an approach to determine the optimal heating conditions of line heating with weaving motions was presented, and some examples were introduced. The maximum angular distortion per unit hour was adopted as an objective function. SUMT algorithm is applied as an optimization tool. To get the optimal heating conditions, equivalent load method based on inherent strain was used. This study also deals with the process of deriving the optimal heating conditions for the specified thickness, heat flux with various torch speeds and weaving breadths as variables. The results of calculated optimal weaving heating conditions were well corresponded to the manufacturing standard. INTRODUCTION The inherent strain method has been used as one of the most efficient analysis method to predict the plate forming deformation by line-heating (Jang, Ko and Seo, 1997). Inherent strain method is an approach to calculate the deformation by elastic equivalent forces which is obtained by integration of inherent (irrecoverable) strain in the HAZ region. Due to its accuracy and efficiency, the inherent strain method will be able to substitute thermal elasto-plastic 3-D FEM analysis which requires much more computing time. It is very important to properly assume the inherent strain region for the precise prediction of plate deformation by line heating. There have been several methods to assume the inherent strain region. Recently, an improved method considering phase transformation effect of steel has been developed (Jang, Ha and Ko, 2003).

ABSTRACT The phase of steel changes from austenite to martensite, bainite, ferrite, and pearlite whether it is a rapid cooling or a slow cooling in the actual cooling process after line heating in shipyards. In order to simulate the cooling process, heat transfer analysis was performed considering the effects of impinging water jet, film boiling, and radiation. From above simulation it is possible to find the cooling speed at the inherent strain region and volume percentage of all phases in that region. By the suggested method based on the precise material properties calculated from volume percentage of all phases, it will be possible to predict the plate deformations by line heating more precisely. It is verified by comparing with some experimental results that the present method is very effective and efficient. INTRODUCTION Hull forming has been done by experts through repeating process in trial and error. So automatic hull forming process is needs to improve ship productivity and it is necessary to predict deformation of hot working precisely. It is possible to predict deformation of hot working precisely when property of hot working part induced precisely. For this, it is required to examine phase transformation in heating line closely. The phase in heating line is transformed in cooling process. Therefore it is required to stimulate heat transfer in cooling process. Until now, it is just focused on study of heating process in heating line, so it is proved to deformation mechanism in thermal elasto-plastic analysis. But, to predict deformation precisely, it is necessary to consider deformation by phase transformation. HEAT TRANSFER ANALYSIS IN COOLING PROCESS OF LINE HEATING Heat transfer is performed by conduction, convection, and radiation. But heat transfer in cooling process of plate surface is usually achieved by convection and radiation.

ABSTRACT During fabrication of deck house block in passenger ships, the problem of unexpected large deformation and distortion frequently occurs. Hence, amending of these deformation become more important in thin plate welding. The spot heating and line heating methods were very widely employed to amend deformation of thin plate structures. Few papers are available on the working conditions of spot heating method but only little information on deformation control. In this study, evaluation was carried out on the temperature distribution of spot and line heating methods using FEA and practical experiments for various heating time. In FEA, heat input model was established using Tsuji's double Gaussian heat input mode (Tsuji, I., 1988). This model was verified by comparing with experimental data. Also radial shrinkage and angular distortion due to spot heating were determined and compared with experimental results. Thermo elasto-plastic analysis was performed using commercial FE code, MSC/MARC. Radial shrinkage and angular distortion were measured using 3D measuring apparatus. Based on these results, criteria for amending thin plate fairing was established in our fabrication yard. INTRODUCTION In recent years of ship building technology, thin plate welding and control of its deformation is considered as a serious problem. During the fabrication of thin plate structures, welding distortions are inevitable and serious problem of whole ship structure in strength. Because of the need to reduce total weight of ships, deck plate thickness has been gradually reduced resulting in use of 5mm thickness plate associated with buckling distortion during deck block fabrication. The best way to control buckling distortion is to optimize welding parameters and structural parameters. But this requires lot of trial and error experiments. In many cases, line heating or triangular heating is not in much correct to control thin plate deformation.

ABSTRACT The inherent strain method is known to be very efficient in predicting the plate deformation by line heating. Traditionally, the inherent strain regions have been determined from the temperature distribution of welding. Though the phenomena of line heating are similar to those of welding, the results cannot reflect the effect of practical line-heating pattern. Furthermore, water-cooling in the actual heating process can change the phase of steel to martensite. In this study, in order to consider plastic strains occurring additionally under phase transformation, inherent strain regions were assumed to expand to Ac1 temperature zone. Also, when calculating inherent strain, material properties of steel in heating and cooling are applied differently considering phase transformation. In this process, a new method which can reflect volume expansion of martensite on thermal expansion is suggested. By the suggested method, the plate deformations by line heating were predicted. It is verified that the predicted results of the present method are in good agreement with those of experiments. INTRODUCTION Plate deformation by line heating has been studied through two approaches which are FEM for thermal elasto-plastic analysis and inherent strain method. Among them, inherent strain method is widely used from the view point of efficiency and accuracy (Jang and Seo, 1997). But there are some limitations to this method with respect to appropriate assumption of inherent strain region, and calculate accurate strain by that region. Satoh (1976) presented the depth and the breath of inherent strain region which were obtained from welding experiments, and assumed that the region is elliptical. In line-heating, Jang and Seo (1997) suggested that inherent strain region can be substituted with mechanical melting point. They obtained inherent strain by adding residual plastic strains in heating and cooling for spot heat source.

ABSTRACT In order to develop a simple method for predicting the twisting deformation of longitudinal stiffeners by line heating, the mechanism of twisting is investigated. This type of forming can be separated into three types, depending on the area to be heated and the external restraint. Simple mechanical models are proposed to clarify the mechanism of the forming. At the same time, the forming process using both the heating and the restraint is numerically analyzed by a thermalelastic- plastic FEM. In this analysis, the compression, the in-plane bending and the twisting of a plate are taken as examples. It is found from this study that the residual deformation after heating is nearly proportional to the forced deformation elastically applied prior to the heating if the forced deformation is small enough. In such a case, the formula derived using the simple mechanical model can be applied. INTRODUCTION Ships are curved thin plate structures consist of outer shell and decks reinforced by many stiffeners. The longitudinal stiffeners at the fore and the aft parts of the ship are curved and twisted due to the complex geometry of the hull. The line heating method is commonly used to twist these longitudinals. The line heating, however, requires skill and experience, especially in making decision regarding the location and magnitude of heating. Due to various factors, the shipbuilding industry is finding it difficult to attract new personal willing to take up such a job. Today, few skilled workmen are capable of forming twisted longitudinals and their numbers are rapidly decreasing. As it takes several years to learn and fully master the technique, it is necessary to clarify the mechanism of the twisting process to shorten the period of learning (Nair and Murakawa, 2001; Nair, Serizawa and Murakawa, 2002).