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Effect of jig constraint position and pitch on welding deformation Highlights Reduction of angular distortion by jig constraint is realized by experiment and simulation. Effect of two types of jig constraint on welding deformations is quantitatively investigated. Relationships between jig position & pitch and welding deformations are explored. Abstract Quantitative study on jig constraint effect on welding deformation was carried out. Welding deformation in a square plate with bead welding under a non-constraint free condition and a jig constraint condition was investigated by experiment. A 3D thermal elastic–plastic FEM program was employed to simulate the transient temperature and deformation occurred in the welding. It is observed that welding angular distortion has been greatly reduced by the jig constraint, and a good agreement was confirmed between simulation and experiment. Three-direction jig constraint and normal direction jig constraint were defined based on typical constraint types in practical engineering. Two parameters?a?and?b, which represent the pitch between two jigs in the welding direction and the distance from the weld line, respectively, were focused. Effect of jig constraint on longitudinal shrinkage, transverse shrinkage and angular distortion were discussed in details. Keywords:Welding deformation;?Jig constraint position;?Constraint pitch;?Measurement;?FEM 1. Introduction Welding process generally produces deformation and residual stresses which are undesired results in engineering. Welding deformation deteriorates the dimensions of structures and influences the appearance of products. Especially the out of plane distortion such as angular distortion and buckling distortion occurs easily in thin-walled structures, and their correcting work is eventually needed. The additional processes will increase not only the production period but also the cost. To reduce the production cost, it is necessary to minimize the welding deformation by some efficient ways. Residual stress degrades the performance of structure in aspects of fatigue strength and bulking strength. Proper post welding heat treatment or mechanical method has to be employed in order to release the residual stresses. Line heating on the reverse side of welding arc can produce an opposite bending moment to correct angular distortion which was reported by?McPherson (2010). As described by?Ando et al. (1982), the use of an induction heating technique has potential benefit in reducing welding residual stress. By altering the stress distribution, buckling distortion can also be mitigated effectively.?Wang et al. (2011)?analyzed welding deformation of a large-scale stiffened structure and proved that buckling distortion can be reduced by line heating process. Additional heating or cooling during welding can be one of the in-process control methods to prevent welding deformation.?Mochizuki et al. (2006)?applied the additional cooling to the weld zone of a T-shape fillet joint and demonstrated that the rotational distortion can be reduced without tacking and external constraint based on the results of numerical simulation.?Guan et al. (1990)?invented a process named as the low stress non distortion (LSND) method based on the cross section thermal tensioning effect. LSND was proved to be superior in preventing buckling distortion in butt welding of thin plates.?Guan and Zhang (1994)?developed a dynamic controlling low stress non distortion (DC-LSND) method as another active in-process buckling control method. In this method, a localized thermal tensioning was realized by a spot heat sink trailing with welding torch, and the longitudinal plastic strain at the zone behind the weld pool was dynamically controlled. Jigs are widely used to assist welding process to avoid rotation distortion in the front of welding heat sources.Hajduk et al. (2009)?described the methodological approach about the design of welding fixtures for robotic cells in spot welding of car bodies based on principles of modularity. Regarding control of welding deformation, there are several reports relating to external constraints and loads.?Park et al. (2012)investigated the angular distortion and residual stress under the various pre-tension states by changing the direction and magnitude of pre-tension stress.?Schenk et al. (2009)?studied the clamping effect on buckling distortion and angular distortion for an overlap joint and T-shape fillet joint. They found that residual stresses and welding distortion were strongly affected by clamping condition.?Shateryana et al. (2012)?investigated the constraint effects on welding deformation and residual stress in aluminum alloy lap joints under three types of local U-shape fixture by performing a 3D finite element analysis.?Ziaee et al. (2009)?studied the influence of boundary conditions on buckling modes during welding thin plates. It was found that external constraint can increase the buckling resistance but can not eliminate buckling. Nevertheless, the quantitative study on control of welding deformation by clamping or jig is rare in literatures. Due to the diversity of design parameters and complexity of welded structures, the limited experimental results at some constraint conditions are not enough to provide an overview of the constraint effect. Since the thermal elastic plastic FEM for welding thermal stress was established by?Ueda and Yamakawa (1971), it has been widely used in researches and in solving engineering problems as described by?Ueda et al. (2012). With the great progress of technology in computer aided engineering (CAE), a series of numerical experiments can be efficiently performed without extra cost when the simulation accuracy was verified previously. In this study, prior to investigate the mechanism of the effect of jig constraint on welding deformation, two testing specimens of bead-on-plate welding at a non-constraint free condition and at a jig constraint condition were prepared and welding deformations were measured by a 3D coordinate measuring device. Then the numerical simulation was performed for the two specimens, respectively. The welding deformation predicted by numerical simulation was compared with the experimental results and the simulation validity was accurately verified. Furthermore, to evaluate the effect of jig constraint quantitatively, the jig constraint is classified into two types named as the normal direction constraint and the three-direction constraint. Totally 41 numerical models under various constraint conditions were analyzed. Two parameters?a?and?b, which represent the pitch between two jigs in welding direction and distance from weld line, respectively, were focused and their effect on welding deformation was investigated in details. 2. Experimental study To investigate the effect of constraint by jigs, two specimens were welded at a non-constraint free condition and at a jig constraint condition as shown in?Fig. 1(a) and (b), respectively. In the jig constraint specimen, the jigs were fastened on the platform and out-of-plane deflection was fixed. The dimensions of the specimens are 400?mm in the length, 400?mm in the width and 9?mm in the thickness. The base material of the plate is SS400 and the material of welding wire with a diameter of 1.2?mm is MG-50T. The rust on the plate surface around the weld line was removed before welding for a good welding quality. The room temperature was about 20?°C during experiment. Fig. 1.?Specimens to be welded: (a) at free condition (b) with jig constraint. The single pass bead-on-plate welding was performed by an automatic MAG welding machine using the same welding conditions (240?A, 25?V, 5?mm/s). The shielding gas was 100% CO2. The constraint jigs were removed about 4?min later from the finishing time of welding. The welded specimens are shown in?Fig. 2(a) and (b), respectively. Fig. 2.?Specimens after welding: (a) at free condition (b) with jig constraint. To obtain the welding deformation, small sized holes were drilled on the plate. The center of each hole was recognized as a measuring point. The coordinates at measuring points on the plate were measured before welding and after cooling. By subtracting the initial coordinates from the final ones, welding deformations were calculated. The three typical welding deformation components, longitudinal shrinkage, transverse shrinkage and angular distortion were evaluated using the measured results. The longitudinal shrinkage at the longitudinal sectionsY?=??190, ?40, 40, 190?mm was, respectively, evaluated as shown in?Fig. 3. The transverse shrinkage and angular distortion were evaluated at the transverse sections?X?=?10, 50, 200, 350, 390?mm as shown in?Fig. 4?and?Fig. 5. The deformation values were the averaged ones at the measuring points on the top surface and bottom surface. Fig. 3.?Longitudinal shrinkage under a non-constraint free condition and a jig constraint condition: (a) four longitudinal sections; (b) longitudinal shrinkage. Fig. 4.?Transverse shrinkage under a non-constraint free condition and a jig constraint condition: (a) five transverse sections; (b) transverse shrinkage. Fig. 5.?Angular distortion under a non-constraint free condition and a jig constraint condition: (a) five transverse section lines; (b) angular distortion. Fig. 3?clearly shows that longitudinal shrinkage near the weld line has much larger value than that far away from the weld line.?Fig. 4?and?Fig. 5?show that the transverse shrinkage and angular distortion at the five sections, respectively, are relatively uniform, since the welding heat input per unit weld length is constant. At the finishing end of the weld line, transverse shrinkage decreased because the compressive transverse plastic strain becomes smaller due to the relatively weaker internal constraint at the end. Through the comparison, it was confirmed that if the constraint jigs are employed to clamp the welding specimen, the angular distortion can be greatly reduced compared with that under a non-constraint free condition. The effect of jig constraint on longitudinal shrinkage and transverse shrinkage was relatively smaller comparing with the effect on angular distortion. 3. Numerical simulation In this study, three-dimensional thermal elastic–plastic FEM was employed to simulate the welding thermal stress and deformation. Constraint jigs were modeled in the simulation following the experimental conditions. The interaction between jigs and specimen was considered by fixing the end of jigs. To accurately model the thermal–mechanical behavior during welding, the temperature dependent material properties were employed. The base metal and filler metal were defined separately in the numerical simulation. Temperature and mechanical analysis were performed sequentially, and iterative substructure method (ISM) proposed byMurakawa et al. (2004)?was used in mechanical analysis to save the computation time. 3.1. Finite element model A solid element formulation is generally necessary to analyze the transient welding thermal stress and strain. To fit the temperature gradient around welding heat source, dense mesh should be made in the vicinity of weld line. In this study, hexahedral elements whose robustness and accuracy in dealing with plasticity behavior were proved well by?Benzley (1995), were employed for welding simulations. The finite element model for the constrained welding specimen is shown in?Fig. 6. The shape of the weld reinforcement in the finite element model was determined from experimental observation, and the width and height are 10?mm and 2.2?mm, respectively. The element size in the weld zone is 5?mm in welding direction, 2?mm in the width direction and 1.8?mm in the thickness direction. The numbers of elements and nodes are 15,736, 20,448, respectively. The jigs are also modeled by solid elements to take into account of its elastic constraint. Due to the complexity of jig geometry, each jig is simplified into two cuboids which have the same length and transverse section as the actual jigs, and the clamping face is approximately 15?mm?×?10?mm. Fig. 6.?Finite element mesh for specimen with jigs and welding heat source zone. 3.2. Welding thermal conduction analysis Before mechanical analysis, thermal conduction analysis was performed to obtain the temperature history for all nodes of solid elements. Welding heat source was represented by uniform heat generation rate within a moving volume as shown in?Fig. 6. The temperature dependent physical properties used in the thermal conduction simulation, are shown in?Fig. 7(a). The thermal properties of weld metal (WM) were assumed to be the same with base metal (BM). At the high temperature over 1000?°C, the material properties were considered to be the same with those at 1000?°C. The ambient temperature was set to be 20?°C and the heat transfer coefficient was assumed to be 24?W/(m2?°C) on all the surfaces (Ueda et al., 2012). Fig. 7.?Material properties of base metal and weld metal: (a) thermal physical properties; (b) mechanical properties. In?Fig. 8, the transient temperature field at 40?s was drawn with cross sectional view, from which it can be seen that, the region near heat source has large temperature gradient, while the rear part showed relatively uniform distribution. The maximum reached temperature distribution on the transverse section which indicates the fusion zone is shown in?Fig. 9. Fig. 8.?Transient temperature distribution at 40?s from start of welding: (a) global view; (b) sectional view. Fig. 9.?The maximum reached temperature distribution on transverse section and fusion zone. 3.3. Thermal stress and deformation analysis By applying the transient temperature, welding thermal stress and deformation were computed incrementally for each time step. The mechanical properties of base metal and filler metal are shown in?Fig. 7(b). The properties of the base metal and filler metal are the same except for the yield stress. The materials follow the isotropic hardening law and related plastic flow rule. For the model welded under a non-constraint free condition, only rigid body motion was restricted in finite element model. For the jig constraint specimen, the end of jigs was constrained in the plate normal direction (Z-direction) during welding. The jig constraint was released after welding. The phase transformation behavior (?Deng, 2009) were not considered in the simulation. The iterative substructure method (ISM) was adopted in order to save computation time without loss of accuracy. Basically, the whole model A was divided into two regions with different level of nonlinearity as shown in?Fig. 10. In the present study, the B region was defined by elements in which the temperature is higher than 300?°C. The remaining region excluding the B region from whole model A is defined as A–B region. The A–B region and B region are solved in an interactive manner, and the unbalanced force on the boundary between the two regions is computed iteratively until equilibrium is satisfied. In this way, total number of iteration steps for whole region will be greatly reduced compared with the straightforward scheme. Fig. 10.?Schematic drawing of regions A, B and A–B in the framework of ISM. 4. Comparison of welding deformation The distributions of computed out-of-plane displacement in the?z?direction under the non-constraint free condition and the jig constraint condition are shown in?Fig. 11. It can be easily observed that the out of plane distortion has been greatly reduced by jig constraint. Fig. 11.?Out-of-plane deformation (unit: mm, deformation scale: 10 times): (a) specimen under free condition; (b) specimen with jigs. The comparisons of welding deformation between simulation and measurement at the non-constraint free condition were shown in?Fig. 12(a)–(c). The computed longitudinal shrinkage as shown in?Fig. 12(a) is symmetrical to the weld line due to the symmetry of the model. The longitudinal shrinkage near the edge of plate is much smaller than that close to weld line. Fig. 12.?Welding deformations at a non-constraint free condition and the comparison between experiment and simulation: (a) longitudinal shrinkage; (b) transverse shrinkage; (c) angular distortion. From the computed and measured results, it can be found that the transverse shrinkage at the middle section of plate is larger than that near the edge as shown in?Fig. 12(b). The smallest value appears at the finishing end of welding. The angular distortion changes a little at all five transverse sections as shown in?Fig. 12(c). If it is observed in detail, the angular distortion at the transverse sections near the terminal of the weld line is larger than that near the starting side of weld line. This is because the pre-heating effect from moving welding heat source is strong near the terminal of the weld line and a pre-angular distortion has been produced in the front of welding heat source. The computed longitudinal shrinkage, transverse shrinkage and angular distortion were very close to the experimental ones. For the specimen under the jig constraint conditions, comparison of angular distortion between experiment and simulation was made and shown in?Fig. 13. Both the experimental and simulation results show that there was about 70% reduction in the angular distortion if constraint jigs were employed. Fig. 13.?Measured and computed welding angular distortion with jig constraint. 5. Parametric study of jig constraint 5.1. Models of jig constraint conditions If jigs constrain the plates through contact, the displacement only in the normal direction of the contact faces between plates and jigs can be assumed to be constrained. If the jigs are rigidly fixed with the plates to be welded, the displacement at the jig constraint positions can be assumed to be fully fixed in the three directions. In this study, two types of constraint from jigs, simply named as the normal direction jig constraint and the three-direction jig constraint, are assumed and schematically shown in?Fig. 14. Fig. 14.?Configuration of jigs and two types of jig constraint. In the modeling of the normal direction jig constraint, nodes on the top and bottom surfaces with distance?baway from weld line, representing the jig constraint position, are fixed only in the normal direction. Additional constraint at nodes 20?mm away from weld line is employed to model supporting base on the bottom surface of plate. In the three-direction jig constraint condition, the displacement at the nodes where jigs were set, is fixed in the three directions. In all cases, the jig constraint at the nodes was applied from the beginning of welding and released after 220?s when the welding was finished. The simulations were performed for a bead-on-plate welding model with dimensions 400?mm?×?400?mm?×?10?mm. The jigs were symmetrically arranged on both sides of welding line. For the sake of simplicity, the constraints are directly applied at the nodes on the top and bottom surfaces for each jig. To investigate the effect of jig position and pitch on welding deformation, totally 41 cases of numerical simulations shown in?Table 1?were performed including one case under a non-constraint free condition. Table 1. Numerical simulation conditions and cases with various jig constraints. Constraint types Jig position?b?(mm) Jig pitch?a?(mm) Total cases Non-constraint free condition None None 1 Normal direction jig constraint 30, 50, 100, 200 5, 20, 40, 80, 200 20 Three direction jig constraint 30, 50, 100, 200 5, 20, 40, 80, 200 20 The welding deformation components, tendon force?F, transverse shrinkage and angular distortion on the middle cross section were investigated. The concept of tendon force was originally proposed by?White et al. (1980)?to represent the lo