Correction of Butt-Welding induced Distortion by Laser Forming

Transcription

1 Correction of Butt-Welding induced Distortion by Laser Forming Peng Cheng, Andrew J. Birnbaum, Y. Lawrence Yao Department of Mechanical Engineering, Columbia University, New York, NY, 127, USA Zhishang Yang, Keith England Technical Center, Caterpillar Inc, Peoria, IL Abstract Welding-induced distortion is an intrinsic problem arising due to the mismatch of thermal expansions in the weld and surrounding material. The distortion can be minimized through the pre-process, in process, or post-process methodology. In the present paper, the laser forming (LF) technology is utilized for the post correction of the welding-induced distortion. Three types of weld paths are applied on the bead-on-plate welding. The induced out-of-plane distortion can be divided into angular distortion and longitudinal distortion. The LF correction paths are determined based on the magnitude and direction of bending angle and the longitudinal residual stresses. The corresponding heating conditions are determined through the heating database established by finite element method (FEM) simulations. Through the experimental validation, it is found that the proposed laser forming strategies can reduce not only the welding-induced distortion, but also the tensile longitudinal residual stress on the welded surface. It is concluded that the laser forming process is effective to reduce the welding induced distortion.. Keywords: Welding-induced Distortion, Correction, Laser Forming, Residual Stress 1

2 1. Introduction Welding induced distortion is a common problem in industry. The fundamental cause of the welding induced distortion is the non-uniform heating of material during the welding process, which in turn produces plastic strains and residual stress due to the mismatch of thermal expansions in the weld and surrounding material. Four types of distortion induced by welding were discovered (Masubuchi, 198). The first two are longitudinal shrinkage and transverse shrinkage that occur in plane. The other two are angular distortion and longitudinal distortion (bowing), which appear out of plane. The angular distortion is mainly caused by the non-uniform extension and contraction through thickness direction due to the temperature gradient. The longitudinal distortion (also called buckling distortion) is generated by the longitudinal tensile residual stress. The distortion causes the degradation of the product performance and the increase of the manufacturing cost due to the poor fit-up, so that it need be eliminated or minimized below a critical level (Michaleris, 1997). During the past few decades, many methods have been proposed to minimize the weldinginduced distortion in large structures. These methods can be classified into pre-process, inprocess and post-process methods. The pre-process approaches attempt to balance the residual stress by optimizing the welding conditions (arc voltage, current, welding speed, electrode material etc.), structural design, fixture design, and welding sequence. These approaches can only reduce the welding induced distortion to certain extents, limited by the original structural and welding process design. In-process approaches, on the other hand, aim to minimize the residual stress during the welding process. Deo and Michaleris (23) proposed a transient thermal tensioning method, which uses two heating torches along the welding path. Xu and Li (25) proposed another dynamic thermal tensioning method which also uses multiple torches 2

3 but the preheating torches are not necessarily along the welding path and the preheating strategy is optimally determined. Most of these methods provide pre-tensions through mechanical or thermal means to compensate for the welding induced mismatch of thermal expansion. In most cases, welding-induced distortions are difficult to predict so that the pre- or inprocess approaches are limit to be implemented. Instead, mechanical or thermal straightening method after welding process can be adopted to reduce or remove the distortions. Compared with mechanical straightening, thermal straightening is the preferred method because the material is handled considerably gently while its shape is being altered. Flame straightening was widely used from the middle of last century. However, this approach is labor intensive, inaccurate and expensive. Many years of experience are usually needed to acquire the skill required for flame straightening complex structures. As a more controllable and repeatable approach, laser forming provides a promising way to eliminate the welding-induced distortion. However, few investigations have been taken during the last two decades since laser forming was proposed. Laser forming is a non-traditional manufacturing technology based on the generation of stress and strain fields by temperature fields, which are due to local laser heating. For two decades, great progress has been made in understanding the underlying mechanism of laser forming. The main advantage of this non-contact forming method is that there is no spring back effect. This brings industrial promise in a wide spectrum of applications, e.g. rapid prototyping, precision adjustment, removing distortion and creating 3D complex shapes (Cheng et. al., 25). Three fundamental mechanisms of elastic-plastic deformation under influence of heating with a laser beam or other heat flux source have been discovered: the temperature gradient mechanism (TGM), the upsetting mechanism (UM), and the buckling mechanism (BM). Geiger et. al. (1993) was the first one to apply laser forming to straightening the car body shells. 3

4 They found that there are the same parameters which control the distortion after welding and the bending angle after laser beam bending, so that the results from laser beam bending may be used to minimize the distortion after welding. However, only angular distortion was accounted for in their investigation. In the present paper, characteristics of distortion and residual stress after laser beam welding are highlighted first. The features of laser forming are also presented. To remove the angular distortion, laser forming under temperature gradient mechanism (TGM) is applied along the welding path on the bottom surface. To remove the longitudinal distortion (buckling distortion), the buckling mechanism (BM) laser forming is applied perpendicular to the welding path on the top surface by counteracting the longitudinal tensioning stress. Corresponding heating conditions can be obtained from the heating database established by FEM simulation. The proposed strategy is verified through the bead-on-plate welding on mild steel plates with three types of weld paths. 2. Experiments and Simulation 2.1 Experiments of welding In this study, bead-on-plate laser welding was carried out to investigate the welding induced distortion. Compared to other conventional welding technology, laser welding offers a number of attractive features such as high weld strength to weld size ratio, reliability, minimal heataffected-zone, and relatively low heat distortion. Even though, the induced distortion is obvious and cannot be neglected. The material investigated is cold-rolled AISI 11 steel with the dimension of 8x8x.89 mm. Before the samples are used in the welding experiment, stress relief annealing is used to reduce the residual stresses due to the previous cold-rolling manufacturing process. Samples are heated to temperature of 6 ~ 625 C, and held for 1 hour 4

5 and then slowly cooled in still air. After this treatment, over 9% of the initial residual stress can be eliminated. The laser system used in both the welding experiments and laser-forming (LF) correction is a PRC-15 CO 2 laser, with a maximum output power of 1.5 kw and power density distribution of TEM. The diameter of the laser beam used in welding is 4mm, which is defined as the diameter 2 at which the power density becomes 1/ e of the maximum power value. Three types of welding paths: straight, curve and circular lines bead-on-plate welding are studied in this paper to develop more general LF correction strategies. A typical heating condition (Laser power=12 W, welding speed=1 mm/s) was applied in the welding experiment. A coordinate measuring machine (CMM) is used to measure the induced out-of-plane distortion. Bending angle may vary along the scanning path, which is known as edge effect (Bao and Yao, 21). Hence, bending angle was measured at equally spaced locations along the scanning path. To enhance laser absorption by the workpiece, graphite coating was applied to the surface exposed to the laser. 2.2 Numerical simulation of welding and laser forming Welding process is a fully coupled thermal, mechanical and metallurgical process. In this study, the problem is simulated as a sequentially coupled thermo-mechanical process neglecting the effect of phase transformation. The solution procedure consists of two steps. First, transient nonlinear heat transfer analysis is performed to determine the temperature distribution and history of the weldment. The temperature history calculated in the heat transfer analysis is then used as a thermal load in the subsequent mechanical elastic-plastic. Temperature-dependent thermo-physical and mechanical properties are used in the simulation. 5

6 In thermal analysis, latent heat and near-melting-temperature material data are accounted for. The thermal conductivity above the melting temperatures is artificially increased to compensate for the convection heat transfer effect in the molten weld pool. The governing equation of the thermal process in the beam is a standard transient heat conduction equation: T ρ c t = q + ( k x x T ) + ( k x y y T ) + ( k y z z T ) z where ρ is the density, c is the heat capacity of the steel, q is the heat generation rate per unit volume, T = T ( x, y, z, t) is the instantaneous temperature at any point in the domain, and k x, k y and k z are the thermal conductivity of the material on x, y, and z directions. Since the steel plate is homogeneous, isotropic material properties k = k = k are used in the model. The heat x y z generation term q in the equation is used as the heat input from the Gaussian distribution heat source. Before welding, the initial temperature on the structure is set to the room temperature. During welding and cooling, convection boundary condition is applied to all the free surfaces of beam structure. The heat loss flux is evaluated as q s = h f ( T T ) s where h f is the film coefficient, T s is the surface temperature, and T is the room temperature. The radiation heat loss is expressed as q r = εσ ( T 4 T 4 ) where ε and σ are the emissivity and Stefan-Boltzmann constant, 6

7 In mechanical analysis, annealing effect and near-melting-temperature material data are considered. The constitutive equations governing mechanical behavior are assumed to be ratedependent elasto-plastic obeying the Von-Mises yield criteria and associated flow rules. In the structural analysis, the plastic deformation of the material is assumed to obey von Mises yield criterion. The total strain is decomposed as the following: & ε = & ε + & ε + & ε ij e ij p ij T ij where e ε ij is the elastic strain, ε& p ij is the plastic strain, and ε T ij is the thermal strain. Plastic strains due to transformation plasticity is not considered in the model. The numerical simulation for laser forming is similar to the welding simulation, except that the peak temperature is always below the melting temperature (for AISI 11 steel, T melting = 152 C ), so that no latent heat or annealing effect is accounted for in the simulation. To numerically simulate the correction effect, a sequentially coupled, multiple-steps weldingforming model is developed in the present study. The mechanical models of welding and laser forming are implemented in the same input file but separated by different steps. In the step of welding mechanical analysis, the load input is only by the welding heat source. The welding residual stress can be accurately predicted and consequently applied in the forming simulation as a pre-stress. Then in the following step of laser forming, the load input includes not only the laser heat input but also the welding-induced residual stresses. The applied laser forming conditions (scanning paths and heating conditions) are determined based on the measured welding distortion and residual stresses. 7

8 ABAQUS 6.4 is used to complement the numerical simulation. The quadratic 2-node brick elements are used in the mechanical analysis because this kind of element has no shear locking and hourglass stiffness and is also suitable for bending-deformation-dominated processes such as laser forming. In order to remain compatible with the structural analysis, an element type, DC3D2, is used in heat transfer analysis. A user subroutine of dflux was developed to model the heat source input from the Gaussian laser beam. 2.3 Residual stress measurement Residual stress arises from the elastic response of the material to an inhomogeneous distribution of nonelastic strains such as thermal expansion strains, plastic strains, precipitation, phase transformation, and misfit, etc. In welding process, concentrated moving heat source causes large residual stress around the welding path, especially in the heat-affected-zone (HAZ). Since the welding process is a plane stress analysis (no stresses in the thickness direction due to the free expansion), only transverse and longitudinal residual stresses are considered. To characterize the distribution of the residual stress, X-ray diffraction (XRD) is adopted to measure the residual stress in different directions. When a polycrystalline piece of metal is deformed elastically in such a manner that the strain is uniform over relatively large distances, this uniform macro-strain may cause a shift in the diffraction lines to new positions. If the metal is deformed plastically, the lattice planes become distorted in such a way that the spacing of any particular (hkl) set varies from one grain to another or from one part of a grain to another. This non-uniform microstrain causes a broadening of the diffraction line. In fact both kinds of strain are superimposed in plastically deformed metals, and diffraction is both shifted and broadened (Cullity, 1978). 8

9 A single stress σ φ acting in some direction φ in the surface can be measured by twomeasurements method, which measures one of the strain ε 3 along the surface normal, and one of the strain along an inclined direction ( Ψ to the normal direction, usually chosen to be 45 ). The direction of the surface normal, the inclined direction Ψ and the direction of σ φ are in the same plane. Elasticity theory for an isotropic solid shows that the strain along the inclined direction Ψ is 1 2 ε Ψ = [ σ φ (1 + v)sin Ψ v( σ 1 + σ 2 )] E Then ε Ψ σ φ ε 3 = ( 1+ v) sin E 2 Ψ σ φ E = (1 + ν ) sin d i d ( ψ d 2 n n ) The above equation allows us to calculate the stress in any chosen direction from plane spacing determined from two measurements. Substituting the Bragg's law λ = 2d sin θ, the measured residual stress is expressed as σ φ = E (1 + v)sin sinθ i sinθ i ( 1) = K( Ψ sinθ sinθ 2 n n 1) where K is defined as the Stress Constant. 3. Results and Discussions 3.1 Characteristics of welding induced distortion and residual stress Fig. 1 shows the welding-induced distortions under typical heating conditions. The out-ofplane distortion can be divided into angular distortion and longitudinal distortion, which is 9

10 defined as perpendicular to and along to the welding path, respectively. The surface, on which the welding path was applied, is referred to as top surface, and the other side of sheet is referred to as bottom surface. The angular distortion is generated due to the non-uniformity of thermal expansion and contraction through the plate thickness. The longitudinal distortion is caused by the tensile residual stresses due to the moving heat source along the longitudinal direction. Under laser welding, due to the high energy density and relative small heat-affected-zone, the weldinginduced distortion is smaller than that of the conventional welding technologies (i.e., Gas Tungsten Arc Welding-GTAW). Even though, Fig.1 still shows that the distortion is obvious and cannot be neglected. Fig.2a shows the distortion of straight-path bead-on-plate welding measured by coordinate measurement machine (CMM). Due to the geometry symmetry, only half plate is shown. The maximum angular distortion (defined by bending angle) is over 3 degree, and the maximum longitudinal distortion (defined by displacement in Z direction) is over 2.2 mm. This distortion was exactly predicted by numerical simulation in ABAQUS, which is shown in Fig. 2b. Fig. 3 shows the time history of temperature at a typical location on the plate. It is found that the peak temperature is over 24 K on top surface. Over 4-degree temperature gradient through the thickness direction caused the non-uniformity of thermal expansion and contraction, resulting in the distortion and residual stresses. Fig. 4 shows the angular distortion (defined by bending angle) distribution along the weld path. It is found that although the heating conditions keep constant along the path, bending angle varies due to the non-uniformity of the inherent constraint (from the surrounding material) and the temperature field. This phenomenon always exists when the moving heat source is applied. It is defined as edge effect in the laser forming process and was thoroughly investigated (Bao 1

11 and Yao, 1999). If the variation of bending angle can be ignored, the average bending angle can be easily calculated either by analytical models or by numerical simulation based on the applied heating conditions and material properties (Vollertsen, 1994). It is also possible to determine the required heating conditions if the bending angle is known although the solution is not unique. Since the samples are annealed to release the residual stress caused by cold rolling before welding, the residual stress measured after welding process can be assumed totally as the result of welding process. X-ray diffraction (XRD) can be used to measure the residual stresses in any direction, as shown in Fig.5. The distribution of longitudinal residual stress and transverse residual stress along Y direction (the direction perpendicular to weld path) was shown in Fig.6 and 7, respectively. Within the heat-affected-zone (HAZ or plastically deformed zone), the longitudinal residual stress on both top surface and bottom surface is tensile because of the plastic compressive deformation within the zone. It is found that the plastic compressive strain within the HAZ on bottom surface is larger than that of the top surface, so that the bending curvature along the weld path is towards the bottom surface, which is shown in Fig.2. Outside the HAZ, only elastic strain exists. The downward curvature causes the tensile longitudinal elastic strain on the top surface, and the compressive longitudinal elastic strain on the bottom surface. So that the longitudinal residual stresses outside the HAZ are tensile on the top surface and compressive on the bottom surface. For the transverse residual stress which is in the direction perpendicular to the weld path, it is found that within the plastic zone, transverse residual stress is compressive on top surface and tensile on bottom surface. If the temperature gradient is large enough (i.e.,tgm laser forming), the induced transverse residual stress is always tensile both on the top and the bottom surface. The reason can be explained as follows. For the welding process, due to the very low scan speed 11

12 and so-caused low temperature gradient through the thickness, the compressive strains in the transverse direction occurring on both top and bottom surface within the plastic zone are in the same order. The relative larger value makes the plate bend upwards. The compressive plastic strain on the bottom surface releases the restraint coming from the neighboring material, so that the remaining elastic strain on the top surface (within plastic zone) is compressive. The similar phenomenon is also found in buckling mechanism (BM) laser forming, and it provides a good way to remove the tensile longitudinal residual stress. This will be explained in the following section. 3.2 Characteristics of laser forming induced distortion and residual stress Three types of mechanisms (Temperature Gradient Mechanism-TGM, Buckling Mechanism- BM, upsetting mechanism-um) were reported in laser forming. The temperature gradient mechanism (TGM) is the most widely used laser-bending mechanism. Large temperature gradient through the thickness direction makes the plate bend upwards. TGM can be utilized to remove the angular distortion in the correction process. In the BM, the laser beam diameter is much larger than the sheet thickness. The diameter is about ten times the sheet thickness. There is no steep temperature gradient through the thickness. The BM is activated by laser parameters that do not yield a temperature gradient in the z direction. Due to heating, thermal compressive stresses develop in the sheet which results in a large amount of thermo-elastic strain which in turn results in local thermo-elasto-plastic buckling of the material. This buckle is generated along the moving direction of the laser beam scanning. When the laser beam leaves the sheet surface, the buckle is generated across the whole sheet. The part can be made to bend in either the positive or the negative z directions depending on a number of factors including the process parameters, the pre-bending orientation of the sheet, the pre-existing residual stresses, the 12

13 direction in which any other elastic stresses are applied, internal stresses, and external or gravitational forces. It is found that through buckling mechanism (BM) laser forming, compressive residual stress perpendicular to the weld path is induced (shown in Fig.8), while in TGM the induced residual stress is always tensile. To reduce the welding-induced tensile longitudinal stress, so as to reduce the caused longitudinal distortion, BM laser forming should be applied. The reason that BM laser forming induces compressive transverse stress can be found from the time history of the transverse residual stress (shown in Fig. 8a). The transverse stress initially increases from zero before the heating source reaches. This is because that the material tends to expand when the heat source is reaching, and the extension strain is only elastic since the temperature is low before heat source reaches. During heating, compressive stresses arise because of the restraint due to the surrounding material and cause local buckling of the sheet because of the geometry of the heated area. When the temperature still increases, the flow stress of the material goes down. Whereas the material in the centre of the buckling area is plastically deformed, the deformation at the sides is still elastic. The neighboring area in the direction of the path feed is already elastically buckled out, whereas the area behind is plastically formed. The restraint of the surrounding material decreases as the beam approaches the second edge. The elastic counter bending of the sides goes down and the bend angle arises. Fig.8 shows the typical residual stress distribution for the BM laser forming. 3.3 Overall strategy The overall strategy for welding distortion correction by laser forming is presented in Fig.9. Firstly the welding-induced distortion can be decomposed into two components: angular 13

14 distortion and longitudinal distortion. The former distortion can be expressed as bending angle and measured by coordinate measurement machine (CMM). For the longitudinal distortion, the surface displacement and residual stress can be measured by CMM and XRD. The angular distortion can be removed by TGM laser forming, while the longitudinal distortion can be removed by releasing the tensile residual stress along the longitudinal direction through the BM laser forming. To remove the angular distortion, the laser-forming path should be along the weld path and applied on the bottom surface. To remove the longitudinal distortion, BM laser forming should be applied on the top surface and the scanning paths are perpendicular to the weld path. The heating conditions (including laser power, scanning speed and beam spot size) can be determined through the database established by FEM. In the database, the bending angle and the transverse residual stress are functions of laser power and scanning speed under the condition of TGM (at a smaller beam diameter and relative large scanning speed) and BM (at a larger beam diameter and relative smaller scanning speed), respectively. By matching the angular distortion and the residual stress between the required values and those of database, the laser power and scanning speed can be determined uniquely if the beam spot size and path spacing are given. Multiple scans may be applied on the same paths if the distortions are not reduced to a critical level. This methodology will be explained in more detail in the following sections. 3.4 LF Correction on straight line bead-on-plate welding Fig. 1 shows the designed paths for the correction of distortion induced by straight line bead-on-plate welding. The path for the angular distortion correction is applied along the weld path on the bottom surface. The paths for the longitudinal distortion correction are applied perpendicular to the weld path and located with equal spacing. In determining the spacing of adjacent scanning paths, a number of guidelines are followed. In general, the paths at the regions 14

15 that have larger longitudinal residual stresses should have denser spacing than regions of smaller stresses. At the same time, due to the practical restrictions such as the cooling issues, the spacing cannot be too close. The spacing between two adjacent paths, d paths, should be equal to the average transverse stress generated by laser forming, s laser, multiplied by the beam spot size d, and divided by the welding-induced longitudinal stress over the spacing, written as d = s d / s. paths laser required If the laser-generated residual stress s laser can fully match the required stress within the range of the heat affected zone (HAZ), the width of HAZ can be adopted as the initial path spacing. The spacing of the paths may vary if the welding induced longitudinal stress varies along the weld path. If this strategy results in a path spacing that is too large to be covered by LFgenerated strain, additional scanning paths should be added. For the length of the BM laserforming path, it can be determined based on the coverage width of the welding-induced longitudinal stress. The coverage width can be defined as the region within which the tensile longitudinal stress is at least 5% of the maximum value occurring in the weld path. Corresponding heating conditions that will apply on the designed LF paths can be determined through the heating database established by FEM simulation. Fig. 11a shows the database that bending angle is a function of laser power and velocity under the condition of TGM. The beam diameter is assumed as constant (i.e., d=4mm). By matching the welding-induced value and the LF-generated value, a group of heating conditions (P and V) can be determined. In general, the combination of large P and V is preferred since it can increase the working efficiency. If the welding-induced bending angle is too large to be recovered by single scan laser forming, multiple scans should be used to avoid melting or material damage. Fig.11b shows the database 15

16 in which the LF-generated residual stress in the direction perpendicular to the scanning path is a function of P and V under the condition of BM. Only under buckling mechanism conditions, the generated transverse residual stress on top surface is compressive and can be used to remove the welding-induced tensile longitudinal residual stress on the welded surface. Experiments were conducted on 11 steel coupons with dimension of 8x8x.89mm The scanning paths and heating conditions in the experiments were determined as described above. The laser system used is a PRC-15 CO 2 laser, which is capable of delivering 1,5 W laser power. The laser beam diameter on the top surface of workpiece is 4mm for welding, 4mm for angular distortion correction, and 8mm for longitudinal distortion correction, respectively. Motion of work pieces was controlled by Unidex MMI5 motion control system, which allows easy specifications of variable velocities along a path with smooth transitions from segment to segment. Figure 12 shows the welded distortion and the remained distortion after LF correction under these conditions. A coordinate measuring machine (CMM) is used to measure the geometry of the formed shapes. Only the top surface of the plate is measured and compared. It is found that over 7% of the angular and longitudinal distortions have been removed. The remained longitudinal residual stress on the top surface is also measured by XRD. About 5% of the tensile residual stress on top surface is removed. The correction procedure is also numerically modeled and good agreement is achieved compared to the experimental result. 3.5 LF Correction on curve path bead-on-plate welding Non-straight line welding often exists due to the complexity of the welded structures. Here a curve line bead-on-plate welding is used to validate the proposed strategy on more general cases. 16

17 In each local region, the curve path still can be assumed as straight line. So that the weldinginduced distortion still can be decomposed into angular distortion and longitudinal distortion. Under curved welding path, the variation of bending angle cannot be neglected any more, so that several segments can be divided along the weld path. The determined heating conditions for removing the angular distortion will vary through each segment. For removing the weld-induced longitudinal residual stress, the paths are still applied in the direction perpendicular to the curve (path extension pass the curvature center). The spacing difference between the regions outside and inside the curve can be neglected, so that the heating conditions may still keep constant along the paths when remove those longitudinal distortions. Since the stress is more localized and not affected much by the geometry and curve path, the heating conditions still can be determined using the same strategy as the straight line welding. Fig. 14a shows the designed LF paths on a curve-path bead-on-plate welding sample. Three segments are divided along the weld path due to the non-uniformity of the angular distortion. Within each segment, the bending angle can be assumed as constant so that the heating conditions are constant. The comparison between the welded sample and the corrected sample is shown in Fig. 14b. It is seen that more than 7% distortions have been removed by the proposed strategy. Better correction result can be achieved by iterative laser forming scans and feedback measurement that requires much more time. 3.6 LF Correction on circular path bead-on-plate welding Both the straight- and curve path welding are open-loop paths so that the induced bending distortion is relatively simple. For a close-loop path welding, the non-uniformity of bending distortion is more serious than the former cases. Fig.15a shows the measurement of distortion on 17

18 a circular-path bead-on-plate welding sample. A saddle shape with negative Gaussian curvature is observed. This type of distortion is also verified by FEM simulation, which is shown in Fig. 15b. It is found that the distorted shape after welding is mainly due to the moving heat source and its scanning direction. From the measured bending angle along the weld path, it is found that the bending direction changes along the path. The reason is due to the adjacent bending effect which is induced by moving heat source, and also due to the direction change of the major inherent mechanical constraint. This non-uniformity is greatly affected by the scanning speed. Assuming an extreme case, that the scanning speed is so fast that the heating energy input is almost instantly applied on the circular path, the bending direction will be the same and towards the heating source. Under current heating conditions, the bending angle variation along the circular path is shown in Fig.16. Four regions are divided according to the bending direction. The size of each region is not even: the region with positive bending angle (bending towards the heat source) is larger than that of the negative bending angle. The paths for correcting the angular distortion are still applied along the weld path, but it is on the different surface in different region according to the direction of bending angle. In the region I and III with positive bending angle (shown in Fig. 17), the laser-forming path is on the bottom surface. While in the region II and IV with negative bending angle, the LF path is on the top surface. Since the longitudinal tensile residual stress is almost constant along the weld path, the laser forming paths to correct the longitudinal distortions can still be equally-space positioned, and are applied on the top surface. All the paths on this circular-path bead-on-plate welding are shown in Fig. 17. Noticing the big variation of bending angle within each region (i.e., region I), the LF scanning path still needs to be divided into several segments. In each segment, the bending distortion can be treated as constant. Then referring to the heating condition databases, the required laser power 18

19 and scanning speed can be determined. For circular-path case, the longitudinal stress inside the circle is larger than that of the outside due to the overlapping accumulation. So that the paths for correction of longitudinal residual stress also need to be divided into 2 segments that are separated by the circle path. Then the heating conditions can be determined as the same strategy used in the above cases. Fig. 18 shows the comparison of the welded distortions before and after LF correction. It is seen that most of the angular and longitudinal distortion was removed. Better removal of the angular and the longitudinal distortion can be achieved by dividing more segments along the circular path, and adding more paths which are perpendicular to the circular welding path, respectively. 3.7 Further discussion For complex welded structures, the welding induced distortion may not be easily decomposed into angular distortion and longitudinal distortion. For those cases, the strain-based methodology which is already applied to the laser forming process design (Liu and Yao, 23; Cheng and Yao, 25) could be a good way to design the correction conditions (including both heating paths and heating conditions). The general principle can be described as follows. From the initial shape and the distorted shape, the strain field that needs to be removed can be calculated through elastic FEM simulation. Accounting for the characteristics of laser forming that the generated strain is mostly perpendicular to the scanning path and is compressive, the LF scanning path can be determined on the concave side and is perpendicular to the principal minimum strain direction. The corresponding heating conditions still can be determined through the databases established by FEM simulation. The challenging issue in this methodology is how to account for the welding induced residual stress when determine the required strain field. More work is needed in future for this strain-based methodology. 19

20 4. Conclusions In this study, the welding distortions induced by straight-, curve- and circular-paths are effectively corrected by the laser forming technology. The out-of-plane distortion can be decomposed into angular distortion and longitudinal distortion. The former distortion can be removed by laser forming under TGM condition. The longitudinal distortion is mainly caused by the tensile longitudinal residual stress on the welding surface. From the characteristics of buckling mechanism (BM) laser forming, it is found that the LF-generated compressive stress can be used to remove the tensile longitudinal residual stress and the caused longitudinal distortions. The corresponding heating conditions for laser forming can be determined by the database of relationship between bending angle, residual stress, laser power, scanning speed and beam spot size. The heating database is established by the laser forming FEM simulation. For curve path welding, the non-uniformity of the induced angular distortion should be considered when determines the heating conditions. For the circular-path welding, even the bending direction may change, so that the paths for removing the angular distortion are still along the weld path, but in different surfaces according to the bending direction. The proposed strategies are validated by experiments and numerical simulation. The result shows that laser forming can be used to effectively remove the distortions induced by butt welding. Acknowledgements The authors acknowledge the support of the NIST and of co-workers within the NIST-sponsored project Laser Forming of Complex Structures (grant number ATP-5269). Help from Mr. Eric Holihan on XRD measurement who is from Columbia University Materials Research Science and Engineering Center (MRSEC) is also appreciated. 2

21 References: 1. Masubuchi, K., 198, Analysis of Welded Structure: Residual Stresses, Distortion, and Their Consequence, Pergamon Press. 2. Michaleris, P. and DeBiccari, A., 1997, Prediction of Welding Distortion Welding Journal, Welding Research Supplement, 76 (4), p 172s-181s 3. Deo, M. V. and Michaleris, P., 23, Mitigation of Welding Induced Buckling Distortion Using Transient Thermal Tensioning, Science and Technology of Welding * Joining, 8(1), pp Xu, J., and Li, W., 25, Welding Induced Distortion Control Using Dynamic Thermal Tensioning, Trans. NAMRI of SME, 33, pp Cheng, P., Mika, D., Graham, M., Yao, Y. L., and Jones, M., 25, Laser Forming of Complex Structures, The 1st International Workshop on Thermal Forming (IWOTF 5), April 13-14, 25, Bremen, Germany 6. Geiger, M., Vollertsen, F., and Deinzer, G., 1993, Flexible Straightening of Car Body Shells by Laser Forming, Sheet Metal and Stamping Symposium, Detroid, Michigan. 7. Cullity, B. D., 1978, Elements of X-ray Diffraction, 2 nd Edition, Addison-Wesley Pub. Co., New York. 8. Bao, J., and Yao, Y. L., 21, Analysis and Prediction of Edge Effects in Laser Bending, ASME J. Manuf. Sci. Eng., 123, pp Vollertsen, F., 1994a, An Analytical Model for Laser Bending, Lasers in Engineering, 2, pp Liu, C., and Yao, Y. L., 23, FEM Based Process Design for Laser Forming of Doubly Curved Shapes, ASME Transactions J. Manu. Science and Engineering, submitted. 11. Cheng, P., Mika, D., and Yao, Y. L., 24, Laser Forming of Varying Thickness Plate, Part II: Process Synthesis, ASME Journal of Manufacturing Science and Engineering, accepted. 12. Dong, P., Ghadiali, P. N., and Brust, F. W., 1998, Residual Stress Analysis of a Multi-pass Girth Weld, ASME PVP- Fatigue, Fracture, and Residual Stresses, 373, pp

22 13. Fisher, J., Broman, R., Thakkar, R., Yang, Y-P., Cao, Z., Zhang, J., and Brust, F., 1999, Numerical Simulation of Distortions and Stresses Due to Welding Thin Gage Steel, International Symposium on Steel for Fabricated Structures, p Fricke, S., Keim, E., and Schmidt, J., 21, Numerical weld modeling-a method for calculating weld-induced residual stresses, Nuclear Eng. Design, 26, pp Junek, L., Slovacek, M., Magula, V., and Ochodek, V., 1999, Residual Stress Simulation Incorporating Weld HAZ Microstructure, ASME PVP- Fracture, Fatigue and Weld Residual Stress, 393, pp Vincent, Y., Jullien, J., Cavallo, N., Taleb, L., Cano, V., Taheri, S., and Gilles, Ph., 1999, On the Validation of the Models Related to the Prevision of the HAZ Behaviour, ASME PVP Fracture, Fatigue and Weld Residual Stress, 393, pp Chang, W. S., and Na, S. J., 22, A Study on Heat Source Equations for the Prediction of Weld Shape and Thermal Deformation in Laser Microwelding, Metallurgical and Materials Transactions B, 33B, pp Nnaji, B. O., Gupta, D., and Kim, K.Y., Welding Distortion Minimization for an Aluminum Alloy Extruded Beam Structure Using a 2D Model, Trans. ASME J. Manu. Sci., 126, pp

23 Fig.1 Samples showing the welding-induced distortions Z (mm) Transverse distance Y(mm) Longitudinal distance X(mm) 4 (a) 23

24 (b) Fig.2 Contour map of straight-path welding sample, showing both angular and longitudinal distortions (a) Experimental measurement by CMM, and (b) Numerical simulation in ABAQUS (Only half plate is shown due to the geometric symmetry, x5 magnification) Fig.3 Typical time history of temperature from welding simulation 24

25 5. By experiment 4.5 By simulation Angular distortion (degree) Power=12 W, V=1 mm/s Beam diameter=4 mm α x schematic of bending angle Location along the weld path (m) (a) By experiment By simulation Longitudinal distortion (mm) Power=12 W, V=1 mm/s Beam diameter=4 mm Location along the weld path (m) (b) 25

26 Fig. 4 Distribution of the welding induced (a) angular distortion and (b) longitudinal disotortion along the direction of weld path 11 Diffraction Intensity In normal direction In tilted direction (5 to normal) stress = MPa Bragg angle(degree) Fig.5 Measurement of the transverse residual stress by XRD at the center of the plate Longitudinal Residual Stress (MPa) Simulation Measure Top surface Bottom surface Distance to Weld Path (m) P=12 W, V=1 mm/s Beam diameter=4 mm Fig.6 Distribution of residual stress in the X direction (direction of welding) for bead-on-plate, straight path welding 26

27 Transverse Residual Stress (MPa) Simulation Measure. Top suface Bottom surface P=12 W, V=1 mm/s Beam diameter=4 mm Distance to Welding Path (m) Fig.7 Distribution of residual stress in the Y direction (direction perpendicular to the direction of welding) for bead-on-plate, straight path welding 2 S22 on Top surface S22 on Bottom surf Temperature on top Temperature on bottom 12 Stress S22 (MPa) LF conditions: Power=8 w Velocity=15 mm/s Spot size=8 mm Temperature (K) Time (Second) (a) 27

28 25 2 On top surface On bottom surf. 15 Stress S22 (MPa) LF conditions: Power=8 w Velocity=15 mm/s Spot size=8 mm Distance to scan path (m) (b) Fig. 8 (a) Time history of transverse stress and temperature in laser forming (b) Distribution of steady state transverse stress along Y direction (under the conditions of power=8 w, scan speed=15mm/s and laser beam diameter=8mm) 28

29 Out-of-Plane Welding distortion Angular Distortion Longitudinal Distortion 1. measured bending angle (normal to path) 2. distribution of pe22 and s22 1. measured longitudinal displacement 2. distribution of pe11 and s11 Correction path: along welding path on the bottom side Correction path: perpendicular to welding path on the top side Determine the heating parameters from process map (Bending angle vs. P, V ) Determine the heating parameters from process map (stress vs. P / V / d, in BM) Check remained distortion Determine scan times Check the property change Fig. 9 Overall Strategy for welding distortion correction 29

30 Fig. 1 Scanning paths of LF to remove welding-induced distortions 3 Bend angle (deg) Power (w) Scan speed (mm/s) 3 (a) 3

31 Z (mm) Stress (MPa) Power (w) Scan speed (mm/s) 3 35 (b) Fig. 11 Process Map to Determine the Heating Conditions (a) bending angle as a function of power and speed (beam spot size=4 mm), (b) transverse stress as a function of power and speed (beam spot size=8mm) Transverse distance (mm) Longitudinal distance (mm) 4 Fig. 12 Measured distortions for straight path bead-on-plate welding before and after LF correction (measured by CMM, x5 magnification) 31

32 Longitudinal Residual Stress (MPa) Before LF: Simulation Measure After LF (Measurement) Distance to Weld Path (m) Fig. 13 Distribution of the remained longitudinal residual stress (a) 32

33 3 Z (mm) Transverse distance (mm) Longitudinal distance (mm) (b) Fig.14 (a) Designed correction paths for curve-path bead-on-plate welding, and (b) Measured distortions for curve-path bead-on-plate welding before and after LF correction (measured by CMM, x5 magnification) Z(mm) 25 Y (mm) X (mm) 2 4 (a) (b) Fig. 15 (a) Measured distortion for circular-path bead-on-plate welding (under welding condition of Power: 12 w, Velocity: 1 mm/s, Beam diameter: 4 mm; measured by CMM) (b) Simulated distortion with contour of minimal principal plastic strain (x5 magnification) 33

34 6 4 Experiment Simulation Bending angle (degree) II III I Schematic of zones I IV II welding conditions: power=12 w speed=1 mm/s spot size=4 mm III Angle to the starting point (degree) IV Fig. 16 Bending angle distribution for the circular-path bead-on-plate welding Fig. 17 Designed correction paths for circular-path bead-on-plate welding 34

35 Fig.18 Experimental validation for LF correction of circular-path bead-on-plate welding (from left to right: welded sample, corrected sample, initial shape) 35