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## An Analytical Model for Tailor Welded Blank Forming”, (2003)

Venue: | J Man Sci Eng, |

Citations: | 4 - 1 self |

### BibTeX

@ARTICLE{Kinsey03ananalytical,

author = {Brad L Kinsey and Jian Cao},

title = {An Analytical Model for Tailor Welded Blank Forming”,},

journal = {J Man Sci Eng,},

year = {2003},

pages = {344--51}

}

### OpenURL

### Abstract

Introduction Automakers are constantly searching for innovative means of reducing vehicle weight and manufacturing costs in order to meet ever-restricting fuel economy standards while remaining economically competitive. A promising opportunity to meet these seemingly conflicting requirements is through the use of Tailor Welded Blanks ͑TWBs͒. TWBs are blanks where multiple sheets of material are welded together prior to the forming process. The differences in the material within a TWB can be in the thickness, grade, or coating of the material, e.g., galvanized versus ungalvanized. Extensive research efforts have focused on TWBs with an emphasis on these formability concerns. From the material point of view, studies have been conducted to investigate the material properties of the weld and in heat affected zone ͓2-4͔ and the effect of post welding processes, e.g. hot and cold planishing ͓5͔. The decreased formability for popular TWB materials and welding combinations were reported in ͓6-10͔. In the previous work ͓11͔, we conducted limit dome height tests of both the base material and TWBs fabricated from 2-mm and 1-mm aluminum 5182-H00 using YAG laser welding with the weld line located in the center of the blank along the major strain direction. From these limit dome height tests, it was determined that the approximate plane strain forming limit was reduced from 22% for the base material to 8% for this TWB combination. Given the reduced formability of TWBs, modifications to the forming process have been proposed to increase the depth of draw of the formed part. One such method is to increase the material flow-in of the thicker, stronger material to reduce the deformation of the thinner, weaker material through the use of a non-uniform binder force, i.e., a lower binder force is applied to the thicker material than the one applied to the thinner material ͓12,13͔. This technique has shown that if the weld line movement can be prevented, deeper depths of draw can be obtained. Another process modification introduced an additional material constraint within the forming area thus preventing the thinner material from taking a majority of the deformation in the process ͓14 -16͔. The additional material constraint method increased the potential depth of draw for a test panel, which included a nonlinear weld line for better material optimization. However, this technique added complexity to the forming process and additional tooling costs. Though TWBs are currently used in industry, the fundamental understanding to quantify material flow in the process, e.g., weld line movement, is lacking. This consequently results in using a trial and error approach, either numerically or in physical die tryouts, to determine the forming height to achieve a desired strain condition at the weld line and the location of the step in the tooling. In order to utilize TWBs to the fullest potential, a means to determine the forming height and to calculate the weld line movement must be developed. With respect to analytical modeling of TWB applications, little work has been reported. Examples of this research, however, include Shi et al. ͓17͔ calculating the limiting thickness and strength difference possible for a TWB application, Cayssials ͓18͔ determining the forming limit curve for TWBs, and Doege et al. ͓4͔ providing analytical work for the weld properties of TWBs. He et al. ͓19͔ used a 2D cross-sectional analysis to determine a non-uniform binder force ratio to improve TWB formability. In their model, the calculations progressed from the edge of the blank to the weld line in order to determine the strain in the 2D cross-section. Good results with respect to determining a non-uniform binder force to prevent weld line movement were obtained and compared with strip and box forming simulations and experiments. The inputs to their model include material In this paper, a 2D sectional analysis on various TWB applications is used to analytically determine the weld line movement and forming height for uniform binder force cases. Also, a method to determine the material flow pattern onto and off the punch face is presented. This analytical model would be beneficial to a designer early in the decision making process, prior to costly and time intensive numerical simulations, to determine the potential depth of draw for a given TWB part and to assure material properties are located where desired in the final part despite weld line movement. Unlike the work presented in the literature, no assumptions regarding material flow in the process are inputted into the model. In order to validate the analytical model, numerical simulations were conducted, and an experimental test panel was formed. Good agreement between the analytical model, the numerical simulations, and test panel forming with respect to weld line movement and forming height demonstrates the effectiveness of this analytical model. Methodology of the Analytical Model The goal of our analytical model is to calculate the weld line movement and forming height for a uniform binder force, TWB application. As was previously mentioned, a 2D sectional analysis greatly simplifies calculations and therefore will be used here. See In our model, we start at location a at the weld line in the 2D cross-section with a known strain level in the 1-direction. Then calculations of force in the 1-direction, T 1 , and strain in the 1-direction, 1 , are determined at all locations indicated in where t thin o is the original thickness of the thinner blank at that location. This relationship is also valid at all locations in the 2D cross-section with the appropriate substitution for variables at the given location. The material is assumed to follow a power hardening law, where is the equivalent stress and is the equivalent strain. Due to force equilibrium across the weld line, the same force exists in the material at A, T 1A , i.e., T 1a ϭT 1A . This fact allows the calculation of the strain at A, 1A , from force equilibrium. Also, plane strain, no shear stress, incompressibility, and negligible thickness stress, 3 ϭ0, are assumed in our model. where t thick o is the original thickness of the thicker blank at section A. Force equilibrium can also be applied to all of the locations in the 2D cross-section. In a straight section, a simple force equilibrium is applied, e.g., T 1a ϭT 1b . This simplification neglects frictional forces in the straight sections of our model, which is a reasonable assumption due to the low value of the frictional forces compared to the forces from material straining. For sections that include a radius, additional force terms for bending, ⌬T bend , and friction, ⌬T f riction , must be included. The appropriate equations for all of the sections on the thinner side of the TWB are The sign of the ⌬T bend and ⌬T f riction terms in the T 1c equation depends on whether the material initially at location b flows onto the punch face ͑negative͒ or into the stretch-draw wall area ͑posi-tive͒. Similar relationships exist for the thicker side as well. At location e, the material is assumed to flow into the stretch-draw wall area. With respect to bending analysis in sheet metal forming, research has investigated using membrane theory in post processing to determine springback ͓23,24͔ and shell theory that considers both bending and stretching effects ͓25-27͔. Also, the calculation of tangential strain has been used to determine springback curvature for plane strain bending ͓19,28͔. Here, Swift's model ͓29͔ for bending in sheet metal forming is used to calculate ⌬T bend . where y is the yield stress of the material, t is the material thickness, and R is the bend radius. This model does not account for increased strain in the material due to bending however. The change in the 1-direction force due to friction, ⌬T f riction , for sections that include a radius is determined from ⌬T f riction ϭTe With values calculated for the forces in the 1-direction at all sectional locations, strain values in the 1-direction, 1 , and stress values in the 2-direction, 2 , can be solved from the material constitutive law presented in the appendix. The strain values in the 1-direction can then be used to determine the draw-in on the thicker, x thick , and thinner, x thin , sides of the 2D cross-section and the weld line movement, x wl . Finally, the force values in the 1-direction at E and e are used to determine the forming height, x FH , for the TWB. Further details for calculating x thick , x thin , x wl , and x FH will be presented in the following sections. Calculations of Forming Height and Weld Line Movement In the deep drawing of sheet metal, material movement from under the binder area and the punch face, along with stretching of the material, is essential to produce the wall of the formed part. In order to calculate the forming height, x FH , at the given strain condition, values for the draw-in of material from under the binder area into the stretch-draw wall are required. For the thinner side of the 2D cross-section, material draw-in, x thin , can be calculated from where L f is the final length of the stretch-draw wall section, L o is the length of the material above the stretch-draw wall prior to forming including the punch and die radii, e be is the engineering strain in the 1-direction from section b to section e of the stretchdraw wall, and x b is the movement of the material initially at location b onto the punch face ͑positive͒ or into the stretch-draw wall ͑negative͒. See A similar equation can be now written for material draw-in on the thicker side of the TWB, x thick . However, for the thicker side, material from the x wl and the stretching of material on the thicker side of the punch face due to engineering strain, e AB , also are assumed to flow into the stretch-draw wall on the thicker side. Therefore, these terms are included in the calculation of x thick . Again, the material draw-in, x thick , is dependent on the forming height through the L f term. Equations ͑7͒ to ͑9͒ provide for a means to calculate x thin and x thick for various forming heights ͑i.e., for various stretch-draw wall length, L f values͒ and for a given value of x b . This data can then be plotted to provide a graph of the draw-in ratio, x thick /x thin , versus forming height for the given x b value. A sample plot is provided in The rationale here is that the forces in the 1-direction at E and e are the forces that draw material into the stretch-draw wall and therefore their ratio is directly proportional to the ratio of the material draw-in on the thicker and thinner sides. Therefore with a polynomial curve fit of the draw-in ratio versus forming height data, such as that given in where X wl o is the initial weld line position offset ͑positive if moved towards the thinner material and negative if moved towards the thicker material͒ and L blank o is the total initial length of the blank. In the preceding paragraphs, an x b value was assumed and the x FH was determined by relating the draw-in ratio, x thick /x thin , to the ratio of forces entering the stretch wall area, T 1E /T 1e , by either Eq. ͑10͒ or ͑11͒. In order to determine the actual x b value for a given TWB application, the x FH values for a range of x b values must be determined and plotted as shown in Numerical Simulations In order to verify our analytical model, numerical simulations were conducted on the commercially available FEM software ABAQUS/Standard. Comparison of Analytical Model and Numerical Simulations In post processing the numerical simulation results, forces and strains in the 1-direction, T 1 and 1 , were extracted to compare with values obtained from the analytical model. Application of Analytical Model to Test Panel As an example of the application of the analytical model to a TWB part, consider the test panel punch and blank geometry shown in Conclusions and Discussion Tailor Welded Blanks offer numerous advantages over the conventional method to fabricate sheet metal parts, e.g., body-inwhite components in the automotive industry. However, decreased formability caused by weld line movement and changes in the material properties in the heat-affected zone of the weld limit their utilization. In order to aid in the design process, an analytical model was developed and presented here to assist the designer in determining the amount of weld line movement and the forming height for a given TWB geometry. Knowledge of these parameters is critical early in the design process so the designer is able to locate the material properties in the formed part where desired and assure the necessary depth of draw is obtainable. A 2D sectional analysis was utilized, and values for material draw-in from under the binder ring were determined in order to obtain the desired parameters. Good agreement between the analytical model and numerical simulations with respect to both weld line movement and forming height verifies the effectiveness of the methodology. While this analytical model was shown to provide good results compared to numerical simulations, there are several aspects of the model that should be noted. First, plane strain and negligible thickness stress assumptions were used to solve the non-linear equations, but these assumptions limit the effectiveness of the model for general cases. In particular, the plane strain assumption could be eliminated to allow for bi-axial straining to be possible, either deep drawing with a negative minor strain or stretch forming with a positive minor strain, at locations on the 2D crosssection. This would allow the model to be used in a more general fashion. Also, the simple bending model used here could be replaced with a model that includes additional stretching of the material due to bending. This would allow the analytical model to follow the numerical simulations more accurately at locations D and d where additional stretching due to bending occurs ͑see