Two-Stage Approach for Improving the Thickness Distribution in Superplastic Forming

Superplastic Forming (SPF) process has many unique advantages over conventional forming operations including ability to produce complex thin shapes and significant cost and weight savings potentials. However, the SPF may result in excessive thinning at certain locations and a non-uniform thickness profile. To address these issues, the two-stage SPF process was developed to improve the uniformity of thickness distribution. In this work, two techniques were considered to improve the final thickness distribution of a complex shape, namely, the license plate pocket potion of an automobile decklid outer panel. These two techniques are the reverse free bulging and sheet preforming. The commercial finite element code, ABAQUS, was used to model the two-stage SPF process of an aluminum alloy AA5083 sheet at 450 °C. The study concluded that reverse free bulging did not result in improvements in the thickness profile compared with that obtained from the single-stage SPF. However, the sheet preforming technique, with an engineered preform cavity, resulted in an almost uniform thickness distribution for the superplastically formed part.


Introduction
Superplasticity is the ability of certain type of materials to exhibit large tensile deformation prior to fracture.While the maximum elongation prior to failure that can be achieved in conventional alloys does not exceed 120%, superplastic materials have the capability to exhibit very large elongations, i.e. >500%, (Pilling & Ridley, 1989).The conditions for superplasticity to occur are forming within a specific range of strain rates, and forming in narrow ranges of temperatures (Pilling & Ridley, 1989).Each material has a unique optimum value of strain rate, and a narrow temperature range which lies above half the material's absolute melting point.
The SPF process is carried out by placing a sheet of superplastic material on a pre-heated single-sided die.The sheet is heated to the required SPF temperature which is specified for that material.Then, an inert gas is applied to one side of the sheet to control the rate of deformation and force the sheet to take the shape of the die cavity.
As a manufacturing process, SPF offers many unique advantages over conventional forming techniques including greater design flexibility, low dies cost, the elimination of spring back, and producing components with complex geometries in one manufacturing step (Kleiner, Geiger, & Klaus, 2003).Accordingly, SPF reduces or eliminates the sub-components and joining operations.In addition, SPF allows for the satisfactory forming of lightweight alloys, which opens the door for substituting steel with lighter weight alloys for automotive components.This would have a huge effect on energy consumption and environment.
The main limitation of SPF is the slow nature of this process compared to other forming operations.Other limitations include the non-uniformity of the produced part thickness, the possibility of severe thinning and necking at certain locations and large amounts of cavities developed in some superplastic alloys, see for example (Jarrar, Liewald, Schmid, & Fortanier, 2014).
An interesting approach to improve the thickness profile of superplastically formed parts is preforming.It was concluded by (Johnson, Al-Naib, & Duncan, 1972) that multistage operations that take advantage of the high friction conditions of SPF were the most effective at producing improved thickness uniformity.Few researchers studied the effect of preforming; (Nakamura, 1989) and (Fischer, 1998) used the preform technique in their works to form simple geometries.In a more recent study (Luckey, Friedman, & Weinmann, 2009), a two-stage SPF process was developed, based on the inventions of (Nakamura, 1989) and (Fischer, 1998).Gas pressure was used to form the blank into a preform die cavity prior to the pressure being reversed to form the sheet into the final component cavity.The preform had been designed to improve the forming of a complex component by providing a superior thickness profile as compared to a single stage forming cycle.Their work was based on finite element analysis and experimental iterations, and focused mainly on the effect of the length of line of the preform cavity.
Abu-Farha and Nazzal (2010) imposed a pre-thinning reverse bulging step before the forward SPF stage.Their results showed that the reverse free bulging approach improved the thickness profile and decreased the severe thinning with specific part geometries and materials.Recently, Lan, Fuh, Lee, Chu, and Chang (2013) used two-stage SPF to form a deep and irregular trough.The sheet was initially bent into a V-shaped groove prior to the gas forming work.They found that preforming of the V blank creates a uniform length of line and improved the thickness profile of the final part.However, a serious wrinkling situation was encountered in their study.
Our main goal is to consider the effect of the shape of the preform cavity on final thickness distribution of the part, and attempt to find an engineered shape for better thickness distribution.We will develop a finite element method predictive tool of the process and suggest certain process guidelines that would overcome some of the limitations of the SPF process.

Constitutive Model
A superplastic aluminum alloy sheet, AA5083, was used in this work which had a nominal thickness of 1.2 mm.The constitutive model used to describe the superplastic deformation here is the power law equation: σ kε ε (1) where σ is the effective flow stress, ε is the effective strain rate, m is the strain rate sensitivity exponent, n is the strain hardening exponent, and k is the strength coefficient.The values of k, m and n were determined by fitting the model to tensile tests taken from (Krajewski and Montgomery, 2004).The obtained values of k, m and n are shown in Table 1.The developed constitutive model was verified by comparing its results with analytical results and experimental data for bulging a sheet with an original thickness of 1.2 mm to form a hemisphere with a radius of 57 mm.
The following equations, taken from (Dutta and Mukherjee, 1992) were used to find the analytical results of the radius of curvature, the pole thickness, and the pressure profile, respectively: where ρ is the radius of curvature, a is the radius of the die, ε is the effective strain rate, S is the thickness after time t, S is the original sheet thickness, σ is the effective flow stress, and P is the applied pressure.
The pole height was found by using the following relationship relating the radius of curvature, ρ, and the height, h, taken from Jovane (1968): Two sets of finite element (FE) simulation runs were performed.In the first set, a constant gas pressure was prescribed during bulge forming.In the second set, the gas pressure profile was computed (rather than prescribed at the outset of the simulation) using an algorithm internal to ABAQUS TM .Simulation results for constant gas pressure were compared with experimental AA5083 data from bulge tests taken from (Bradley, 2004).Figures 1(a-b) show the FE predicted dome pole height at the two gas pressures (solid curves).The triangles correspond to the experimental data.Figures 2(a-b) show the dome pole thickness evolution at the same pressures considered in Figure 1.Figures 1 and 2 show that the developed material model leads to FE predictions that follow the experimental trends.ABAQUS TM results for constant strain rate forming were compared with the analytical results.Figure 3 shows the FE predicted dome pole height at a strain rate of 0.0005 1/sec (solid curve), the triangles correspond to the analytical results.Figure 4 shows the dome pole thickness evolution at the same strain rate considered in Figure 3. Figures 3 and 4 show that the developed material model leads to FE predictions that follow the analytical trends.

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Results
Table 2     Table 3 Co and the tw  The reason fo er, its resistanc the other hand MPa.dels used for th e four models nd 3 made the ing at these reg tretching, the models.stretching, required the longest forming time of 1351 seconds.The first three models did not achieve a uniform thickness distribution.On the other hand, the fourth model resulted in an almost uniform thickness distribution for the superplastically formed part.The improvement in the minimum thickness was 3.5%, and in the thinning factor it was 4.4%.In order to achieve a wrinkle-free component, the preform length of line was calculated to ensure that it did not exceed the final part cross-section length of line.
Figure 6 sh the die are 306.32 mm both 6 mm corner.Th approxima ability to (ABAQUS The gas pr rate of 0.0 0.2 coeffic Figure Figure 12 Figure

Table 1 .
The obtained m, n, and k values for the constitutive model

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