Superplasticity is the deformation behavior that produces essentially neck-free elongation of many hundreds of percent in metallic materials. The development of superplastic materials has provided new opportunities to produce complex components using forming techniques that are not possibel with conventional metals and alloys. Superplastic forming (SPF) has been widely used in the aviation and the aerospace industry since it has gret advantages to produce very complicated, light and strong components. The application of SPF today has expanded very quickly in the aerospace industry and it has been recently used to produce some consumer goods such as golf clubs and cookeryware.
Different types of SPF processes have been evolved for various superplastic materials. The simplest form of the superlastic sheet forming is the female forming. A number of superplastic forming processes have been developed and designed to avoid severe thickness deviation that is inevitable in simple female forming. Some of forming processes require tool movements for fetter thickness distribution than the simple female forming. On the other hand, superplastic forming/diffusion bonding (SPF/DB) process has been developed at Rockell, providing a means to inexpensively utilize a structurally efficient material heretofore inhibited by high fabrication and material costs.
In such processes, it is necessary to control the temperature and the strain rate for good stability of the plastic deformation and the large elongation less susceptible to localized necking. In order to successfully produce a complex sheet metal component by superplastic forming, the optimum condition of the pressure cycle to gain the maximum strain rate sensitivity has to be sought by numerical simulation. Although many effort has been made in the optimization of SPF processes with various methods, researches on the optimum forming condition of the moving-tool forming process and the SPF/DB process are still needed for successful application.
Computer simulations of three dimensional superplastic sheet forming processes have been carried out by the finite element method with a membrane element or a shell element. In general superplastic sheet forming processes, the bending effect due to the sheet thickness is not negligible since the sheet is not thin compare to the other dimensions. In the real process modeling, a membrane element is regarded as more preferable rather than a shell element because of the computing efficiency and the easy contact treatment. Nevertheless, a membrane element has a disadvantage of disregarding the bending effect during the deformation. To overcome such a deficit in using a membrane element, a modified membrane element may be required in the finite element formulation procedure to take the bending effect into account.
In this dissertation, superplastic forming processes are simulated by the use of a finite element method in the convective coordinates system. The finite element formulation is derived from the equilibrium equations as a weak form of Lagrangian formulation for the incremental analysis. The inelastic behavior of the superplastic material is described as incompressible, nonlinear, viscous flow. The formulation derived has been implemented into a finite element code with a modified membrane finite element which approximates the bending energy term with the kink angle. The formulation is associated with an algorithm to consider properly contact between dies and materials and an algorithm to control the pressure cycle for the optimization of the forming time. The calculation deals with maximization of the stain rate sensitivity, protection of the localized deformation, and consistency of the desired strain rate. The code calculates the deformed shapes, the thickness distribution, and the strain rates as well as the optimum pressure cycle. The validity of the present code is demonstrated by comparing numerical results with experimental results in a simple female forming process.
Analysis of moving-tool forming processes is carried out with the present finite element code. The result is compared with blow forming processes with a fixed female die to demonstrate that the thickness distribution with a moving die is different from that with a fixed die. Results show that the thickness distribution of a part can be improved by using a moving-tool forming process with the same part shape.
Analysis of a superplastic forming/diffusion bonding (SPF/DB) process is also carried out for a 4-sheet sandwich part. The result shows that the deformed shape with the three dimensional analysis is different from that with the two dimensional plane strain analysis because of the end effect. The result demonstrates that three dimensional analysis is indispensable for simulation of SPF/DB to provide the accurate pressure cycle and deformed shapes. Remarkable deviation of the thickness distribution along the corridor direction also demonstrates the necessity of three dimensional analysis. The present analysis enables to predict accurate thickness distribution, which is necessary for good design of multi-sheet sandwich parts as an aircraft part.
