3. Numerical simulation in ISMF method

Numerical simulations for ISMF are still one of the challenges that need to be solved due to the loss of time in the simulation process, and the contact between the tool and the forming surface is always replaced. Therefore, the meshed surfaces in the simulation should not be too complicated, and the tool paths must be programmed and imported into the input files of CAE software such as ABAQUS, DEFORM, LS-DYNA, and so on. This software can provide a simulation of elastic and plastic deformation of the sheet metal forming process. Characteristics such as stress distribution, deformation, ductile fracture, etc. can be easily inspected through the simulation process. The results of the simulation process can then be used to obtain the optimal shape as well as the material properties required for the final product. Before simulating the process of forming deformation, mechanical properties of 3D models, geometric profiles of products, and contact surfaces must be built. Elastoplastic model is often selected to simulate through material properties such as elastic modulus, Poisson's coefficient, and density of materials. The flow stress curve equations of materials and anisotropic models must be applied to describe the plastic flow rule of materials.

#### 3.1 Select simulation elements

position at each Z layer, the points are projected in the radial direction from the center axis and calculate their intersection with the created surface. Those intersec-

> c ¼ m þ Rnv t ¼ c � Rn j j CE ¼ j j CG ¼ j j Rnvn e ¼ c � j j CE n

j j ET ¼ j j E � T

j j ST <sup>¼</sup> ð Þ j j ET <sup>2</sup> j j HT cl ¼ m þ j j ST nxoy

h ¼ e � j j ET nv

where c, m, t, e, h, and cl are vectors corresponding to peak points of C, M,T, E, H, and CL; R is the radius of forming tool; nn is a unit normal vector; nv is the vector along the unit axis; and nxoy is a projection of the nn vector on the (XoY) bottom

(6)

tion points must be checked to see whether they are inside or outside of corresponding triangular elements as illustrated in Figure 9. After finding the points in the inner domain of the triangle, it is possible to calculate the position

points of the tool according to Eq. (6) and Figure 10.

Calculation of tool location points (CL data).

Mass Production Processes

plane.

Figure 11.

106

Tool path generated from CAM software.

Figure 10.

Meshed elements used in finite element simulation of ISMF are often shell element models with more than five integral points according to the thickness of the shell. Using the integral points in the thickness direction of the shell element could be replaced by the solid element and described the effects of the tension and compression area on the simulation results. Most shell elements consider the normal stress to be zero in the direction of the thickness, but because the shear stress in that direction may be not zero, then the stress state is not plane stress. Some shell elements consider the normal stress in the thick direction, and they are called thick shell elements. Figure 12 shows the finite element model for the ISMF simulation process, in which forming tools and supported molds are designed and calibrated with 3D software, the blank is modeled with shell elements (S4R), and tools and

Figure 12. Finite element model for simulation.

molds are modeled by rigid surface elements (R3D4). The average size of the elements can be selected to suit the calculation time and desired accuracy.
