incompressibility。 Thus, the variation form as a basis for finite element discretization is given by this equation [22]:

Fig。 4。   The resulted embossed pin head and the geometries to be measured。

cavity represent by 1。 Therefore the lower the ratio, the higher the unfilled region depicting the larger defect。 Filling ratio can be obtained from the ratio of filled region to the fully-filled region, or AR = Filled Region/Fully-Filled Region。 Similarly, in Fig。 4, bulging is measured from the image of the forged pin head obtained from the FE result。 In the current work, two features are measured: A and

B。 For consistent calculation, a simple program is developed using Matlab。 The image of the embossed pin head is captured from FE simulation, and the geometry of the part is determined using an ordinary program developed using Matlab。 For the fabrication of the blade, the 100-tone c-type mechanical press machine is used (Fig。 5)。

4。Results and discussion

In the embossing process of the pin head, the stress distribution shows the concentrated tensile stress around the sliding region。 This tensile stress increases as the punch stroke increased。 At lower

stroke, the stress concentration is more localized at the right sec- tion and the largest stress can be found near this region (Fig。 6)。 The localization continues until the end of the press, resulting in

where  ε˙ v  = ε˙ ii   is  the  volumetric  strain  rate  and  k  is  the  penalty

constant, a very large positive number。 Eqs。 (1) and (2) are the basic equations for the finite element formulation。

The two-dimensional (2D) model of the simulation is shown in Fig。 3。 The model consists of a preform/workpiece, top die, and bottom die。 Both dies are considered as rigid bodies。 The preform is placed in between the dies before the embossing takes place。 In this process, the workpiece is pressed by a punch at a constant speed of 250 mm/s。 The thickness of the AA6061 workpiece is 3。0 mm。 Since the process does not use any lubricant and the material to be formed is aluminum, the friction coefficient is assumed to be 0。4。 The ini-

tial temperature of the workpiece, punch, and die is set at room temperature or at 25 ◦C。 The rigid-plastic finite element method is

applied in the analysis of the deformation involving 3000 elements for the preform。 The material properties are listed in Table 1。 The material used for the punch and die is the D2 tool steel, which is suitable for cold working processes。

In the present study, two major defects are considered, i。e。, unfilled region and bulging。 The unfilled region is quantified based on the filling ratio。 The filling ratio is described as the ratio of the filled region to the fully filled or defect-free part。 The  fully-filled

Table 1

Material properties of the workpiece。

Parameter Workpiece

the decrease of distribution area。 In the present study, the flow of the material in the right section of the pin head is the main focus。

Material type AISI 6061

Modulus Young (GPa) 70

Yield strength (MPa) 386

Poisson ratio 0。35

Hardness HRC-24

  Fig。 5。   The 100 tone c-type mechanical press machine used in the fabrication。

Fig。 6。  The stress distribution of the pin head embossing at different punch stroke at diameter = 3 mm, distance to edge = 0。7 mm and depth = 2 mm。