Example of Grid Analysis
Occasionally a problem is found, such as an automotive instrument panel mounting plate, which is ideally suited for grid analysis. Certain lots of electro galvanized steel encounter severe breakage for this part. A gridded stamping is shown in Fig. 7; the area of interest is shown within the dashed lines. The breakage location is indicated by the solid black line. An initial conclusion might be that the metal is restricted in the blank and that the maximum strain direction is perpendicular to the failure.
An examination of the grids within the critical area indicates quite an opposite condition (Fig. 8). The maximum strain direction is diagonal across the flat and at 45 degrees to the failure. This is characteristic of the failure found in a tension specimen. Maximum strain values are +80% along the major axis and 25% along the minor axis. The ratios of the two strains are identical to those found in a tension test. This stamping is, in fact, pulling a tensile test along axis A C. Because the strain values are tension compression, Fig. 6 is not applicable. However, the strain is critical based on the tension compression curve of Goodwin . (2)
In order to evaluate whether die or blank changes can reduce breakage, it is necessary to understand the metal flow. Partial stages of formation are not available to generate the strain history. The metal flow, however, can be stimulated by forcing a sheet of polyethylene over the stamping. This sheet of polyethylene represents the original flat sheet of steel. A series of ink circles are stamped in the polyethylene sheet to help visualize the deformation. Two pieces of thick cardboard are cut to the horizontal profile of the sidewall; these duplicate the die radius and hold down plate. The polyethylene is sandwiched between the two "cardboard dies" and the composite is pulled down the sidewall; the polyethylene is allowed to slip between the cardboard dies. At the bottom position, the polyethylene has stretched (elongated circles) along the diagonal A C and compressed into wrinkles along B D. The polyethylene model duplicates to some degree the deformation required of the steel.
The deformation pattern of the polyethylene can be analyzed and simplified. Fig. 9 illustrates the results. A section of the blank A' BPQ' is merely folded down to form the wall A B P Q; strain within this area is approximately zero. There is, of course, a bending and unbending of the steel in this section as it passes from the blank over the die and then flattens out into the wall. However, the initial and final states may be visualized by the flap being folded down. A similar process takes place to form wall C D M L. To maintain geometrical continuity of the blank, the middle section A' BCD' must therefore deform to fill space A B C D of the final part.
Further visualization will show that line A' C will elongate to become diagonal A C. This agrees exceptionally well with an average strain of 63% measured between A and C on the stamping. The other diagonal B D has a calculated strain of 22% and a measured strain of 25%. Because the strains are generated only from material being forced to conform to the geometric shape, changes in the die radii, blank size, lubrication, etc., would not radically affect the press performance. Changes in part dimensions, however, would have a very great effect.
Apart from any geometrical considerations, there remains the problem of various lots of material generating radically different breakage statistics. From the previous analysis, it can be determined that the stamping is actually tensile testing the steel along axis A C. Therefore, press performance data on the various lots of steel should be in direct correlation to the stretching ability of the steel, as evidenced by a steep stress strain curve, a high tensile-to-yield stress ratio (TS/YS), and a high uniform elongation. Such a material would tend to distribute the strain more uniformly in the presence of a stress gradient. The mechanical property results in Table 1 confirm the relationship. In this particular case, the mechanical properties required for a successful stamping are now determined.