# Out with Boxes—In with a Continuum

February 1, 2008

Boxes are useful for organizing storage of millions of items. Seasonal clothing, holiday decorations, toys, photographs and junk are items commonly found in boxes in the home. At work the stored items range from old files to inventory of parts. Storing in boxes can create some real dilemmas and serious conflicts. Does this item fit the description of items in box No. 8? What does one do with an item that belongs in both box No. 8 and box No. 15? Should one obtain a duplicate and store one in each box or store the item in box No. 8 with a descriptive note in box No. 15?

Unfortunately, these and other problems exist in the metalforming arena. Too many times a person uses boxes in an attempt to simplify difficult or complex concepts and questions. A decade ago, a seminar targeted forming of large parts. Does your company make large or small parts? If you can answer that question, what sized part is the dividing line? Probably the dividing line is a sliding scale depending on the background of the person asking the question.

A common use of boxes is to separate various industries. Here boxes become barriers to discourage the transmission of information across different industries. An expert in designing or forming automotive parts often has little credibility in the appliance, aerospace or consumer-product industries. Yet, a tiny grain of metal alloy responds to a force (stress) and deforms (strains) according to equations of physics. The grain does not know or care what industry is applying the force nor does it behave differently in a car door compared to a refrigerator door.

 Fig. 1—Boxes representing different strength levels suggest a discontinuous drop in formability. The dashed line portraying a continuum is more accurate.

Examine this list of parts:

• Tank for welding gas (construction),

• Scuba tank (sports),

• Oil filter (automotive),

• Two-piece beer can (food/drink),

• 1-in. drawn cup (education),

• 0.06-in. dia. cup (electronic).

These parts have a large range of sizes—from feet to hundredths of an inch in diameter. The consumer industry certainly varies. Varieties of material are possible specifications. What is the common thread among all these parts? All are blanked and deep-drawn cylindrical cups with the same design rules and forming limits. Identical troubleshooting procedures are applicable to all of the parts. Unfortunately, each industry usually stays within its own box without information interchange between boxes.

A different use of boxes can lead to wrong conclusions. Fig. 1 shows a common portrayal of different-strength steels. While this figure shows four boxes, some other sources use only three. Looking at just the boxes, too many people conclude that moving from lower-strength to higher-strength steel results in a discontinuous drop in formability as measured by the total elongation. The correct picture should be one of a continuous decrease in total elongation (shown by the dashed curve) as a function of either yield or tensile strengths. The work-hardening exponent (n value) follows the same shape curve. Nature generally operates as a gradual continuum like dawn and dusk, not like instantaneous discontinuous changes of a light switch.

 Fig. 2—The curve shows a continuum between total elongation and yield strength for a large number of steel grades.

The concept of boxes in Fig. 1 poses yet another problem. The current definition for the top of low-strength range is 30.5 Ksi, which is the minimum yield strength of bake-hardenable 210-MPa steel. That means the aluminum-killed, draw-quality (AKDQ) steel is both a low-strength and a medium- (or high-) strength steel. A coil of 29-Ksi yield strength steel is low strength, while a coil of 31 Ksi yield strength steel is medium strength according to Fig. 1. The dividing line is arbitrary and, in fact, was higher than 30.5 Ksi many years ago.A popular current example of the continuum of formability properties is the banana curve shown in Fig. 2. Again, the overlapping range of properties of the various types of steels is evident. One can anticipate the changes in steel formability as the yield or tensile strength increases.

A final example is splits or tears in sheetmetal parts as the strain level exceeds the forming limit. Generally, one has only two boxes. The first is obvious—the parts have exceeded the allowable strain level and split. The second box causes the trouble. The parts have not split. However, that box is so large it encompasses parts ranging from almost ready to split to overly safe from splitting. Instead, the proximity of the parts to failure requires a continuum type of measurement, such as a safety factor, to be useful.

Thinking out of the box serves a useful purpose. In metalforming, we must throw out the boxes and replace them with a continuum. Then die tryout, troubleshooting, process tracking and other press-shop needs will become more accurate and meaningful. MF

Industry-Related Terms: , , ,
View Glossary of Metalforming Terms

Technologies: Quality Control