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Sheet Metal Forming: Circle Grid Analysis

Posted October 04, 2012 3:00 PM by psikorsky

There are three fundamental processes that can occur during sheet metal forming and they are: 1) Bending, 2) Stretching and 3) Drawing. Any formed sheet metal component is made by a combination of these three processes. To help understand what these processes are consider a sheet of unformed metal onto which you have embossed a pattern of circles as shown in the figure at the left. Let's call this a state of zero strain, i.e., all of the circles on the metal surface are in their original shape and size

BENDING

If we are to form a part solely by bending, say by using a brake press, it is equivalent to pulling the sheet metal in one direction so that circles we've embossed on the metal surface elongate in the direction we've pulled but remain unchanged perpendicular to the direction we've pulled. In this case we say we have positive major strain and zero minor strain.

STRETCHING

If we form a part by stretching, i.e., by pulling the sheet metal simultaneously in two directions at 90 degrees to one another, our embossed circles will grow in both directions. In this case we say we have positive major strain and positive minor strain. Imagine a piece of sheet metal held rigidly on all four edges while pressing a hemispherical punch into the center as an example of this forming process.

DRAWING

In the case of drawing, the sheet metal is pulled on one direction with the perpendicular direction unrestrained. Thus, as the material stretches in one direction it actually contracts in the other direction. This is what happens during the formation of a beer or soda can - a cylindrical punch is pressed into a piece of sheet metal that is unrestrained or only partly restrained along the edges. In this case we have positive major strain and negative minor strain.

THE REAL WORLD

In the real world, actual sheet metal parts are formed by a combination of these three fundamental processes, i.e., different regions of any given part may be formed by bending, stretching or drawing. Also, in the real world, we use a tool called Circle-Grid Analysis, where we physically etch a pattern of circles and square grids onto the surface of a piece of sheet metal prior to forming parts, much like in the illustrations above. We then form that etched piece of sheet metal into the finished part, physically measure the major and minor strains on our now distorted circles, and plot them on something called a Forming Limit Diagram.

If the strains that are plotted for a given area on a plot show positive major strain and positive minor strain, that area of the part is formed primarily by stretching. If the major strain is positive, but the minor strain is near zero, you are in the bending region of the Forming Limit Diagram. Finally, if the minor strain is negative, you are in the drawing region of the diagram. If the strains that are plotted are above the red line in the diagram you are at risk of fracturing the sheet metal during the forming process. If you are below the red line, the part can be formed safely without fear of fracture.

Each type and grade of sheet metal has a unique forming limit diagram. Depending on which forming process is predominant in making a specific part you may want to optimize specific material properties. For example, for parts that are formed primarily by bending, the key material property is total elongation. For parts formed by stretching the key property is the work hardening exponent, usually called the n-value. Finally, for drawn parts the most important material property is the resistance to thinning, called the r-value.

Oftentimes we do not have the ability to change materials, or we have a very limited number of materials to select from; when we do our circle-grid analysis we find that the strains we measure are very near to the problem region on our forming limit diagram. In other cases, our circle-grid analysis tells us we should not be having any problems but we are fracturing parts in manufacturing. In either of these cases we would look at other factors aside from material, such as lubrication or tooling condition, or hold down pressures as ways to get us away from failure.

The bottom line is that there are very useful tools for analyzing sheet metal forming that can be used to optimize material, part design, and/or sheet metal processing.

Editor's Note: CR4 would like to thank PJ Sikorsky of GEA Consulting for contributing this blog entry

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