The Science of Forming

Do higher strength steels exhibit reduced formability? The most honest answer is: “It depends.” The relationship between yield strength and formability is complex. First, the term formability encompasses widely differing primary forming modes, including tensile stretching, bending and cup drawing. Some modes depend highly on yield strength, while others are completely independent.

Fig. 1—A pure bend has a convex half in tension, a neutral-axis central boundary with zero deformation, and a concave half in compression. Failure occurs with the highest tensile stretching located at the surface of the convex half.

Many complex stampings contain all three of the listed forming modes. Interaction and interference among these modes in a single stamping makes failure analysis extremely difficult. Also, formability of several steel types with the same yield strength will vary with different microstructures. What processes were utilized to achieve the given yield strength? Is failure caused by work hardening, inclusions, precipitates, voids or simply grain size?

Last month we showed that failure during simple tensile stretching results from the reduction in sheet thickness due to excessive major and minor stretching in the plane of the sheet. Once sheet thinning reaches the critical value, a local (through-thickness) neck forms that restricts additional deformation within the local neck, creating failure.

The bending mode of deformation differs greatly (Fig. 1). The outer (concave) half of the bend undergoes tensile stretching and the inner (convex) half undergoes compressive shrinking; the dividing line between the two is a neutral axis with zero deformation. We achieve a pure bending mode without a change in sheet thickness due to the balance between the thinning of the outer tensile elements and a thickening of the compressive inner elements. Failure, therefore, occurs without thinning of the sheetmetal, and the onset of failure cannot be predicted by the forming-limit diagram.

Instead, the tensile stretching of the outer layer of the convex surface of the bend simulates a tensile test (Fig. 1). The highest tensile stretch localizes at the peak of the bend. Quantify the severity of the bend using the ratio of punch radius (r) to sheet thickness (t) in the following equation:

Percent stretch = 100 x 1/ (1+r/t)

Fig. 2—Higher yield-strength materials create a higher forming force (FF) due to increased force to achieve flange deformation, bend/unbend over the die radius plus greater friction. However, the pulling force (FP) also is strengthened by the higher yield strength to balance out the higher forming forces.

A small punch radius for a given sheet thickness creates a high peak stretch. Moving away from the peak reduces the amount of stretch, so that the allowable stretch then depends on the microstructure of the steel near the convex surface. The amount and thickness of inclusions, porosity, grain size, work hardening and other features can strengthen or degrade the amount of allowable stretch prior to tearing or cracking of the sheet surface. Studies show that the amount of peak stretch in a bend at fracture is proportional to the total elongation determined by a tensile test. If blanks fail during bending, a common press-shop troubleshooting procedure is to turn the blanks over. If only one surface exhibits poor stretchability due to inclusions, subjecting that weak surface to compression on the concave side may save the blanks.

In contrast, the cup-drawing forming mode provides some fascinating results. By designing a cup that forms well with low-strength steel, the forming mode proves insensitive to yield strength and will form well with high-strength steel. The binder area (Fig. 2) requires more force (FF) to pull the higher strength material toward the die opening as the surface area compresses. And, the material workhardens during the bend/unbend sequence as the workpiece moves over the die radius into the cup wall. However, the material transmitting the pulling force of the punch (FP) also has a higher strength. Therefore, the cup can be successfully drawn to its same depth.

These results have been proven mathematically and experimentally. Two-piece steel beverage cans are produced by a sequence of draw, redraw, three ironing stages and a bottom-dome forming operation. The DR-9 steel grade is cold-rolled to a thin sheet, annealed and then given another 35-percent cold reduction. The steel forms in the full-hard condition without failure. The secret in making the beverage cans: use of compressive-forming processing stages.

Instead of the plastic (permanent) deformation previously discussed, stiffness and springback relate to elastic stresses. Pressing down on a flat surface, such as a car roof or refrigerator door, with a force less than the yield strength causes an elastic bowing of the sheetmetal. Resistance to the force is the material’s stiffness. Releasing the force allows the elastic bowing to spring back to its initial configuration.

The amount of deformation created by a specific force (stress) depends on the elastic modulus, or Young’s Modulus, of the material. Steel has a high modulus (30 million) that creates a relatively stiff panel. Many nonferrous materials, such as aluminum alloys, have an elastic modulus of only 10 million. For the same force placed on a panel, an aluminum alloy will exhibit three times the amount of deflection or reduction in stiffness as steel. Likewise, when the force is released, springback from aluminum is three times that of steel.

Increasing the yield strength of the material does not change its elastic modulus. It merely allows more panel deflection and springback before the onset of plastic (permanent) deformation. Weight-reduction programs increase yield strength to offset the reduction in sheet thickness. This may balance load-carrying capacity, but the thinning of the panel reduces its geometric stiffness. This limits the amount of panel weight reduction, unless additional design changes are incorporated.

Whether designing a new panel with higher-strength steel or upgrading an existing panel, designers must start by analyzing the stamping to identify the forming modes, and understand the interactions among adjoining modes. Then we can acquire strain directions and magnitudes for analysis, and make decisions about forming severity and necessary design changes. MF

Keeler, Peter Ulintz and Ed Tarney will present the popular Deep Draw seminar on March 13, 2013 in Livonia (Detroit), MI. Learn more and register to attend at www.pma.org/meetings.