Eren Billur
Technical Manager

# Predicting Springback with Simulation

September 2, 2021

Sounds quite easy, doesn’t it? After all, there are papers from the 1980s on predicting springback using finite-element analysis (FEA), and many commercially available software packages offer die designers easy access to FEA capabilities. Yet with all of these advancements, we still hear of shops machining die surfaces two or more times. What goes wrong?

Springback—Simple Mathematics

To understand the challenges with springback prediction, let us understand the simplest math behind it. Consider the tensile test—pulling a test specimen causes it to elongate. If the test keeps the specimen below its yield point, when removing the load the specimen’s total length should equal its original length (i.e., before the tensile test).

However, if the tensile-test load exceeds the specimen’s yield strength, its final length depends on:

1) Stress condition before load removal (σr)

Calculating Stress

Correctly calculating the stress before removing the load requires use of a hardening curve and yield locus (see Cutting Edge, June 2021 issue of MetalForming). If the material is simply stretched (as with a tensile test), the hardening curve would be sufficient. However, if forming occurs along two axes, we also require the yield locus.

Further, if the material undergoes a bending-unbending cycle, as with a draw bead for example, we may require more complex data to predict the stress level. A material’s flow stress may be lower than expected under compression if it is applied after tension, due to Bauschinger effect, also known as kinematic hardening. The most advanced model for determining flow stress of sheet metals has been proposed by Yoshida and Uemori, known as the Y-U model, used by most sheet forming-simulation software. Generating the necessary data requires a tension-compression test, which can be tricky for thin-gauge, high-strength alloys as the specimen may buckle under high compressive loads. In these cases, we use specially designed and fabricated grips and anti-buckling devices.

Stretching a Gen3 advanced high-strength steel (AHSS) to about 4 percent of true plastic strain and then compressing it back to 3 percent results in an approximate 40-percent reduction in the flow stress (Fig. 1). Compressing the same steel back to its original shape, the experimental flow stress is approximately 15 percent less than the prediction without kinematic hardening (Fig. 1).

Should the flow stress fall below expectation, a die designer should overpredict springback. However, we often will underestimate it because we assume a constant unloading modulus, which may decrease with plastic strain. Catching this effect requires a load-unload tensile test—relatively easier than a tension-compression test as it does not require anti-buckling precautions. Fig. 2 illustrates the output of such a test on a TWIP950 AHSS specimen. Unloading moduli then are fit to the Y-U model (Fig. 3).

Effects of These Models

It is clear and convincing that the unloading modulus significantly affects the ability to predict springback. Still not convinced? See Fig. 4.

How important is the tension-compression data? Without it, it would be nearly impossible to predict the twists and curls observed in the press shop.

Without these two datasets, springback prediction almost always will differ greatly from the reality on the shop floor. Both models may require significant time and effort in order to conduct the necessary experiments and then fit the raw data into the models.

However, several software packages exist for fitting the raw data. Compared to the cost and time required to rework a die set, developing the experimental data for simulation may still be a worthwhile investment. MF

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