A Finite Element Study of the Deformability of Steel Jingyi Wang Qi Rui Jiadi Fan

Background punch die holder  A real-life problem  Use finite element analysis software to simulate the stamping process of bakeware

Background  Improper forming condition will lead to defect. The wrinkling and fracture defect during deep drawing process  Manufacturing and fixing stamping mold is expensive  Simulation needed to test whether certain mold and forming condition is reasonable before manufacturing

Method  Experimental and Empirical Analysis  3D model with different parts under dynamic loading– Use ABAQUS  Different forming conditions Temperatures Strain rates Holding force  Compare, design and optimize forming condition to avoid possible defect

ABAQUS

Wrinkling Why wrinkling happens?  During the deep drawing process, metal flows inside. From large perimeter area to small perimeter area.  Under minimum principal stress, the blank will be thickened. Uneven thickening will lead to wrinkling.  We need a reasonable holding force to provide a restriction.

Why fracture happens?  The friction between holder and blank, die and blank will block metal from flowing.  If the friction is too big, the metal at the corner will fracture because of over-thinning.  If the thickness after deformation reduces to 70% of the original thickness or less, we treat it as fracture. Fracture

 As temperature rises, the deformability of metal will improve.  However, good deformability may lead to the over-thinning at the corner.  Higher temperature is also more energy expensive. So, forming temperature is a parameter that need to be balanced.  Suggested temperature (dependent on holding force, material, etc): ℃ Temperature effect Temperature ℃ Maximum stretch depth (mm) Simulation Experiment

 Under large strain rate, the deformability of metal is poor. It will be more likely to generate fracture.  Small strain rate decreases the productivity.  In industrial process, strain rate is also a design parameter. Strain rate effect

 Oversize holding force can lead to fracture defect  An undersize holding force can lead to wrinkling defect  Dependent on details of the object Holding force effect Holding Force (MPa) Maximum stretch depth (mm) Simulation Experiment

Element type  S4R: 4-node general-purpose shell, reduced integration with hourglass control, finite membrane strains  Membrane theory

Target geometry after deep drawing A realistic geometry 2D and 3D model Animation

One quarter of the entire model holderpunchdie Simulation model

42CrMo high-strength steel Young’s moldus: 210Gpa Poison's ratio: 0.31 Density: 7,830 kg/m^3 True stress-strain curve Material property

Result—different temperatures The thickness at the corner is smaller under higher temperature. As the thickness ratio are both lower than 70%. It’s unnecessary to simulate a higher temperature. Strain rate: 1, holding force: 10,000N Temperature: 600 ℃ and 650 ℃ T=600 ℃ T=650 ℃

The thickness at the corner is smaller under higher strain rate Result—different strain rates

Result–different holding forces Reasonable holding force range: 7,000~13,000N F=5000N F=10,000N F= 30,000N

Refine the size of blank  After the deep drawing process, the extra blank needs to be cut off.  The former blank is 400*400mm, it will cause a huge waste of material.  Refine it to 300*300mm and 240*240mm.

400*400mm 300*300mm 240*240mm Result–size of the blank 240*240mm good enough for our bakeware

Conclusion

This is just a simple FE application. ABAQUS is able to do very complicated problems. In our case, the geometry of production is simple. However, in more complicated cases, we need to consider much more.

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