⚡ electrical engineering

Numerical and Experimental Analysis of Stretch Flanging of AISI 304 Stainless Steel Sheet with Complex Geometry: FEM Validation via CMM

This study validates a finite element model of stretch flanging for a complex AISI 304 stainless steel component against CMM measurements, revealing that while the isotropic simulation generally achieves high accuracy, discrepancies in critical edge positions are primarily driven by friction sensitivity rather than material anisotropy.

Original authors: Alireza Hashemi, hassan karimi

Published 2026-07-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alireza Hashemi, hassan karimi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a piece of metal, like a thick cookie dough, and you want to punch a hole in it. But instead of just making a hole, you want to stretch the edges of that hole outward to create a flared rim, like the lip of a flower pot. This is called stretch flanging.

Now, imagine that this "cookie" isn't just a simple circle. It has a big hole in the middle, but it also has six smaller, pear-shaped holes scattered around it, like little islands. The goal is to stretch the big central hole without tearing the thin strips of metal (the "bridges") that connect the big hole to these little islands.

This paper is a story about how two researchers, Alireza and Hassan, tried to predict exactly how this metal would behave using a super-computer simulation, and then checked if their prediction was right by actually making the part in a real factory.

Here is the breakdown of their journey:

1. The Computer Guess (The Simulation)

The researchers built a digital twin of the metal part using software called LS-DYNA. Think of this software as a high-tech video game engine that simulates physics.

The Setup: They created a digital version of a 3mm-thick stainless steel sheet with the complex hole pattern.
The Action: They simulated a giant punch pushing through the center hole, forcing the metal to stretch outward.
The Simplification: To keep the math manageable, they treated the metal as if it behaved the same way in every direction (isotropic), even though real metal has a tiny bit of "grain" or directionality. They decided this was a safe bet because the metal's grain wasn't very strong.

2. The Real-World Test (The Experiment)

You can't just trust a computer guess; you have to test it.

They took a real 120-ton press machine and physically stamped the metal part.
They made three copies of the part.
They used a CMM (Coordinate Measuring Machine), which is like a super-precise robotic arm with a needle that touches the part to measure its size down to the micrometer. They checked nine different spots on the part.

3. The Results: How Close Was the Guess?

When they compared the computer's measurements to the robot's measurements, the results were mostly impressive:

The Good News: For 8 out of the 9 spots they measured, the computer was less than 2% off. That's like guessing the length of a football field and being off by only a few inches.
The Bad News: One specific spot, called J2, was off by 10.9%. This spot was the narrow "bridge" of metal between the big hole and one of the small pear-shaped holes.

4. The Detective Work: Why Was One Spot Wrong?

The researchers didn't just shrug and say, "Oops." They played detective to find out why the computer missed that one spot.

The Suspect: They suspected friction.
The Theory: In the simulation, they told the computer that the metal slides against the tool with the same amount of "stickiness" (friction) everywhere. But in reality, in those tight, narrow bridges, the metal gets squished harder, and the lubricant (oil) can't get in as easily. This means the metal is actually stickier in those tight spots than the computer thought.
The Proof: They ran the simulation again, but this time they told the computer to assume the metal was stickier in those tight spots. When they did this, the computer's prediction for that tricky spot (J2) suddenly matched the real-world measurement perfectly.
The Lesson: The error wasn't the computer's fault; it was the assumption that friction is the same everywhere.

5. The Safety Check: Will It Tear?

The most important question in metal forming is: Will it rip?

The computer calculated that the metal stretched the most in those narrow bridges, reaching a strain (stretch) of 27%.
The researchers know that AISI 304 stainless steel usually starts to tear around 35–40%.
The Verdict: The part is safe! It has a "safety margin" of about 8 to 13%. However, the researchers warn that this is a predicted safety margin. To be 100% sure, they suggest using a high-speed camera system (called DIC) in the future to watch the metal stretch in real-time and confirm the numbers.

6. The Takeaway for Engineers

The paper ends with a simple piece of advice for anyone designing tools to shape metal:

Don't guess one number for friction. Instead of picking one "average" friction value, run your computer simulations using a range of friction values (from very slippery to very sticky).
Why? Because if you only guess one number, you might miss the fact that a tiny, critical part of your design could fail under specific conditions. By testing the "worst-case" friction, you ensure your tool is safe no matter what happens.

In summary: The researchers successfully used a computer to predict how a complex metal part would look, proving the method works very well for overall size. They found that the only major mistake came from underestimating how "sticky" the metal gets in tight corners, and they learned that testing a range of conditions is better than guessing a single average.

Technical Summary: Numerical and Experimental Analysis of Stretch Flanging of AISI 304 Stainless Steel Sheet with Complex Geometry

Problem Statement
Stretch flanging involves enlarging a pre-existing hole using a punch larger than the hole diameter, subjecting the material edge to circumferential tensile strain. While standard flanging of a single hole is well-understood, this study addresses a specific industrial challenge: the PGL sectioner flange used in 20 kV medium-voltage switchgear. This component features a central Ø73 mm hole surrounded by six pear-shaped auxiliary holes. These auxiliary holes disrupt material flow, forcing the metal to navigate around them during circumferential stretching. Consequently, strain concentrates in the narrow "bridges" between the central and auxiliary holes, creating a high risk of tearing that is absent in simple, axisymmetric studies. The core problem is predicting the forming behavior and dimensional accuracy of this complex geometry, particularly given the sensitivity of local strain concentrations to process variables like friction.

Methodology
The study employs a combined numerical and experimental approach to validate a Finite Element Method (FEM) model against physical production data.

Experimental Setup: A 3-mm-thick AISI 304 stainless steel blank was manufactured on a 120-ton mechanical press. The material was characterized via uniaxial tensile tests in three orientations (0°, 45°, 90°), revealing a mean yield strength of 327 MPa, UTS of 641 MPa, and a modest planar anisotropy ( $\Delta r = -0.12$ ). Notably, the blank holder was omitted from the tooling setup because the auxiliary holes would be crushed under pressure; instead, locating pins maintained sheet position.
Numerical Simulation: An explicit dynamic FEM model was constructed in LS-DYNA using 45,670 Belytschko-Tsay shell elements with five integration points through the thickness. The model utilized the von Mises isotropic yield criterion and isotropic hardening (MAT_024). This simplification was deliberate, serving as a baseline given the modest anisotropy and to isolate friction effects.
Validation and Sensitivity: Three replicates of the part were produced and measured at nine specific locations using a Coordinate Measuring Machine (CMM). These measurements were compared against FEM predictions. A mesh sensitivity study (coarse 1.5 mm, medium 1.0 mm, fine 0.45 mm) and a friction sensitivity analysis ( $\mu = 0.10, 0.125, 0.15$ ) were conducted to ensure convergence and diagnose prediction errors.

Key Results

Global Dimensional Accuracy: The FEM model demonstrated high predictive accuracy for global dimensions. The mean absolute error across nine measured parameters was 1.86%. Eight of the nine parameters showed errors below 2%, with outer diameter (K) parameters predicted with sub-percent accuracy.
Local Prediction Discrepancy: A significant outlier was observed at parameter J2 (the outer edge position aligned with an auxiliary hole), which exhibited a 10.9% error. This location corresponds to the narrow bridge where material flow is most constrained.
Friction Sensitivity: A sensitivity analysis revealed that J2 is highly sensitive to the friction coefficient. Varying $\mu$ from 0.10 to 0.15 shifted the J2 prediction by 22%, whereas global parameters like h1 shifted by only 1.1%. The study concludes that the 10.9% error at J2 stems from the assumption of a constant friction coefficient; in reality, restricted lubricant penetration in the narrow bridge likely results in a locally higher effective friction.
Strain Analysis: The maximum predicted plastic strain was 27%, located in the bridge between the central and auxiliary holes. This value is below the estimated Forming Limit Diagram zero ( $FLD_0$ ) of 35–40% for AISI 304, suggesting a safe but narrow processing window with a margin of approximately 8–13 percentage points. Mesh convergence was confirmed, with peak strains stabilizing at 27% for the fine mesh (0.45 mm).

Significance and Contributions
The paper claims to provide a validated framework for simulating complex stretch flanging operations where standard axisymmetric assumptions fail. Its primary contributions are:

Diagnostic of Error Sources: It isolates the constant-friction assumption as the primary cause of local prediction errors in complex geometries, demonstrating that global accuracy can mask significant local discrepancies.
Practical Engineering Guidelines: The authors recommend that die designers execute FEM simulations across a friction interval ( $\mu_{min}$ to $\mu_{max}$ ) rather than relying on a single-point assumption. This approach reveals the sensitivity of critical local parameters and prevents unconservative tooling design.
Baseline for Future Work: By adopting the von Mises isotropic criterion despite known modest anisotropy, the study establishes a clear isotropic baseline for future research involving more complex anisotropic yield criteria (e.g., Hill's 1948 or Barlat's Yld2000-2d).

The study maintains a modest stance on its strain predictions, noting that while the 27% strain suggests safety, direct experimental validation via Digital Image Correlation (DIC) is required to confirm the true peak strain and safety margins definitively. Similarly, limitations regarding springback and through-thickness strain measurement are acknowledged as areas for future investigation.