This post presents a simulation model for crack propagation in welded joints with holes composed of both weld and base metal. The study investigates the impact of hole shape, size, and position on the stress intensity factor at the crack tip in 6061 aluminum alloy welded joints used in aviation.

Flanging special-shaped holes in sheet metal is a challenging task. Mainstream methods, such as neutral layer unfolding and 3D software sheet metal unfolding, are commonly used for typically formed parts. However, irregular surfaces require post-optimization and may not even be feasible.

Additionally, there is an unconventional one-step forming expansion method that belongs to the rough type. While it is fast and widely applicable, it has a significant dimensional deviation and is generally only used as a reference for hole shape expansion.

**Limitations of conventional deployment**

**Limitations of neutral layer deployment**

The special-shaped hole is composed of convex arcs, concave arcs, and straight lines with varying radii. The stress state and deformation properties of each component differ from one another.

- The straight part can be regarded as bending deformation;
- The convex arc part can be regarded as hole turning deformation;
- The concave arc part can be regarded as drawing deformation.

The 8228 mesh cover’s drawing cavity has a circular top and a rounded rectangle bottom. The flanging of the oil tank hole is inclined at a 5° angle to the vertical direction, composed mainly of straight lines on both sides and concave arcs at both ends.

To achieve conventional expansion, one needs to find the corresponding formula for each arc or straight line of the hole-turning form and obtain the expansion size of each section.

The joints between each section of the unfolding line calculated by the theory are generally not smooth, so it is necessary to obtain a high-quality unfolding line through post-transition treatment.

The entire process is relatively complex and time-consuming. As shown in Fig. 1, there are 52 such holes in the 8228 mesh cover.

Fig. 1 3D drawing of 8228 mesh cover product

Based on the consistency of the hole shape, 26 holes require expansion, which in turn demands 26 calculations. It is evident that the calculation workload for the entire oil tank hole is substantial.

Moreover, theoretically, the concave arc needs to be computed based on the flanging of the circular hole. However, upon checking the corresponding formulas, only three cases were found, namely (a) flanging of the flat section, (b) flanging of the deep drawing part, and (c) flanging after deep drawing.

In this particular example, the flanging of the oil groove hole on the quadrangular surface can only be approximately estimated since there is no specific formula to accurately calculate it.

Therefore, the expansion of the neutral layer has certain limitations.

For developing special-shaped holes on irregular surfaces, this approach will not only take a considerable amount of time, but also the flanging concave arc section of four-corner oil tank holes is not applicable, or may require later-stage improvements and adjustments.

**Limitations of general 3D sheet metal unfolding**

Using UG 3D software as an example, 3D sheet metal unfolding can be divided into two categories: parametric sheet metal unfolding and non-parametric sheet metal unfolding.

Whether it is parametric or non-parametric, personnel dealing with flanging and unfolding are required to possess professional sheet metal knowledge and a solid foundation in 3D modeling.

Parametric sheet metal unfolding requires that certain operations such as bending and edge bending must be completed using the “sheet metal module” during the 3D modeling process. The modeler’s comprehensive quality requirements are relatively high, mainly reflected in the setting of specific parameters.

If relevant experience is not accumulated, there may be significant deviations in the size of the expanded product in parametric sheet metal modeling.

Parameterless sheet metal unfolding has less strict requirements for existing three-dimensional products. It does not require parameters and does not have to be generated under the “sheet metal module”. However, recognizable bending edges are required for automatic recognition and expansion.

In general, 3D sheet metal unfolding is more practical for single-stage or multi-stage bending parts whose main surface is a plane. It is difficult to unfold a special-shaped hole on an irregular surface using only a three-dimensional “sheet metal module” or the corresponding non-parametric unfolding function.

**Limitations of one-step forming deployment**

One-step forming and unfolding is generally used to approximate the unfolding shape of special-shaped holes.

In the actual operation process, its accuracy and operation time depend directly on the size of the surface virtual mesh.

The finer the mesh, the higher the precision of the expansion line, but the corresponding operation time will increase. Conversely, the larger the mesh, the lower the accuracy but the faster the speed. Each approach has its own advantages and disadvantages.

**A new method of small slice subdivision expansion**

The flanging of the oil tank hole on the 8228 mesh cover cannot be accomplished well using the current expansion methods, thus it is necessary to investigate a new method.

Is it possible to simplify this oil tank hole flanging into an ordinary bending process?

Undoubtedly, the straight edge segment can be achieved, but dealing with the arcs at both ends requires further consideration.

Taking inspiration from the one-step forming technique, the surface of the oil groove hole can be divided into five, ten, or even more smaller segments.

By doing this, it can be approximated infinitely as a straight edge flanging with a very narrow width. Moreover, a more precise expansion size of the straight edge flanging can be obtained through the neutral layer expansion method.

**Expansion of lines on both sides**

Although the flanging of the oil tank hole may be irregular, it can be simplified by flanging the two straight lines approximately.

Based on previous experience with sheet metal unfolding of mesh covers, it can be simplified by unfolding according to the inner material and adding compensation, without the need to consult tables or apply complex formulas.

Regarding the angle, the hole turning die’s direction must be optimized to be vertical upward, and the included angle of the hole is 10°, causing the two side surfaces composed of straight lines to become variable angle surfaces. The specific deployment process is as follows:

(1) Rotate the outer edge of the flanging along the bending line (the orange surface in Fig. 2) and offset it by 0.12mm for compensation.

Fig. 2 Simplified expanded partial view of lines on both sides

- Intersect with the drawing surface of the substrate to obtain an intersecting curve, that is, straight edge expansion.

(3) In the later stages, the intersecting curve and two end arcs need to be simplified into straight line segments and arcs.

The unfolding of the straight-line part is usually straightforward, and those with experience in general bending unfolding can easily handle this step.

In fact, this process can be completed using AutoCAD in a 2D environment, but working in a 3D environment should be more convenient, faster, more intuitive, and efficient.

**Expansion of concave arc at both ends**

The curved surface at both ends is not an arc but a conic, which means that the previously introduced neutral layer expansion method is not strictly applicable.

To use the neutral layer method for expansion, the concave arc needs to be segmented and approximated into small concave arcs, and then the formula needs to be applied after referring to the table for calculation.

Although this method provides relatively accurate results, the process is complex and not user-friendly.

In this case, we introduce a new method called “small slice subdivision expansion.” The curved surface at both ends is divided into infinite pieces, and we extract 7 equidistant pieces.

Since the sheet is small enough, we can assume that the width of these 7 pieces is zero, which means they can be treated as 7 straight lines.

As shown in Fig. 2, we use the three-dimensional bisection command to divide the curved surface at both ends into 7 reference points. We then measure and record the length of the line from these points to the flanging contour line in turn.

Next, we enter the UG sketch, and the datum plane is perpendicular to the blanking direction. The length of the line segment just measured corresponds to the radius value of the diameter marked by the dotted circle in Fig. 3.

According to the process requirements, we make negative compensation for the arc flanging height at both ends, and the green thin solid line indicates the compensated position.

Finally, we use the spline curve to approximate the tangent lines of each arc and obtain the orange line in Figure 3, which is the expansion line of the arc segment. We apply the same process to the other concave arc to obtain the final complete expansion line.

Fig. 3 Simplified expanded view of concave arc at both ends

**Post optimization of expansion line**

After processing, we obtain expansion lines for both lines and arcs, but these lines are splines, which may not be ideal for post-processing.

Previously, developers projected other construction lines onto the two-dimensional plane based on the blanking direction, and then transformed them smoothly into straight lines and arcs one by one. This method was time-consuming.

On the other hand, the spline expansion lines we obtain can be easily simplified into lines and arcs using the “simplify curve” command in UG 3D software, while still maintaining a smooth transition.

**Conclusion**

Our company has officially adopted the new method of “small piece subdivision” in some of our recent products.

The oil groove holes of the mesh covers 9100, 8325, and others are irregular curved surface special-shaped hole flanging.

We have obtained the unfolding through this method, and the sheet metal parts produced from the trial meet the design requirements.

The entire process, from product modeling to sheet metal unfolding, can be completed within the same three-dimensional environment.

We have eliminated the need for mutual conversion between software, and there is no significant calculation involved. The whole process is straightforward.

The most significant advantage of this method is that the simplified line obtained is already the expansion line in space.

While the AutoCAD environment can only process the expansion on the plane, the real expansion line can only be obtained through post-projection conversion.

This new expansion method effectively eliminates unnecessary errors in the conversion process, making it easier to ensure the quality of the expansion line.

We believe that this new method of “small piece subdivision” will inevitably form a new trend in the increasingly modern and high-end sheet metal industry, leading to the future development of sheet metal parts.