Forming Strains under ASME VIII-1 vs ASME VIII-2 2

[MchA]

Hello everyone,

I am seeking clarification on the classification of forming strains under ASME VIII-1 UG-79 and ASME VIII-2 Table 6.1, particularly for spherical caps, such as those used in floating head heat exchangers or intermediate heads with Y-forgings.

Under ASME VIII-1 Table UG-79-1, these components appear to fall under Case 2, which applies to parts with double curvature (e.g., heads). This typically includes elliptical and torispherical heads, but would it also apply to hemispherical heads or spherical caps, despite having a constant radius of curvature?

My interpretation is that hemispherical and spherical caps are still double-curved since they have curvature in both the meridional and circumferential directions. Can anyone confirm whether this is correct? Or is Case 2 specifically intended for heads with two different radii (i.e., crown and knuckle)?

Turning to ASME VIII-2 Table 6.1, classification seems to depend on the fabrication process. If a spherical cap is formed from a single plate, would it fall under the first row:

“For all one-piece, double-curved circumferential products, formed by any process that includes dishing or cold spinning (e.g., dished heads or cold spun heads)”

Could a spherical cap, even with a constant radius of curvature, qualify as a “one-piece, double-curved circumferential product” under this definition?
Alternatively, if the cap is formed from multiple segments, I assume it would fall under the third row:

“For heads that are assembled from formed segments (e.g., spherical dished shell plates or dished segments of elliptical or torispherical heads)”

Could one argue that a spherical cap, even when formed from a single piece, is conceptually similar to the top portion of a segmented head and therefore classified under the third row? Or is classification strictly based on the fabrication method (i.e., one-piece vs. welded segmented)?

I’d appreciate any feedback or insights based on your experience.
Thanks in advance!

 

[TGS4]

My interpretation is that hemispherical and spherical caps are still double-curved since they have curvature in both the meridional and circumferential directions. Can anyone confirm whether this is correct?

Correct. Cylinders would have single-curvature, but any head would be doubly-curved.

Could a spherical cap, even with a constant radius of curvature, qualify as a “one-piece, double-curved circumferential product” under this definition?

Yes

Could one argue that a spherical cap, even when formed from a single piece, is conceptually similar to the top portion of a segmented head and therefore classified under the third row? Or is classification strictly based on the fabrication method (i.e., one-piece vs. welded segmented)?

For Table 6.1, classification is strictly based on the fabrication method.

 

[r6155]

"For Table 6.1, classification is strictly based on the fabrication method" : Incorrect
The difference is ONE-PIECE or segments.

 

[TGS4]

"For Table 6.1, classification is strictly based on the fabrication method" : Incorrect
The difference is ONE-PIECE or segments.

Which is what I said, in the context of the question asked.

 

[r6155]

The calculated strain is an estimate and must be verified with post-forming measurements. A procedure is required for this.

 

[MchA]

Thank you so much, TGS4 and r6155.

I now understand that the classification in ASME VIII-2 Table 6.1 is based strictly on the "fabrication method", rather than geometric or strain-related considerations.

That said, I still find this a bit counterintuitive from an engineering standpoint. A spherical cap formed from a single plate generally undergoes much less forming strain than an elliptical or torispherical head — especially in the knuckle region, where strain tends to concentrate due to abrupt curvature transitions. A spherical cap, having a constant radius of curvature, typically results in a more uniform and lower forming strain distribution.

Another point: the crown portion of a spherical head might be formed in a single piece, but if it is later welded to the rest of the head, it would fall under the “segmented” category, even though the forming process itself hasn’t changed. This classification seems driven solely by post-forming welding, rather than the actual deformation the material experiences.

Would there be any technical justification or background guidance explaining this conservative stance in the code — especially considering that it may not always correlate with the actual severity of the forming strain?

The calculated strain is an estimate and must be verified with post-forming measurements. A procedure is required for this.

Also, thank you for pointing out that the calculated strain is just an estimate and must be verified through post-forming measurements, with a defined procedure in place.

This leads me to another question regarding the ordering and manufacturing process. Since the actual forming strain must be confirmed and potentially requires heat treatment based on the verified value, should I explicitly request my fabricator to perform the post-forming heat treatment according to the actual measured strain?

I’m asking because this would likely impact both the manufacturing route and the cost — especially if the actual strain turns out to exceed the threshold defined in the code. In that case, proper documentation and agreement during the ordering phase would seem essential.

Is it typical to include this requirement upfront in the purchase specification, or is it usually left to the fabricator to decide once the forming is completed?

Thanks again for your continued guidance, it’s extremely helpful.

 

[TGS4]

I don't necessarily disagree with your contention that this is a blunt and potentially highly-conservative (but also potentially under-conservative) approach.

Your ID says that you are from Italy - is that correct? If so, I would recommend that you get involved in the ASME Section VIII, Italy IWG (International Working Group) and start working towards a recommendation for a change to the Code.

 

[r6155]

Additional clarification. ASME VIII Div 2
Example 1: ONE PIECE hemispherical head, press formed. Use the formula in the first row of Table 6.1.
Example 2: Segmented hemispherical head, each segment press formed and then welded. Use the formula in the third row of Table 6.1.

Both examples use the same fabrication method. Therefore, the fabrication method is not the difference.

 

[Trestala]

A spherical cap formed from a single plate generally undergoes much less forming strain than an elliptical or torispherical head — especially in the knuckle region, where strain tends to concentrate due to abrupt curvature transitions

The radius you use in the formula in Table UG-79-1 or Table 6.1 for an ellipsoidal head is the mean radius of the knuckle (Rf), not the radius of the head measured in the straight flange or cylindrical part (Dm/2). The radius you use in the formula for a spherical head would be the mean radius of the sphere itself. So, even if you have the same formula being used, you will still have higher calculated forming strain values in an ellipsoidal and torispherical head since you are using a smaller radius.

Another point: the crown portion of a spherical head might be formed in a single piece, but if it is later welded to the rest of the head, it would fall under the “segmented” category, even though the forming process itself hasn’t changed. This classification seems driven solely by post-forming welding, rather than the actual deformation the material experiences.

Segmented heads in which each segment are dished (formed by dishing press) and then welded together will have different strains compared to a dished+cold spun heads from a single/welded flat plate.

This leads me to another question regarding the ordering and manufacturing process. Since the actual forming strain must be confirmed and potentially requires heat treatment based on the verified value, should I explicitly request my fabricator to perform the post-forming heat treatment according to the actual measured strain?

You can decide the stress relieving based on the calculated forming strains. You only measure the curvature, radius of the knuckle, and after-forming thickness of a head, not the strains. UG-81(a) requires knuckle radius should not be less than what is specified, so actual forming strain can be assumed not exceeding the calculated strain.

 

[r6155]

"You only measure the curvature, radius of the knuckle, and after-forming thickness of a head, not the strains": INCORRECT
Measure of strain is part of dimensional control, The procedure is simple and is included in the Inspection Plan prepared by the Pressure Vessel design engineering.

 

[r6155]

If the measured strain is below the limit, stress relieving can be avoided.

 

[MchA]

Thank you all for your kind replies,

The radius you use in the formula in Table UG-79-1 or Table 6.1 for an ellipsoidal head is the mean radius of the knuckle (Rf), not the radius of the head measured in the straight flange or cylindrical part (Dm/2).

I fully agree with this when referring to Table UG-79-1. However, I still have some doubts regarding the first row of Table 6.1 for one-piece heads, because in this case, the forming strain appears to be defined by the following parameters:

• Db = diameter of the blank plate (or of the intermediate product)
• Df = final outside diameter of the component after forming

In this context, I would assume that Df refers to the external diameter at the tangent line (TL) for an ellipsoidal head, for example — which is formed from a blank plate with diameter Db. If that's the case, the calculated forming strain would not differentiate between a spherical cap, a hemispherical head, or an ellipsoidal head, since they could all share the same final outside diameter (Df) and be formed from similarly sized blanks (Db).
For this reason, the formulas used for multi-piece heads (which are similar to those in UG-79) actually make more sense to me, as they more directly account for geometry-related strain.

Segmented heads in which each segment are dished (formed by dishing press) and then welded together will have different strains compared to a dished+cold spun heads from a single/welded flat plate.

That makes sense, and I agree — segmented heads formed by dishing individual segments and then welding them together will likely experience different strain distributions compared to heads formed as a single piece (whether dished or cold-spun from a flat plate).

That said, I remain a bit puzzled when it comes to spherical caps, particularly in the case of hemispherical heads.
In practice, the crown portion of a hemispherical head — effectively a spherical cap — is often formed from a single plate by cold spinning or dishing. This cap is then welded to other shell segments to complete the head assembly.

Here’s where the confusion arises: even though this top spherical cap is formed as a single piece, it would be classified under multi-piece construction in Table 6.1 simply because it is later welded to the remaining parts of the head. As a result, the allowable forming strain limit changes — not due to any actual difference in the forming strain, but purely because of how the head is categorized: one-piece vs. multi-piece.
So even if the forming method, geometry, and even the strain level remain the same (or lower), the classification as a multi-piece head leads to different, often more conservative, limits.
This is where I find the logic somewhat counterintuitive — since the Code’s categorization seems to be based more on assembly method than on the actual mechanical strain experienced during forming.

This seems to suggest that the simplified approach in the first row of Table 6.1 may not fully capture geometry-specific strain differences, which can be mechanically significant.

 

[Trestala]

INCORRECT
Measure of strain is part of dimensional control, The procedure is simple and is included in the Inspection Plan prepared by the Pressure Vessel design engineering.

You should mention where exactly strain measurement is required and how do you measure the strain. I have reviewed hundreds of inspection and tests plans of fabricators and strains are not measured directly. Only the shape, radius, and thickness are measured after forming. The strain is calculated which already corresponds to the extreme fiber elongation. You always mention something without providing any clear reference. Read VIII-1, UG-81 and VIII-2, 6.1.2.

 

[Trestala]

If that's the case, the calculated forming strain would not differentiate between a spherical cap, a hemispherical head, or an ellipsoidal head, since they could all share the same final outside diameter (Df) and be formed from similarly sized blanks (Db).
For this reason, the formulas used for multi-piece heads (which are similar to those in UG-79) actually make more sense to me, as they more directly account for geometry-related strain.

I agree, the formula should be based on the radius of the curve of the head, not the before and after diameters of the plate. I checked with Compress and they still use the 3rd formula in Table 6.1. instead of the first one which is the same as UG-79.

As a result, the allowable forming strain limit changes — not due to any actual difference in the forming strain, but purely because of how the head is categorized: one-piece vs. multi-piece.

The extreme fiber elongation limit will still be the same, e.g. 5%. The difference would be on how it is calculated. But I get your point, it should be clear when to use the first formula compared to the 3rd formula for double-curved heads.

 

[r6155]

@ Trestala

1. The elliptical head has no knuckle radius.
   
2. From what you say, I assume you've never performed a tension test in the lab.
   
3. The formula in UG-79 and Table 6.1 are predictions: need to be checked.
   
4. Yes, I've seen many incomplete inspection plans and several inspectors without the necessary knowledge.
   
5. More: do you perform any checks after the stress relieving the head?

 

[Trestala]

The elliptical head has no knuckle radius.

 

[r6155]

Trestala, you said "The radius you use in the formula in Table UG-79-1 or Table 6.1 for an ellipsoidal head is the mean radius of the knuckle (Rf)"

Did you confess that?. Are you sure the ellipsoidal head has a knuckle radius?
Ummmmm !!!!