Elongation in plate rolling process

[Faiz vhora]

I am looking for an formula to determine elongation of plate during rolling process in pressure vessel manufacturing process so that we cannot have to cut the extra material later and dont have to do shell setup
P.s. Material Mild steel

 

[bmoorthy]

ASME Sec VIII Div 1 Table UG 79-1 and clause UG 79 may help.
Let us assume the thickness is 25 mm and the shell diameter is 2500 ID then the % strain as per UG 79-1 for a cylindrical shell (Being formed from a flat plate)= 50 * 25/2500 % = 0.5% (Strain). While you may use the above to find the ultimate elongation that may happen to the plate by the virtue of rolling/bending, it may be noted that, if one just calculates the required circumference using the mid-diameter (ID + t/2) and cut the plate for bending, it will still work.

 

[CuMo]

You best speak to the company that will roll the material for you.
They will give you the best answer based on experience.

 

[DriveMeNuts]

Where the rolling machine needs to plastically deform the plate, there isn't a formula.
A very arduous Elastic-Plastic analysis is your only port of call, which I'm not sure if it will even spit out the number that you want.
A company that roll plate will have a spreadsheet of results from a long history of actual experience. If you can get your hands on that (Good Luck!) then you will need to interpolate to get a result for your geometry.

 

[Some Curious Guy]

I agree with @CuMo and @DriveMeNuts reply. There is no formula to predict elongation of plate during rolling. Manufacturers will have a database of actual measurement and they will use this database to predict elongation. This is will change from manufacturer to manufacturer and also from one rolling machine to another. Speak with the rolling subcontractor. If its your own shop , then start collecting data for a database.
All the best.

 

[r6155]

@ Faiz vhora
Can you tell us thickness and outside diameter ?

Regards

 

[chicopee]

You can ESTIMATE by a strain analysis along the longitudinal and lateral directions. You,ll need to know the poisson ratio.

 

[Faiz vhora]

@r6155
OD-500 mm
Thickness- 20

 

[Faiz vhora]

Thank you all for your response .

 

[Faiz vhora]

Yes i am currently working on data analysis and trying to do something with scatter diagram which help me to establish relation between length of plate and elongation. Thank you.
Is i am going in correct direction by drawing scatter plot?

 

[r6155]

See ROARK´S, digital seventh edition.
Chapter 9 Curved Beams
9.1 Tables formulas for curved beams subjected to bending in the plane of the curve.

In your example the radius of neutral axis is 239.861 mm.
Length of plate (20 mm) = 2 . Pi. 239.861 = 1507.09 mm minus gap of bevel for welding.

Regards

 

[DriveMeNuts]

I think Section 9.1 of Roarks is for the stress analysis of beams which have already been formed into curves, but I may be wrong.
All of the examples in Section 9.1 of Roarks have stress results less than yield, suggesting that Plastic deformation isn't being considered.
Therefore I question how useful Roarks would be where the rolling of plate requires plastic deformation.

 

[FacEngrPE]

Some companies have the ability to roll steel plate tubes without flatspots adjacent to the weld. Unless you are rolling in house, you can order per the required diameter, and make the plate length the suppliers responsibility. The gap and any weld prep should also be specified.

If you are rolling in house, working up the data as a scatter plot should help calibrate your rolling process and calculations to each other. You will also want to make sure your shop can roll "pipes" without flatspots on the ends. (Example - DAVI Plate Roll - 4 Roll in Action in Finland

https://youtu.be/1yzdyNNpHv4

) It may take a while, but bending without margins at the ends of your plates is entirely practical.

 

[r6155]

@ DriveMeNuts
All steels, aluminums, and even plastics exhibit springback upon release from the bending forces. Springback is the release of elastic strain and is related directly to the material yield strength.

Please, as an example, refer to ASME VIII Div.1 Mandatory Appendix 44 Cold Stretching of Austenitic Stainless Steel Pressure Vessels. Just as a reading information.

Regards

 

[DriveMeNuts]

r6266,
I associate springback with elastic behaviour.
Plastic deformation removes spring back.
The geometric in 9.1 of Roarks are curved shapes under no stress. The OP geometry is a flat plate needing to be curved with plastic deformation. 9.1 of Roarks doesn't cater for Plastic deformation
I am unable to comprehend how your point relates to the OP.

 

[r6155]

@ DriveMeNuts
If the load is removed when the specimen is in the plastic range, it retraces a straight line path parallel to the initial line and reaches zero stress at a finite value of deformation after elastic part of deformation is recovered.

1)“I think Section 9.1 of Roarks is for the stress analysis of beams which have already been formed into curves, but I may be wrong.”
Yes, you are wrong.
You are confusing table 9.1 with table 9.2

2) So a plate rolled to make a cylinder (permanent deformation) could not be used for a pressure vessel. Won't you be wrong?

3) what is your proposal to help (OP)?

4) Did you read Appendix 44 in ASME VIII Dv.1?

Regards
r6155

 

[DriveMeNuts]

r6155,
I think you are just making everything up. This feels like deja vu.

Roarks Sections for Flat Plate, Curved Beams and Circular Rings assumes that there is zero initial stress, and do not consider Plastic Deformation when a load is applied. The only mention of Plastic deformation in Roarks is for calculating the Shape factor (= Plastic Modulus/Elastic Modulus), which predicts the Bending moment where Plastic Hinge Collapse will happen. It doesn't predict deflection or elongation of the beam during plastic deformation. Roarks does not predict the elongation of a flat plate experiencing extensive plastic deformation as it is formed into a cylinder (i.e. the OP). Therefore Roarks is not relevant to the OP.

I am very familiar with Appendix 44 which relates to plastic deformation, and it doesn't predict elongation during Plastic deformation (where predicting elongation during plastic deformation is the subject of this thread). It therefore has no relation to the OP.

Obviously, plate needs to be plastically deformed into a Pressure Vessel cylinder. The question raised by the OP is, how do you predict the elongation of the plate during the rolling process.

If you actually do have any interest in this thread, you will find an education in my first post above where I provide my recommendations, which are agreed with by others.

 

[r6155]

@ DriveMeNuts
No company that makes cylinders cares about the elongation to know the length of sheet metal to cut to make a cylinder.
You have no manufacturing experience.

Regards

 

[DriveMeNuts]

r6155,
From your reply, it is clear that you didn't read the OP and just started to randomly write fiction. Your knowledge of Roarks is zero and Appendix 44 is irrelevant to the OP.

The manufacturers which I have worked for need an accurate plate length for large thickness cylinders to minimise the need for cutting and grinding the ends of the plate after rolling. They find this length from experience, not analysis.

As per my first post.