Calculation of deformation rate

Heat treatment for recovery performance

According to Article 8.1 of GB150.4-2011, when the steel plate cold forming pressure components meet any of the following a) – e) conditions and the deformation rate exceeds the range in Table 4, corresponding heat treatment shall be carried out after forming to restore the material properties.

8.1. Recovery performance heat treatment of formed pressure parts

8.1.1 When the cold formed steel plate pressure element meets any of the following conditions (a)~e) and the deformation rate exceeds the range in Table 4, corresponding heat treatment shall be carried out after forming to restore the material properties.

a) Containers containing extremely toxic or highly hazardous media;

b) Vessels with stress corrosion indicated in the drawing;

c) For carbon steel and low alloy steel, the thickness before forming is greater than 16 mm;

d) For carbon steel and low alloy steel, the thinning amount after forming is greater than 10%;

e) Impact tester is required for carbon steel and low alloy steel.

The deformation rate control indexes of cold formed parts are as follows:

Material Carbon steel, low alloy steel and other materials Austenitic stainless steel
Deformation rate/% 5 15a
Calculation of deformation rate:
Uniaxial tension (for example, cylinder forming, see Figure 12): deformation rate (%)=508 [1 – (R;/R)]/ R,
Biaxial tension (see Figure 12 for head forming): deformation rate (%)=758 [1 – (R;/R)]/ R;
In the formula:
8 — Plate thickness, mm;
R — radius of the middle surface after forming, mm;
R– Radius of middle surface before forming (∞ for flat plate), mm
a: When the design temperature is lower than – 100C or higher than 675C, the deformation rate control value is 10%.

5% for carbon steel, low alloy steel and other materials, and 15% for austenitic stainless steel. In the remarks, when the design temperature is lower than – 100 ° C or higher than 675 ° C, the deformation rate control value is 10%.
The specification provides illustrations for the barrel and head.

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Figure.12 Uniaxial and biaxial stretch forming

How to calculate the deformation rate of each component?

Calculation of cylinder deformation rate

Deformation rate, also known as extreme fiber elongation. For the cylinder, it is unidirectional tension, and the formula is:
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Uniaxial tension formula of cylinder

Rf is the middle radius and Ro is the middle radius before forming. For the cylinder, Ro is infinite. Therefore, the deformation rate formula of the cylinder can be further simplified:

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Further Simplification of the Deformation Rate Formula of the Cylinder
The deformation rate can be obtained when the inner diameter and thickness of the cylinder are known.
In Article 10.4.2 of GB150-1998, the index of carbon steel cylinder is: the thickness is not less than 3% of the inner diameter of the cylinder, which is basically equivalent to the deformation rate of 3%.

10.4.2 The cold formed or medium temperature formed pressure components that meet one of the following conditions shall be heat treated after forming. The thickness of round steel is 8, which meets the following conditions:

The thickness of carbon steel and 16MnR shall not be less than 3% of cylinder inner diameter D;

The thickness of other low alloy steels shall not be less than 2.5% of the inner diameter D of the cylinder.

According to GB150-2011, it is uniformly changed to 5%, and the post forming heat treatment is required only when other requirements are matched. Relatively speaking, the standard requirements are more relaxed.

Deformation rate of elliptical head

Elliptical head is a biaxial stretching element, so it is calculated according to the following formula:

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Ro is infinite, so the key point is the calculation of Rf.
The source of Rf of elliptical head is mainly approximate ellipse drawing method and four center method.

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Four mind method

In ASME VIII I, UG32, for standard elliptical heads, the radii of small arcs and large arcs obtained by four center method are 0.17D and 0.90D respectively:

An acceptable approximation ofa 2:1 ellipsoidal head is one with a knuckle radius of 0.17D and a spherical radius of 0.90D.

The deformation rate corresponds to a small arc radius of 0.17D, so for a standard ellipse, Rf is 0.17D+0.5 δ。
The large arc radius 0.9D also appears repeatedly in the equivalent spherical shell radius of the external pressure elliptical head, the calculated thickness of the hole reinforcement in the center of the elliptical head and the equivalent diameter of the head in WRC107297.
For elliptical heads of other shapes (D/2h is not 2), refer to Table 1-4.4 of ASME VIII.

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The derivation process can refer to:

Calculation of cold forming deformation rate of elliptical head

For the rest of dished heads, spherical heads, conical heads, Rf is easy to determine, and no examples will be given.

Elbow deformation rate

In ASME VIII I, Table UG79-1, in addition to unidirectional and bidirectional stretching, the formula for calculating the deformation rate of heat exchange pipe bends and elbows is also given.

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ASME VIII I, Table UG79-1

In the GB151-1999 version, for the heat exchange tubes of low temperature heat exchangers, when the bending radius is required to be less than 10 times the outer diameter of the heat exchange tubes, stress relief heat treatment is required.

A4.2.3 When the U-bend is cold bent and the bending radius is less than 10 times the outer diameter of the heat exchange tube, stress relief heat treatment must be carried out after cold bending. For the heat treated pipes, after hot bending or cold bending when the bending radius is less than 10 times the outer diameter of the heat exchange pipe, the same heat treatment process as the original heat treatment process must be carried out again.

It can be obtained by substituting the formula into the calculation formula of the deformation rate. When the bending radius is 10 times the outer diameter of the heat exchange tube, the corresponding deformation rate is 5%, meeting the requirements of GB150.4. This provision is set to meet the requirements of the deformation rate.
Low temperature heat exchanger has been deleted in the new version of GB151-2014, which means that the requirements of GB150 can be followed.

8.10.3 U-tube

When stress corrosion resistance is required or residual stress is required to be eliminated, carbon steel and low alloy steel U-shaped heat exchange pipe bends and straight pipe sections of at least 150mm shall be subject to heat treatment. The reason for the hot spot of U-shaped heat exchange pipe bend section made of other materials shall be negotiated by the Supplier and the Demander.

However, the deformation rate formula of elbow is not available in GB150 for the time being, so we can consider referring to the old specification or other specifications.

ASME Code Requirements

In the corresponding chapters of ASME, UG-79, UCS-79, UHA-44, UNF-79 and UHT-79, there are heat treatment requirements for the forming of pressure parts of various materials and components, which are different from GB and can be used as a reference for designing similar equipment.
For example, for the most widely used carbon steel, according to UCS-79:
For P-No 1 material (SA-516 70) cold formed or cold bent elbows and heat exchange tubes, with a thickness of no more than 19mm, do not need post forming heat treatment. That is, common carbon steel heat exchange tubes do not need to consider forming heat treatment. For example, if the fiber elongation is greater than 40%, forming heat treatment is required. Of course, it is difficult to reach 40% in general.

(1) Cold- formed and bent P-No.1 pipe and tube ma-terial having a nominal thickness not greater than /4 in. (19 mm) does not require post-forming heat treatment.

[2) For P-No. 1, Group Nos. 1 and 2 materials othernthan those addressed by (1), post- forming heat treatmentnis required when the extreme fiber elongation exceedsn40% or if the extreme fiber elongation exceeds 5% andnany of the following conditions exist:

When the deformation rate is greater than 5% and the forming temperature is between 120-480 ° C, post forming heat treatment is required:

(-b) The material is not exempt from impact test-ing by the rules of this Division, or impact testing is re-quired by the material specification.

(-c) The nominal thickness of the part before cold forming exceeds 7/8 in. (16 mm).

(-d) The reduction by cold forming from the nom-inal thickness is more than 1 0% at any location where the extreme fiber elongation exceeds 5%.

(-e) The temperature of the material during form-ing is in the range of 250°F to 900°F (120°C to 480°C].

The corresponding standard definition of GB150 and the description of warm forming:

2. Warm formed pressure parts

When the forming temperature is low, the influence of cold work hardening still exists. It is advisable to refer to the heat treatment conditions and requirements for cold formed pressure parts to determine whether performance recovery heat treatment is required after forming. When the forming temperature is high, if the heat treatment state of the material supply is changed, and the heat treatment state of the material required by the design is the same as the heat treatment state of the material supply, the heat treatment shall be conducted again to restore the heat treatment state of the material supply.

In the design of different specifications, the basic requirements of this specification must be considered.

Requirements of EN13445

In the process of a foreign project, the overall equipment is designed according to ASME, but the owner is from Europe. There are engineering regulations in the project that the deformation rate needs to be calculated according to EN13445.4, and it is stipulated that all carbon steel equipment with a deformation rate of more than 5% needs heat treatment.
At the beginning, it did not cause vigilance. It was designed, ordered and manufactured according to ASME requirements.
It was not until the Employer’s Engineer requested one day to submit the calculation sheet of fiber elongation according to the requirements of the project regulations that it was found that:
All carbon steel heads need post forming heat treatment.
The calculation formula of EN13445 is as follows, and the diameter ratio before and after forming is logarithmic:
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Dished circular products

The diameter Db before forming and the diameter De after forming are shown in the figure below.

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Forming of dished circular products

For an elliptical head with a diameter of 2000 and a thickness of 10mm, it is a relatively thin head. According to ASME, the deformation rate is 2.17%, less than 5%.
However, according to EN, the deformation rate is 19.2%, nearly 9 times that of ASME.

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In fact, it can be seen from the formula that the head is thick wall and thin wall, even if the head thickness is 0, the formula is simplified as:

  • 100*ln(1.21)=19%

Therefore, no convex head can be spared.
After discussion with the Owner, considering that heat treatment is not required in ASME and GB codes, this article has no impact on safety. In addition, some heads have been bought back and welded with the cylinder, whether it can be omitted.

It was ruthlessly rejected by the owner.

Source: China Pipe Fittings Manufacturer – Yaang Pipe Industry Co., Limited (

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)

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