Vessel Low-cycle Fatigue | Online Calculator

Fatigue Calculators







Low-cycle Fatigue of Vessels

This calculation determines the cyclic strength of the pressure vessels within < 105 loading cycles. To perform calculations, it is necessary to specify the principal cycle stresses σ1 ÷ σ3 during loading and unloading, service temperature T, parameters of welds, then select a material category and tensile strength Rm/t.

The calculation is based on ISO 16528-1: 2007, ISO 16528-2: 2007. Following the results of calculations, the number of loading cycles to failure N is determined. The calculation is made for vessels and apparatuses that meet the strength conditions under static load.

INITIAL DATA

T - Vessel wall temperature;


σ1c - First principal stress at charge;


σ2c - Second principal stress at charge;


σ3c - Third principal stress at charge;


σ1d - First principal stress at discharge;


σ2d - Second principal stress at discharge;


σ3d - Third principal stress at discharge;


ξ - Coefficient, depending on the type of welded joint (see table below);


Rm/t - Tensile strength of material at service temperature.

RESULTS DATA

N - Number of cycles to failure.

Wall temperature (T)


STRESSES AT CHARGE

First principal (σ1c)

Second principal (σ2c)

Third principal (σ3c)


STRESSES AT DISCHARGE

First principal (σ1d)

Second principal (σ2d)

Third principal (σ3d)


Type welging coefficient ξ

Welded seams are ground


MATERIAL

Ultimate strength (Rm/t)

Carbon steel

Alloy steel

Austenitic steel

High strength steel (σв > 700 МПа)

Aluminium alloy AlMg2, AlMg3

Aluminium alloy AlMg6

Copper alloy

Brass alloy

Titanium alloy ERTi-1


Number of cycles (N)

BASIC FORMULAS

Number of cycles:

N = (1 / nN)*[A*C / (σa - B/nσ)]

nN - Safety factor for the number of loading cycles;

nσ - Safety factor for permissible stresses;

σa - Equivalent amplitude of stresses;

A, B, C - coefficients, depending on material and vessel wall temperature.

INITIAL DATA

T - Vessel wall temperature;


σ1c - First principal stress at charge;


σ2c - Second principal stress at charge;


σ3c - Third principal stress at charge;


σ1d - First principal stress at discharge;


σ2d - Second principal stress at discharge;


σ3d - Third principal stress at discharge;


ξ - Coefficient, depending on the type of welded joint (see table below);


Rm/t - Tensile strength of material at service temperature.

RESULTS DATA

N - Number of cycles to failure.

WELD TYPE FACTOR

Weld type

Figure

ξ

Full penetration butt weld

1

Welded seam with backing sheet

1.2

Full penetration T-weld

1.2

One-sided weld seam without backing sheet

1.5

Welded seams of flat flanges

1.5

WELD TYPE FACTOR

Weld type

Figure

ξ

Full penetration butt weld

1

Welded seam with backing sheet

1.2

Full penetration T-weld

1.2

One-sided weld seam without backing sheet

1.5

Welded seams of flat flanges

1.5

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