GB/T 4732.4-2024 Pressure vessels design by analysis - Part 4: Stress classification method
1 Scope
This document specifies a stress classification design method based on elastic stress analysis and plastic failure criteria to prevent plastic collapse failure, excessive local strain failure, ratchet failure and fatigue failure of vessels.
This document is applicable to thin-walled plates and shells or pressure-bearing structures dominated by thin-walled plates and shells which are elastic or locally become plastic but generally remain elastic. The use of stress classification methods for thick-walled structures (such as cylinders with R/δ ≤ 4) may produce uncertain results, in this case, the analysis method in GB/T 4732.5 should be adopted.
Note: Unless otherwise specified, this document applies only where the design temperature is below the temperature at which the allowable stress is controlled by the creep limit or the durable strength of the material.
2 Normative references
The following documents contain provisions which, through reference in this text, constitute provisions of this document. For dated references, only the edition cited applies. For undated references, the latest edition (including any amendments) applies.
GB/T 4732.1-2024 Pressure vessels design by analysis - Part 1: General requirements
GB/T 4732.2 Pressure vessels design by analysis - Part 2: Materials
GB/T 4732.3 Pressure vessels design by analysis - Part 3: Formulae method
GB/T 4732.5 Pressure vessels design by analysis - Part 5: Elastic plastic analysis method
GB/T 4732.6-2024 Pressure vessels design by analysis - Part 6: Fabrication, inspection and testing and acceptance
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in GB/T 4732.1-2024 and the following apply.
3.1.1 loading histogram
statistical graph obtained by processing the load cycle of the vessel by cycle counting method
Note: In the loading histogram, the load cycle is represented by a rectangular block. The height and width of the block represent the range of loads in the cycle and the number of cycles, respectively. A rectangular block represents a constant amplitude cycle. When multiple different constant amplitude cycles are included in the loading history, the loading histogram consists of a series of juxtaposed rectangular blocks of unequal height and width.
3.1.2 event
one or several fatigue damage-producing event(s) that may be included in the user’s design specification (UDS), each of which consists of specified load components at several points in time over a period of time, and alternates a specified number of times
Note: The event can be a startup, a shutdown, an accident state, or any other cyclic action. The sequence of multiple events may be regular or random.
3.1.3 cycle
relationship between stress and strain established by a specified load at a location of the vessel or component More than one stress-strain cycle can be generated at a location during an event or at the transition between two events, and the cumulative fatigue damage from these stress-strain cycles determines whether the specified operation is applicable at that location. The judgment of applicability is based on a stable stress-strain cycle
3.1.4 proportional loading
loading where the value of the applied stress varies with time and the stress Mohr’s circle also varies with time during constant amplitude load. In some cases, although the size of the Mohr’s circle changes during the cycle, this loading is still a proportional loading as long as the direction of the principal stress axis remains fixed
Note: An example of proportional loading is a rotating shaft subjected to in-phase torsion and bending where the ratio of axial and torsional stresses during cycles remains constant.
3.1.5 non-proportional loading
loading where the direction of the principal stress axis is not fixed but changes direction during the cycle
Note: An example of non-proportional loading is a rotating shaft subjected to out-of-phase torsion and bending where the ratio of axial and torsional stresses continuously changes during cycles.
3.1.6 peak
point where the first derivative of the load or stress histogram changes from a positive value to a negative value
3.1.7 valley
point where the first derivative of the load or stress histogram changes from a negative value to a positive value
3.2 Symbols
For the purposes of this document, the following symbols apply.
a——Radius of the heated spot or heated zone in the plate, mm.
α——Linear expansion factor of the material at the average temperature of two adjacent points at the average cycle temperature, 10-6mm/mm·℃.
a1——Linear expansion factor of material 1 at average cycle temperature, 10-6mm/mm·℃.
a2——Linear expansion factor of material 2 at average cycle temperature, 10-6mm/mm·℃.
C₁——Factor in fatigue assessment exemption criterion 2.
C₂——Factor in fatigue assessment exemption criterion 2.
Ec——Elastic modulus of a given material in the design fatigue curve, MPa.
ET——Elastic modulus of the material at temperature T, MPa.
Ey1——Elastic modulus of material 1 at the average cycle temperature, MPa.
Ey2——Elastic modulus of material 2 at the average cycle temperature, MPa.
Eym——Elastic modulus of material at the average cycle temperature, MPa.
F——Peak stress, MPa.
K——Load combination factor.
Ke, k——Fatigue loss factor.
Kf——Fatigue strength weakening factor.
M——Number of stress cycles at the fatigue failure check point determined by the cycle counting method.
Mb——Axial bending moment per unit circumferential length at the weld joint of multi-layer cylindrical shell, spherical shell or head, N·mm.
——Number of cycles obtained from the design fatigue curve adopted when the stress amplitude is .
N(Se)——Number of cycles obtained from the design fatigue curve adopted when the stress amplitude is Se.
Nk——Number of allowable cycles of the kth constant amplitude cycle.
nk——Number of cycles of the estimated operating load given by the cycle counting method.
——Expected (design) number of cycles for the full-range including startup and shutdown.
——Number of valid cycles corresponding to △PN.
——Estimated (design) number of operating pressure cycles.
——Number of valid cycles corresponding to SML.
——Effective number of metal temperature difference fluctuation △TE between any two adjacent points.
——Number of valid cycles corresponding to △TM.
——Number of cycles corresponding to △TN.
——Number of valid cycles corresponding to △TR.
——Number of cycles of temperature difference fluctuation of assemblies composed of materials with different linear expansion factors.
P——Specified design pressure, MPa.
Pb——Primary bending stress, MPa.
PL——Primary local membrane stress, MPa.
Pm——General primary membrane stress, MPa.
Q——Secondary stress, MPa.
Contents
1 Scope
2 Normative references
3 Terms, definitions and symbols
4 Stress analysis
5 Stress classification
6 Design evaluation
7 Other requirements
Annex A (Informative) Loading histogram formulation and cycle number calculation for fatigue evaluation
Annex B (Informative) Linearization of elastic nominal stress
Annex C (Normative) Experimental stress analysis
Annex D (Normative) Stress index method for nozzle analysis
GB/T 4732.4-2024 Pressure vessels design by analysis - Part 4: Stress classification method
1 Scope
This document specifies a stress classification design method based on elastic stress analysis and plastic failure criteria to prevent plastic collapse failure, excessive local strain failure, ratchet failure and fatigue failure of vessels.
This document is applicable to thin-walled plates and shells or pressure-bearing structures dominated by thin-walled plates and shells which are elastic or locally become plastic but generally remain elastic. The use of stress classification methods for thick-walled structures (such as cylinders with R/δ ≤ 4) may produce uncertain results, in this case, the analysis method in GB/T 4732.5 should be adopted.
Note: Unless otherwise specified, this document applies only where the design temperature is below the temperature at which the allowable stress is controlled by the creep limit or the durable strength of the material.
2 Normative references
The following documents contain provisions which, through reference in this text, constitute provisions of this document. For dated references, only the edition cited applies. For undated references, the latest edition (including any amendments) applies.
GB/T 4732.1-2024 Pressure vessels design by analysis - Part 1: General requirements
GB/T 4732.2 Pressure vessels design by analysis - Part 2: Materials
GB/T 4732.3 Pressure vessels design by analysis - Part 3: Formulae method
GB/T 4732.5 Pressure vessels design by analysis - Part 5: Elastic plastic analysis method
GB/T 4732.6-2024 Pressure vessels design by analysis - Part 6: Fabrication, inspection and testing and acceptance
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in GB/T 4732.1-2024 and the following apply.
3.1.1 loading histogram
statistical graph obtained by processing the load cycle of the vessel by cycle counting method
Note: In the loading histogram, the load cycle is represented by a rectangular block. The height and width of the block represent the range of loads in the cycle and the number of cycles, respectively. A rectangular block represents a constant amplitude cycle. When multiple different constant amplitude cycles are included in the loading history, the loading histogram consists of a series of juxtaposed rectangular blocks of unequal height and width.
3.1.2 event
one or several fatigue damage-producing event(s) that may be included in the user’s design specification (UDS), each of which consists of specified load components at several points in time over a period of time, and alternates a specified number of times
Note: The event can be a startup, a shutdown, an accident state, or any other cyclic action. The sequence of multiple events may be regular or random.
3.1.3 cycle
relationship between stress and strain established by a specified load at a location of the vessel or component More than one stress-strain cycle can be generated at a location during an event or at the transition between two events, and the cumulative fatigue damage from these stress-strain cycles determines whether the specified operation is applicable at that location. The judgment of applicability is based on a stable stress-strain cycle
3.1.4 proportional loading
loading where the value of the applied stress varies with time and the stress Mohr’s circle also varies with time during constant amplitude load. In some cases, although the size of the Mohr’s circle changes during the cycle, this loading is still a proportional loading as long as the direction of the principal stress axis remains fixed
Note: An example of proportional loading is a rotating shaft subjected to in-phase torsion and bending where the ratio of axial and torsional stresses during cycles remains constant.
3.1.5 non-proportional loading
loading where the direction of the principal stress axis is not fixed but changes direction during the cycle
Note: An example of non-proportional loading is a rotating shaft subjected to out-of-phase torsion and bending where the ratio of axial and torsional stresses continuously changes during cycles.
3.1.6 peak
point where the first derivative of the load or stress histogram changes from a positive value to a negative value
3.1.7 valley
point where the first derivative of the load or stress histogram changes from a negative value to a positive value
3.2 Symbols
For the purposes of this document, the following symbols apply.
a——Radius of the heated spot or heated zone in the plate, mm.
α——Linear expansion factor of the material at the average temperature of two adjacent points at the average cycle temperature, 10-6mm/mm·℃.
a1——Linear expansion factor of material 1 at average cycle temperature, 10-6mm/mm·℃.
a2——Linear expansion factor of material 2 at average cycle temperature, 10-6mm/mm·℃.
C₁——Factor in fatigue assessment exemption criterion 2.
C₂——Factor in fatigue assessment exemption criterion 2.
Ec——Elastic modulus of a given material in the design fatigue curve, MPa.
ET——Elastic modulus of the material at temperature T, MPa.
Ey1——Elastic modulus of material 1 at the average cycle temperature, MPa.
Ey2——Elastic modulus of material 2 at the average cycle temperature, MPa.
Eym——Elastic modulus of material at the average cycle temperature, MPa.
F——Peak stress, MPa.
K——Load combination factor.
Ke, k——Fatigue loss factor.
Kf——Fatigue strength weakening factor.
M——Number of stress cycles at the fatigue failure check point determined by the cycle counting method.
Mb——Axial bending moment per unit circumferential length at the weld joint of multi-layer cylindrical shell, spherical shell or head, N·mm.
——Number of cycles obtained from the design fatigue curve adopted when the stress amplitude is .
N(Se)——Number of cycles obtained from the design fatigue curve adopted when the stress amplitude is Se.
Nk——Number of allowable cycles of the kth constant amplitude cycle.
nk——Number of cycles of the estimated operating load given by the cycle counting method.
——Expected (design) number of cycles for the full-range including startup and shutdown.
——Number of valid cycles corresponding to △PN.
——Estimated (design) number of operating pressure cycles.
——Number of valid cycles corresponding to SML.
——Effective number of metal temperature difference fluctuation △TE between any two adjacent points.
——Number of valid cycles corresponding to △TM.
——Number of cycles corresponding to △TN.
——Number of valid cycles corresponding to △TR.
——Number of cycles of temperature difference fluctuation of assemblies composed of materials with different linear expansion factors.
P——Specified design pressure, MPa.
Pb——Primary bending stress, MPa.
PL——Primary local membrane stress, MPa.
Pm——General primary membrane stress, MPa.
Q——Secondary stress, MPa.
Contents of GB/T 4732.4-2024
Contents
1 Scope
2 Normative references
3 Terms, definitions and symbols
4 Stress analysis
5 Stress classification
6 Design evaluation
7 Other requirements
Annex A (Informative) Loading histogram formulation and cycle number calculation for fatigue evaluation
Annex B (Informative) Linearization of elastic nominal stress
Annex C (Normative) Experimental stress analysis
Annex D (Normative) Stress index method for nozzle analysis
