A method for predicting creep damage of high-temperature pressure-bearing structures

Abstract

The present invention relates to a method for predicting creep damage in high-temperature, pressure-bearing structures. The creep damage of high-temperature structures is assessed using a creep deformation prediction model. The creep damage value D is the ratio of the creep strain value ε of the equipment at time t to the creep ductility parameter εD of the pressure-bearing equipment material. The creep ductility parameter is the creep strain value corresponding to the intersection of the extended deformation curve of the material in creep stage II and the material's fracture life at time t. The creep deformation prediction model provided by the present invention can accurately predict the entire creep deformation process of a material within a wide stress range. The model parameter identification process is simple, and the evaluation results are safe and reliable. The model is suitable for evaluating the creep damage state of key high-temperature structural components.

Description

Technical Field

[0001] The present invention belongs to the field of high-temperature structural integrity, and in particular relates to a method for predicting creep damage of a high-temperature pressure-bearing structure. Background Art

[0002] Creep damage is one of the important damage mechanisms of high-temperature pressure-bearing structures. Its accurate assessment is crucial to ensuring the long-term safe operation of key structures such as high-temperature pressure vessels and pipelines, power plant boilers, etc. At the same time, the accurate assessment of creep damage is also involved in the creep fatigue life assessment. From a macroscopic phenomenological point of view, creep is the slow inelastic deformation behavior of materials under high-temperature constant load conditions. It is a time-dependent deformation process. The whole process can usually be divided into three stages, namely stage I (deceleration creep stage), stage II (constant rate creep stage) and stage III (accelerated creep stage). From a microscopic perspective, the creep process is related to a variety of slow microstructural rearrangements, such as dislocation movement, microstructural degradation, grain boundary void nucleation and growth, etc.

[0003] To predict the creep behavior of materials, various constitutive models for creep deformation have been proposed, such as the time-hardening model, the strain-hardening model, and the Norton-Bailey power-law creep model. However, these models often only describe a certain stage or the first two stages of the creep process. Subsequently, Evans and Wilshire et al. proposed the θ parameter method, which can describe the entire creep deformation process. However, the numerous parameters in their prediction model make it difficult to accurately identify the θi parameter in practical applications. With the development of continuum damage mechanics, researchers have analyzed the physical mechanisms of creep damage, introduced corresponding internal damage variables, and then developed dynamic equations for the evolution of creep strain and damage. These models, such as the Kachanov-Robatnov-Hayhurst model, have been developed based on the physical mechanisms of creep damage, enabling prediction of all three stages of creep. However, these models involve numerous material parameters, and the differential equations describing the evolution of creep strain and internal variables are rigid and coupled, making accurate model parameter identification difficult and hindering their application in engineering. Therefore, it is necessary to develop a simple and practical creep damage prediction method. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method for predicting creep damage of high-temperature pressure-bearing structures, in which the creep model can accurately predict the entire process of material creep deformation within a wide stress range, and the model parameter identification process is simple. This method can be applied to evaluate the creep damage of high-temperature pressure-bearing structures.

[0005] The present invention adopts the following technical solutions:

[0006] A method for predicting creep damage of high-temperature pressure-bearing structures is proposed. The creep damage value D at a certain point of the pressure-bearing structure is expressed as follows:

[0007]

[0008] Where ε is the creep strain value of the pressure-bearing structure at time t, ε D The creep ductility parameter of the material of the pressure-bearing structure is defined as: the slope of the creep deformation curve of the material in stage II Extend the deformation curve of stage II, and the extension line is connected with the fracture life time t of the material. f The intersection point corresponds to the creep strain value.

[0009] When the creep damage value D is less than 1, the high-temperature structure can be considered safe and will not creep crack.

[0010] Since the deformation curve of stage II is a straight line, it can also be understood that the slope of the creep curve at the intersection of stages I and II is The creep strain value corresponding to the creep rupture life time t is the creep ductility parameter, where is the minimum creep strain rate of the creep curve.

[0011] Furthermore, the method comprises the following steps:

[0012] S1. Analyze the specified temperature T and different stress levels σ i The creep strain curve of the material under the conditions of (i=1, 2, ..., n) is used to distinguish the creep stages I, II and III of the material according to the curve of the change of creep strain rate over time. m data points are selected from each creep deformation stage to obtain the given stress level σ i Creep strain data set P under (i=1, 2, ..., n) i ,Right now

[0013]

[0014] in, and Represent the creep strain data of creep stage I, stage II and stage III respectively. The superscripts I, II and III represent the creep deformation stages respectively. The subscript i represents the corresponding stress level. The subscript j represents the serial number of the selected creep strain data point.

[0015] S2: According to the specified temperature T, different stress levels σ i The creep strain curve of the material under the conditions of (i=1, 2, ..., n) is used to obtain the corresponding creep rupture life t fi, slope is the minimum creep strain rate and creep ductility parameters Then the average value of creep ductility parameter ε is calculated D , which is expressed as follows:

[0016]

[0017] S3: Establish a strain-based creep strain prediction model to obtain the creep strain value ε at time t. The prediction model expression is as follows:

[0018]

[0019] Where t is the creep time, t f is the creep rupture life, A and B are model parameters;

[0020] S4: Based on the creep strain value ε determined in S3 and the creep ductility parameter ε determined in S2 D , the corresponding creep damage D is calculated using formula (1).

[0021] Furthermore, the model parameters A and B in Equation (3) are functions of the stress level σ, and they can be expressed as follows:

[0022]

[0023] B(σ)=b0+b1σ+b2σ 2 (5)

[0024] Among them, a1, a2, a3, b0, b1 and b2 are fitting parameters.

[0025] Furthermore, in formula (3) f is a function of the stress level σ and is calculated using the Larson-Miller formula:

[0026] LMP=β0+β1(lgσ)+β2(lgσ) 2 +β3(lgσ) 3 (6)

[0027] t f =10 LMP / (T+273.15)-C (7)

[0028] Where T is temperature in °C, C is the Larson-Miller constant, LMP is the time-temperature parameter, and β0, β1, β2, and β3 are cubic polynomial coefficients.

[0029] Furthermore, the calculation method of the cubic polynomial coefficients β0, β1, β2 and β3 and the Larson-Miller constant C is as follows: Get different temperatures Tp (p=1, 2, ..., r), different stress levels σ q Creep rupture life of materials under (q=1, 2, ..., s) conditions This r×s group of data Substitute into equation (6) and equation (7) for nonlinear fitting, and the cubic polynomial coefficient β is obtained according to the fitting results. i (i=0, 1, 2, 3) and the numerical value of the Larson-Miller constant C.

[0030] Furthermore, the calculation method of the fitting parameters a1, a2, a3, b0, b1 and b2 is as follows: Formula (3) is re-expressed as follows:

[0031]

[0032] The creep rupture life t fi and creep strain data set P i As input data, the least square method is used to fit Equation (8), and the i-th stress level σ is obtained. i The corresponding parameter A i and B i , denoted as (σ i , A i ) and (σ i , B i ); using the least square method to (σ i , A i ) is fitted to equation (4) to obtain the specific values ​​of parameters a1, a2 and a3; (σ i , B i ) is fitted to equation (5) to obtain the specific values ​​of parameters b0, b1 and b2, and then the functional relationships between A, B and stress level σ are determined respectively.

[0033] Furthermore, step S5 is included. Specifically, step S5 is as follows: for the creep strain prediction model of formula (3) and the creep damage formula of formula (1), a creep finite element simulation is performed on the pressure-bearing structure using finite element software to obtain a distribution cloud diagram of the creep strain ε and the creep damage variable D of the pressure-bearing structure at different times t.

[0034] Furthermore, the finite element simulation is specifically to use Fortran language to write a numerical integration algorithm of the model, perform creep finite element simulation on the pressure-bearing structure according to the output results of the algorithm, and obtain the creep damage value D corresponding to a certain time t; the finite element simulation uses the finite element software ANSYS, and the numerical integration algorithm is written into the usercreep user subroutine of the finite element software ANSYS.

[0035] Furthermore, the numerical integration algorithm is as follows:

[0036] S51. According to steps S1-S4, it is known that t n The variable {σ n , ε n , D n}, calculate the current time t n+1 =t n +Δt, namely

[0037]

[0038] S52. Calculate the current time t n+1 =t n +Δt creep strain increment Δε n+1 ,Right now

[0039]

[0040] S53. Calculate the current time t n+1 =t n +Δt creep damage increment ΔD n+1 ,Right now

[0041]

[0042] S54. Update current time t n+1 =t n +Δt{ε n+1 , D n+1},Right now

[0043]

[0044] t n+1 The corresponding {ε n+1 , D n+1} is the desired output variable.

[0045] The present invention also provides a device for predicting creep damage of a high-temperature pressure-bearing structure, which has a built-in program for running the above-mentioned method for predicting creep damage of a high-temperature pressure-bearing structure.

[0046] The beneficial effects of the present invention are:

[0047] The main materials of high-temperature pressure-bearing structures such as high-temperature pressure vessels and high-temperature pressure pipelines in the fields of petrochemicals, electric power, etc. are metal materials. When the service temperature exceeds 0.3 to 0.5 times the melting point of the metal material, creep deformation and damage usually need to be considered.

[0048] This paper proposes a simple and practical model for predicting creep damage in high-temperature, pressure-bearing structures. It accurately predicts the entire creep deformation process within a wide stress range. The model's parameter identification process is simple. A finite element user subroutine developed based on this model, combined with damage variables based on creep strain and creep ductility parameters, can perform structural creep finite element analysis. This model can predict creep deformation at different times and assess creep damage at specific locations. The assessment results are reliable and secure, making it suitable for evaluating the creep damage state of critical high-temperature structural components. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 1 is the creep strain curve of 2.25Cr1Mo0.25V steel at 455°C and different stress levels (340 MPa, 360 MPa, 380 MPa and 400 MPa) in the embodiment.

[0050] Figure 2 In order to select an appropriate amount of creep strain data from the four creep strain curves with stress levels of 340 MPa, 360 MPa, 380 MPa and 400 MPa, there are 10 data points in the creep stages I, II and III.

[0051] Figure 3 To extend the deformation curve of creep stage II and obtain the creep strain value corresponding to the creep rupture moment

[0052] Figure 4 The creep rupture life data of 2.25Cr1Mo0.25V steel at different temperatures and stress levels and the fitting curve based on the Larson-Miller formula are shown.

[0053] Figure 5 The creep deformation curves of the material under different stress levels predicted by the model are in the range of 250 MPa to 400 MPa. The rightmost part of the figure corresponds to the 250 MPa curve, and the stress levels increase from left to right.

[0054] Figure 6 This figure shows the von Mises equivalent creep strain distribution of the 1 / 4 finite element model of the reactor cylinder structure in the example after 8760 hours of service. In the figure, EPCREQV represents the von Mises equivalent creep strain, and MN (outside the image, corresponding to 0.537E-03) and MX (inside the image, corresponding to 0.700E-03) indicate the minimum and maximum values ​​of EPCREQV, respectively.

[0055] Figure 7This figure shows the creep damage distribution of the finite element model of the reactor cylinder structure in the example after 8760 hours of service. SVAR1 represents the creep damage variable D, while MN (outside the image, corresponding to 0.031578) and MX (inside the image, corresponding to 0.041188) indicate the minimum and maximum values ​​of the creep damage variable D, respectively. DETAILED DESCRIPTION

[0056] The technical solution of the present invention is described in more detail below with reference to the embodiments and drawings:

[0057] A method for predicting creep damage of a high-temperature pressure-bearing structure comprises the following steps:

[0058] S1. Analyze the specified temperature T and different stress levels σ i The creep strain curve of the material under the conditions of (i=1, 2, ..., n) is used to distinguish the creep stages I, II and III of the material according to the curve of the change of creep strain rate over time. m data points are selected from each creep deformation stage to obtain the given stress level σ i Creep strain data set P under (i=1, 2, ..., n) i ,Right now

[0059]

[0060] in, and Represent the creep strain data of creep stage I, stage II and stage III respectively. The superscripts I, II and III represent the stages of creep deformation, respectively. The subscript i represents the corresponding stress level, and the subscript j represents the sequence number of the selected creep strain data point.

[0061] In this embodiment, the pressure-bearing structure is a hydrogenation reactor, the main material is 2.25Cr1Mo0.25V steel, the service temperature T is 455°C, the stress levels σ are 340MPa, 360MPa, 380MPa and 400MPa, and the corresponding creep strain curves are as follows: Figure 1 As shown. Taking the creep strain curve corresponding to the stress level of 340MPa as an example, the creep stage I, stage II and stage III are divided according to the change of creep strain rate with time. For each stress level, 10 data points are selected from creep stages I, II and III respectively, thereby obtaining the creep strain data set under different stress levels, as shown in Figure 2 As shown (due to the proportion in the figure, some points overlap and are not fully displayed).

[0062] S2: According to the specified temperature T, different stress levels σ iThe creep strain curve of the material under the conditions of (i=1, 2, ..., n) is used to obtain the corresponding creep rupture life t fi ; Extend the creep stage II deformation curve to t = t fi The creep strain is obtained as Then the creep ductility parameter ε is calculated D , creep ductility parameter ε D The expression is as follows:

[0063]

[0064] In this embodiment, the creep rupture life under stress levels of 340 MPa, 360 MPa, 380 MPa and 400 MPa is 5333 h, 3247 h, 596 h and 159 h respectively. fi ,like Figure 3 As shown, the creep strain obtained are equal to 1.51%, 1.54%, 1.65%, and 2.09% respectively, from which the creep ductility parameter ε is calculated. D The average value is 1.70%.

[0065] S3: Establish a strain-based creep deformation prediction model to obtain the creep strain value ε at time t. The prediction model expression is as follows:

[0066]

[0067] Among them, t f is the creep rupture life, ε is the creep strain value at time t, and A and B are both model parameters. In this model, the parameters A and B are functions of the stress level σ, so they can be expressed as follows:

[0068]

[0069] B(σ)=b0+b1σ+b2σ 2 (5)

[0070] Among them, a1, a2, a3, b0, b1 and b2 are fitting parameters.

[0071] In this model, t f It is also a function of the stress level σ and can be calculated using the following Larson-Miller formula:

[0072] LMP=β0+β1(lgσ)+β2(lgσ) 2 +β3(lgσ) 3 (6)

[0073] t f =10LMP / (T+273.15)-C (7)

[0074] Where T is temperature in °C, C is the Larson-Miller constant, LMP is the time-temperature parameter, and β0, β1, β2, and β3 are cubic polynomial coefficients. p (p=1, 2, ..., r), different stress levels σ q Creep rupture life of materials under (q=1, 2, ..., s) conditions This r×s group of data Substitute into equation (6) and equation (7) for nonlinear fitting, and the cubic polynomial coefficient β is obtained according to the fitting results. i (i=0, 1, 2, 3) and the numerical value of the Larson-Miller constant C.

[0075] In this embodiment, if Figure 4 The data points shown are fitted with Equations (6) and (7) based on the creep rupture life data of structural materials under different temperature / stress level combinations, and the values ​​of β0, β1, β2 and β3 are 2.54483×10 5 、-2.88052×10 5 , 1.20976×10 5 and -1.7366×10 4 , the value of the Larson-Miller constant C is 22.12.

[0076] S4: To facilitate identification of the model parameters A and B in step S3, formula (2) is re-expressed as follows:

[0077]

[0078] The creep rupture life t fi and creep strain data set P i As input data, the least square method is used to fit Equation (8), and the i-th stress level σ is obtained. i The corresponding parameter A i and B i , denoted as (σ i , A i ) and (σ i , B i ); using the least square method to (σ i , A i ) is fitted to equation (4) to obtain the specific values ​​of parameters a1, a2 and a3; (σ i , B i) is fitted to equation (5) to obtain the specific values ​​of parameters b0, b1 and b2, and then the functional relationships between A, B and stress level σ are determined respectively.

[0079] In this embodiment, the fitting parameters a1, a2, a3, b0, b1 and b2 are -0.31444, -8.69×10 -23 、9.11863、40.18、-0.223、3.71×10 -4 From this, the creep deformation curves under different stress levels can be predicted, such as Figure 5 Shown is the creep deformation curve predicted by the model under stress levels of 250MPa to 400MPa.

[0080] S5: Based on the creep strain determined in step S3 and ε determined in step S2 D , the corresponding creep damage D can be calculated, and its expression is as follows:

[0081]

[0082] In this embodiment, the creep ductility parameter ε D It is 1.70%, so the calculation expression of creep damage D is D = ε / 0.017.

[0083] S5: For the creep deformation prediction model of formula (3), the numerical integration algorithm of the model is written using Fortran language. The designed algorithm is as follows:

[0084] S51. According to steps S1-S4, it is known that t n The variable {σ n , ε n , D n}, calculate the current time t n+1 =t n +Δt, namely

[0085]

[0086] S52. Calculate the current time t n+1 =t n +Δt creep strain increment Δε n+1 ,Right now

[0087]

[0088] S53. Calculate the current time t n+1 =t n +Δt creep damage increment ΔD n+1 ,Right now

[0089]

[0090] S54. Update current time t n+1 =t n +Δt{ε n+1 , D n+1},Right now

[0091]

[0092] The numerical integration algorithm is written into the usercreep subroutine of the finite element software ANSYS using Fortran language, and t can be obtained during creep finite element simulation. n+1 The corresponding {ε h+1 , D n+1}, which are the required output variables, thereby obtaining the distribution cloud diagram of the creep strain ε and creep damage variable D of the structure at different times t.

[0093] In this embodiment, creep finite element simulation is performed on a reactor cylinder structure subjected to internal pressure. The service temperature is 455° C., the internal pressure load is 21.7 MPa, and the inner diameter and wall thickness of the cylinder are 5200 mm and 360 mm, respectively. Figure 6 This is the distribution of the creep strain (represented by EPCREQV in the figure) of the predicted 1 / 4 finite element model of the cylinder structure after one year (i.e., 8760 hours) of service. It can be seen from the figure that the creep strain of the reactor cylinder structure gradually increases from the outer wall to the inner wall. Figure 7 This is the distribution of the creep damage variable D (denoted by SVAR1 in the figure) of the cylinder structure. The maximum creep damage of the structure is located on the inner wall of the cylinder, and its maximum value is 0.041. Since this value is less than 1, the reactor structure is safe after one year of service and will not creep crack.

[0094] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting creep damage of high-temperature pressure-bearing structures, characterized in that: The creep damage value D at a certain point of the pressure-bearing structure is expressed as follows: Where ε is the creep strain value of the pressure-bearing structure at time t, ε D is the creep ductility parameter of the material of the pressure-bearing structure, which is defined as: the creep ductility parameter of the material is defined as: the creep strain value corresponding to the intersection of the deformation curve of stage II of the material creep deformation curve with the slope of the stage II of the material creep deformation curve and the fracture life of the material at time t; The following steps are involved: S1. Analyze the specified temperature T and different stress levels σ i , i=1,2,...,n The creep strain curve of the material under the conditions of creep strain rate is used to distinguish the creep stages I, II and III of the material. m data points are selected from each creep deformation stage to obtain the given stress level σ i , the creep strain data set P under i=1,2,...,n i ,Right now in, and Represent the creep strain data of creep stage I, stage II and stage III respectively. The superscripts I, II and III represent the creep deformation stages respectively. The subscript i represents the corresponding stress level. The subscript j represents the serial number of the selected creep strain data point. S2: According to the specified temperature T, different stress levels σ i , i=1,2,...,n, the creep strain curve of the material under the conditions of, i=1,2,...,n, and the corresponding creep rupture life t fi , slope is the minimum creep strain rate and creep ductility parameters Then the creep ductility parameter ε is calculated D , which is expressed as follows: S3: Establish a strain-based creep strain prediction model to obtain the creep strain value ε at time t. The prediction model expression is as follows: Where t is the creep time, t f is the creep rupture life, A and B are model parameters; S4: Based on the creep strain value ε determined in S3 and the creep ductility parameter ε determined in S2 D , the corresponding creep damage D is calculated using formula (1).

2. The method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 1, wherein: The model parameters A and B in formula (3) are functions of the stress level σ and are expressed as follows: B(σ)=b0+b1σ+b2σ 2 (5) Among them, a1, a2, a3, b0, b1 and b2 are fitting parameters.

3. The method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 1, wherein: In formula (3), t f is a function of the stress level σ and is calculated using the Larson-Miller formula: LMP=β0+β1(lgσ)+β2(lgσ) 2 +β3(lgσ) 3 (6) t f ＝10 LMP / (T+273.15)-C (7) Where T is temperature in °C, C is the Larson-Miller constant, LMP is the time-temperature parameter, and β0, β1, β2, and β3 are cubic polynomial coefficients.

4. A method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 3, characterized in that: The calculation method of the cubic polynomial coefficients β0, β1, β2 and β3 and the Larson-Miller constant C is as follows: Get different temperatures T p ,p=1,2,...,r, different stress levels σ q ,q=1,2,...,s creep rupture life of materials This r×s group of data Substitute into equation (6) and equation (7) for nonlinear fitting, and the cubic polynomial coefficient β is obtained according to the fitting results. i ,i=0,1,2,3 and the numerical value of Larson-Miller constant C.

5. The method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 2, wherein: The calculation method of the fitting parameters a1, a2, a3, b0, b1 and b2 is as follows: Formula (3) is re-expressed as follows: The creep rupture life t fi and creep strain data set P i As input data, the least square method is used to fit Equation (8), and the i-th stress level σ is obtained. i The corresponding parameter A i and B i , denoted as (σ i ,A i ) and (σ i ,B i ); using the least square method to (σ i ,A i ) is fitted to equation (4) to obtain the specific values ​​of parameters a1, a2 and a3; (σ i ,B i ) is fitted to equation (5) to obtain the specific values ​​of parameters b0, b1 and b2.

6. The method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 1, wherein: The method further includes step S5, which specifically comprises: performing creep finite element simulation on the pressure-bearing structure using finite element software for the creep strain prediction model of formula (3) and the creep damage expression of formula (1), and obtaining distribution cloud diagrams of the creep strain ε and creep damage variable D of the pressure-bearing structure at different times t.

7. A method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 6, characterized in that: Specifically, the finite element simulation includes writing a numerical integration algorithm for the model in Fortran language, performing a creep finite element simulation on the pressure-bearing structure based on the output results of the algorithm, and obtaining a creep damage value D corresponding to a certain time t; the finite element simulation uses the finite element software ANSYS, and the numerical integration algorithm is written into the usercreep user subroutine of the finite element software ANSYS.

8. The method for predicting creep damage of a high-temperature pressure-bearing structure according to claim 7, wherein: The numerical integration algorithm is as follows: S51. According to steps S1-S4, it is known that t n The variable at the moment {σ n ,ε n ,D n }, calculate the current time t n+1 =t n +Δt, namely S52. Calculate the current time t n+1 =t n +Δt creep strain increment Δε n+1 ,Right now S53. Calculate the current time t n+1 =t n +Δt creep damage increment ΔD n+1 ,Right now S54. Update current time t n+1 =t n +Δt{ε n+1 ,D n+1 },Right now t n+1 The corresponding {ε n+1 ,D n+1 } is the desired output variable.

9. A device for predicting creep damage of high-temperature pressure-bearing structures, characterized in that: It has a built-in program for running the high-temperature pressure-bearing structure creep damage prediction method according to any one of claims 1 to 8.

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