High-temperature pressure vessel creep strength design and assessment method considering probability dispersibility

Abstract

The invention relates to a high-temperature pressure vessel creep strength design and assessment method considering probability dispersity. The method comprises the following steps: acquiring monotonic thermal tensile stress strain data of a material at a preset temperature and N groups of creep deformation data at the preset temperature; performing parameter fitting on the elastic-plastic model to obtain elastic-plastic model parameters; sampling based on the N groups of creep deformation data to obtain z samples; performing parameter fitting on the creep constitutive model based on the z samples to obtain z groups of creep constitutive model parameters; obtaining probability distribution of the creep constitutive model parameters based on the z groups of creep constitutive model parameters; and drawing an isochronous stress-strain curve under specific reliability, and performing finite element analysis on the high-temperature pressure vessel based on the isochronous stress-strain curve to obtain a creep strength assessment result.

Description

Technical Field

[0001] This invention relates to the field of creep strength design for high-temperature structures or components, and more specifically to a method for designing and evaluating the creep strength of high-temperature pressure vessels that takes into account probabilistic dispersion. Background Technology

[0002] High-temperature pressure vessels in next-generation nuclear power and other fields are exhibiting an extreme development trend, characterized by high temperature, high pressure, large size, and long service life. For example, the main vessel of a sodium-cooled fast reactor has an service temperature of 550℃, a design pressure of 0.3MPa, and a design life of 40 years. Under these stringent conditions, creep is a significant damage mode for high-temperature pressure vessels. Therefore, it is necessary to research creep strength assessment methods for high-temperature pressure vessels to verify whether their creep strength meets design requirements during the design phase. This is crucial for ensuring the integrity of high-temperature pressure vessels and the long-term safe operation of energy systems.

[0003] Currently, methods for assessing the creep strength of high-temperature pressure vessels mainly fall into three categories: elastic analysis methods, inelastic analysis methods, and isochronous stress-strain curve methods. Among these three methods, the isochronous stress-strain curve method directly incorporates the creep effect of high-temperature materials into the elastoplastic constitutive model, significantly reducing the burden of inelastic analysis such as creep and shortening the strength design cycle of high-temperature pressure vessels. Based on these advantages, this method has received widespread attention and focused research from industry professionals.

[0004] Research has found that existing isochronous stress-strain curve methods are still deterministic isochronous stress-strain curves, meaning the curve represents the average trend line of the material response. This method cannot introduce the influence of probabilistic dispersion into the material constitutive model, making it difficult to assess the creep strength of high-temperature pressure vessels that takes into account the uncertainty of the material response. Summary of the Invention

[0005] The purpose of this invention is to provide a design and evaluation method for the creep strength of high-temperature pressure vessels that takes into account the probability dispersion, so as to solve the problem that the prior art does not take into account the uncertainty of material response.

[0006] To achieve the above objectives, this invention provides a method for designing and evaluating the creep strength of high-temperature pressure vessels that considers probabilistic dispersion, comprising the following steps:

[0007] S100: Obtain monotonic thermal tensile stress-strain data and N sets of creep deformation data of high-temperature pressure vessel material at a preset temperature. Each set of creep deformation data includes stress load and creep strain time data under that stress load; where N is a positive integer greater than 1.

[0008] S200: Based on the monotonic thermal tensile stress-strain data of high-temperature pressure vessel materials at a preset temperature, the parameters of the preset elastoplastic model are fitted to obtain the elastoplastic model parameters of the high-temperature pressure vessel materials at the preset temperature.

[0009] S300: Sample N sets of creep deformation data of high temperature pressure vessel material at a preset temperature to obtain z samples. Each sample includes Na sets of creep deformation data, where z and a are preset positive integers and a is less than N.

[0010] S400: For each of the z samples, the parameters of the preset creep constitutive model are fitted using that sample to obtain the creep constitutive model parameters of the high-temperature pressure vessel material at the preset temperature based on that sample.

[0011] S500: Determine the probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature based on the creep constitutive model parameters of z samples.

[0012] S600: Based on the elastoplastic model parameters and the probability distribution of creep strain of high-temperature pressure vessel materials at a preset temperature, determine the isochronous stress-strain curve of high-temperature pressure vessel materials under specific reliability and preset design life.

[0013] S700: Based on the design physical dimensions of the high-temperature pressure vessel, a finite element model of the high-temperature pressure vessel is established; according to the design service conditions of the high-temperature pressure vessel, boundary conditions and load conditions are set for the finite element model, including temperature loads, which are preset temperatures; material parameters are assigned to the finite element model, including elastoplastic parameters, where the elastoplastic parameters are isochronous stress-strain curves under specific reliability and preset design life; finite element analysis is performed on the finite element model to obtain the finite element analysis results.

[0014] S800: Determine the assessment results based on the finite element analysis results.

[0015] Optionally, the elastoplastic model is:

[0016] ,

[0017] in, For strain amplitude, To stabilize the cyclic stress amplitude; E is the elastic modulus; This is the cyclic hardening coefficient; The cyclic hardening index; and These are the parameters of the elastoplastic model to be determined.

[0018] Optionally, the creep constitutive model is:

[0019] ,

[0020] in, σ represents creep strain; σ represents stress in MPa; t represents time in hours; A, n, and m are all parameters of the creep constitutive model to be determined.

[0021] Optionally, step S500 specifically includes:

[0022] For each sample, the creep strain data at different stress levels corresponding to the sample are calculated based on the creep constitutive model parameters of the high-temperature pressure vessel material at a preset temperature; wherein, the creep strain data at each stress level corresponding to the sample includes the creep strain at each time point under that stress level.

[0023] The probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature is determined based on creep strain data of z samples under different stress levels.

[0024] Optionally, step S600 specifically includes the following steps:

[0025] S610: Determine the monotonic thermal tensile stress-strain curve of high-temperature pressure vessel material based on the elastoplastic model parameters of the high-temperature pressure vessel material at a preset temperature.

[0026] S620: Determine the creep stress-strain curve of high-temperature pressure vessel material under specific reliability and preset design life based on the probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature.

[0027] S630: Based on the monotonic thermal tensile stress-strain curve of the high-temperature pressure vessel material and the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life, determine the isochronous stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

[0028] Optionally, step S630 specifically includes:

[0029] The monotonic thermal tensile stress-strain curve of the high-temperature pressure vessel material and the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life are added together to obtain the isochronous stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

[0030] Optionally, step S800 specifically includes:

[0031] Determine whether the finite element analysis results converge. If they do, the assessment result is that the creep strength of the high-temperature pressure vessel meets the design requirements; otherwise, the assessment result is that the creep strength of the high-temperature pressure vessel does not meet the design requirements.

[0032] Optionally, the monotonic thermal tensile stress-strain data and creep deformation data of the high-temperature pressure vessel material are obtained by performing monotonic thermal tensile tests and creep tests on standard samples of high-temperature pressure vessels, respectively.

[0033] Optionally, the standard sample of the high-temperature pressure vessel is a round bar sample. Attached Figure Description

[0034] Figure 1 A flowchart illustrating the design and evaluation method for creep strength of high-temperature pressure vessels considering probabilistic dispersion according to an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of a typical high-temperature pressure vessel according to an embodiment of the present invention;

[0036] Figure 3 This is a probability distribution diagram of the creep constitutive model parameter A of a typical high-temperature pressure vessel material according to an embodiment of the present invention;

[0037] Figure 4 This is a probability distribution diagram of the creep constitutive model parameter n of a typical high-temperature pressure vessel material according to an embodiment of the present invention.

[0038] Figure 5 This is a probability distribution diagram of the creep constitutive model parameter m of a typical high-temperature pressure vessel material according to an embodiment of the present invention;

[0039] Figure 6 The isochronous stress-strain curves of high-temperature pressure vessel materials under different design lives at 95% reliability, according to embodiments of the present invention.

[0040] Figure 7 This is a schematic diagram of the finite element analysis results of a typical high-temperature component according to an embodiment of the present invention. Detailed Implementation

[0041] The preferred embodiments of the present invention are given below with reference to the accompanying drawings and described in detail.

[0042] like Figure 1 As shown in the figure, this invention provides a method for designing and evaluating the creep strength of high-temperature pressure vessels that considers probabilistic dispersion, which includes the following steps:

[0043] S100: Obtain monotonic thermal tensile stress-strain data and N sets of creep deformation data of high-temperature pressure vessel material at a preset temperature. Each set of creep deformation data includes stress load and creep strain time data under that stress load.

[0044] S200: Based on the monotonic thermal tensile stress-strain data of high-temperature pressure vessel materials at a preset temperature, the parameters of the preset elastoplastic model are fitted to obtain the elastoplastic model parameters of the high-temperature pressure vessel materials at the preset temperature.

[0045] The elastoplastic model can be the Ramberg-Osgood model shown below:

[0046]

[0047] in, For strain amplitude, To stabilize the range of cyclic stress; To stabilize the cyclic stress amplitude; E is the elastic modulus; This is the cyclic hardening coefficient; This is the cyclic hardening index. and These are the parameters for the elastoplastic model to be determined. The elastic modulus can be obtained using a dynamic thermomechanical analyzer.

[0048] After obtaining the monotonic thermal tensile stress-strain data, parameter fitting was performed to obtain the elastoplastic model parameters of the high-temperature pressure vessel material at a preset temperature. and .

[0049] S300: Sample N sets of creep deformation data of high-temperature pressure vessel material at a preset temperature to obtain z samples. Each sample includes Na sets of creep deformation data, where z and a are preset positive integers and a is less than N.

[0050] The specific values ​​of z and a can be selected as needed. In some embodiments, a bootstrap method can be used to sample N sets of creep deformation data to obtain the required number of samples.

[0051] S400: For each of the z samples, the parameters of the preset creep constitutive model are fitted using that sample to obtain the creep constitutive model parameters of the high-temperature pressure vessel material at the preset temperature based on that sample.

[0052] The creep constitutive model can be represented by the Norton-Bailey equation as shown below:

[0053]

[0054] in, σ is the creep strain; σ is the stress (MPa); t is the time (h); A, n, and m are all parameters of the creep constitutive model to be determined, which are related to the material type and temperature.

[0055] Each sample includes multiple sets of creep deformation data. Creep constitutive model parameters are fitted to each sample separately using a pre-defined method (e.g., least squares method). This allows us to obtain the creep constitutive model parameters for the high-temperature pressure vessel material based on that sample at a pre-defined temperature. Ultimately, z sets of creep constitutive model parameters are obtained.

[0056] S500: Determine the probability distribution of creep constitutive model parameters based on the creep constitutive model parameters of high-temperature pressure vessel materials at a preset temperature using z samples, and determine the probability distribution of creep strain of high-temperature pressure vessel materials at a preset temperature based on the creep constitutive model parameters of high-temperature pressure vessel materials at a preset temperature using z samples.

[0057] After obtaining the probability distribution of the creep constitutive model parameters, the parameters can be sampled a target number of times to obtain multiple sets of new creep constitutive model parameters, thereby increasing the number of creep constitutive model parameters and improving the accuracy of the probability distribution of creep strain. The probability distribution of creep strain of a high-temperature pressure vessel material at a preset temperature is determined based on the creep constitutive model parameters of z samples at a preset temperature. Specifically, this includes:

[0058] For each sample, creep strain data at different stress levels is calculated based on the creep constitutive model parameters of the high-temperature pressure vessel material at a preset temperature. Each creep strain data point at each stress level includes the creep strain at each time point within that stress level. Different stress levels are multiple stress values ​​obtained within a preset stress range, using a preset step size. For example, within the 0-100 MPa range, values ​​are taken in 0.5 MPa steps, resulting in 201 stress levels. At each stress level, creep strain at different time points can be calculated based on the creep constitutive model parameters of the high-temperature pressure vessel material at the preset temperature. Different time points can be selected as needed, such as 1h, 10h, 100h, 1000h, 10000h, etc.

[0059] The probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature is determined based on creep strain data at different stress levels corresponding to z samples. As described above, each sample corresponds to a creep strain at the same stress level and time point, and z samples correspond to z creep strains. Based on these z creep strains, the probability distribution of creep strain at the stress level and time point can be calculated. Therefore, each stress level and each time point can be combined in pairs to form different stress level-time groups. The probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature includes the probability distribution of creep strain under each stress level-time group.

[0060] S600: Based on the elastoplastic model parameters and the probability distribution of creep strain of high-temperature pressure vessel materials at a preset temperature, determine the isochronous stress-strain curve of high-temperature pressure vessel materials under specific reliability and preset design life.

[0061] Step S600 specifically includes:

[0062] S610: Determine the monotonic thermal tensile stress-strain curve of high-temperature pressure vessel material based on the elastoplastic model parameters of the high-temperature pressure vessel material at a preset temperature.

[0063] S620: Determine the creep stress-strain curve of high-temperature pressure vessel material under specific reliability and preset design life based on the probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature.

[0064] S630: Based on the monotonic thermal tensile stress-strain curve of the high-temperature pressure vessel material and the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life, determine the isochronous stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

[0065] In step S610, once the parameters of the elastoplastic model are determined, they can be substituted into the elastoplastic model to obtain the relationship between tensile stress and tensile strain, i.e., the monotonic thermal tensile stress-strain curve.

[0066] In step S620, since the creep strain probability distribution under each stress level-time group has been obtained previously, the creep strain probability distribution at the time point corresponding to each stress level and the preset design life can be extracted from it. Based on this, the creep strain at a specific reliability (e.g., 95%) at the time point corresponding to the stress level and the preset design life can be determined. Thus, different stress levels and their corresponding creep strains under the preset design life and specific reliability can be obtained, that is, the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

[0067] In step S630, the strain under a certain stress in the isochronous stress-strain curve under a specific reliability and preset design life is obtained by adding the strain (elastic-plastic strain) in the monotonic thermal tensile curve under that stress and the creep strain.

[0068] S700: Based on the design physical dimensions of the high-temperature pressure vessel, a finite element model of the high-temperature pressure vessel is established; according to the design service conditions of the high-temperature pressure vessel, boundary conditions and load conditions are set for the finite element model, including temperature load, which is a preset temperature; material parameters are assigned to the finite element model, including elastoplastic parameters, where the elastoplastic parameters are the isochronous stress-strain curves under specific reliability and preset design life; finite element analysis is performed on the finite element model to obtain the finite element analysis results.

[0069] Finite element analysis can be performed in existing finite element software such as ABAQUS.

[0070] S800: Determine the assessment results based on the finite element analysis results.

[0071] Step S800 specifically includes:

[0072] Determine whether the finite element analysis results converge. If they do, the assessment result is that the creep strength of the high-temperature pressure vessel meets the design requirements; otherwise, the assessment result is that the creep strength of the high-temperature pressure vessel does not meet the design requirements.

[0073] The creep strength assessment method for high-temperature pressure vessels in this invention takes into account the uncertainty of material creep performance. It assesses the strength of high-temperature pressure vessels based on isochronous stress-strain curves under specific reliability. Compared with existing deterministic methods, it can more accurately quantify the uncertainty of creep constitutive model parameters, improve structural safety and reliability through probabilistic assessment, and avoid overly conservative or aggressive designs.

[0074] The following example uses a typical high-temperature pressure vessel (e.g.) Figure 2 As shown in the figure, the creep strength test is carried out using the method of the present invention, and the main process flow is as follows:

[0075] I. Typical high-temperature pressure vessels are made of high-temperature alloy materials. Using their monotonic thermal tensile data, elastic-plastic model parameters are fitted to obtain the elastic-plastic model parameters at a preset temperature of 750℃. , The elastic modulus E is taken as 210000MPa.

[0076] 2. There are 14 sets of creep deformation data at 750℃ (i.e., N=14). The capacity of each sample is set to 11 sets (i.e., Na=11). Based on the bootstrap method, 2000 samples are taken from the 14 sets of creep deformation data to obtain 2000 samples, i.e., z=2000.

[0077] Third, based on 2000 samples, the parameters of the creep constitutive model are fitted, resulting in 2000 sets of creep constitutive model parameters (including A, n, and m). Counting these 2000 sets of creep constitutive model parameters yields the probability distributions of A, n, and m, as follows: Figure 3 , Figure 4 and Figure 5 As shown.

[0078] IV. Based on Elastic-Plastic Model Parameters and Using 2000 sets of A, n, and m values, we determined the isochronous stress-strain curves under 95% reliability and the preset design life (10h), as follows: Figure 6 As shown.

[0079] V. For example Figure 2 As shown, the dimensions of a typical high-temperature pressure vessel are: δ1=8mm, h1=4000mm, L=2000mm, h2=2000mm, R1=1000mm, r1=200mm, δ2=8mm, ρ1=20mm, ρ2=10mm. Finite element analysis is performed on the typical high-temperature pressure vessel. The isochronous stress-strain curves under 95% reliability and preset design life (10h) are used as elastoplastic parameters and input into the finite element model. The time length of the static analysis step is set to 36000s (10h).

[0080] VI. The finite element analysis results of typical high-temperature pressure vessels converge, such as... Figure 7 As shown, the creep strength of a typical high-temperature pressure vessel meets the design requirements at 95% reliability.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. That is, all simple and equivalent changes and modifications made based on the claims and description of this invention fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion, characterized in that, Includes the following steps: S100: Obtain monotonic thermal tensile stress-strain data and N sets of creep deformation data of high-temperature pressure vessel material at a preset temperature. Each set of creep deformation data includes stress load and creep strain time data under that stress load; where N is a positive integer greater than 1. S200: Based on the monotonic thermal tensile stress-strain data of high-temperature pressure vessel materials at a preset temperature, the parameters of the preset elastoplastic model are fitted to obtain the elastoplastic model parameters of the high-temperature pressure vessel materials at the preset temperature. S300: Sample N sets of creep deformation data of high temperature pressure vessel material at a preset temperature to obtain z samples. Each sample includes Na sets of creep deformation data, where z and a are preset positive integers and a is less than N. S400: For each of the z samples, the parameters of the preset creep constitutive model are fitted using that sample to obtain the creep constitutive model parameters of the high-temperature pressure vessel material at the preset temperature based on that sample. S500: Determine the probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature based on the creep constitutive model parameters of z samples. S600: Based on the elastoplastic model parameters and the probability distribution of creep strain of high-temperature pressure vessel materials at a preset temperature, determine the isochronous stress-strain curve of high-temperature pressure vessel materials under specific reliability and preset design life. S700: Based on the design physical dimensions of the high-temperature pressure vessel, a finite element model of the high-temperature pressure vessel is established; according to the design service conditions of the high-temperature pressure vessel, boundary conditions and load conditions are set for the finite element model, including temperature loads, which are preset temperatures; material parameters are assigned to the finite element model, including elastoplastic parameters, where the elastoplastic parameters are isochronous stress-strain curves under specific reliability and preset design life; finite element analysis is performed on the finite element model to obtain the finite element analysis results. S800: Determine the assessment results based on the finite element analysis results.

2. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion as described in claim 1, characterized in that, The elastic-plastic model is as follows: ， in, For strain amplitude, To stabilize the cyclic stress amplitude; E is the elastic modulus; This is the cyclic hardening coefficient; The cyclic hardening index; and These are the parameters of the elastoplastic model to be determined.

3. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion as described in claim 1, characterized in that, The creep constitutive model is as follows: ， in, σ represents creep strain; σ represents stress in MPa; t represents time in hours; A, n, and m are all parameters of the creep constitutive model to be determined.

4. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion as described in claim 1, characterized in that, Step S500 specifically includes: For each sample, the creep strain data at different stress levels corresponding to the sample are calculated based on the creep constitutive model parameters of the high-temperature pressure vessel material at a preset temperature; wherein, the creep strain data at each stress level corresponding to the sample includes the creep strain at each time point under that stress level. The probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature is determined based on creep strain data of z samples under different stress levels.

5. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion according to claim 1, characterized in that, Step S600 specifically includes the following steps: S610: Determine the monotonic thermal tensile stress-strain curve of high-temperature pressure vessel material based on the elastoplastic model parameters of the high-temperature pressure vessel material at a preset temperature. S620: Determine the creep stress-strain curve of high-temperature pressure vessel material under specific reliability and preset design life based on the probability distribution of creep strain of high-temperature pressure vessel material at a preset temperature. S630: Based on the monotonic thermal tensile stress-strain curve of the high-temperature pressure vessel material and the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life, determine the isochronous stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

6. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion as described in claim 5, characterized in that, Step S630 specifically includes: The monotonic thermal tensile stress-strain curve of the high-temperature pressure vessel material and the creep stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life are added together to obtain the isochronous stress-strain curve of the high-temperature pressure vessel material under specific reliability and preset design life.

7. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion according to claim 1, characterized in that, Step S800 specifically includes: Determine whether the finite element analysis results converge. If they do, the assessment result is that the creep strength of the high-temperature pressure vessel meets the design requirements; otherwise, the assessment result is that the creep strength of the high-temperature pressure vessel does not meet the design requirements.

8. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion according to claim 1, characterized in that, The monotonic thermal tensile stress-strain data and creep deformation data of the high-temperature pressure vessel material were obtained by performing monotonic thermal tensile tests and creep tests on standard samples of high-temperature pressure vessels, respectively.

9. The method for designing and evaluating the creep strength of high-temperature pressure vessels considering probabilistic dispersion as described in claim 8, characterized in that, The standard sample for the high-temperature pressure vessel is a round bar sample.

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