Prediction Method of Low Cycle Fatigue Life of Thermally Aged Materials

Abstract

The present invention provides a method for predicting the low cycle fatigue life of thermally aged materials, comprising: S1 determining the fatigue strength coefficient σ' of the material before aging f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, determine the fatigue strength coefficient σ' of the material at different aging times f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, and establish a functional relationship with aging time; S2 determines the relationship between fatigue ductility coefficient ε'f and fatigue ductility index c and aging time according to K, n, σ'f, b; S3 substitutes σ'f, b, ε'f, c into the Basquin‑Manson‑Coffin equation to obtain a low-cycle fatigue life prediction equation suitable for different aging times. The present invention effectively solves the problem that the low-cycle fatigue life of materials in thermal aging in the prior art cannot be accurately predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue life prediction methods, and in particular to a method for predicting the low-cycle fatigue life of thermally aged materials. Background Art

[0002] Nuclear power materials are subject to harsh service environments and are exposed to high temperature (280-320°C) and high pressure (around 15MPa) conditions for long periods of time. Under these conditions, the materials are prone to microstructural changes that lead to thermal embrittlement, which reduces the plasticity and toughness of the materials while increasing their hardness and brittleness. This greatly increases the risk of sudden failure of structural components and is an important factor affecting the safe operation of nuclear power plants.

[0003] Fatigue damage refers to the process in which a material continuously produces permanent cumulative damage under cyclic loads far below the tensile strength level, and the material locally cracks or suddenly breaks completely after a number of cycles. Fatigue damage is the main failure form of nuclear power materials, and low-cycle fatigue damage under thermal aging conditions is the most important failure form of nuclear power materials. Therefore, low-cycle fatigue analysis under thermal aging occupies an important position in the design. In the prior art, it is carried out by actual detection during use, and there is no method for theoretical prediction. Summary of the invention

[0004] The invention provides a method for predicting the low cycle fatigue life of thermally aged materials, which solves the problem in the prior art that the low cycle fatigue life of thermally aged materials cannot be accurately predicted.

[0005] According to the present invention, a method for predicting the low-cycle fatigue life of thermally aged materials is provided, comprising: S1 determining the fatigue strength coefficient σ' of the material before aging; f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, determine the fatigue strength coefficient σ' of the material at different aging times f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, and establish a functional relationship with aging time; S2 is based on K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time; S3 will be σ' f , b, ε' f Substituting c into the Basquin-Manson-Coffin equation, the low-cycle fatigue life prediction equation applicable to different aging times is obtained.

[0006] Furthermore, the prediction method also includes: S4 measuring the strain-life curve of the unaged material and the aged material.

[0007] Furthermore, the strain-life curves of the unaged and aged materials are specifically as follows: when the material is not aged, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after the material is aged for 1000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after the material is aged for 3000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after the material is aged for 5000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively.

[0008] Furthermore, the cyclic stress-strain behavior of the material reflects the true stress-strain characteristics of the material under low-cycle fatigue loading conditions. The stress amplitude and strain amplitude under stable conditions can usually be expressed by the Ramberg-Osgood law:

[0009]

[0010] Among them, ε a is the total strain amplitude, σ a / E is the elastic strain part, (σ a / K) 1 / n is the plastic strain part, and the stress amplitude is the stress amplitude at half life. By fitting the data of plastic strain and stress amplitude under different strain amplitudes, the cyclic strength coefficient K and cyclic strain hardening exponent n can be obtained.

[0011] Furthermore, according to the Basquin-Manson-Coffin and Ramberg-Osgood formulas, the corresponding fatigue strength coefficient σ' can be obtained by fitting the strain amplitude and strain amplitude data of unaged and different aging times by the least squares method. f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening exponent n.

[0012] Furthermore, the fatigue strength coefficient σ' f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening exponent n are associated with aging time, and these parameters have a similar exponential relationship with aging time.

[0013] Furthermore, the same equation form is used to fit the relationship between each parameter and the aging time. After fitting, the fatigue strength coefficient σ' fThe relationship between the fatigue strength index b and the aging time is shown in formula (3), the relationship between the fatigue strength index b and the aging time is shown in formula (4), the relationship between the cyclic strength coefficient K and the aging time is shown in formula (5), and the relationship between the cyclic strain hardening index n and the aging time is shown in formula (6).

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Furthermore, according to K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time;

[0020] Substituting Ramberg-Osgood into the Basquin-Manson-Coffin equation, we can obtain the fatigue ductility coefficient ε' f , the relationship between the fatigue ductility index c and the other four parameters:

[0021]

[0022]

[0023] Substitute formulas (3)-(6) into formulas (7)-(8).

[0024] Furthermore, the relationship between the fatigue ductility coefficient εf, the fatigue ductility index c and the aging time is obtained:

[0025]

[0026]

[0027] Furthermore, by substituting formulas (2), (3), (7), and (8) into the Basquin-Manson-Coffin equation, we can obtain the fatigue life prediction equation for material 16MND5 at different thermal aging times:

[0028]

[0029] Furthermore, the low cycle fatigue life of the material is predicted according to formula (11) and compared with the actual test results. The prediction model results are compared with the test results.

[0030] By applying the technical solution of the present invention, the low-cycle fatigue life of thermal aging materials can be predicted by deriving the actual low-cycle fatigue life through tests or actual fatigue and establishing a functional relationship with parameters, so that it is possible to predict in advance whether the use of the material is safe. The technical solution of the present invention effectively solves the problem that the low-cycle fatigue life of thermal aging materials in the prior art cannot be accurately predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] By reading the detailed description below with reference to the accompanying drawings, the above and other purposes, features and advantages of the exemplary embodiments of the present disclosure will become readily understood. In the accompanying drawings, several embodiments of the present disclosure are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:

[0032] Figure 1 A schematic diagram showing the change of fatigue life with thermal aging time at different amplitudes of the method for predicting low-cycle fatigue life of thermal aging materials in this embodiment;

[0033] Figure 2 Shows Figure 1 Schematic diagram of the relationship between aging and time for the prediction method of low cycle fatigue life of thermally aged materials;

[0034] Figure 3 Shows Figure 1 Schematic diagram of the test life of the prediction method for low cycle fatigue life of thermally aged materials. DETAILED DESCRIPTION

[0035] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0036] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0037] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" may include both "above" and "below". The device may also be positioned in other different ways, rotated 90 degrees or in other orientations, and the spatially relative descriptions used herein are interpreted accordingly.

[0038] Now, exemplary embodiments according to the present disclosure will be described in more detail with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in a variety of different forms and should not be construed as being limited to the embodiments described herein. It should be understood that these embodiments are provided to make the disclosure of the present application thorough and complete, and to fully convey the concepts of these exemplary embodiments to those of ordinary skill in the art. In the accompanying drawings, for clarity, the thickness of the layers and regions is enlarged, and the same reference numerals are used to represent the same devices, and thus their descriptions will be omitted.

[0039] like Figures 1 to 3 As shown, in this embodiment, the constant amplitude uniaxial tensile and compressive strain load spectrum of the medium carbon steel 16MND5 material commonly used in nuclear power under unaged and aged conditions is taken as an example, and the prediction method of low cycle fatigue life is as follows:

[0040] (1) Measure the strain-life curves of unaged and aged materials;

[0041] (2) Determine the fatigue strength coefficient σ' of the material before aging and at different aging times f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, and determine the relationship with aging time;

[0042] (3) According to K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time;

[0043] (4) σ' f , b, ε' f Substituting c into the Basquin-Manson-Coffin equation, the low-cycle fatigue life prediction equation applicable to different aging times is obtained.

[0044] in:

[0045] (1) Measure the strain-life curves of unaged and aged materials

[0046] The fatigue life of the material changes with the thermal aging time when the strain amplitude is 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively when it is not aged, aged for 1000 hours, aged for 3000 hours and aged for 5000 hours. Figure 1 shown.

[0047] (2) Determine the fatigue strength coefficient σf, fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening exponent n of the material before aging and at different aging times, and determine their relationship with aging time.

[0048] The cyclic stress-strain behavior of a material reflects the true stress-strain characteristics of the material under low-cycle fatigue loading conditions. The stress amplitude and strain amplitude under stable conditions can usually be expressed by the Ramberg-Osgood law:

[0049]

[0050] Among them, ε a is the total strain amplitude, σ a / E is the elastic strain part, (σ a / K) 1 / n is the plastic strain part, and the stress amplitude is the stress amplitude at half life. By fitting the data of plastic strain and stress amplitude under different strain amplitudes, the cyclic strength coefficient K and cyclic strain hardening exponent n can be obtained.

[0051] According to the Basquin-Manson-Coffin and Ramberg-Osgood formulas, the corresponding fatigue strength coefficient σ' can be obtained by fitting the strain amplitude and strain amplitude data of unaged and different aging times by the least squares method. f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n. The results are shown in Table 1.

[0052] Table 1 Material parameters at different heat aging times

[0053] Aging time (h) K(MPa) n <![CDATA[σ' f (MPa)]]> b 0 645.3 0.0779 601.0 -0.0439 1000 753.3 0.1072 663.0 -0.0568 3000 746.6 0.1063 652.2 -0.0555 5000 695.4 0.1037 623.1 -0.0542

[0054] The fatigue strength coefficient σ' f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n are associated with aging time. These parameters have a similar exponential relationship with aging time, such as Figure 2 shown.

[0055] Using the same equation form, the relationship between each parameter and aging time is fitted. After fitting, the fatigue strength coefficient σ' f The relationship between the fatigue strength index b and the aging time is shown in formula (3), the relationship between the fatigue strength index b and the aging time is shown in formula (4), the relationship between the cyclic strength coefficient K and the aging time is shown in formula (5), and the relationship between the cyclic strain hardening index n and the aging time is shown in formula (6).

[0056] Formulas (2)-(6) can accurately describe the influence of thermal aging on the material parameters. As the thermal aging time increases, the mechanical properties of the material show the characteristics of first hardening and then softening. At the same time, the critical aging time T in formulas (2)-(6) s The aging range that can reflect the effect of initial hardening on the material parameters, T s The larger the value, the larger the time range of the impact, which has certain physical significance. The formula is concise and the parameters are easy to obtain.

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] (3) According to K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time;

[0063] Substituting Ramberg-Osgood into the Basquin-Manson-Coffin equation, we can obtain the fatigue ductility coefficient ε' f , the relationship between the fatigue ductility index c and the other four parameters:

[0064]

[0065]

[0066] Substituting formula (3)-(6) into formula (7)-(8), we can obtain the relationship between fatigue ductility coefficient εf, fatigue ductility index c and aging time:

[0067]

[0068]

[0069] (4) Substituting formulas (2), (3), (7), and (8) into the Basquin-Manson-Coffin equation, the fatigue life prediction equation for material 16MND5 applicable to different thermal aging times can be obtained as follows:

[0070]

[0071] According to formula (11), the low cycle fatigue life of the material is predicted and compared with the actual test results, such as Figure 3 As shown. Compared with the test results, the prediction model results are all within the range of 2 times the fatigue life, proving that the model can well predict the actual results. When using this model, only the aging time and strain load conditions need to be entered to obtain the corresponding material life. The calculation is fast and easy to use.

[0072] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0073] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein, for example. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0074] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the low cycle fatigue life of thermally aged materials, characterized in that: include: S1 determines the fatigue strength coefficient σ' of the material before aging f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, determine the fatigue strength coefficient σ' of the material at different aging times f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n, and establish a functional relationship with aging time; S2 according to K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time; The fatigue strength coefficient, fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening index n are correlated with the aging time. These parameters have a similar exponential relationship with the aging time. Using the same equation form, the relationship between each parameter and the aging time is fitted respectively; after fitting, the relationship between the fatigue strength coefficient and the aging time is shown in formula (3), the relationship between the fatigue strength index b and the aging time is shown in formula (4), the relationship between the cyclic strength coefficient K and the aging time is shown in formula (5), and the relationship between the cyclic strain hardening index n and the aging time is shown in formula (6); According to K, n, σ' f , b Determine the fatigue ductility coefficient ε' f and the relationship between fatigue ductility index c and aging time; Substituting Ramberg-Osgood into the Basquin-Manson-Coffin equation, we can obtain the fatigue ductility coefficient ε' f , the relationship between the fatigue ductility index c and the other four parameters: Substitute formula (3)-(6) into formula (7)-(8); The relationship between fatigue ductility coefficient εf, fatigue ductility index c and aging time is obtained: S3 will σ' f , b, ε' f Substituting c into the Basquin-Manson-Coffin equation, the low-cycle fatigue life prediction equation applicable to different aging times is obtained.

2. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 1, characterized in that: The prediction method further includes: S4 measuring the strain-life curve of the material before and after aging.

3. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 2, characterized in that: The strain-life curves of the material before and after aging are specifically as follows: when the material is not aged, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after aging for 1000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after aging for 3000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively; after aging for 5000 hours, the fatigue life changes with the thermal aging time when the strain amplitudes are 0.2%, 0.3%, 0.4%, 0.6% and 0.8% respectively.

4. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 3, characterized in that: The cyclic stress-strain behavior of a material reflects the true stress-strain characteristics of the material under low-cycle fatigue loading conditions. The stress amplitude and strain amplitude under stable conditions can usually be expressed by the Ramberg-Osgood law: Among them, ε a is the total strain amplitude, σ a / E is the elastic strain part, (σ a / K) 1 / n For the plastic strain part, the stress amplitude is the stress amplitude at half life; by fitting the data of plastic strain and stress amplitude under different strain amplitudes, the cyclic strength coefficient K and cyclic strain hardening exponent n can be obtained.

5. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 4, characterized in that: According to the Basquin-Manson-Coffin and Ramberg-Osgood formulas, the corresponding fatigue strength coefficient σ' can be obtained by fitting the strain amplitude and strain amplitude data of unaged and different aging times by the least squares method. f , fatigue strength index b, cyclic strength coefficient K and cyclic strain hardening exponent n.

6. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 5, characterized in that: Substituting formulas (2), (3), (7), and (8) into the Basquin-Manson-Coffin equation, we can obtain the fatigue life prediction equation for material 16MND5 at different thermal aging times:

7. The method for predicting the low cycle fatigue life of thermally aged materials according to claim 6, characterized in that: The low cycle fatigue life of the material is predicted according to formula (11). The predicted model results are within the range of 2 times the fatigue life compared with the test results.

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