Metal material compression creep constitutive model construction method

Abstract

The invention provides a method for constructing a constitutive model of compression creep of a metal material. The method comprises the following steps: 1) constructing the constitutive model of the metal material under nominal compression stress; 2) determining a creep time threshold value of the metal material; 3) determining creep characteristic constants A and B and creep time influence parameters n and m of the material; and 4) substituting the determined material parameters A, n, m and B into the constitutive model under the nominal compression stress to obtain the compression creep constitutive model of the metal material. According to the method, the change relation of the creep strain of the metal material under the constant compression load along with time can be described, and the creep deformation behavior of the metal material under the long-term compression load can also be predicted, so that the design of a structural member is optimized, and the service reliability of the structural member is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of material and component testing and analysis, and particularly to a method for constructing a constitutive model of compressive creep of metal materials. Background Art

[0002] In recent years, with the application of titanium alloys in the main pressure-resistant structures of deep-sea major equipment, the compressive creep behavior of titanium alloys has gradually become a hot topic in creep research. However, there is currently a lack of an effective mathematical model to describe the compressive creep deformation behavior of titanium alloys, that is, the compressive creep constitutive model. By using the creep constitutive model, the deformation and life of materials under long-term actual service conditions can be simulated or predicted, thereby reducing the failure risk of engineering structural components caused by long-term deformation. Therefore, establishing a compressive creep constitutive model for metal materials has important scientific significance and engineering application value. Summary of the Invention

[0003] Aiming at the technical problems existing in the above background art, the present invention proposes a method for constructing a constitutive model of compressive creep of metal materials, which can describe the relationship between strain and time of metal materials under a constant compressive load, and can also predict the deformation behavior of metal materials under a long-term compressive load, thereby optimizing the design of structural components and improving their service reliability.

[0004] To solve the above technical problems, a method for constructing a constitutive model of compressive creep of metal materials provided by the present invention mainly includes the following steps: Step 1: Construct a constitutive model of the metal material under the nominal compressive stress. The specific process is as follows: Ignoring the change in the mechanical properties of the metal material during the compressive creep process, a creep time threshold related to the nominal compressive stress σ is introduced. When the creep time exceeds the creep time threshold , it is considered that creep deformation no longer occurs under this compressive load. Further assume that the compressive creep constitutive model is expressed as: ; where σ pc is the compressive yield strength of the material, ε is the creep strain, t is the creep time, is the cumulative creep strain of the material when the creep time reaches the time threshold σ under the nominal compressive stress , A , n , m and B are material parameters; When only considering a certain nominal compressive stress, the above formula (1) can be simplified to: ; wherein, is the creep time threshold related to the nominal compressive stress; Step 2: Determine the creep time threshold of the metallic material; Step 3: Determine the creep characteristic constant A and B and the creep time influence parameter n and m ; Step 4: Substitute the determined material parameters A , n , m and B into the constitutive model under the nominal compressive stress to obtain the compressive creep constitutive model of the metallic material.

[0005] For the method for constructing the compressive creep constitutive model of the metallic material, wherein: the creep time threshold in the Step 2 is determined according to the test results of creep strain - time, or estimated according to the change trend of creep strain - time.

[0006] For the method for constructing the compressive creep constitutive model of the metallic material, wherein: if it is necessary to obtain the constitutive model under different nominal compressive stresses in the Step 3, that is, the above formula (1), select the creep strain - time test data at not less than two stress levels, and discretize A , n , m and B within the value range of the preset parameters. For any A , n , m and B combination, calculate the sum of the squares of the errors between the model prediction value and the test value at the selected stress levels, and screen out the A , n , m and B combination with the minimum sum of the squares of the errors as the values of the parameters A , n , m and B .

[0007] For the method for constructing the compressive creep constitutive model of the metallic material, wherein: if it is only necessary to obtain the constitutive model under a certain nominal compressive stress in the Step 3, that is, the above formula (2), discretize A , n and m within the value range of the preset parameters. For any A , n andm combinations, calculate the sum of the squares of the errors between the model prediction values and the test values at this stress level, and select the A and n and m combinations as the values of the parameters A and n and m .

[0008] For the method for constructing the constitutive model of the compression creep of the metal material, wherein the formula for calculating the sum of the squares of the errors between the model prediction values and the test values at the calculated stress level is: ; In the above formula (3), y ( σ i , t k ) represents the creep strain measured in the test at the stress σ i and the time t k , f ( σ i , t k ) represents the creep strain value predicted by using formula (1) at the stress σ i and the time t k , M is the number of selected creep stress levels, N is the total number of moments used to calculate the creep strain.

[0009] For the method for constructing the constitutive model of the compression creep of the metal material, wherein: in step 4, the material parameters A and n and m and B determined according to the constitutive model under different nominal compression stresses are substituted into the above formula (1), and the constitutive model of the compression creep of the metal material can be obtained.

[0010] For the method for constructing the constitutive model of the compression creep of the metal material, wherein: in step 4, the material parameters A and n and m determined according to the constitutive model under a certain nominal compression stress are substituted into the above formula (2), and the constitutive model of the compression creep of the metal material can be obtained.

[0011] Adopting the above technical solution, the present invention has the following beneficial effects: The method for constructing the constitutive model of the metal material under compression creep can describe the relationship between the creep strain and time of the metal material under a constant compression load; by using the present invention, the relationship between the creep strain and time under other different compression loads can be predicted based on the test data under two compression loads, greatly saving the test cost; by using the present invention, the creep deformation behavior of the material under a long-term compression load can be predicted, so as to optimize the design of the structural member and improve its service reliability. A creep time threshold related to the nominal compression stress is introduced in the model of the present invention. When the creep time threshold is exceeded, creep deformation no longer occurs under this compression load, which can better describe the results of the creep test of the metal material under a constant compression load. Description of the Drawings

[0012] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0013] Figure 1 It is a comparison diagram between the compression creep constitutive model of Ti-6Al-4V ELI titanium alloy involved in the method for constructing the constitutive model of the metal material under compression creep of the present invention and the test results. Detailed Embodiments

[0014] The following will clearly and completely describe the technical solutions of the present invention with reference to the drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0015] The following will further explain and illustrate the present invention in combination with specific embodiments.

[0016] A method for constructing a constitutive model of a metal material under compression creep provided in this embodiment includes the following steps: 1) Ignoring the change in the mechanical properties of the metal material during the compression creep process, a creep time threshold related to the nominal compression stress σ is introduced . When the time is exceeded, it is considered that creep deformation no longer occurs under this compression load. Further assume that the constitutive model of compression creep can be expressed as: ; Wherein, σ pc is the compression yield strength of the material, εis the creep strain, t is the creep time, is the cumulative creep strain of the material when the creep time reaches the time threshold σ under the nominal compressive stress , A , n , m and B are material parameters.

[0017] When only considering a certain nominal compressive stress, Equation (1) can be simplified as: ; where is the creep time threshold related to the nominal compressive stress.

[0018] 2) Determine the creep time threshold

[0019] The creep time threshold is determined according to the test results of creep strain - time, or estimated according to the change trend of creep strain - time.

[0020] 3) Determine the creep characteristic constants A and B of the material and the creep time influence parameters n and m If it is necessary to obtain the constitutive model under different nominal compressive stresses, that is, Equation (1), select the creep strain - time test data at no less than two stress levels, and discretize A , n , m and B within the value range of the preset parameters. For any combination of A , n , m and B , calculate the sum of the squares of the errors between the model prediction values and the test values at the selected stress levels, and screen out the combination of A , n , m and B with the minimum sum of the squares of the errors as the values of the parameters A , n , m and B . If it is only necessary to obtain the constitutive model under a certain nominal compressive stress, that is, Equation (2), discretize A , n and m within the value range of the preset parameters. For any combination of A , n and mCombine to calculate the sum of the squares of the errors between the model predictions and the experimental values at this stress level, and select the combination with the smallest sum of the squares of the errors A and n and m as the values of the parameters A and n and m .

[0021] 4) Substitute the obtained material parameters A and n and m and B into Equation (1), or substitute the material parameters A and n and m into Equation (2) to obtain the compression creep constitutive model

[0022] The following takes obtaining the compression creep constitutive model of Ti-6Al-4V ELI titanium alloy in the literature (Wang et al. Journal of Ship Mechanics, 2018, 22(4):464-474) as an example for specific illustration

[0023] Figure 1 The "○" in it represents the creep strain-time test data of Ti-6Al-4V ELI titanium alloy under different compression stresses. It can be seen that for a 0.7 σ pc compression creep stress, when the creep time is about 1000 h, the creep strain no longer increases with the increase of the creep time, that is, the creep time threshold of Ti-6Al-4V ELI titanium alloy under a 0.7 σ pc compression creep stress is 1000 h. When the compression creep stress is 0.8 σ pc , 0.85 σ pc and 0.9 σ pc , during the tested time, the creep strain still has an increasing trend with time. According to the trend of the creep strain changing with time, it is estimated that the creep time thresholds under 0.8 σ pc , 0.85 σ pc and 0.9 σ pc compression creep stresses are 2000 h, 2500 h and 5000 h respectively

[0024] Here, 0.7 σ pc and 0.9 σpc Parameter fitting for the test data under compressive creep stress A 、 n 、 m and B . The preset parameter ranges of A 、 n 、 m and B are [-0.1:0.1], [-0.9:0], [-0.1:0.1] and [1.4:1.8] respectively, and the parameters A 、 n 、 m and B are discretized with step sizes of 0.01, 0.01, 0.02 and 0.01 respectively. For any combination of A 、 n 、 m and B , calculate the sum of the squares of the errors between the predicted values and the experimental values of the model under 0.7 σ pc and 0.9 σ pc compressive creep stress, as shown in Equation (3), i.e.: ; where, in the above Equation (3), y ( σ i , t k ) represents the creep strain measured experimentally at stress σ i and time t k , f ( σ i , t k ) represents the creep strain value predicted by Equation (1) at stress σ i and time t k , M is the number of selected creep stress levels (here M = 2), N is the total number of time instants used to calculate the creep strain.

[0025] The corresponding A 、 n 、 m and BThey are 0.03, -0.57, 0.06, and 1.48 respectively. Substituting these parameters and the creep time thresholds under different compressive creep stresses into Equation (1), the compressive creep constitutive model of Ti-6Al-4V ELI titanium alloy is obtained.

[0026] Figure 1 The lines in σ pc and 0.9 σ pc are the compressive creep constitutive models of Ti-6Al-4V ELI titanium alloy obtained by fitting the creep-time test data under 0.7 σ pc and 0.85 σ pc compressive creep stresses, as well as the constitutive prediction results for the compressive creep at 0.8

[0027] It can be seen that the constitutive model proposed in the present invention can well describe the relationship between the creep strain and time of Ti-6Al-4V ELI titanium alloy under different stress levels.

[0028] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a constitutive model of metal material compression creep, characterized in that, It mainly includes the following steps: Step 1: Construct a constitutive model of the metal material under the nominal compressive stress. The specific process is as follows: Ignoring the change in the mechanical properties of metallic materials during the compression creep process, a creep time threshold related to the nominal compressive stress σ is introduced. When the creep time exceeds the threshold , it is considered that creep deformation no longer occurs under this compressive load. Further assume that the constitutive model of compression creep is expressed as: ； Among them, σ pc is the compressive yield strength of the material, ε is the creep strain, t is the creep time, is the nominal compressive stress σ under which the creep time reaches the time threshold and the cumulative creep strain of the material at this time, A , n , m and B are material parameters; When only considering a certain nominal compressive stress, the above formula (1) can be simplified as: ； Among them, is the creep time threshold related to the nominal compressive stress; Step 2: Determine the creep time threshold of the metal material; Step 3: Determine the creep characteristic constants of the material A and B and the creep time influence parameter n and m ; Step 4: Substitute the determined material parameters A , n , m and B into the constitutive model under nominal compressive stress to obtain the compressive creep constitutive model of the metallic material.

2. The method for constructing a constitutive model of compression creep of a metallic material according to claim 1, wherein: The creep time threshold in the said step 2 is determined according to the test results of creep strain-time or estimated according to the change trend of creep strain-time.

3. The method for constructing a constitutive model of compression creep of a metallic material according to claim 1, wherein: In step 3, if the constitutive model under different nominal compressive stresses, i.e., the above formula (1), is to be obtained, creep strain-time test data at no less than two stress levels are selected, and for A , n , m and B , they are discretized. For any combination of A , n , m and B , the sum of the squared errors between the model prediction values and the test values at the selected stress levels is calculated, and the combination of A , n , m and B with the minimum sum of the squared errors is selected as the values of the parameters A , n , m and B .

4. The method for constructing a constitutive model of compression creep of a metallic material according to claim 1, characterized in that: If only the constitutive model under a certain nominal compressive stress, i.e., the above formula (2), is required in step 3, within the value range of the preset parameters, A and n and m are discretized. For any combination of A and n and m , the sum of the squared errors between the model prediction value and the experimental value at this stress level is calculated, and the combination of A and n and m with the smallest sum of squared errors is selected as the values of the parameters A and n and m .

5. The method for constructing the constitutive model of metal material compression creep according to claim 3 or 4, characterized in that The formula for calculating the sum of the squares of the errors between the model prediction value and the experimental value at the calculated stress level is: ； In the above formula (3), y ( σ i , t k ) represents the creep strain measured in the test at stress σ i and time t k . f ( σ i , t k ) represents the value of the creep strain predicted by using formula (1) at stress σ i and time t k . M is the number of selected creep stress levels, N is the total number of moments used to calculate the creep strain.

6. The method for constructing the constitutive model of metal material compression creep according to claim 1, characterized in that: In step 4, the material parameters determined according to the constitutive model under different nominal compressive stresses A , n , m and B are substituted into the above formula (1), and the compressive creep constitutive model of the metallic material can be obtained.

7. The method for constructing a constitutive model of compression creep of a metal material according to claim 1, characterized in that: In step 4, the material parameters determined according to the constitutive model under a certain nominal compressive stress A , n and m are substituted into the above formula (2), and the compressive creep constitutive model of the metallic material can be obtained.

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