A statistical analysis method for creep deformation

Abstract

The application discloses a creep deformation statistical analysis method, and specific steps are as follows: step 001, obtaining creep deformation and time relationship of not less than three same size samples of same batch material or same batch parts under the same condition; step 002, selecting some typical time and corresponding creep strain, selecting a suitable statistical distribution function to statistically analyze the creep strain under the typical time, and fitting the distribution parameters; step 003, calculating the survival rate of the tested sample or part not more than a certain creep strain or the creep strain of the tested sample or part under a certain survival rate under the selected statistical distribution function, and drawing a P-C-T curve; through the method, the creep deformation of the material or the part can be statistically analyzed, and then the survival rate of the material or the part not more than a certain creep strain under a given condition can be calculated, which has important significance for accurately evaluating the creep performance of the material or the part.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material analysis, and particularly relates to a creep deformation statistical analysis method. BACKGROUND

[0002] Many materials (such as metals, rocks, etc.) exhibit creep properties under certain conditions. Accurate evaluation of the creep properties of materials is crucial for the safety and reliable service of engineering structures.

[0003] However, due to the differences between individual samples or parts, even samples of the same size from the same batch of materials exhibit significant differences in creep deformation under the same conditions (such as stress, temperature, and time).

[0004] Therefore, there is an urgent need to establish a creep deformation analysis method that takes into account the individual differences of samples. SUMMARY

[0005] The present application aims to provide a creep deformation statistical analysis method that takes into account the creep deformation under the condition of individual differences of samples to solve the technical problems existing in the prior art.

[0006] To solve the above technical problems, the present application specifically provides the following technical solutions:

[0007] A creep deformation statistical analysis method, comprising the following steps:

[0008] Step 001: performing creep experiments on multiple samples under the same experimental conditions, wherein the materials of the multiple samples are the same batch of materials, and the sizes of the multiple samples are consistent; recording the creep strain values of the multiple samples at typical times respectively, and making a creep strain value-time change curve graph;

[0009] Step 002: selecting a suitable distribution function, fitting the creep strain values using the selected distribution function, and obtaining distribution parameters;

[0010] Step 003: using the selected distribution function, calculating the survival rate of samples not exceeding a certain creep strain value at a typical time, or the creep strain value of samples at a certain survival rate, and drawing a P-C-T curve;

[0011] Step 004: if the time point of the creep strain required for the sample is not within the range of the typical time, obtaining the creep strain value of the sample at that time point from the creep strain value-time change curve graph made in step 001, or obtaining the creep strain value of the sample at that time point according to step 001; repeating steps 002 and 003 to obtain the survival rate of samples not exceeding a certain creep strain value at a specific time, or the creep strain value of samples at a certain survival rate.

[0012] Further, in the step 001, the experimental conditions include creep temperature, creep stress, and creep time.

[0013] Further, in the step 002, based on the cumulative probability, the calculation is performed according to formula (1):

[0014]

[0015] Wherein, n is the total number of samples, P i is the estimated probability less than or equal to the i-th number of samples, each data is numbered from small to large, that is, x1≤x2≤x3≤x4≤x n ;

[0016] Then draw the data points (x1, P1), (x2, P2),..., (x n , P n ), if the creep strain values at these typical times correspond to the data points approximately forming a straight line, it is indicated that the distribution function can better describe the creep strain statistical distribution characteristics of the samples.

[0017] Further, in the step 002, the mean μ and the standard deviation σ of the normal distribution function are calculated according to formula (2) and (3):

[0018]

[0019]

[0020] Wherein, n is the total number of test samples, x i is the creep strain data of sample i at a certain typical time.

[0021] Compared with the prior art, the present application has the following beneficial effects:

[0022] The creep deformation statistical analysis method provided by the present application proposes the P-C-T (Probabilistic-Creep strain-Time) curve concept considering the creep deformation dispersion of samples or parts, and then provides a creep deformation statistical analysis method based on the same. Through the method, the creep deformation of materials or parts can be statistically analyzed, and the occurrence probability (survival rate) of the materials or parts not exceeding a certain creep strain value under given conditions can be calculated, which is of great significance for accurately evaluating the creep performance of materials or parts. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those skilled in the art, other drawings can also be obtained from the provided drawings without creative labor.

[0024] Figure 1 Schematic diagram of shape and size of Ti-6Al-4V alloy compression creep sample

[0025] Figure 2 Graph of creep strain value of Ti-6Al-4V alloy sample under compression stress of 912 MPa versus time

[0026] Figure 3 Schematic diagram of normal distribution fitting result of creep strain of Ti-6Al-4V alloy sample under different creep times

[0027] Figure 4 Schematic diagram of creep test result and P-C-T curve of Ti-6Al-4V alloy sample under compression stress of 912 MPa. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0029] The following will take the compression creep deformation of Ti-6Al-4V alloy sample at room temperature as an example for specific description. Figure 1

[0030] Step 001, using MTS Landmark testing machine to perform compression creep experiment on Ti-6Al-4V alloy sample shown in Figure 1 at room temperature for 50h, and the stress level is compression yield strength 912 MPa.

[0031] A total of 3 parallel experiments are performed, and all the experiments are completed on the same machine; some typical times and their corresponding creep strains are selected.

[0032] In this embodiment, the typical times are 10h, 20h, 30h, 40h, 50h, and the obtained graph of creep strain value of Ti-6Al-4V alloy sample versus time is as shown in Figure 2 ​It can be seen that the creep strain of the Ti-6Al-4V alloy sample presents a certain dispersion.

[0033] In step 002, a suitable distribution function is selected, and the creep strain values are fitted by using the selected distribution function, and distribution parameters are obtained.

[0034] In this embodiment, the distribution function is selected based on the cumulative probability, and the cumulative probability is calculated according to formula (1):

[0035]

[0036] Wherein, n is the total number of samples, P i is the estimated probability less than or equal to the ith number, and each data is numbered from small to large, that is, x1≤x2≤x3≤x4≤x n ;

[0037] Then draw the data points (x1, P1), (x2, P2),..., (x n , P n ), if the creep strain values at these typical times correspond to the data points that are approximately straight lines, it indicates that the distribution function can well describe the statistical distribution characteristics of the creep strain of the samples.

[0038] In this embodiment, the cumulative probability of the creep strain values of the Ti-6Al-4V alloy sample at 10h, 20h and 40h is calculated, as shown in Figure 3 It can be seen that the creep strain of the three Ti-6Al-4V alloy samples at different times well obeys the normal distribution, and the determination coefficient R 2 all exceed 0.98.

[0039] Therefore, in this embodiment, the normal distribution is used to statistically analyze the creep strain of the Ti-6Al-4V alloy sample at different times.

[0040] The normal distribution is used to fit the creep strain of different samples at different creep times in Figure 2 , and the normal distribution parameters are obtained; wherein, the mean μ and the standard deviation σ of the normal distribution function are calculated according to formula (2) and (3):

[0041]

[0042] Wherein, n is the total number of test samples, x i is the creep strain data of sample i at a certain typical time.

[0043] Step 003, according to the normal distribution function to calculate the Ti-6Al-4V alloy sample at different survival rate (such as 50%, 90%, 95% and 99%) under the creep strain, the same survival rate of different time creep strain is connected, the P-C-T curve of the Ti-6Al-4V alloy sample is obtained, as shown in Figure 4

[0044] Step 004, taking the survival rate of the Ti-6Al-4V alloy sample at 50h under room temperature compression creep strain not more than 2.5% as an example.

[0045] First, according to step 001, using MTS Landmark testing machine to carry out 50h compression creep experiment on Ti-6Al-4V alloy sample at room temperature, as shown in Figure 1 , the compression creep strain value of different Ti-6Al-4V alloy samples at 50h is obtained; or directly obtain the compression creep strain value of different Ti-6Al-4V alloy samples at 50h. Figure 2

[0046] Then according to step 002, the parameters of the normal distribution function are fitted according to the creep strain values of a plurality of different Ti-6Al-4V alloy samples; and according to step 003, the survival rate of the Ti-6Al-4V alloy sample at room temperature compression creep strain not more than 2.5% is calculated by the normal distribution function to be 92%.

[0047] Similarly, the compression creep strain value of the Ti-6Al-4V alloy sample at a given survival rate is calculated by the normal distribution function.

[0048] In this application, P-C-T of P-C-T curve refers to three elements of probability (Probabilistic), creep strain (Creep strain) and time (Time), wherein the probability refers to the occurrence probability (survival rate) of not more than a certain creep strain value.

[0049] The P-C-T curve can be used to evaluate and study the creep performance of materials or parts.

[0050] Consider the uncertainty factor: the curve can consider the influence of some uncertainty factors in the creep process of materials or parts, such as the non-uniformity of the microstructure of materials or parts, and more truly reflect the creep performance of materials or parts than the traditional deterministic creep strain-time curve.

[0051] Determine the material property parameters: through the probability analysis and curve fitting of a large amount of test data, the creep characteristic parameters of the material can be more accurately determined, and more reliable basis is provided for the creep constitutive model establishment and performance evaluation of the material.

[0052] ​​The P-C-T curve can also be used to predict the reliability and life of the structure.

[0053] In engineering applications, it is important to know the creep strain of a material after long-term use to assess the reliability and life of the structure. The creep life of a component, i.e. the time during which the creep strain of the component does not exceed a certain critical value, can be more accurately predicted by the P-C-T curve, so that a reasonable maintenance and replacement plan can be made to provide safety for engineering.

[0054] The above examples are only exemplary embodiments of the present application and are not intended to limit the present application, and the protection scope of the present application is defined by the claims. Those skilled in the art can make various modifications or equivalent replacements to the present application within the spirit and protection scope of the present application, and such modifications or equivalent replacements shall also be considered to fall within the protection scope of the present application.

Claims

1. A method of statistical analysis of creep deformation, characterized in that, The method comprises the following steps: Step 001, performing a creep experiment on a plurality of samples under the same experimental conditions, wherein the materials of the plurality of samples are the same batch of materials, and the sizes of the plurality of samples are consistent; and recording the creep strain values of the plurality of samples at typical times respectively, and making a creep strain value-time curve graph; Step 002, selecting a normal distribution function to fit the creep strain values and obtaining the mean value of the normal distribution function μ and the standard deviation σ ; Step 003, using a normal distribution function to calculate the survival rate of the sample under a certain creep strain value at a typical time, or the creep strain value of the sample under a certain survival rate, and drawing a P-C-T curve; Step 004, if a time point of a required creep strain of the sample is not within the range of the typical time, obtaining the creep strain value of the sample at the time point from the creep strain value-time curve graph made in step 001, or obtaining the creep strain value of the sample at the time point according to step 001; and repeating steps 002 and 003 to obtain the survival rate of the sample under a certain creep strain value at a specific time, or the creep strain value of the sample under a certain survival rate.

2. The creep deformation statistical analysis method according to claim 1, characterized in that, In the step 001, the experimental conditions include a creep temperature, a creep stress and a creep time.

3. The creep deformation statistical analysis method according to claim 1, characterized by, In the step 002, the calculation is performed according to formula (1) based on a cumulative probability: ； wherein, n is the total number of samples, P i is the estimated probability of being less than or equal to the i order, each data is numbered from small to large, that is x 1≤ x 2≤ x 3≤ x 4≤ x n ; Then draw the data points on the probability coordinate paper of the normal distribution function to be used x 1, P 1), ( x 2, P 2),..., ( x n , P n ) If the data points corresponding to the creep strain values at these typical times are approximately in a straight line, it indicates that the normal distribution function can better describe the creep strain statistical distribution characteristics of the samples.

4. The creep deformation statistical analysis method according to claim 1, characterized by, In the step 002, the mean value of the normal distribution function μ and standard deviation σ Calculated according to equations (2) and (3): ； ； wherein, n is the total number of test specimens, x i is the creep strain data for a test specimen at a certain typical time. i is the creep strain data for a test specimen at a certain typical time.

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