CN116911022A - Method for describing medium-temperature, low-stress and long-time creep curve of high-temperature alloy - Google Patents
Method for describing medium-temperature, low-stress and long-time creep curve of high-temperature alloy Download PDFInfo
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Abstract
The invention provides a medium-temperature, low-stress and long-time creep curve description method for a high-temperature alloy, and relates to the technical field of high-temperature alloys. Firstly, obtaining a plurality of creep curves of the alloy under different temperatures and stress conditions; calculating calculated values of threshold stress, minimum creep rate and initial creep strain in a fitting mode; then determining a creep time-strain experimental curve fitting equation of the alloy; calculating parameters in creep time-strain experiment curve fitting equations under different creep conditions; and substituting parameters in the creep time-strain experimental curve fitting equation under different creep conditions into the creep time-strain experimental curve fitting equation to predict creep curves under different temperatures and stresses. The method can accurately describe the complete long-time creep curve, and improves the prediction accuracy of the creep curve of the high-temperature alloy under a certain creep condition and the creep interruption time corresponding to a certain strain quantity.
Description
Technical Field
The invention relates to the technical field of high-temperature alloy, in particular to a method for describing a medium-temperature, low-stress and long-time creep curve of a high-temperature alloy.
Background
Since the thirty decades of the last century, high-temperature alloys have become a research hotspot for people due to their excellent high-temperature strength, oxidation resistance and corrosion resistance, and are widely used as candidate materials for hot-end components of aerospace engines and high-temperature corrosion-resistant components in industrial gas turbines, energy and chemical fields.
Creep refers to slow plastic deformation of a material under high temperature and constant stress, and failure of an actual engineering component is often caused by creep deformation under high temperature conditions, so that failure and fracture of a superalloy can generate a series of problems of service safety and economic loss. Superalloys require thousands to tens of thousands of hours of operation on an aeroengine, even more than 30 years of safe operation in a coal-fired power plant, creep life is one of the key parameters indispensable for material design, but it is difficult to conduct creep testing for such a long time under laboratory conditions. It is therefore necessary to describe the long-term creep curve of an alloy under existing experimental conditions and to effectively predict the creep life, while avoiding alloy failure, and at the same time maximizing the utilization of the alloy.
Description methods and life prediction models for superalloy creep curves have been proposed in large numbers since the fifties of the twentieth century. In 1963, j.c.m.li et al proposed a predictive equation for creep curves of alloy deceleration and steady state phases by counting time and strain parameters on the creep curves, which studied the creep curves based solely on stress and temperature dependence of dislocation proliferation and hardening rate, and thus described poorly the acceleration phase of creep damage generation. In 2005 lupin et al, a continuous impairment mechanical equation was proposed that is suitable for describing creep behavior under different creep conditions, and the model can be applied to complex load and temperature conditions, e.g. constant load creep, constant strain rate and stress relaxation tests, etc. But the model is established based on an alloy strain-rate curve, the strain of the alloy in the acceleration stage accounts for the main part of the alloy strain, the curve fitting is relatively fit only in the acceleration stage, and the fitting result is poor. Both the above methods are only suitable for describing partial stages of the existing creep curve, but have poor description effect on the complete creep curve, and cannot predict the creep curve under other creep conditions, so that the creep life cannot be predicted.
Evans et al in 1982 proposed using the theta projection method to describe the creep curve of an alloy and correlating the relevant parameters in the method with creep conditions to achieve predictions of creep curves and life under other creep conditions. According to the method, material softening and material hardening in the alloy creep process are comprehensively considered, and the two factors are overlapped by an exponential equation to obtain a theta projection equation. However, this method is based on ideal creep conditions and does not take into account the change in true creep stress due to the formation of creep damage during creep, and is therefore not suitable for long-life or large-strain creep deformation. The factor of creep stress change caused by section loss in a creep experiment is introduced on the basis of the theta projection method in 2016, feng Jiang and the like, so that the theta projection method is corrected, but the method is established on the basis of a creep curve with small strain, and the creep life of the alloy is very short, so that the method is not suitable for creep curve description and life prediction with large strain or long time.
In summary, the prior art does not consider describing the complete creep curve of the superalloy, and does not consider describing the creep curve with large strain and long service life, and cannot obtain the creep time corresponding to the large strain under a certain creep condition. Meanwhile, the prior art has less consideration on the creep characteristic parameters of the alloy, only describes the creep curve shape, and has larger method limitation, low accuracy and low practicability.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for describing a medium-temperature, low-stress and long-time creep curve of a high-temperature alloy for describing the creep curve of the high-temperature alloy aiming at the defects of the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme: a method for describing medium-temperature, low-stress and long-time creep curves of high-temperature alloy,
obtaining creep curves of the alloy under different temperatures and stress conditions;
calculating calculated values of threshold stress, minimum creep rate and initial creep strain in a fitting mode;
determining a creep time-strain experimental curve fitting equation of the alloy;
parameters in creep time-strain experimental curve fitting equations under different creep conditions are calculated, and are substituted into the creep time-strain experimental curve fitting equations to predict creep curves under different temperatures and stresses.
The method specifically comprises the following steps:
step 1, obtaining at least nine creep curves of the alloy under different temperatures and stress conditions by using a high-temperature creep testing machine, wherein each creep curve comprises temperature, stress, creep strain, creep time and minimum creep rate;
step 2, threshold stress sigma th According to the formula sigma th Fitting with =ft+h, where T is the creep temperature, F, H is a constant related to the alloy material, and calculating the parameter F, H in the formula to obtain the threshold stress σ th Calculating a value;
step 3, the minimum creep rateAccording to the formula->Fitting, wherein G is shear modulus, R is gasThe body constant, n is the stress index, sigma is the creep stress, Q is the creep activation energy, D is the constant related to the alloy material, the parameters D, n and Q in the formula are calculated to obtain the minimum creep rate +.>Calculating a value;
step 4, the initial creep strain epsilon i According to the formula epsilon i ＝Eσ m Fitting, wherein E, m is a constant related to the alloy material, and calculating a parameter E, m in the formula to obtain initial creep strain epsilon i Calculating a value;
step 5, the creep time-strain experimental curve of the alloy is formulated
Fitting, wherein t is creep time, epsilon is creep strain, A, B, C is a constant related to creep conditions, and obtaining parameters A, B, C in a formula to obtain a creep time-strain experimental curve fitting equation of the alloy;
step 6, fitting the constant A, B, C obtained in the step 5 according to a formula log (X) =a×σ+b, and x= A, B, C, wherein a and b are constants related to the alloy material, and obtaining parameters a and b in the formula;
step 7, calculating the parameters A, B, C under different creep conditions by using the formula log (X) =a×σ+b obtained in step 6, and introducing the parameters into the formulaThe method is used for predicting creep curves under different temperatures and stresses, and comprises the step of predicting alloy fracture time under certain creep conditions and interruption time corresponding to certain creep strain.
Preferably, the parameters F, H, E, m are obtained by regression of T, sigma and ε by least squares using mathematical analysis software i Carry over formula sigma th =ft+h and formula ε i ＝Eσ m Obtaining the product.
Preferably, the parametern, Q and D are obtained by using mathematical analysis software and performing regression according to a least square method to obtain T,R, G and the calculated sigma th Carry formula->Obtaining the product.
Preferably, the parameter A, B, C is calculated by least squares regression using mathematical analysis softwareε i Substitution of creep time-strain experiment curve into formula +.> Obtaining the product.
Preferably, the parameters a and b are obtained by using mathematical analysis software to carry A, B, C fitting values into the formula log (X) =a×σ+b by least squares regression, and x= A, B, C.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: the method for describing the medium-temperature, low-stress and long-time creep curves of the high-temperature alloy can accurately describe the complete long-time creep curve, and improves the prediction precision of the creep curve of the high-temperature alloy under a certain creep condition and the creep interruption time corresponding to a certain strain. The method is simple and reliable, the data processing process is tight, the accuracy is high, the service process and the service time of the high-temperature alloy can be effectively evaluated by using the method, the harm is reduced, the cost is reduced, and the method is suitable for different types of high-temperature alloys. Meanwhile, parameters in each variable fitting formula are derived from creep data obtained by the alloy on a conventional creep testing machine, and the reliability is high.
Drawings
FIG. 1 is a graph of creep time versus strain for GH984G alloys provided by embodiments of the invention under different creep conditions;
FIG. 2 is a graph showing a comparison of a GH984G alloy short-life experimental curve and a predicted curve provided by an embodiment of the invention and a curve made by a comparative example; FIG. 3 is a graph showing the comparison of the experimental and predicted curves of the medium life of GH984G alloy provided in the examples and the curves made in the comparative examples;
FIG. 4 is a graph comparing the experimental curve and the predicted curve of the GH984G alloy with the curves of the comparative example;
FIG. 5 is a graph of GH984G alloy creep curves under different conditions predicted according to fit equation provided by the examples.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
In the embodiment, GH984G alloy is taken as an example, and creep curves of the alloy under different conditions are predicted by adopting the medium-temperature, low-stress and long-time creep curve description method of the high-temperature alloy.
In this embodiment, a method for describing a medium-temperature, low-stress and long-time creep curve of a superalloy includes the following steps:
step 1, obtaining at least nine creep curves of the alloy under different temperatures and stress conditions by using a high-temperature creep testing machine, wherein each creep curve comprises temperature, stress, creep strain, creep time and minimum creep rate;
step 2, threshold stress sigma th According to the formula sigma th Fitting with =ft+h, where T is the creep temperature, F, H is a constant related to the alloy material, and calculating the parameter F, H in the formula to obtain the threshold stress σ th Calculating a value;
step 3, the minimum creep rateAccording to the formula->Fitting, wherein G is shear modulus, R is gas constant, n is stress index, sigma is creep stress, Q is creep activation energy, D is constant related to alloy material, parameters D, n and Q in a formula are calculated to obtain minimum creep rate +.>Calculating a value;
step 4, the initial creep strain epsilon i According to the formula epsilon i ＝Eσ m Fitting, wherein E, m is a constant related to the alloy material, and calculating a parameter E, m in the formula to obtain initial creep strain epsilon i Calculating a value;
step 5, the creep time-strain experimental curve of the alloy is formulated
Fitting, wherein t is creep time, epsilon is creep strain, A, B, C is a constant related to creep conditions, and obtaining parameters A, B, C in a formula to obtain a creep time-strain experimental curve fitting equation of the alloy;
step 6, fitting the constant A, B, C obtained in the step 5 according to a formula log (X) =a×σ+b, and x= A, B, C, wherein a and b are constants related to the alloy material, and obtaining parameters a and b in the formula;
step 7, calculating the parameters A, B, C under different creep conditions by using the formula log (X) =a×σ+b obtained in step 6, and introducing the parameters into the formulaThe method is used for predicting creep curves under different temperatures and stresses, and comprises the step of predicting alloy fracture time under certain creep conditions and interruption time corresponding to certain creep strain.
Wherein the parameters F, H, E, m are obtained by regression of T, sigma and ε by least squares using mathematical analysis software i Carry over formula sigma th =ft+h and formula ε i ＝Eσ m Obtaining the product.
Parameters n, Q and D are subjected to regression by using mathematical analysis software according to a least square method, and T,R, G and the calculated sigma th Carry formula->Obtaining the product.
The parameters A, B, C are calculated by the least square regression by using mathematical analysis softwareε i Creep time-strain experimental curve brought into the formula +.>Obtaining the product.
Parameters a, b were calculated by using mathematical analysis software and by least squares regression to bring the A, B, C fit into the formula log (X) =a σ+b, x= A, B, C.
In this embodiment, firstly, a GH984G alloy is taken as a research object, and a high-temperature creep testing machine is utilized to obtain creep curves of the alloy under nine different temperature and stress conditions. In this example, the experimental curves of the alloy under the conditions of 700 ℃/350MPa, 700 ℃/250MPa and 750 ℃/300MPa are shown in FIG. 1.
By using different temperaturesThe intersection point of the curve and the abscissa obtains the threshold stress sigma of the GH984G alloy th Using the formula sigma th Let ft+h give σ th After the relation with T, the relation is brought into the formula +.>The stress index n, the creep activation energy Q and the material parameter D of the alloy are obtained by inputting sigma, T, G and R. Using the formula epsilon i ＝Eσ m By passing throughInputting epsilon i And σ may result in parameter E. After all unknown parameters in the above relation are confirmed, the corresponding sigma is obtained by inputting the corresponding creep condition th 、/>Epsilon i And calculating a value. Sigma (sigma) th 、/>Epsilon i The experimental and calculated values of (2) are shown in Table 1. The specific fitting process is implemented by a linear fitting tool of Origin software.
TABLE 1 sigma th 、ε i Determination of calculated values
The epsilon obtained by calculation is calculated i 、Carry formula->And fitting each creep curve using the formula. The specific operation is that a non-linear fitting tool of Origin software is used, a formula is written into and a proper A, B, C initial value is selected, a curve is fitted, and a creep curve fitted by the formula and a curve and experiment curve pair made by a comparative example are shown in fig. 2, 3 and 4. It can be seen from the graph that the formula accurately describes the creep curve, whether it is short-lived (fig. 2), medium-lived (fig. 3) or long-lived (fig. 4). Existing projectionThe method and the modified theta projection method cannot describe long-term creep curves (fig. 3, 4), whereas the j.c.m.li and v.lupin equations describe curves that are unstable and less accurate. Compared with the different methods, the creep curve accuracy made by the formula provided by the invention is greatly improved, and the long-time creep curve can be accurately described. The coefficients a, b were obtained by fitting parameters A, B, C under different creep conditions and the formula log (X) =a×σ+b (x= A, B, C), and the fitting values and calculated values of the parameters are shown in table 2. The specific fitting process is implemented by a linear fitting tool of Origin software.
TABLE 2 fitting and calculated values for parameters A, B, C
By using the method and the result, sigma under different temperature and stress conditions is calculated th 、ε i 、A. B, C, a corresponding fitting equation can be obtained, so as to achieve the purpose of predicting creep curves under different conditions, as shown in fig. 5.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (6)
1. A method for describing medium-temperature, low-stress and long-time creep curves of a high-temperature alloy is characterized by comprising the following steps of:
obtaining creep curves of the alloy under different temperatures and stress conditions;
calculating calculated values of threshold stress, minimum creep rate and initial creep strain in a fitting mode;
determining a creep time-strain experimental curve fitting equation of the alloy;
parameters in creep time-strain experimental curve fitting equations under different creep conditions are calculated, and are substituted into the creep time-strain experimental curve fitting equations to predict creep curves under different temperatures and stresses.
2. The method for describing the medium-temperature, low-stress and long-time creep curve of the superalloy according to claim 1, wherein the method comprises the following steps: the method comprises the following steps:
step 1, obtaining at least nine creep curves of an alloy under different temperatures and stress conditions, wherein each creep curve comprises temperature, stress, creep strain, creep time and minimum creep rate;
step 2, threshold stress sigma th According to the formula sigma th Fitting with =ft+h, where T is the creep temperature, F, H is a constant related to the alloy material, and calculating the parameter F, H in the formula to obtain the threshold stress σ th Calculating a value;
step 3, the minimum creep rateAccording to the formula->Fitting, wherein G is shear modulus, R is gas constant, n is stress index, sigma is creep stress, Q is creep activation energy, D is constant related to alloy material, parameters D, n and Q in a formula are calculated to obtain minimum creep rate +.>Calculating a value;
step 4, the initial creep strain epsilon i According to the formula epsilon i ＝Eσ m Fitting, wherein E, m is a constant related to the alloy material, to obtain parameters in the formulaNumber E, m, initial creep strain ε i Calculating a value;
step 5, the creep time-strain experimental curve of the alloy is formulatedFitting, wherein t is creep time, epsilon is creep strain, A, B, C is a constant related to creep conditions, and obtaining parameters A, B, C in a formula to obtain a creep time-strain experimental curve fitting equation of the alloy;
step 6, fitting the constant A, B, C obtained in the step 5 according to a formula log (X) =a×σ+b, and x= A, B, C, wherein a and b are constants related to the alloy material, and obtaining parameters a and b in the formula;
step 7, calculating the parameters A, B, C under different creep conditions by using the formula log (X) =a×σ+b obtained in step 6, and introducing the parameters into the formulaThe method is used for predicting creep curves under different temperatures and stresses, and comprises the step of predicting alloy fracture time under certain creep conditions and interruption time corresponding to certain creep strain.
3. The method for describing the medium-temperature, low-stress and long-time creep curve of the superalloy according to claim 2, wherein the method comprises the following steps: the parameters F, H, E, m are obtained by regression of T, sigma and epsilon by least squares using mathematical analysis software i Carry over formula sigma th =ft+h and formula ε i ＝Eσ m Obtaining the product.
4. The method for describing the medium-temperature, low-stress and long-time creep curve of the superalloy according to claim 2, wherein the method comprises the following steps: the parameters n, Q and D are obtained by using mathematical analysis software to carry out regression according to a least square method, and T is,R, G and calculatedSigma of arrival of th Carry formula->Obtaining the product.
5. The method for describing the medium-temperature, low-stress and long-time creep curve of the superalloy according to claim 2, wherein the method comprises the following steps: the parameter A, B, C is calculated by using mathematical analysis software according to least square regressionε i Creep time-strain experimental curve brought into the formula +.> Obtaining the product.
6. The method for describing the medium-temperature, low-stress and long-time creep curve of the superalloy according to claim 2, wherein the method comprises the following steps: the parameters a and b are obtained by using mathematical analysis software and carrying out regression according to a least square method to obtain a A, B, C fitting value into a formula log (X) =a sigma+b, wherein X= A, B, C.
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