CN113008677B - Creep endurance prediction method of nickel-based superalloy - Google Patents

Creep endurance prediction method of nickel-based superalloy Download PDF

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CN113008677B
CN113008677B CN202110229187.2A CN202110229187A CN113008677B CN 113008677 B CN113008677 B CN 113008677B CN 202110229187 A CN202110229187 A CN 202110229187A CN 113008677 B CN113008677 B CN 113008677B
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黄佳
贺斟酌
孙燕涛
杨晓光
石多奇
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Abstract

The invention provides a prediction method of creep endurance of a nickel-based superalloy, which is characterized in that a crystal orientation function is defined by introducing a tensile limit, a corresponding minimum creep strain rate in a correction state is provided, the anisotropic characteristic of the minimum creep strain rate is successfully verified through mathematical transformation and minimum creep strain rate data, and the direction factor description defined by tensile strength can be better passed; finally, two permanent life prediction equations of anisotropic correction are derived based on the derivation ideas of the Larson-Miller method and the Wilshire equation. The prediction method provided by the invention can be used for better predicting the creep endurance property of the nickel-based superalloy.

Description

Creep endurance prediction method of nickel-based superalloy
Technical Field
The invention belongs to the technical field of service life prediction, and particularly relates to a creep endurance prediction method of a nickel-based superalloy.
Background
Nickel-based superalloys are used as high temperature structural materials due to their excellent properties of strength, hardness, toughness, corrosion resistance, and high temperature resistance. Under wider temperature and load conditions, the nickel-based superalloy needs to have enough endurance performance reserve and can fully exert the potential of the material, and meanwhile, the pure dependence on experimental performance tests brings ultra-long test period and cost, so that a prediction technology with simple application and clear and steady physical basis for creep endurance performance is needed. The Larson-Miller parameter method is based on the Arrhenius equation and extrapolation parameters derived therefrom and has long been widely used. On the basis of long-term research, Wilshire et al at Swansea university in UK proposes an exponential-form endurance life model which considers temperature influence and utilizes tensile strength to perform stress normalization treatment on the basis of a Monkman-Grant relational expression, and the model can reflect the endurance performance rule of a wide stress range. However, neither of these two types of classical prediction methods can uniformly predict crystal orientation-related creep-endurance performance.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting creep rupture property of a nickel-based superalloy, and the method provided by the present invention can uniformly predict creep rupture property related to crystal orientation of the nickel-based superalloy.
The invention provides a method for predicting creep endurance of a nickel-based superalloy, which comprises the following steps:
the anisotropy characteristic of the minimum creep strain rate is described according to a direction factor defined by tensile strength;
introducing the anisotropic characteristic of the minimum creep strain rate into a Larson-Miller method or a Wilshire equation to obtain a prediction equation of the creep endurance performance of the nickel-based superalloy;
and predicting the creep endurance performance of the nickel-based superalloy according to the prediction equation.
Preferably, the method for characterizing the anisotropy of minimum creep strain rate in terms of a directional factor defined by tensile strength comprises:
defining a crystal orientation function to obtain an expression of the minimum creep strain rate with the tensile limit of the crystal orientation function;
the anisotropic character of the minimum creep strain rate described by the orientation factor defined by the tensile strength is obtained by mathematical transformation from an expression of the minimum creep strain rate with the tensile limit of the crystallographic orientation function.
Preferably, the expression of the minimum creep strain rate includes formula (1) and formula (2):
Figure BDA0002958269570000021
Figure BDA0002958269570000022
in the formula (1), f (A)hkl) As a function of crystal orientation, σTS,[001]A stretch limit in a reference direction; sigmaTS,[hkl]Is [ hkl]The stretch limit of the direction;
in the formula (2), the reaction mixture is,
Figure BDA0002958269570000023
for minimum creep strain rate, C is a material parameter dependent on temperature and stress, f (A)hkl) As a function of crystallographic orientation, σ is stress, n is a stress and temperature dependent material parameter, QcThe creep activation energy in the reference direction is R is constant and T is temperature.
Preferably, the method of mathematical transformation comprises:
taking logarithm on two sides of the equal sign of the formula (2), converting the exponential relation into a linear relation, and obtaining the anisotropy characteristic of the minimum creep strain rate described by the direction factor defined by the tensile strength, wherein the anisotropy characteristic is shown in a formula (3):
Figure BDA0002958269570000024
in the formula (3), the reaction mixture is,
Figure BDA0002958269570000025
for minimum creep strain rate, n is a stress and temperature dependent material parameter, σ is stress, f (A)hkl) As a function of crystal orientation, QcFor creep activation energy in the reference direction, R is a constant, T is temperature, and C is a material parameter dependent on temperature and stress.
Preferably, the anisotropy characteristic of the minimum creep strain rate is introduced into the Wilshire equation to obtain formula (4):
Figure BDA0002958269570000026
in the formula (4), σ is stress, σTSAs tensile strength under corresponding temperature conditions, k1And u is the material parameter, f (A)hkl) As a function of crystal orientation, tfIn order to last the life of the fracture,
Figure BDA0002958269570000027
in a modified form of creep activation energy, R is a constant and T is temperature.
Preferably, in the Larson-Miller method: the activation energy of the minimum creep strain rate conforms to the Arrhenius equation, the endurance life and the minimum creep rate conform to the Monkman-Grant relationship, and the following formulas (5) and (6) are shown:
Figure BDA0002958269570000031
Figure BDA0002958269570000032
in the formula (5), the reaction mixture is,
Figure BDA0002958269570000033
for minimum creep strain rate, A1For the kinetic parameters, f (σ) is a function of stress, and T is temperature;
in the formula (6), the reaction mixture is,
Figure BDA0002958269570000034
for minimum creep strain rate, A2To destroy the strain parameter, tfFor a long life at break.
Preferably, the method further comprises the following steps:
the minimum creep rate is eliminated by the equations (5) and (6), and the minimum strain rate is expressed as an exponential relation of a stress function and a temperature function, as shown in the equation (7):
Figure BDA0002958269570000035
in the formula (7), f (sigma) is a function of stress, T is temperature, A1As a kinetic parameter, A2To destroy the strain parameter, tfFor a long life at break.
Preferably, the method further comprises the following steps:
in the formula (7): let CL-M＝lg(A1/A2)，PL-M(vi)/2.303, to give formula (8):
PL-M＝T(CL-M+lgtf) (8)
in the formula (8), CL-MAs a kinetic parameter A1And failure strain parameter A2Exponential function of, CL-MRegarded as a constant;
PL-Mas a function of stress.
Preferably, the method further comprises the following steps:
expression (8) is expressed as an expression in engineering applications, as shown in formulas (9) and (10):
PL-M＝T(20+lgtf)/1000 (9)
lgσ＝a0+a1P+a2P2+a3P3 (10)
in formula (9), PL-MIs a function of stress, T is temperature, TfFor a long life at break;
in the formula (10), σ is stress, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method.
Preferably, the method further comprises the following steps:
introducing a tensile strength dependent directional correction factor to said equation (10)
Figure BDA0002958269570000041
To give formulae (11) and (12):
PL-M＝T(20+lgtf)/1000 (11)
lg(σf(Ahkl))＝a0+a1P+a2P2+a3P3 (12)
in the formula (11), PL-MAs a function of stress, T is temperature, TfFor a long life at break;
in formula (12), σ is stress, f (A)hkl) As a function of crystal orientation, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method.
The invention provides a method for predicting creep endurance performance related to orientation of nickel-based superalloy, which finds that the characteristic relation of the temperature and anisotropy of the nickel-based superalloy is quite consistent with the anisotropy correlation of a stretching limit by data analysis, thus defining a crystal orientation function related to the stretching limit and providing a minimum creep strain rate expression modified by the stretching limit; through mathematical transformation and minimum creep strain rate data, the anisotropic characteristic of the minimum creep strain rate is successfully verified and can be better described through a direction factor defined by tensile strength; subsequently, two kinds of anisotropy-corrected persistent life prediction equations were derived based on the derivation ideas of the Larson-Miller method and the Wilshire equation. The prediction method provided by the invention can uniformly predict the creep endurance quality related to the crystal orientation of the nickel-based superalloy and has a good prediction effect.
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FIG. 1 is a flow chart of a method for predicting the orientation-dependent creep rupture property of a nickel-base superalloy provided in an embodiment of the present invention;
FIG. 2 is an anisotropy plot of the permanence properties of a DZ125 alloy and a GTD-111 alloy in accordance with an embodiment of the present invention;
FIG. 3 is a graph of the tensile limit and elastic modulus of a DZ125 alloy as a function of temperature for an example of the present invention;
FIG. 4 is a graph of tensile strength and elastic modulus of a GTD-111 directionally solidified superalloy as a function of temperature for an embodiment of the present invention;
FIG. 5 is a diagram illustrating the adaptive evaluation of crystal orientation factors according to an embodiment of the present invention;
FIG. 6 is a diagram illustrating the prediction of the anisotropy Wilshire method based on the orientation factor in an embodiment of the present invention;
FIG. 7 is a prediction chart of the anisotropy Larson-Miller method based on the crystal orientation factor in the example of the present invention (in (a), a)1＝-4.004，a2＝0.862，a3＝-0.032，a4＝0.00033，R20.996; (b) in (a)1＝-18.049，a2＝2.70，a3＝-0.112，a4＝0.001485，R2＝0.980)；
FIG. 8 is a two-fold life dispersion band diagram of the DZ125 alloy in the example using the modified Wilshire method;
FIG. 9 is a two-fold life dispersion band diagram of the GTD-111 alloy of the example using the modified Larson-Miller method.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other examples, which may be modified or appreciated by those of ordinary skill in the art based on the examples given herein, are intended to be within the scope of the present invention. It should be understood that the embodiments of the present invention are only for illustrating the technical effects of the present invention, and are not intended to limit the scope of the present invention. In the examples, the methods used were all conventional methods unless otherwise specified.
The invention provides a method for predicting creep endurance quality related to orientation of a nickel-based superalloy, which comprises the following steps: experiments show that the characteristic relation of the temperature and the anisotropy of the nickel-based superalloy is quite consistent with the anisotropy correlation of the tensile limit, so that a related crystal orientation function is defined, a minimum creep strain rate expression modified by the tensile limit is provided, and the anisotropy characteristic of the minimum creep strain rate can be successfully verified to be better described by a direction factor defined by the tensile strength through mathematical transformation and minimum creep strain rate data; based on the derivation thought of the Larson-Miller method and the Wilshire equation, two permanent life prediction equations with anisotropy correction are derived.
The present invention is not particularly limited in terms of the composition of the nickel-base superalloy, and any nickel-base superalloy known to those skilled in the art may be used, such as the DZ125 alloy or the GTD-111 alloy.
In the present invention, the method for predicting the orientation-dependent creep rupture property of a nickel-base superalloy preferably comprises:
through analyzing the lasting fracture life of the nickel-based high-temperature alloy (such as DZ125 alloy) in different directions and at different temperatures, the anisotropic characteristic of the alloy is obvious at lower temperature and is not obvious at higher temperature; this is consistent with the temperature dependence of the anisotropy of the stretching limit.
Accordingly, a crystal orientation function is defined, and a minimum creep strain rate expression of tensile limit correction is provided, which is expressed by the following formula (1) and formula (2):
Figure BDA0002958269570000061
Figure BDA0002958269570000062
in the formula (1), f (A)hkl) As a function of crystal orientation, σTS,[001]A stretch limit in a reference direction; sigmaTS,[hkl]Is [ hkl]The stretch limit of the direction;
in the formula (2), the reaction mixture is,
Figure BDA0002958269570000063
for minimum creep strain rate, C is a material parameter dependent on temperature and stress, f (A)hkl) As a function of crystallographic orientation, σ is stress, n is a stress and temperature dependent material parameter, QcThe creep activation energy in the reference direction is R is constant and T is temperature.
By taking logarithm of both sides of formula (2), can be used
Figure BDA0002958269570000067
Is ordinate, ln [ f (A)hkl)σ]The complex exponential relation of the original formula (2) is converted into a linear relation as an abscissa so as to ensure that the minimum creep strainThe anisotropy of the ratio can be better characterized by the orientation factor defined by the tensile strength, and the mathematical transformation (logarithm) of equation (2) is shown in equation (3):
Figure BDA0002958269570000064
in the formula (3), the reaction mixture is,
Figure BDA0002958269570000065
for minimum creep strain rate, n is a stress and temperature dependent material parameter, σ is stress, f (A)hkl) As a function of crystal orientation, QcFor creep activation energy in the reference direction, R is a constant, T is temperature, and C is a material parameter dependent on temperature and stress.
Similar to the derivation idea of the willire equation, the modified form of the willire equation is derived from equation (3) as shown in equation (4):
Figure BDA0002958269570000066
in the formula (4), σ is stress, σTSAs tensile strength under corresponding temperature conditions, k1And u is the material parameter, f (A)hkl) As a function of crystal orientation, tfIn order to last the life of the fracture,
Figure BDA0002958269570000068
in a modified form of creep activation energy, R is a constant and T is temperature.
Mathematically transforming equation (4) to yield equation (a):
ln(-ln(σ/σTS))＝ln(k1)+uln[f(Ahkl)tfexp(-Qc */RT)]formula (A);
in the formula (A), ln (-ln (sigma/sigma TS)) is used as a vertical coordinate; ln [ f (A)hkl)tfexp(-Qc */RT)]As an abscissa, the energy can be calculated from data known in the art (e.g., property data published publicly or obtained by experimental testing for certain nickel-base superalloys)A series of ordinate data and abscissa data can be obtained, scatter diagrams are drawn according to the data, then a linear equation is fitted to the formula (A) according to the scatter diagrams to obtain a fitted straight line, and the abscissa and ordinate values of any point on the straight line can be obtained according to the fitted straight line, so that the creep endurance performance of the nickel-based superalloy under different conditions can be predicted.
In the present invention, the Larson-Miller method preferably sets the activation energy for minimum creep strain rate to conform to the Arrhenius equation, and the endurance life and minimum creep rate to conform to the classical Monkman-Grant relationship, as shown in equations (5) and (6):
Figure BDA0002958269570000071
Figure BDA0002958269570000072
in the formula (5), the reaction mixture is,
Figure BDA0002958269570000073
for minimum creep strain rate, A1For the kinetic parameters, f (σ) is a function of stress, and T is temperature;
in the formula (6), the reaction mixture is,
Figure BDA0002958269570000074
for minimum creep strain rate, A2To destroy the strain parameter, tfFor a long life at break.
In the present invention, equation (5) and equation (6) eliminate the minimum creep rate, which can be expressed as an exponential relationship between the stress function and the temperature, as shown in equation (7):
Figure BDA0002958269570000075
in the formula (7), f (sigma) is a function of stress, T is temperature, A1As a kinetic parameter, A2To destroy the strain parameter, tfFor a long life at break.
Setting constant CL-M＝lg(A1/A2)，PL-MIf f (σ)/2.303, equation (7) is transformed into:
PL-M＝T(CL-M+lgtf) (8)
in the formula (8), the parameter CL-MAs a kinetic parameter A1And failure strain parameter A2When studying a certain class of materials, CL-MThe parameter can be considered as a constant, CL-MPreferably 18 to 22, and more preferably 20; pL-MAs a function of stress.
In the present invention, the general expression of formula (8) in specific engineering applications is given accordingly, as shown in formulas (9) and (10):
PL-M＝T(20+lgtf)/1000 (9)
lgσ＝a0+a1P+a2P2+a3P3 (10)
in the formula (9), PL-MAs a function of stress, T is temperature, TfFor a long life at break;
in the formula (10), σ is stress, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method.
In the present invention, a tensile strength dependent directional correction factor is introduced into equation (10)
Figure BDA0002958269570000081
Further modifications of the Larson-Miller method are available as shown in equations (11) and (12):
PL-M＝T(20+lgtf)/1000 (11)
lg(σf(Ahkl))＝a0+a1P+a2P2+a3P3 (12)
in the formula (11), PL-MAs a function of stress, T is temperature, TfFor a long life at break;
in formula (12), σ is stress, f (A)hkl) As a function of crystal orientation, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method.
T and T in formula (11) can be obtained from data known in the art (e.g., published or experimentally tested performance data for certain nickel-base superalloys)fData, and further P in the formula (11)L-MData; p in formula (11)L-MData is substituted into formula (12) as P data, and σ and f (A) in formula (12)hkl) Fitting the formula (12) to obtain a third-order polynomial curve for known data in the prior art, and obtaining a horizontal and vertical coordinate value of any point on the curve according to the obtained third-order polynomial curve, so that the creep endurance property of the nickel-based superalloy under different conditions can be predicted.
The invention provides a method for predicting creep endurance performance related to orientation of nickel-based superalloy, which finds that the characteristic relation of the temperature and anisotropy of the nickel-based superalloy is quite consistent with the anisotropy correlation of a stretching limit by data analysis, thus defining a crystal orientation function related to the stretching limit and providing a minimum creep strain rate expression modified by the stretching limit; through mathematical transformation and minimum creep strain rate data, the anisotropic characteristic of the minimum creep strain rate is successfully verified to be described better through a direction factor defined by tensile strength; subsequently, two kinds of anisotropy-corrected persistent life prediction equations were derived based on the derivation ideas of the Larson-Miller method and the Wilshire equation. The prediction method provided by the invention can uniformly predict the creep endurance quality related to the crystal orientation of the nickel-based superalloy and has a good prediction effect.
Examples
By analyzing the endurance performance of the DZ125 alloy and the GTD-111 alloy in different directions and at different temperatures, as shown in FIG. 2, it is found that the anisotropy characteristic is obvious at a lower temperature and is not obvious at a higher temperature, which is consistent with the temperature dependence of the anisotropy of the stretching limit, as shown in FIGS. 3 and 4; then, a crystal orientation function is defined, and a minimum creep strain rate expression of tensile limit correction is proposed, which is expressed by the following formula (1) and formula (2):
Figure BDA0002958269570000091
Figure BDA0002958269570000092
in the formulae (1) and (2), the function f (A)hkl) Is a function of the crystal orientation, the parameter C is a temperature and stress dependent material parameter, QcIs a reference direction ([001 ]]Direction) of the creep activation energy, σTS,[hkl]Is [ hkl]Tensile limit of direction, σTS,[001]The stretch limit in the reference direction.
The evaluation was made with reference to publicly published data for two oriented crystal materials, DS GTD-111 alloy and DZ125 alloy.
To verify the accuracy of this amendment, the evaluation was made with reference to the published data for two oriented crystalline materials, DS GTD-111 alloy and DZ17G alloy.
Taking logarithm of two sides of the formula (2) respectively, can use
Figure BDA0002958269570000095
Is ordinate, ln [ f (A)hkl)σ]In the abscissa, this converts the original complex exponential relationship into a linear relationship, as shown in fig. 5 in particular, whereby the anisotropic character of the minimum creep strain rate can be better described by the directional factor defined by the tensile strength.
Subsequently, similar to the derivation idea of the willire equation, a modified form of the willire equation is obtained, as shown in formula (4):
Figure BDA0002958269570000093
in the formula (4), the reaction mixture is,
Figure BDA0002958269570000094
modified form of creep activation energy, σTSTensile Strength at corresponding temperature conditions, tfFor long life at break, k1And u is a material parameter; therefore, the corrected Wilshire equation can well consider the influence of anisotropy, namely the persistence of other crystal directions can be converted by the direction factor and solved by the model parameters of the reference direction.
As can be seen from FIG. 4, the DS GTD-111 alloy has obviously different temperature dependencies of tensile strength and elastic modulus under different temperature conditions, and meanwhile, the permanent data of the alloy under different temperatures and orientations shows strong consistency with the tensile strength. Thus, for further validation of the modified Wilshire equation, the creep and creep properties of the DS GTD-111 and DZ125 alloys were predicted and evaluated in view of the completeness of published data:
mathematically transforming equation (4) to yield equation (a):
ln(-ln(σ/σTS))＝ln(k1)+uln[f(Ahkl)tfexp(-Qc */RT)]formula (A);
in the formula (A), ln (-ln (sigma/sigma TS)) is used as a vertical coordinate; ln [ f (A)hkl)tfexp(-Qc */RT)]As the abscissa, a series of ordinate data and abscissa data in the formula (A) can be obtained from data known in the art (publicly published performance data of DS GTD-111 and DZ 125), scatter plots are drawn from these data, then a straight line equation is fitted to the formula (A) from these scatter plots to obtain a fitted straight line, and creep activation energy equivalent to the DS GTD-111 alloy can be obtained by data fitting
Figure BDA0002958269570000102
The value is 263.02kJ/mol, and the obtained fitting straight line is shown in FIG. 6 (in FIG. 6, (a) is the fitting result of the DZ125 alloy, and (b) is the fitting result of the DS GTD-111 alloy). in the fitting process, the scatter diagram is not a single straight line rule, but satisfies the two-line ruleAccording to the regularity, the two lines of character marks with different colors in the figure 6 are respectively the conditions before and after the inflection point, have different coefficient values, and the creep endurance performance of the DS GTD-111 and DZ125 alloy under different conditions can be predicted through the figure 6.
According to the DZ125 alloy data, a double-life dispersion band is drawn, as shown in FIG. 8, the abscissa in FIG. 8 is the predicted data obtained by the prediction method in the embodiment, and the ordinate is known published actual data, and it is found that most data points of the predicted life obtained by the prediction method in the embodiment are within a double line, so that the modified Wilshire method provided by the invention has good prediction performance.
By introducing tensile strength dependent directional correction factors
Figure BDA0002958269570000101
A modified form of the Larson-Miller method can be obtained, as shown in equations (11) and (12):
PL-M＝T(20+lgtf)/1000 (11)
lg(σf(Ahkl))＝a0+a1P+a2P2+a3P3 (12)
t and T in equation (11) can be obtained from data known in the art (e.g., publicly published performance data for DZ125 alloy and DS GTD-111 alloy) by predicting and evaluating the anisotropic creep and creep properties of DZ125 alloy and DS GTD-111 alloy, respectively, in consideration of the anisotropyfData, and further P in the formula (11)L-MData; p in formula (11)L-MData is substituted in expression (12) as P data, and σ and f (A) in expression (12)hkl) For the data known in the prior art, fitting formula (12) to obtain a third-order polynomial curve, and the specific results are shown in fig. 7, wherein the creep endurance performance of the DZ125 alloy and the DS GTD-111 alloy under different conditions can be predicted by the graphs (a) and (b) in fig. 7.
According to DS GTD-111 alloy data, a double life dispersion band is drawn, as shown in FIG. 9, the abscissa in FIG. 9 is the predicted data obtained by the prediction method in the embodiment, and the ordinate is known published actual data, and it is found that most data points of the predicted life obtained by the prediction method in the embodiment are within a double line, so that the corrected Larson-Miller method provided by the invention has good prediction performance.
The invention provides a method for predicting creep endurance performance related to orientation of nickel-based superalloy, which finds that the characteristic relation of the temperature and anisotropy of the nickel-based superalloy is quite consistent with the anisotropy correlation of a stretching limit by data analysis, thus defining a crystal orientation function related to the stretching limit and providing a minimum creep strain rate expression modified by the stretching limit; through mathematical transformation and minimum creep strain rate data, the anisotropic characteristic of the minimum creep strain rate is successfully verified to be described better through a direction factor defined by tensile strength; subsequently, two kinds of anisotropy-corrected persistent life prediction equations were derived based on the derivation ideas of the Larson-Miller method and the Wilshire equation.
While only the preferred embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (1)

1. A method for predicting creep endurance of a nickel-based superalloy, comprising:
the anisotropy characteristic of the minimum creep strain rate is described according to a direction factor defined by tensile strength;
introducing the anisotropic characteristic of the minimum creep strain rate into a Larson-Miller method or a Wilshire equation to obtain a prediction equation of the creep endurance performance of the nickel-based superalloy;
predicting the creep endurance property of the nickel-based superalloy according to the prediction equation;
the method for characterizing anisotropy of minimum creep strain rate in terms of a directional factor defined in terms of tensile strength includes:
defining a crystal orientation function to obtain an expression of the minimum creep strain rate with the tensile limit of the crystal orientation function;
obtaining the anisotropic characteristic of the minimum creep strain rate described by the direction factor defined by the tensile strength through mathematical transformation according to the expression of the minimum creep strain rate of the tensile limit with the crystal orientation function;
the expression of the minimum creep strain rate includes formula (1) and formula (2):
Figure FDA0003547172560000011
Figure FDA0003547172560000012
in the formula (1), f (A)hkl) As a function of crystal orientation, σTS,[001]A stretch limit in a reference direction; sigmaTS,[hkl]Is [ hkl]The stretch limit of the direction;
in the formula (2), the reaction mixture is,
Figure FDA0003547172560000013
for minimum creep strain rate, C is a material parameter dependent on temperature and stress, f (A)hkl) As a function of the crystallographic orientation, σ is the stress, n is a stress and temperature dependent material parameter, QcAs the creep activation energy in the reference direction, R is a constant and T is temperature;
the method of mathematical transformation comprises:
taking logarithm on two sides of the equal sign of the formula (2), converting the exponential relation into a linear relation, and obtaining a transformation formula of the anisotropic characteristic of the minimum creep strain rate described by the direction factor defined by the tensile strength, wherein the transformation formula is shown as a formula (3):
Figure FDA0003547172560000021
in the formula (3), the reaction mixture is,
Figure FDA0003547172560000022
for minimum creep strain rate, n is a stress and temperature dependent material parameter, σ is stress, f (A)hkl) As a function of crystal orientation, QcAs the creep activation energy in the reference direction, R is a constant, T is temperature, C is a material parameter dependent on temperature and stress;
introducing the anisotropic characteristic of the minimum creep strain rate into a Wilshire equation to obtain formula (4):
Figure FDA0003547172560000023
in the formula (4), σ is stress, σTSAs tensile strength under corresponding temperature conditions, k1And u is the material parameter, f (A)hkl) As a function of crystal orientation, tfIn order to maintain the fracture life for a long time,
Figure FDA0003547172560000024
in a modified form of creep activation energy, R is a constant and T is temperature;
in the Larson-Miller method: the activation energy of the minimum creep strain rate conforms to the Arrhenius equation, the endurance life and the minimum creep strain rate conform to the Monkman-Grant relationship, and the following formulas (5) and (6) are shown:
Figure FDA0003547172560000025
Figure FDA0003547172560000026
in the formula (5), the reaction mixture is,
Figure FDA0003547172560000027
for minimum creep strain rate, A1For the kinetic parameters, f (σ) is a function of stress, T is temperature;
in the formula (6), the reaction mixture is,
Figure FDA0003547172560000028
for minimum creep strain rate, A2To destroy the strain parameter, tfFor a long life at break;
the minimum creep strain rate is eliminated by the equations (5) and (6), and is expressed as an exponential relation of a stress function and a temperature function, as shown in the equation (7):
Figure FDA0003547172560000029
in formula (7), f (σ) is a function of stress, T is temperature, A1As a kinetic parameter, A2To destroy the strain parameter, tfFor a long life at break;
in the formula (7): let CL-M＝lg(A1/A2)，PL-M(vi)/2.303, to give formula (8):
PL-M＝T(CL-M+lg tf) (8)
in the formula (8), CL-MAs a kinetic parameter A1And failure strain parameter A2Exponential function of, CL-MRegarded as a constant;
PL-Mis a stress function;
expression (8) is expressed as an expression in engineering applications, as shown in formulas (9) and (10):
PL-M＝T(20+lgtf)/1000 (9)
lgσ＝a0+a1P+a2P2+a3P3 (10)
in the formula (9), PL-MIs a function of stress, T is temperature, TfFor a long life at break;
in the formula (10), σ is stress, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method;
introducing a tensile strength dependent directional correction factor to said equation (10)
Figure FDA0003547172560000031
To give formulae (11) and (12):
PL-M＝T(20+lgtf)/1000 (11)
lg(σf(Ahkl))＝a0+a1P+a2P2+a3P3 (12)
in the formula (11), PL-MAs a function of stress, T is temperature, TfFor a long life at break;
in formula (12), σ is stress, f (A)hkl) As a function of crystal orientation, a0、a1、a2And a3Is a constant term of a fitting polynomial, and P is a heat intensity comprehensive parameter established based on a Larson-Miller method.
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