CN105910921B - A method of prediction DZ125 alloy creep curves - Google Patents
A method of prediction DZ125 alloy creep curves Download PDFInfo
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Abstract
A method of prediction DZ125 alloy creep curves,（1）In predicted temperature TmAnd stressmLower measurement alloy short time tensile creep curve, until creep curve is walked surely substantially；（2）Least square fitting creep data is used by the model, determines parameter betai（i=0,1,2,3）Value；（3）Judge creep curve type：Work as β2＜ 0 or β3When ＜ 0, creep curve does not have the tertiary creep stage, this is the first type；Work as β2＞ 0 while β3When ＞ 0, creep curve contains the tertiary creep stage, this is second of type；The present invention can relatively accurately express the creep curve of DZ125 and similar alloy；The dispersibility for fundamentally significantly limiting Prediction Parameters is conducive to improve precision of prediction.In addition, model parameter is few, operating performance is strong；Invention creates a kind of completely new, simple and direct, high-precision creep curve prediction techniques.
Description
Technical field
The invention belongs to high temperature alloy mechanical property research fields, are related to a kind of new side of nickel-base alloy creep curve prediction
Method.
Background technology
DZ125 is one of highest directional solidification nickel-base high-temperature alloy of current performance level, with good medium and high temperature
Comprehensive performance and thermal fatigue property are widely used in the key areas such as aero-engine, special to the prediction in such alloy creep service life
It is not that the prediction of creep curve has become important topic, however there is no the model of accurate description creep curve at present, therefore accurate
Really predict that the creep curve of alloy is extremely difficult.So far, it answers about creep curve prediction technique is most representational
Belong to θ and hints obliquely at method.Last century the eighties, Evans R W and Wilshire B etc. is based on time hardening and strain hardening principle carries
The θ for having gone out description creep curve hints obliquely at method, and model is：
In formula, ε is strain, and t is creep time,WithRespectively reflection material creep hardening and it is compacted
Become softening process, θi(i=1,2,3,4) is undetermined parameter, can be obtained by analyzing measured data.
θ equations can preferably reflect primary creep behavior and second stage, and and creep phase III deviation it is very big.Patent
Number CN 102331377 is proposed in the croop property of assessment T-P92 steel：6 groups of creep curves are first tested, and according to θ equation models
Go out corresponding θ parameter θsi(i=1,2,3,4) is then fitted multiple spot creep data and determines θiFactor is asked further according to these factors
Go out θi(i=1,2,3) value, finally by θi(i=1,2,3) value substitutes into θ equations, finds out θ4.On the one hand this method increases operation
Process, meanwhile, the parameter being related to is more, large dispersion.Importantly, due to θ3And θ4It the common description creep phase III, misses
Difference is larger, therefore passes through θ3Seek θ4, elementary error can not avoid, meanwhile, this method also has certain limitation.
Maruyama K and Oikawa H et al. improves θ equations, enables θ4=θ2, obtain correcting θ equations：
They have carried out creep life prediction with the equation to the steel such as CrMoV and 12Cr (H46), and precision is up to 90%.But thing
In reality, general material can only be reflected second stage and the phase III of creep by correcting θ equations, and first stage error compared with
Greatly, be especially beyond expression the creep process of not no phase III, therefore limits its use.Nevertheless, this method is still not
With degree it is used.
Invention content：
Goal of the invention：
A method of prediction DZ125 alloy creep curves are stretched to the short time through newly-built creep curve model
Creep curve analyzes and determines creep curve type, targetedly carries out creep test using specific method on this basis,
And creep parameters are determined by corresponding technological means, obtain prediction creep curve equation and prediction creep rate equation, purpose
It is to create a kind of completely new, simple and direct, high-precision creep curve prediction and creep rate evaluation method.
Technical solution：
Experiment proves, utilizes model ε=β0+β1ln(t+1)+β2exp(β3T) Ni based alloys can be almost fully described by
The overall process of creep, the model have the very high goodness of fit compared with currently used other models.In formula：ε is strain, and t is
Creep time, βi(i=0,1,2,3,4) is constant, i.e. parameter.Experience have shown that usually | β2|<<1, and | β3| also very little, therefore
β0It is related with initial strain, while playing the role of equilibrium equation, it is little with creep curve form, tendency relationship；β1Ln (t+1) is retouched
State creep hardening process；β2exp(β3T) creep softening process is described, and related with creep curve form.Therefore, β1、β2And β3With
Creep curve is in close relations, especially β2With β3Size combinations reflect the form and variation tendency of creep curve.
Experiment and analysis shows：Due to | β2| and | β3| equal very little, therefore：1. working as β3When ＜ 0, creep curve does not accelerate
Creep stage, creep later stage strain mainly by β1Ln (t+1) determines that creep rate variation tendency is ε '=β1/(t+1)；2. when
β2＜ 0, β3When ＞ 0, still without the tertiary creep stage, creep early period, strain mainly by β1Ln (t+1) determines that creep rate is main
Depending on β1/ (t+1), creep later stage, strain are ε=β with time relationship1ln(t+1)+β2exp(β3T), creep rate be ε '=
β1/(t+1)+β2β3exp(β3T), strain is still mainly by β1Ln (t+1) determines that creep rate equally depends primarily on β1/(t+1)；
3. working as β2＞ 0, β3When ＞ 0, creep curve contains the tertiary creep stage：In creep early period, strain mainly by β1Ln (t+1) decisions,
Creep rate depends primarily on β1/(t+1)；In the creep later stage, strain mainly by β2exp(β3T) it determines, creep rate mainly takes
Certainly in β2β3exp(β3t)；In creep mid-term, by β1The creep that ln (t+1) is represented hardens and by β2exp(β3T) creep represented is soft
Change tends to balance, and works as β1/(t+1)2≈β2β3 2exp(β3When t), creep rate is minimum.
In terms of prediction, creep curve can be divided into two types, i.e., first type in no tertiary creep stage and
Second of type containing the tertiary creep stage.For the creep curve of the first type, due to the creep later stage, strain mainly by
β1Ln (t+1) determines that creep rate depends primarily on β1/ (t+1), therefore, after creep curve enters stable region, β1Value Ying Ji
This is constant.Estimate once it is determined that under predicted temperature and stress creep curve parameter β1It, can be by creep curve end after value stabilization
Thus the parameter value of creep data obtains prediction creep curve equation and predicts creep rate equation as predicted parameter value, from
And achievees the purpose that predict creep curve equation and estimate creep rate.
For the creep curve of second of type, parameter value can refer to θ under constant temperature and hint obliquely at method parameter extrapolation formula lg βi
=ai+biσ (i=0,1,2,3) is determined.It is to be noted that：The study found that wherein using β1=a1+b1σ formula ratios use lg β1
=a1+b1σ formula are more accurate.
The present invention is based on principles above, first pass through creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) to prediction
Short time creep curve at temperature and stress is fitted, and determines model parameter, according to the pass of model parameter and creep curve
System judges creep curve type, carries out creep test using corresponding method according still further to creep curve type and creep curve is pre-
It surveys.
Steps are as follows：
(1) basis《GB/T2039-2012 metal material simple tension creep test methods》, in predicted temperature TmAnd stress
σmLower measurement short time tensile creep curve, until creep curve is walked surely substantially；
(2) with ε=β0+β1ln(t+1)+β2exp(β3T) it is creep curve model, in formula：ε is strain, when t is creep
Between, βi(i=0,1,2,3) is constant, i.e. parameter；The above-mentioned creep data of least square fitting is used by the model, is determined
Parameter betai(i=0,1,2,3) value；
(3) judge creep curve type：Work as β2＜ 0 or β3When ＜ 0, creep curve does not have the tertiary creep stage, this is first
Type；Work as β2＞ 0 while β3When ＞ 0, creep curve contains the tertiary creep stage, this is second of type；
(4) prediction of creep curve
1. the prediction of the first type creep curve
Continue in temperature TmAnd stress σmLower measurement tensile creep curve, in the creep stable region of creep curve, from creep song
Line end starts to choose three groups or more creep datas by different time, according to creep curve model ε=β0+β1ln(t+1)+β2exp
(β3T) the above each group creep data is fitted using least square method respectively, determines corresponding parameter value；If β in each group parameter1
Value fluctuation is larger, also needs to continue creep test, and choose three groups from creep curve tip forward again according to the method described above
The above creep data, meanwhile, each group creep data that least square fitting is selected again is used according to creep curve model, really
Fixed corresponding parameter value, β of this process until each group parameter1Value is 10-4In accuracy rating it is equal until；
By the parameter value β of one group of creep curve end creep data1i(i=0,1,2,3) it is used as predicted parameter value substitution compacted
Varied curve model obtains prediction creep curve equation：ε=β10+β11ln(t+1)+β12exp(β13t)；According to prediction creep curve
Equation draws creep curve, which is to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein ε '
For creep rate, creep rate is estimated according to prediction creep rate equation combination creep time；
2. the prediction of second of type creep curve
In temperature TmUnder, it measures three kinds or more and is more than σmThe creep curve of stress, until breaking sample.It is required that：It is selected
Stress is uniformly distributed, and maximum stress cannot be more than σmN times, n=1.5-2, σmBigger, n is smaller；
According to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) use least square method respectively to above different
The creep data of stress is fitted, and determines corresponding parameter value；According to determining parameter value in lg βi(i=0,2,3)-σ and
β1Corresponding data point is found in σ coordinate system, and lg β are determined by linear fiti(i=0,2,3)-σ and β1- σ relational expressions, by σmGeneration
Enter the relational expression, finds out Tm、σmUnder predicted parameter value β σmi(i=0,1,2,3)；The predicted parameter value is substituted into creep curve
Model obtains prediction creep curve equation：ε=βσm0+βσm1ln(t+1)+βσm2exp(βσm3t)；According to prediction creep curve equation
Creep curve is drawn, which is to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein
ε ' is creep rate, and creep rate is estimated according to prediction creep rate equation combination creep time, according to the minimum creep speed of estimation
Rate predicts secondary creep rates.
This method is suitable for the prediction of a variety of Ni based alloys creep curves within the scope of 600-1100 DEG C, 0-1100MPa.
Beneficial effects of the present invention：
(1) the creep curve model structure that the present invention uses is simple, and parameter is few, can relatively accurately express DZ125 and class
Like the creep curve of alloy；
(2) by creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) short time creep curve is analyzed,
Judge creep curve type, creep curve measurement is targetedly carried out using specific method on this basis, and pass through one
Fixed technological means determines prediction creep parameters, obtains prediction creep curve equation and prediction creep rate equation, fundamentally
The dispersibility for significantly limiting Prediction Parameters is conducive to improve precision of prediction.In addition, model parameter is few, operating performance is strong；
(3) it is completely new that invention creates one kind, and simple and direct, high-precision creep curve prediction technique provides for related field
Valuable reference；
(4) this prediction technique can be used for the prediction of a variety of Ni based alloys creep lines, therefore, the research and development to Ni based high-temperature alloys
And product design and use provide effective technical support.
Description of the drawings：
125 alloy 418h and 750h creep matched curves of DZ under 980 DEG C of Fig. 1,90MPa；
The comparison of DZ 125 alloy 3000h prediction creep curves and actual measurement creep curve under 980 DEG C of Fig. 2,90MPa；
The creep matched curve of 125 alloys of DZ under the different stress of 980 DEG C of Fig. 3；
β at 980 DEG C of Fig. 4i(i=0,1,2,3) and stress σ relation curves；
Prediction creep curve and actual test creep curve under 980 DEG C of Fig. 5,160MPa compare.
Specific implementation mode：
A method of prediction DZ125 alloy creep curves are by being stretched to the short time under predicted temperature and stress
Creep data analysis judges creep curve type, and corresponding creep test and creep number are taken further according to creep curve type
According to processing method, to achieve the purpose that predict long-time creep curve.Steps are as follows：
(1) basis《GB/T2039-2012 metal material simple tension creep test methods》, in predicted temperature TmAnd stress
σmThe lower short time tensile creep curve for measuring Specimens, until creep curve is walked surely substantially；
(2) with ε=β0+β1ln(t+1)+β2exp(β3T) it is creep curve model, in formula：ε is strain, when t is creep
Between, βi(i=0,1,2,3) is constant, i.e. parameter；The above-mentioned creep data of least square fitting is used by the model, is determined
Parameter betai(i=0,1,2,3) value；
(3) judge creep curve type：Work as β2＜ 0 or β3When ＜ 0, creep curve does not have the tertiary creep stage, this is first
Type；Work as β2＞ 0 while β3When ＞ 0, creep curve contains the tertiary creep stage, this is second of type；
(4) prediction of creep curve
1. the prediction of the first type creep curve
Continue in temperature TmAnd stress σmLower measurement tensile creep curve, in the creep stable region of creep curve, from creep song
Line end starts to choose three groups or more creep datas by different time, according to creep curve model ε=β0+β1ln(t+1)+β2exp
(β3T) the above each group creep data is fitted using least square method respectively, determines corresponding parameter value；If β in each group parameter1
Value fluctuation is larger, also needs to continue creep test, and choose three groups from creep curve tip forward again according to the method described above
The above creep data, meanwhile, each group creep data that least square fitting is selected again is used according to creep curve model, really
Fixed corresponding parameter value, β of this process until each group parameter1Value is 10-4In accuracy rating it is equal until；
By the parameter value β of one group of creep curve end creep data1i(i=0,1,2,3) it is used as predicted parameter value substitution compacted
Varied curve model obtains prediction creep curve equation：ε=β10+β11ln(t+1)+β12exp(β13t)；According to prediction creep curve
Equation draws creep curve, which is to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein ε '
For creep rate, creep rate is estimated according to prediction creep rate equation combination creep time；
2. the prediction of second of type creep curve
In temperature TmUnder, it measures three kinds or more and is more than σmThe creep curve of stress, until breaking sample.It is required that：It is selected
Stress is uniformly distributed, and maximum stress cannot be more than σmN times, n=1.5-2, σmBigger, n is smaller；
According to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) use least square method respectively to above different
The creep data of stress is fitted, and determines corresponding parameter value；According to determining parameter value in lg βi(i=0,2,3)-σ and
β1Corresponding data point is found in σ coordinate system, and lg β are determined by linear fiti(i=0,2,3)-σ and β1- σ relational expressions, by σmGeneration
Enter the relational expression, finds out Tm、σmUnder predicted parameter value β σmi(i=0,1,2,3)；The predicted parameter value is substituted into creep curve
Model obtains prediction creep curve equation：ε=βσm0+βσm1ln(t+1)+βσm2exp(βσm3t)；According to prediction creep curve equation
Creep curve is drawn, which is to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein
ε ' is creep rate, and creep rate is estimated according to prediction creep rate equation combination creep time, according to the minimum creep speed of estimation
Rate predicts secondary creep rates.
This method is suitable for the prediction of a variety of Ni based alloys creep curves within the scope of 600-1100 DEG C, 0-1100MPa.
Application example：
Prediction of the example 1. to 980 DEG C of 125 alloys of DZ, 90MPa creep curves
(1) basis《GB/T2039-2012 metal material simple tension creep test methods》Using single head testing machine, pre-
125 alloy short time tensile creep curves of DZ are measured under 980 DEG C of testing temperature, stress 90MPa, until creep curve is walked surely substantially,
Sample is " work " shape plate Specimens, specification：Gauge length is 15mm, and wide, thick size is respectively 4.5mm, 2.5mm, refers to Tian Ning, field
Your of element " microscopic structure and creep behaviour of DZ125 alloys "《China YouSe Acta Metallurgica Sinica》2014,24(5):1232-1239.
It was found that tending to walk to creep curve when 418h steady.Pass through creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) above-mentioned 418h creep datas are fitted using least square method, determine parameter value βi(i=0,1,2,3) it is respectively：-
0.0774, shown in 0.1075,0.0774, -10.3724, creep matched curve such as Fig. 1 (a).Sentenced according to creep curve type
According to：β3＜ 0, creep curve do not have the tertiary creep stage, are the first type.
(2) continue to measure tensile creep curve at 980 DEG C, 90MPa to 750h, creep matched curve such as Fig. 1 (b) institutes
Show.In the creep stable region of creep curve, from creep curve tip forward choose successively creep time be 750h, 675h,
5 groups of creep datas of 600h, 517h and 475h, according to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) using most
Small square law is fitted the above each group of data respectively, determines that corresponding parametric values are as shown in table 1.As it can be seen that the β of each creep curve1Value is very
Stablize, respectively：0.0992,0.0992,0.0993,0.0993,0.0993, and β3Respectively less than 0, further prove creep curve
For the first type；By the parameter beta of 750h creep curvesi(i=0,1,2,3) value substitutes into creep curve mould as predicted parameter value
Type obtains prediction creep curve equation：ε=- 0.0314+0.0992ln (t+1) -0.0024exp (0.0019t)；According to the party
Journey draws creep curve, and the strain of prediction creep 3000h is 0.75015604%, compared with actual measurement strain 0.76157%, prediction
Precision is illustrated in figure 2 prediction creep curve and surveys the comparison of creep curve up to 98.5%.
(3) according to creep rate equation：Predict creep 3000h creep speed
Rate is 3.219 × 10-5%/h, and it is 3.349548 × 10 to survey creep rate-5%/h, error are only 3.8%.
125 alloy creep different time creep curve fit parameter values of DZ under 1 980 DEG C of table, 90MPa
Prediction of the example 2. to 980 DEG C of 125 alloys of DZ, 160MPa creep curves
(1) basis《GB/T2039-2012 metal material simple tension creep test methods》Using single head testing machine, and with
1 identical sample specification of example measures 125 alloy tensile creep curves of DZ at 980 DEG C of predicted temperature, stress 160MPa, sees
Discovery is examined, enters stable state to creep when 260h.Pass through creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) it uses
Least square method is fitted the creep data of above-mentioned 260h, determines parameter betai(i=0,1,2,3) value is：0.0873、
0.5500,0.3795,0.0042, according to creep curve type criterion：β2＞ 0 while β3＞ 0, creep curve contains tertiary creep
Stage is second of type；
(2) at 980 DEG C, 180MPa, 200MPa, 220MPa stress is selected to carry out creep curve measurement, until breaking sample
Until product；
(3) according to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) use least square method respectively to 980
DEG C, tri- groups of creep datas of 180MPa, 200MPa, 220MPa are fitted, and determine that corresponding parameter value is as shown in table 2, creep
Matched curve is as shown in Figure 3；
(4) according to the parameter value in table 2, in lg βi(i=0,2,3)-σ and β1Corresponding data point is found in σ coordinate system, is led to
It crosses linear fit and obtains β at 980 DEG Ci(i=0,1,2,3) is with stress σ relation curves as shown in figure 4, thereby determining that lg βi(i=0,
2,3)-σ and β1- σ relational expressions are as follows：
lgβ0=-4.72844+0.0175 σ degrees of fitting：98.47%
β1=-0.5990+0.00566 σ degrees of fitting：99.89%
lgβ2=-2.82386-0.00269 σ degrees of fitting：99.31%
lgβ3=-3.46545+0.1252 σ degrees of fitting：99.12%
By σmAbove-mentioned relation formula is substituted into, 980 DEG C, the predicted parameter value β under 160MPa are found outi(i=0,1,2,3) it is respectively：
0.00400,0.30660,0.000556852,0.034494512, it is substituted into creep curve model and obtains prediction creep curve
Equation：
ε=0.3066ln (1+t)+0.000556852exp (0.01464512t)+0.004；
(5) prediction creep curve is drawn according to prediction creep curve equation, with actual test creep curve comparison such as Fig. 5
It is shown.It can be seen that practical creep life is 711h, and predict that the same strain time is 692h, precision of prediction is up to 97%.
According to prediction creep rate equationPredict secondary creep rates
For 0.003687%/h, compared with surveying creep rate 0.003915%/h, error is only 5.8%.
The different creep under variable stress curve fitting parameter values of 2 980 DEG C of table
Claims (2)
1. a kind of method of prediction DZ125 alloy creep curves, it is characterised in that：This approach includes the following steps：
(1) basis《GB/T2039-2012 metal material simple tension creep test methods》, in predicted temperature TmAnd stress σmUnder
Alloy short time tensile creep curve is measured, until creep curve is walked surely substantially；
(2) with ε=β0+β1ln(t+1)+β2exp(β3T) it is creep curve model, in formula：ε is strain, and t is creep time, βi(i
=0,1,2,3) it is constant, i.e. parameter；Least square fitting creep data is used by the model, determines parameter betai(i=0,
1,2,3) value；
(3) judge creep curve type：Work as β2＜ 0 or β3When ＜ 0, creep curve does not have the tertiary creep stage, this is the first type
Type；Work as β2＞ 0 while β3When ＞ 0, creep curve contains the tertiary creep stage, this is second of type；
(4) prediction of creep curve
1. the prediction of the first type creep curve
Continue in temperature TmAnd stress σmLower measurement tensile creep curve, in the creep stable region of creep curve, from creep curve end
End starts to choose three groups or more creep datas by different time, according to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) the above each group creep data is fitted using least square method respectively, determines corresponding parameter value；If β in each group parameter1Value
Fluctuate larger, also need to continue creep test, and according to the method described above again from creep curve tip forward choose three groups with
Upper creep data, meanwhile, each group creep data that least square fitting is selected again is used according to creep curve model, is determined
Corresponding parameter value, β of this process until each group parameter1Value is 10-4In accuracy rating it is equal until；
By the parameter value β of one group of creep curve end creep data1i(i=0,1,2,3) predicted parameter value is used as to substitute into creep song
Line model obtains prediction creep curve equation：ε=β10+β11ln(t+1)+β12exp(β13t)；According to prediction creep curve equation
Creep curve is drawn, which is to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein ε ' is compacted
Variable Rate estimates creep rate according to prediction creep rate equation combination creep time；
2. the prediction of second of type creep curve
In temperature TmUnder, it measures three kinds or more and is more than σmThe creep curve of stress, until breaking sample.It is required that：Selected stress
It is uniformly distributed, and maximum stress cannot be more than σmN times, n=1.5-2, σmBigger, n is smaller；
According to creep curve model ε=β0+β1ln(t+1)+β2exp(β3T) use least square method respectively to the above different stress
Creep data be fitted, determine corresponding parameter value；According to determining parameter value in lg βi(i=0,2,3)-σ and β1- σ is sat
Corresponding data point is found in mark system, lg β are determined by linear fiti(i=0,2,3)-σ and β1- σ relational expressions, by σmSubstitute into the pass
It is formula, finds out Tm、σmUnder predicted parameter value β σmi(i=0,1,2,3)；Predicted parameter value substitution creep curve model is obtained
Predict creep curve equation：ε=βσm0+βσm1ln(t+1)+βσm2exp(βσm3t)；Creep is drawn according to prediction creep curve equation
Curve, the curve are to predict creep curve；
By predicting that creep curve equation finds out prediction creep rate equation：Wherein ε ' is
Creep rate estimates creep rate according to prediction creep rate equation combination creep time, pre- according to the minimum creep rate of estimation
Survey secondary creep rates.
2. a kind of method of prediction DZ125 alloy creep curves according to claim 1, it is characterised in that：This method is suitable
It shares in the prediction of DZ125 alloys creep curve within the scope of 600-1100 DEG C, 0-1100MPa.
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