CN105842087A - Designing and prediction method for converting high-temperature stress relaxation data into creep data - Google Patents

Abstract

The invention discloses a designing and prediction method for converting high-temperature stress relaxation data into creep data. The method mainly comprises the following steps: establishing a stress relaxation two-stage superposition model; creating the concepts of equivalent full relaxation time and equivalent relaxation creep rates, carrying out simulation of an equivalent relaxation creep rate in two integrated relaxation stages to obtain a steady-state creep rate under constant stress and establishing a stress relaxation-creep conversion model; acquiring stress relaxation performance data of a high-temperature component material; subjecting the data and the stress relaxation two-stage superposition model to fitting so as to obtain a corresponding material constant; and carrying out calculating according to a numerical analysis program, solving the stress relaxation-creep conversion model and eventually converting stress relaxation data into creep data so as to obtain a steady-state creep rate curve and a steady-state creep curve. According to the invention, accurate association between stress relaxation data and creep data behaviors is established; a prediction method for converting single relaxation data into creep data under any stress is constructed; so a novel approach is provided for designing of creep strength of a high-temperature member and for evaluation of the service life of the high-temperature member.

Description

High-temperature stress relaxation data are converted to the design Forecasting Methodology of creep data

Technical field

The invention belongs to the testing of materials and engineering structure Intensity Design technical field, be specifically related to a kind of by the high temperature of material Stress relaxation test data are converted to the method for high-temerature creep data, especially equivalent and relax the height on creep rate basis The design Forecasting Methodology of temperature creep.

Background technology

High-temerature creep fracture is the fields such as Aero-Space, petrochemical industry, dynamic power, and high-temperature service and component failure lost efficacy Principal mode, material at high temperature creep data is the necessary basis of creep strength and Life Design.But, traditional high-temerature creep The life test method time is long, uses parameter extrapolation to be only capable of realizing limited extrapolation to the data obtained.Longer examination Both cause the consuming of a large amount of manpower and materials with life test, again limit exploitation and the popularization and application of new material.Stress relaxation It is material two kinds of performance characteristics at high operating temperatures with creep.It is the most continuous that creep characterizes irreversible transformation under constant stress The process increased, stress relaxation then reflects the phenomenon that under constant strain, stress the most constantly reduces.The two naturally occurring Plant corresponding relation.Then, set up the association between the two data and conversion, be then possible not only to reduce hot test amount, Er Qieke To accelerate the CREEP DESIGN of high-temperature material, there is great academic significance and construction value.

Currently, with respect to high-temperature material performance relaxstion-creep conversion method, main employing calculates the side combined with mapping Method.The method substantially is tried to gather out the creep ratio under stress different under equality of temperature relatively by doing several relaxation tests Close relaxation test, or simply only carry out a relaxation test, directly derive the artificial stable pine assert by this relaxation data The stress-strain Rate Relationship in relaxation stage simulates the stress-strain Rate Relationship in steady creep stage, thus carries out creep and set Meter.But, first, initial strain (stress) is different, and its stress-strain Rate Relationship is the most different, although all long time lax strain Speed all goes to zero；Secondly, it is impossible to define and stably relax the stage, particularly with less than 24 hours even stress relaxation of a few hours Test；Its three, lax initial strain is promoted to 1% and even reaches 1.5%, 2% more than by existing method, enters from the beginning Overall plastic property or yield strain process even fracture process, have no way of producing the lax behavior that elastic strain converts to plastic strain.Institute In this way scientific and feasibility receives query.The present inventor once disclosed the creep life prediction side of a kind of material Method, according to the lax relation with creep, substep carry out numerical computations and combine with diagram method obtain material steady state creep should Variable Rate.All these methods are all not carried out the ultimate function that stress relaxation changes with creep and associate, and do not establish lax-compacted Become transformation model.Therefore, need badly develop based in stress relaxation and creep physical interconnection function resolve relation conversion pre- Survey technology.

Summary of the invention

It is an object of the invention to overcome the problem in the presence of existing stress relaxation creep conversion estimation technology and defect, Propose and build equivalent full slack time and the concept of equivalent relaxation rate, setting up the exact correlation of stress relaxation and creep Stress relaxation-creep transformation model, thus realize the high-temperature stress relaxation data accurate transformation to creep data.

For solving the problems referred to above, the technical solution adopted in the present invention is:

A kind of method that material high-temperature stress relaxation data are converted to creep data, it is characterised in that described method includes Following steps:

1) stress relaxation behavior model two-stage superposition equation is set up；

2) set up equivalent full slack time and equivalent relaxes the concept of creep rate, set up equivalent and relax creep rate model With equivalent creep increment model；

3) stress relaxation ability data and the curve of existing high-temperature component material are directly gathered；Or use pole stretching examination Sample, utilizes high-temerature creep testing machine to obtain stress relaxation ability data and the curve of high-temperature component material at a certain temperature；

4) according to acquired stress relaxation ability data, the stress relaxation two-stage superposition corresponding material of equation is simulated Constant；Described material constant includes material constant k, p, t₀；Elasticity modulus of materials E directly uses existing performance data, or Drawn with strain calculation by the load measuring the loading procedure of stress relaxation experiment；

5) applying step 4) equivalent set up relaxes creep rate model, or equivalent creep increment model, carries out numerical value Analyze and program calculates, obtain the material at high temperature secondary creep rates data under constant stress, or creep strain data, thus be compacted Intensity adjustable, biometry and design provide foundation.

Say further, described step 1) in set up stress relaxation behavior model two-stage superposition equation, including with Lower step:

Stress relaxation is carried out the most in two stages.

A. first stage equation: the incipient stage i.e. first stage shows as diffusion process, represents with diffusion equation:

${\mathrm{\σ}}_1={\mathrm{\σ}}_0\exp (-\frac{kt}{1+pt})$

σ in equation₁It is the relaxed stress of first stage t, σ₀Initial stress, k and p for reflection metal essence and The material constant relevant with relaxation condition.

B. second stage equation: stress relaxation second stage is for stably to relax the stage, and its equation is:

${\mathrm{\σ}}_2={\mathrm{\σ}}_r+({\mathrm{\σ}}_0-{\mathrm{\σ}}_r)\frac{{{\mathrm{\σ}}_0}^{\′}}{{\mathrm{\σ}}_0}\exp (-\frac{t}{t_0})$

In formula, σ₂It is the relaxed stress of the 2nd stage t, σ_rIt is Relaxation Limit, t₀Lax stable for reflection metal intracrystalline The material constant of property.σ′₀It is the initial stress of second stage, namely the Relaxation Limit of first stage, therefore have as t → ∞, by step Rapid a diffusion equation can obtain:

${{\mathrm{\σ}}_0}^{\′}={\mathrm{\σ}}_0\exp (-\frac{k}{p})$

Research before this shows: if there is stress relaxation limit, then its value should be zero.In view of σ_rEven if existing, its value Smaller, also for simplifying lax equation, it is possible to approximation takes σ_r=0, thus second stage equation is:

${\mathrm{\σ}}_2={{\mathrm{\σ}}_0}^{\′}\exp (-\frac{t}{t_0})$

Equation shows, stress relaxation second stage residual stress and time exponentially relation.

C. stress relaxation general equation is:

σ=σ₁-(σ′₀-σ₂)

Being substituted in above formula by first and second stage equation, collated, stress relaxation equation is eventually:

$\mathrm{\σ}={\mathrm{\σ}}_0\[e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})\]$

Furthermore, described step 4) in set up equivalent and relax creep rate model and equivalent creep increment model, Comprise the following steps:

D. stress relaxation equation ε₀=ε_e+ ε=Const, ε₀For overall strain, ε_eFor elastic strain, ε is creep strain, to it Make the differential of time t, and divided by elastic modulus E, obtain lax creep rate equation:

$\stackrel{\·}{\mathrm{\ϵ}}=-\stackrel{\·}{\mathrm{\σ}}/E$

In formula,For stress relaxation rate,For lax creep rate, E is elastic modelling quantity.

E. by stress relaxation general equation differential and substitute in above formula, can obtain

$\stackrel{\·}{\mathrm{\ϵ}}=\frac{{\mathrm{\σ}}_0}{E}\[\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}\]$

Arrange above formula in conjunction with stress relaxation general equation, eliminate initial stress σ₀, then the creep rate that relaxes is:

$\stackrel{\·}{\mathrm{\ϵ}}=\frac{\mathrm{\σ}}{E}\[\frac{\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}}{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})}\]$

The relation of the creep strain ε vs. time t that this model is represented by under any stress σ:

$d\mathrm{\ϵ}=\frac{\mathrm{\σ}}{E}\[\frac{\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}}{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})}\]dt$

F. mean creep rate

To lax creep rateFull strain in the τ time under 0～τ time inner product gets certain stress σ:

${\mathrm{\ϵ}}_{\mathrm{\τ}}={\∫}_0^{\mathrm{\τ}}\frac{\mathrm{\σ}}{E}\[\frac{\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}}{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})}\]dt=\frac{\mathrm{\σ}}{E}(e-e^{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1+e^{-\frac{t}{t_0}})})$

Again divided by τ, i.e. obtain the Mean Speed in the τ time, i.e. stress relaxation one, average creep in time two-stage τ Speed:

${\stackrel{\·}{\mathrm{\ϵ}}}_{av}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})})/\mathrm{\τ})$

G. equivalent τ full slack time_eq

Take the logarithm in the counter stress second stage equation both sides that relax,I.e. in single pair of number coordinate system, Ln σ Yu t is in line relation.Ln σ is i.e. approximately equivalent τ full slack time with the intersection point of time coordinate_eq, as shown in Figure 1.

Thus have τ_eq=t₀lnσ′₀, by equationSubstitute into, and transformed cancellation σ₀, collated Arrive:

${\mathrm{\τ}}_{eq}={t_0}^{\′}(ln\mathrm{\σ}-ln(e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}\left(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}}\right))-\frac{k}{p})$

H. equivalent secondary creep rates

With equivalent τ slack time_eqSubstitute into mean creep rate equation, finally give approximation and include lax first and second process Equivalent relax creep rate (model), in order to simulate secondary creep rates, i.e.

$\stackrel{\·}{\mathrm{\ϵ}}={\stackrel{\·}{\mathrm{\ϵ}}}_{eq}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}})})/{\mathrm{\τ}}_{eq})$

Equivalent creep increment model i.e. shows themselves in that

$d\mathrm{\ϵ}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}})})/{\mathrm{\τ}}_{eq})dt$

Numerical analysis and program computational methods described in furthermore: step 5) are, programming τ_eqPass through iteration The numerical analysis methods such as method solve；Step 5) described in stress-secondary creep rates that result of calculation is creepNumber According to and curve, and creep strain-time (ε-t) data and curve.Material at high temperature creep is carried out according to these data and curve Intensity Design and biometry assessment.

Compared with prior art, the present invention has the following advantages:

1. the equivalent that the present invention is established relaxes creep rate, designs for high-temerature creep and provides new route.

The most up to now, there is no any one for realizing the pine that relaxation data is set up to the conversion of creep data Relaxation-creep transformation model, prior art does not sets up stress relaxation and associates with the physics parsing of creep, can only use calculating and mapping The method combined, or use excessive initial plastic deformation, or artificial examination gathers lax creep rate, blindly forced what is called The method of accelerated test is changed, so conversion accuracy is relatively low.The present invention proposes and constructs equivalent full slack time and works as The concept of amount relaxation rate, is modeled as the creep rate under constant stress the equivalent relaxation rate planning as a whole the lax two-stage, based on Stress relaxation and the relation of creep, construct relaxstion-creep transformation model, and relaxstion-creep is changed as support, scientific meaning Clearly, Technology Ways is reasonable, the most reliably.

3., according to the relaxstion-creep transformation model of the creep rate that relaxes based on equivalent, it is possible not only to characterize and prediction creep Stress-secondary creep ratesData and curve, it is also possible to characterize and predict creep strain-time (ε-t) data And curve, relaxstion-creep conversion range is the most wide, greatly facilitates high temperature creep strength design.

The most existing relaxstion-creep conversion method needs many group stress relaxation test data, and when test to have certain Long, consume more human and material resources and financial resources.And the present invention have only to one shorter time relaxation test, i.e. can calculate appoint Creep data under what stress, carries out creep strength design, greatly reduces high-temperature time correlation test, greatly reduce people Power, material resources and time cost, bring great convenience for high temperature design.

5. the present invention is possible not only to carry out relaxstion-creep data conversion estimation, the stress relaxation two-stage superposition set up Equation can also carry out stress relaxation behavior prediction, residual stress prediction and high temperature fastening design.

6. the present invention not only provides concrete stress relaxation-creep transformation model, additionally provides concrete prediction and calculates Method.The programming system simultaneously designed and developed, effectively reduces workload and the requirement to operator's Professional knowledge.

Accompanying drawing explanation

Fig. 1 is equivalent schematic diagram full slack time.

Fig. 2 is stress relaxation experimental data figure.

Fig. 3 is creep test datagram.

Fig. 4 is the present invention based on equivalent to relax the high temperature of stress relaxation-creep transformation model conversion estimation of creep rate Material secondary creep rates and the schematic diagram compared with result of the test thereof.

Fig. 5 is the present invention based on equivalent to relax the high temperature of stress relaxation-creep transformation model conversion estimation of creep rate Material steady state creep behavior and the schematic diagram compared with result of the test thereof.

Detailed description of the invention

The present invention is a kind of to utilize equivalent to relax the high-temperature material stress relaxation creep conversion estimation method of creep rate, examines Consider the essential connection of creep rate between stress relaxation and creep, set up based on equivalent relax creep rate creep model this One creep and lax between exact correlation, and then make full use of the test of existing high-temperature stress relaxation, or only need to carry out shorter Relaxation test, it is achieved the high accuracy conversion of creep-lax, it is provided that arbitrarily creep data during long under stress, compacted for high-temperature component Intensity adjustable design and biometry provide new way and new method.

Forecasting Methodology of the present invention is divided into six steps, based on diffusion principle and Maxwell equation including setting up Stress relaxation two-stage superposition equation；Carry out short time high temperature stress relaxation test, or directly utilize existing high-temperature component material Relaxation property data；Relaxation property data are processed, simulates corresponding material constant；Set up and relax creep based on equivalent The lax creep transformation model of speed；Elasticity modulus of materials E directly uses existing performance data, or by measuring stress relaxation The load of the loading procedure of experiment draws with strain calculation；Calculated stress relaxation by numerical analysis and program according to transformation model Data are converted to creep data, it was predicted that creep behaviour.Particularly as follows:

1., according to stress relaxation two-stage behavioral mechanism, set up stress relaxation two-stage superposition equation.

$\mathrm{\σ}={\mathrm{\σ}}_0\[e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}\left(1-e^{-\frac{t}{t_0}}\right)\]$

2., according to stress relaxation behavior characteristic, establish equivalent full slack time and equivalent and relax creep rate, this equivalent Lax creep rate is modeled as creep speed of steady state, sets up equivalent and relaxes creep rate model, and equivalent creep increment model.

3. use single pole tensile sample, utilize creep testing machine, test to obtain the stress relaxation ability data of material. As ready-made data can be found, and allowed, can directly quote and utilize.

4. process by stress relaxation two-stage superposition equation counter stress relaxation property data, matching or calculate corresponding Material constant k, p, t₀；Directly quote current material elastic modulus E, or by measuring the loading procedure of stress relaxation experiment Elastic load draws with strain calculation.

5. previous materials constant and elasticity modulus of materials E substitute into relax creep rate model and the equivalent creep of this equivalent increase Amount model:

$\stackrel{\·}{\mathrm{\ϵ}}={\stackrel{\·}{\mathrm{\ϵ}}}_{eq}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}})})/{\mathrm{\τ}}_{eq})$

With

Wherein,

Thus obtain corresponding equivalent and relax creep rate model and the concrete manifestation formula of equivalent creep increment model.

6. utilize the relax concrete manifestation formula of creep rate model and equivalent creep increment model of above equivalent to change Calculating, concrete calculating process is as follows:

Determine corresponding creep stress σ and incremental time dt, carry out programming by the iterative method in numerical analysis techniques And calculate, first solve τ_eq, followed by solve equivalent secondary creep ratesWith equivalent creep increment d ε, finally give corresponding bar Stress-secondary creep rates under partData and curve and creep strain-time (ε-t) data and curve, real Existing creep to the conversion of creep, carries out creep strength analysis and design to stress relaxation.

Embodiment 1:

Domestic 1Cr10NiMoW2VNbN steel, for less than 600 DEG C turbine rotors, blade and bolt, as a example by this material It is described further.Should be understood that the purpose that following example are merely to illustrate, not for limiting the scope of the present invention.

1. set up stress relaxation two-stage equation

$\mathrm{\σ}={\mathrm{\σ}}_0\[e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})\]$

2. obtain stress relaxation data

Stress relaxation test is unidirectional stress relaxation tension test at 600 DEG C, and lax initial stress is 300MPa, test data As shown in Figure 2.

3. parameter fitting

Utilize stress relaxation two overlapping of order equationTo relaxation test data acquisition with many Level linear processes returns the mode combined and obtains each material constant.K, p, t₀It is respectively 5.49,10.02,3700.8； At 600 DEG C, elasticity modulus of materials E is 1.68 × 10⁵MPa。

4. establish equivalent steady state creep model concrete manifestation formula

The material parameter obtained by aforementioned 3rd step parameter fitting respectively substitutes into aforementioned equivalent steady state creep model and equivalent Stable state increment creep model:

With

5. carry out conversion Calculation

Take at 600 DEG C four creep stress σ=200,210,225,240MPa, carry out programming and computer calculate, Finally give the stress-secondary creep rates under corresponding conditionsData and curve and creep strain-time (ε-t) Data and curve, as shown in accompanying drawing 3,4.

Embodiment 2:

In order to verify transformation result, carried out at 600 DEG C four stress levels 200,210,225, the creep examination of 240MPa Test, as shown in Figure 3；Transformation result of the present invention and experimental result are plotted in the most respectively in accompanying drawing 4,5 and compare, and figure dotted line is Result of the test, solid line is transformation result.Can be seen that from accompanying drawing 4,5, transformation result quite well is in actual creep number generally According to, this explanation, this relaxstion-creep conversion method is reliable.This also indicates that, plans as a whole lax two stage equivalent creep rate, Be relatively more suitable for simulate secondary creep rates, can with this transformation model and method carry out high temperature creep strength design with Biometry.Also indicate that simultaneously, utilize the stress relaxation test of single 1000 hours, multiple compacted under the most measurable any stress Parameter evidence, the creep data of the most up to ten thousand hours, save time, save trouble, laborsaving, greatly facilitate acquisition and the creep of creep data Prediction of strength and design.

In a word, the present invention relaxes that the stress relaxation-creep transformation model basis of creep rate is deep based on equivalent, closes Reason, computational methods are simple, convenient, complete, and conversion accuracy, reliability and usefulness are higher, can be used for the engineering of high-temerature creep design Practice.

Claims (5)

1. high-temperature stress relaxation data are converted to the design Forecasting Methodology of creep data, it is characterised in that described method bag Include following steps:

1) stress relaxation two-stage Additive Model is set up；

2) establish equivalent full slack time and equivalent to relax the concept of creep rate, set up based on equivalent relax creep rate should Power relaxstion-creep transformation model；

3) use pole tensile sample, utilize creep testing machine to obtain one group of stress relaxation at a certain temperature of high-temperature component material Data；

4) according to acquired stress relaxation ability data, use stress relaxation two-stage Additive Model, simulate corresponding material Material constant, obtains material parameter；

5) acquired material constant and parameter are substituted into the stress relaxation-creep transformation model set up, use numerical analysis Technology, by programming and calculating, solves this model, obtains corresponding creep data.

The method that high-temperature material stress relaxation data the most according to claim 1 are converted to creep data, it is characterised in that: Step 1) described in set up stress relaxation two-stage Additive Model, particularly as follows:

A. first stage equation:

σ therein₁It is the relaxed stress of first stage t, σ₀Being initial stress, k and p is for reflection metal essence and with lax The material constant that condition is relevant；

B. second stage equation:

In formula, σ₂It is the relaxed stress of second stage t, σ_rIt is Relaxation Limit, t₀For reflection metal intracrystalline relaxation stability Material constant；σ₀' it is the initial stress of second stage, namely the Relaxation Limit of first stage, therefore have as t → ∞, by step a side Journey can obtain:

${{\mathrm{\σ}}_0}^{\′}={\mathrm{\σ}}_0\exp (-\frac{k}{p})$

In view of σ_rEven if existing, its value is smaller, and also for simplifying lax equation, approximation takes σ_r=0, thus second stage Equation shows themselves in that

${\mathrm{\σ}}_2={{\mathrm{\σ}}_0}^{\′}\exp (-\frac{t}{t_0})$

C. stress relaxation general equation: its equation is, σ=σ₁-(σ₀′-σ₂)

Being substituted in general equation by first and second stage equation, collated, stress relaxation equation is eventually:

$\mathrm{\σ}={\mathrm{\σ}}_0\[e^{-\frac{kt}{1+pt}}-e^{\frac{k}{p}}(1-e^{-\frac{t}{t_0}})\]$

High-temperature stress relaxation data the most according to claim 1 are converted to the design Forecasting Methodology of creep data, its feature Be: step 2) described in foundation relax based on equivalent the stress relaxation-creep transformation model of creep rate, particularly as follows:

D. stress relaxation equation ε₀=ε_e+ ε=Const, wherein, ε₀For overall strain, ε_eFor elastic strain, ε is creep strain, to this Equation makees the differential of time t, and divided by elastic modulus E, obtains lax creep rate equation::

$\stackrel{\·}{\mathrm{\ϵ}}=-\stackrel{\·}{\mathrm{\σ}}/E$

In formula,For stress relaxation rate,For lax creep rate, E is elastic modelling quantity；

E. by lax to stress relaxation differential equations substitution creep rate equation, can obtain

$\stackrel{\·}{\mathrm{\ϵ}}=\frac{{\mathrm{\σ}}_0}{E}\[\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}\]$

In conjunction with stress relaxation equation, arrange lax creep rate equation, eliminate initial stress σ₀, then the creep rate that relaxes is:

$\stackrel{\·}{\mathrm{\ϵ}}=\frac{\mathrm{\σ}}{E}\[\frac{\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}}{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})}\]$

The relation of the creep strain ε vs. time t that this model is represented by under any stress σ:

$d\mathrm{\ϵ}=\frac{\mathrm{\σ}}{E}\[\frac{\frac{k}{{(1+pt)}^2}{e}^{-\frac{kt}{1+pt}}+\frac{1}{t_0}{e}^{-\frac{k}{p}}{e}^{-\frac{t}{t_0}}}{e^{-\frac{kt}{1+pt}}-e^{-\frac{k}{p}}(1-e^{-\frac{t}{t_0}})}\]dt$

F. mean creep rate

To lax creep rateFull strain in the τ time under 0～τ time inner product gets certain stress σ:

Again divided by τ, i.e. obtain the Mean Speed in the τ time, i.e. stress relaxation one, mean creep rate in time two-stage τ:

G. equivalent τ full slack time_eq

Take the logarithm in the counter stress second stage equation both sides that relax,I.e. in single pair of number coordinate system, ln σ and t Be in line relation；Ln σ is i.e. approximately equivalent τ full slack time with the intersection point of time coordinate_eq, as shown in Figure 2；

Thus have τ_eq=t₀lnσ₀', by equationSubstitute into, and transformed cancellation σ₀, collated:

${\mathrm{\τ}}_{eq}=t_0(ln\mathrm{\σ}-ln(e^{\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}\left(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}}\right))-\frac{k}{p})$

H. equivalent secondary creep rates

With equivalent τ slack time_eqSubstitute into mean creep rate equation, finally give approximation and include working as of lax first and second process The lax creep rate model of amount, in order to simulate the secondary creep rates in creep process, i.e.

$\stackrel{\·}{\mathrm{\ϵ}}={\stackrel{\·}{\mathrm{\ϵ}}}_{eq}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}})})/{\mathrm{\τ}}_{eq})$

Equivalent creep increment model i.e. shows themselves in that

$d\mathrm{\ϵ}=\frac{\mathrm{\σ}}{E}\left(\right(e-e^{e^{-\frac{{\mathrm{k\τ}}_{eq}}{1+{\mathrm{p\τ}}_{eq}}}-e^{-\frac{k}{p}}(1-e^{-\frac{{\mathrm{\τ}}_{eq}}{t_0}})})/{\mathrm{\τ}}_{eq})dt$

High-temperature stress relaxation data the most according to claim 1 are converted to the design Forecasting Methodology of creep data, its feature Be: step 4) described in material constant include k, p, t₀；Step 4) described in material parameter include elasticity modulus of materials E, directly Connect the existing performance data of employing, or drawn with strain calculation by the load measuring the loading procedure of stress relaxation experiment.

High-temperature stress relaxation data the most according to claim 1 are converted into the design Forecasting Methodology of creep data, its feature Be: step 5) described in numerical analysis and program computational methods be, programming equivalent τ full slack time_eqPass through iterative method Solve Deng numerical analysis method, then solve equivalent equivalent and relax creep rate and equivalent creep increment；Step 5) described in meter Calculate stress-secondary creep rates that result is creepData and curve, and creep strain-time (ε-t) data And curve.