CN104156577A - Service life evaluation method of ultra-supercritical boiler special steel pipe welding connector - Google Patents

Abstract

The invention relates to a service life evaluation method of an ultra-supercritical boiler special steel pipe welding connector. The method includes the steps of firstly: using an NSW-MOD theoretical model to determine mathematic relation between a creep damage accumulation process and crack growth rate on the basis of a crack tip creep damage accumulation process; secondly, using a polynomial to fit a da/dt-a curve to obtain a maximum curvature point, namely the turning point a of creep crack growth; thirdly, calculating to obtain the ratio a/(S-a0), namely the creep crack growth service life loss a/(S-a0) of the special steel pipe welding connector under high temperature and high pressure, of special steel pipe welding connector pipeline wall thickness S to the difference (S-a0) of S and initial crack length a0; acquiring the creep crack growth residual service life of the special steel pipe welding connector under high temperature and high pressure by numerical integration between the crack length a at the turning point and the pipe wall thickness S. The method has strict physical and theoretical basis, and service life predication is highly matched with actual service life.

Description

A kind of ultra-supercritical boiler heterogenous steel pipe welding joint lifetime estimation method

Technical field

The present invention relates to the On Creep Crack Growth life-span prediction method of a kind of ultra-supercritical boiler heterogenous steel pipe welding joint under high-temperature and high-pressure conditions.

Background technology

China is that thermal power generation, within current and following significant period of time, still in occupation of leading position, is still most important power source in whole electrical production taking coal as main energy country.The approach that various countries' thermal power generation is raised the efficiency in the world is at present mainly by improving steam parameter, improves the vapor pressure and the temperature that enter steam turbine, and therefore, super (super-) critical thermal power generation unit has obtained greatly developing.

Thermal power generation unit steam parameter, as the raising of temperature, pressure, has all proposed stricter requirement to performances such as the opposing of boiler high temperature pressure-containing member creep, high-temperature oxydation and corrosion.Meanwhile also there is series of new heat-resisting steel material, such as T91, T92, HR3C, Super304H etc. are novel martensite, the austenitic heat-resistance steel of representative, become the main use material of the pressure-containing members such as super (super-) critical unit reheater, superheater.Austenitic heat-resistance steel is mainly used in the high temperature position of equipment, and from the viewpoint of cost, lower temperature position still adopts martensite heat-resistant steel.Therefore,, for high-temperature surface, dissimilar steel pipeline welding joint is also apparent.All kinds of defects that these materials are prone to pit/indenture, crackle or cause because thermal treatment is improper in manufacture processing, installation and use procedure.

Under long-time high temperature or overtemperature, easily there is creep strain in the high-temperature heating parts in station boiler.Creep failure not only with the performance of material itself, at high temperature support creep resisting ability relevant, but also with material internal with defect relevant.Along with the continuous prolongation of time, in material, existing creep hole is easy to forming core on grain boundary, hole will expand connect form new for macroscopic void, grow up to a certain extent after just the creep that is joined together to form slowly breed crackle, be finally gathered into micro-crack or macroscopic cracking.

Because the performance such as thermal expansivity, creep rupture strength of Dissimilar Steel Welded Joint, mother metal and each mother metal heat-affected zone differs greatly, at high temperature there is the difference of croop property, material between the each region of welding joint is interrupted and expand and produce internal stress.One of feature of station boiler is exactly High Temperature High Pressure, therefore, is also subject to by the creep stress producing under high temperature stress for the pressure-containing member of station boiler.Under high temperature or overtemperature, move for a long time, to forming the Dissimilar Steel Welded Joint of fine cracks,, there is a creep impairment region in the stress complexity of crack tip, and creep impairment region can further expand, expansion.In On Creep Crack Growth, crack tip creep loss constantly expands, and micro-crack forms time main crackle gradually, when inferior main crackle reaches critical, interconnects towards the inferior main crackle of beneficial direction, finally forms main crackle and expands forward.Whole process is exactly the accumulation creep impairment of so continuous repetition, and back and forth constantly expansion forward, until fracture.

At present, both at home and abroad the prediction of boiler tubes of power plant and pipeline creep life is adopted to the extrapolation technique method and the method relevant to creep process based on mechanical performance data more, as the measurement technology of the metallographic changing features such as cavity nucleation and growth, free carbide composition.Extrapolation technique based on mechanical performance data has experienced parameter Extrapolation method, creep rupture strength isotherm linear extrapolation method.

Parameter extrapolation method need to be carried out matching to experimental data, lack tighter physics and theoretical foundation, therefore its life prediction is mainly experience, and ordinary test carries out under uniform temperature, load, adopts the method bimetry obviously with actual inconsistent.Creep rupture strength isotherm linear extrapolation method is to adopt the method that improves stress and temperature to obtain the relation between material stress and rupture time and temperature in short-term, relation between extrapolated long-time stress and rupture time and temperature again, this Extrapolation method is the basic methods of current high-temperature component design, but because forecasting techniques is more responsive to working stress, the relation of creep life and stress is quite queried, therefore there is more deficiency for the life appraisal of high-temperature component in this technology.

Ultra supercritical thermal power generation unit high temperature position adopts different heat-resisting steel, in welding and use procedure, cause composition, institutional framework and the poor mechanical property mutation of welding joint large, exist higher stress to concentrate at welding joint, supporting creep resisting performance weakens gradually, creep hole forming core is easy to form, and grows up and be gathered into micro-crack, easily produces creep damage failure.Therefore, said method has larger discrepancy for predicting the outcome of Dissimilar Steel Welded Joint On Creep Crack Growth life-span.

Feature of the present invention is based on crack tip stress-strain field, think creep damage mechanism control creep open split, Crack Extension until lost efficacy whole process, determine in conjunction with method for numerical simulation the turning point that crackle accelerates expansion under high-temperature and high-pressure conditions according to the theoretical model of On Creep Crack Growth, pass judgment on the residual life of Dissimilar Steel Welded Joint.To generating plant metal supervision and life-span management, no matter from economy, or from safe operation and how the arranged rational time between overhauls(TBO) consider, prediction has safely very important realistic meaning to the long-term operation of thermal power generation unit.

Summary of the invention

Technical matters to be solved by this invention, is just to provide a kind of ultra-supercritical boiler heterogenous steel pipe welding joint lifetime estimation method, and it has tighter physics and theoretical foundation, therefore its life prediction and the actual goodness of fit are higher.

Solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A kind of ultra-supercritical boiler heterogenous steel pipe welding joint lifetime estimation method, is characterized in that comprising the following steps:

S1 sets up On Creep Crack Growth model

To the evaluation of high-temperature material creep resistant Crack Extension performance, C ^*being similar in elastic-plastic fracture mechanics and the J integration of path independence, is the stress-strain field parameter through theoretical Strict Proof, for the description of crack tip region stress-strain field when high-temerature creep in steady state creep situation, also has the integral characteristic of path independence; Now use C ^*the expression formula that characterizes field of stresses and strains near crack tip is as follows:

${\mathrm{\σ}}_{\mathrm{ij}}={\mathrm{\σ}}_0{\left(\frac{C^{*}}{{\stackrel{\·}{\mathrm{\ϵ}}}_0{\mathrm{\σ}}_0{I}_{n}r}\right)}^{\frac{1}{n+1}}{\widetilde{\mathrm{\σ}}}_{\mathrm{ij}}(\mathrm{\θ},n)---\left(1\right);$

${\stackrel{\·}{\mathrm{\ϵ}}}_{\mathrm{ij}}={\stackrel{\·}{\mathrm{\ϵ}}}_0{\left(\frac{C^{*}}{{\stackrel{\·}{\mathrm{\ϵ}}}_0{\mathrm{\σ}}_0{I}_{n}r}\right)}^{\frac{n}{n+1}}{\widetilde{\mathrm{\ϵ}}}_{\mathrm{ij}}(\mathrm{\θ},n)---\left(2\right);$

In formula, r is illustrated in crack tip θ angular direction apart from splitting sharp distance; σ ₀it is yield strength; it is the strain rate under corresponding effect of stress; for angle factor, it is the dimensionless function of θ and n; I _nbeing the n dimensionless function of considering stress state, is the function of n;

In On Creep Crack Growth process, crack tip exists a creep control zone, and the expansion of creeping crack is mainly because the damage accumulation in creep control area causes; Nikbin, Smith and Webster think at a damage field of the most advanced and sophisticated existence of creeping crack, in crack propagation process, as long as enter this region, damage accumulation will occur; In the time that the toughness of crack tip near zone is exhausted completely, this region is just considered to lose efficacy, and crack tip will be expanded forward; Because damage is relevant with creep strain, the creep stage that therefore the accumulation degree of damage is experiencing with material is relevant; In the subordinate phase of the deformation of creep, creep rupture strain is constant; In the steady creep Crack Extension stage, crack growth rate is also constant; In sum, based on the stress field of crack tip under hot conditions, the creep crack growth rate that Nikbin, Smith and Webster propose the stabilization sub stage can utilize following formula to calculate, i.e. NSW model:

$\frac{\mathrm{da}}{\mathrm{dt}}=\frac{n+1}{{\mathrm{\ϵ}}_f^{*}}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}---\left(3\right);$

In formula, r _cbe crack tip creep loss area size, generally equate with the average grain size of material; for multiaxis fracture toughness; It is generally acknowledged that multiaxis fracture toughness can be thought and the breaking strain ε of single shaft creep _fidentical; And the in the situation that of plane strain, can think ε _f/ 30; Breaking strain ε _fdetermine by fracture tension test;

It in NSW model, is hypothesis reaching peaked position in crack tip equivalent stress lost efficacy; But test and result of finite element all show that the stress state On Crack Propagation of crack tip has a great impact; In order to describe better the propagation behavior of crack tip region crackle, the stress state of crack tip is taken into account in NSW theoretical prediction model, i.e. NSW-MOD model, expression formula is as follows:

$\frac{\mathrm{da}}{\mathrm{dt}}=\frac{n+1}{{\mathrm{\ϵ}}_f}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}{\frac{\widetilde{\mathrm{\σ}}(\mathrm{\θ},n)}{f(\mathrm{\θ},n)}|}_{\max }---\left(4\right);$

NSW-MOD model takes into full account the stress field of crack tip, the stress state containing crackle welding joint of dissimilar steel under high temperature can better be described, do not carrying out On Creep Crack Growth test condition with almost harmless method but also can realize, the residue of the service structure containing defect is being predicted creep life;

In NSW-MOD model, first material failure occurs obtain peaked position, obtain by method of value solving;

The calculating of On Creep Crack Growth Model Parameter

(1) creep strain speed

Material generation creep process is generally divided into three phases, describes the creep behaviour of material for describing the general Norton of the employing laws of this structure of creep of steady-state process more, and its expression formula is:

$\stackrel{\·}{\mathrm{\ϵ}}={\mathrm{A\σ}}^n---\left(5\right);$

σ is respectively steady state creep rate of strain and the stress in creep process; A, n is material creep performance parameter, determines by creep test;

(2) dimensionless function I _n

I _nbeing the n dimensionless function of considering stress state, is the function of n, and the expression formula under plane strain state is:

$I_n=10.3{(0.13+\frac{1}{n})}^{1/2}-\frac{4.6}{n}---\left(6\right);$

Expression formula under plane stress state is:

$I_n=7.2{(0.12+\frac{1}{n})}^{1/2}-\frac{2.9}{n}---\left(7\right);$

(3) multi axial strain factor f (θ, n)

Identical in multi axial strain factor f (θ, n) and creep ductility exhaustion damage constitutive equation, growing up and assembling the stress three axle degree R that depend primarily on material creep intensified index n and material based on creep hole _σ;

Its expression formula of multi axial strain factor f (θ, n) is:

$f(\mathrm{\θ},n)=\frac{{\mathrm{\ϵ}}_f^{*}}{{\mathrm{\ϵ}}_f}=\sinh \left[\frac{2}{3}\left(\frac{n-0.5}{n+0.5}\right)\right]/\sinh \left[2\frac{{\widetilde{\mathrm{\σ}}}_m}{{\widetilde{\mathrm{\σ}}}_e}\left(\frac{n-0.5}{n+0.5}\right)\right]---\left(8\right);$

In formula, $h={\widetilde{\mathrm{\σ}}}_m/{\widetilde{\mathrm{\σ}}}_e;$

Stress three axle degree R _σexpression formula be:

$R_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_m}{{\mathrm{\σ}}_{\mathrm{eq}}}=\frac{\sqrt{2}({\mathrm{\σ}}_1+{\mathrm{\σ}}_2+{\mathrm{\σ}}_3)}{3\sqrt{{({\mathrm{\σ}}_1-{\mathrm{\σ}}_2)}^2+{({\mathrm{\σ}}_2-{\mathrm{\σ}}_3)}^2+{({\mathrm{\σ}}_3-{\mathrm{\σ}}_1)}^2}}---\left(9\right);$

In formula, σ _mfor hydrostatic stress; σ _eqfor equivalent stress;

(4) creep rupture parameter C ^*calculating

Creep rupture parameter C ^*calculate by ABAQUS software, or by obtaining based on Reference Stress method (RSM);

The R5 of central power office of front Britain and R6 code are promoted the use of the success that RSM method has been described widely, creep rupture parameter C ^*method by Reference Stress under steady state creep condition is described; For describing creep rupture mechanical parameter C by Reference Stress method under steady state conditions ^*, the computing method of this and J integration are similar;

Method estimation C based on Reference Stress ^*expression formula as follows:

$C^{*}={\mathrm{\σ}}_{\mathrm{ref}}\·\stackrel{\·}{\mathrm{\ϵ}}\·{\left(\frac{K}{{\mathrm{\σ}}_{\mathrm{ref}}}\right)}^2---\left(10\right);$

In formula, σ _reffor Reference Stress, obtain by ultimate load, or obtain by theoretical calculation formula; Stress strength factor K calculates and calculates by theoretical formula, also can obtain by numerical evaluation;

Determining of the definition of 3 On Creep Crack Growth turning points and critical crack length

The length of determining critical crack is generally to determine after obtaining fracture toughness according to crack expansion test, but the validity of acquisition fracture toughness is more difficult; As everyone knows, crackle continue expansion process in, under a certain crack length, cause creep crack growth rate da/dt to change suddenly and accelerate expansion, i.e. the turning point of Crack Extension, so, be corresponding critical crack length at crack length corresponding to this turning point place;

According to station boiler the various different temperatures of reality from different in depress, through type (4) calculate obtain various different temperatures from different in the creep crack growth rate da/dt that depresses, then adopt multinomial model to carry out matching to da/dt-a curve, try to achieve turning point and can obtain the crack length a at turning point place that creep crack growth rate accelerates; Wherein, adopt polynomial regression function to be:

da/dN＝c ₀+c ₁a+c ₂a ²+c ₃a ³+c ₄a ⁴+c ₅a ⁵(11)；

In formula, c ₀, c ₁, c ₂, c ₃, c ₄, c ₅for fitting coefficient;

After three order derivatives of formula (11) solved function curve, try to achieve turning point, then obtain the corresponding crack length a of this turning point;

4 On Creep Crack Growth residual life evaluation

Heating surface tube is in harsh working environment, the easily germinating of induced defect, the macroscopic cracking that is continued expansion generation by this class defect is one of main Types mainly with multiple cracks or crackle group's form existence and radial cracking, and the wall thickness of heating surface tube will be much smaller than its axial length, therefore be, one of the most dangerous form containing the heating surface tube of radial cracking; Fig. 1 is for containing crackle heating surface tube figure;

If heating surface tube wall thickness is S, Initial crack length is a ₀; By determining after the crack length a at turning point place, the life consumption P after experience turning point is a/ (S-a ₀); So, the On Creep Crack Growth time t after experience turning point, residual life is:

$t={\∫}_a^S\frac{1}{\frac{n+1}{{\mathrm{\ϵ}}_f}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}{\frac{\widetilde{\mathrm{\σ}}(\mathrm{\θ},n)}{f(\mathrm{\θ},n)}|}_{\max }}\mathrm{da}---\left(12\right);$

In formula, under integration, be designated as the corresponding crack length a in turning point place, be above designated as-reheater heating surface tube wall thickness S;

S2 obtains the croop property parameter A of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature by creep test, n, set up Creep Equation, and obtain the performance parameter elastic modulus E of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature; Poisson ratio v, fracture toughness ε _f;

S3 calculates I according to formula (6) or formula (7) _n, and calculate acquisition by Finite Element Method value;

S4 adopts Finite Element Method or theoretical formula to calculate high temperature fracture parameters C ^*, and obtain high temperature fracture parameters C ^*relational expression C with crack length a ^*(a);

S5 is by high temperature fracture parameters C ^*relational expression C with crack length a ^*(a) after substitution formula (4), obtain creep crack growth rate da/dt;

S6 adopts multinomial model matching da/dt-a curve, and obtaining solved function curve break after the fitting expression of curve is the turning point that creep crack growth rate da/dt accelerates, and to obtain the corresponding crack length a in this turning point place be critical crack length;

It is S that S7 establishes heating surface piping wall thickness, and Initial crack length is a ₀; Life consumption P after experience turning point a is a/ (S-a so ₀);

S8 through type (4) carries out numerical integration between the crack length a at turning point place and pipe thickness S, and formula (12) obtains On Creep Crack Growth residual life t.

Basic ideas of the present invention are:

On Creep Crack Growth is the most advanced and sophisticated process of creep damage failure continuously of hardware internal fissure, based on the continuous accumulation of crack tip creep impairment, adopts NSW-MOD theoretical model, establishes the mathematical relation between creep impairment accumulation and crack growth rate.(2) adopt multinomial model to carry out matching to da/dt-a curve, try to achieve curve break and can obtain the turning point a of On Creep Crack Growth.(3) determine after the crack length a at turning point place, try to achieve and Dissimilar Steel Welded Joint pipeline wall thickness S and Initial crack length a ₀poor (S-a ₀) ratio a/ (S-a ₀), and then the life consumption of the On Creep Crack Growth of acquisition Dissimilar Steel Welded Joint under high-temperature and high-pressure conditions is a/ (S-a ₀).Obtain Dissimilar Steel Welded Joint On Creep Crack Growth residual life under high-temperature and high-pressure conditions by carrying out numerical integration between the crack length a from turning point and pipe thickness S.

Beneficial effect: the method combining by numerical evaluation and theoretical model, calculate micro-crack extension process under various service conditions (pressure and temperature), obtain the residual life of welding assembly.Avoid being undertaken by destructive test the not enough and too large problem of traditional appraisal procedure error that method is time-consuming and cost is high of life prediction.

Brief description of the drawings

Fig. 1 a is for dividing one of figure containing Cracked pipe sectional view and mesh of finite element;

Fig. 1 b is for dividing two of figure containing Cracked pipe sectional view and mesh of finite element;

Fig. 2 is da/dt-a curve map.

Embodiment

The On Creep Crack Growth life-span prediction method implementing procedure of ultra supercritical Dissimilar Steel Welded Joint of the present invention under high-temperature and high-pressure conditions is as follows: (theoretical derivation as summary of the invention, this does not repeat)

(1) obtain the croop property parameter A of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature by creep test, n, set up Creep Equation, and obtain the performance parameter elastic modulus E of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature; Poisson ratio v, fracture toughness ε _f;

(2) calculate I according to formula (6) or formula (7) _n, and obtain by numerical evaluation value;

(3) adopt Finite Element Method or theoretical formula to calculate high temperature fracture parameters C ^*, and obtain high temperature fracture parameters C ^*relational expression C with crack length a ^*(a);

(4) by high temperature fracture parameters C ^*relational expression C with crack length a ^*(a) after substitution formula (4), obtain creep crack growth rate da/dt;

(5) adopt multinomial model matching da/dt-a curve, obtaining solved function curve break after the fitting expression of curve is the turning point that creep crack growth rate da/dt accelerates, and to obtain the corresponding crack length a in this turning point place be critical crack length;

(6) establishing heating surface tube wall thickness is S, and Initial crack length is a ₀.Life consumption P after experience turning point a is a/ (S-a so ₀);

(7) through type (4) carries out numerical integration between the crack length a at turning point place and pipe thickness S, and formula (12) obtains On Creep Crack Growth residual life t.

Calculated examples

The present invention is taking the weld metal zone (WM) in certain 1000MW ultra supercritical unit T92/HR3C dissimilar steel welded pipe line as calculated examples, outlet steam parameter 26.25MPa, and 603 DEG C/605 DEG C, pipeline specifications is (Φ × S/mm) 48.3 × 7.82.

Because welding joint pipeline is very long along pipeline axial length, for internal diameter of the pipeline, axial dimension is much larger than its caliber, and strain that can negligible axial length direction, therefore can be plane strain problems by this problem reduction.Two dimension is containing Cracked pipe, as shown in Figure 1.Initial crack is positioned at pipeline radial outer wall, and Initial crack length is 0.1mm.When calculating, taking interior pressure as 25MPa, it is explanation that temperature is 600 DEG C.The chemical composition of T92/HR3C dissimilar steel weld pipe is as shown in table 1.

The chemical composition (wt%) of table 1 HR3C, T92, WM

The croop property parameter A that obtains Dissimilar Steel Welded Joint welding material under high temperature by creep test, n, sets up Creep Equation, and obtains the performance parameter elastic modulus E of Dissimilar Steel Welded Joint welding material under high temperature; Poisson ratio v, fracture toughness ε _f.

Under plane strain condition, calculate I according to formula (6) _n, and obtain by numerical evaluation value.The material parameter of weld metal zone and NSW/NSW-MOD model parameter are as shown in table 2 below.

The material parameter of table 2 weld metal zone and NSW/NSW-MOD model parameter

For the pipe that bears interior pressure, as follows containing the expression formula of the Reference Stress of outer wall radial cracking pipe

${\mathrm{\σ}}_{\mathrm{ref}}=\frac{P}{\frac{M_1}{R_2-a}+\ln \left(\frac{R_2-a}{R_1}\right)}---\left(14\right)$

M ₁for correction factor, its expression formula is

$M_1=\sqrt{1+1.61\frac{a^2}{R_{1}t}}---\left(15\right)$

Adopt stepping analytic approach, obtain the stress strength factor K under different crack lengths by numerical evaluation, then through type (10), (14), (15) calculate for weld metal zone high temperature fracture parameter C ^*with the pass of crack length a be

C ^*(a)＝-1.87125E-9+8.85825E-9a-5.45487E-9a ²+1.13359E-9a ³

Wherein, polynomial expression linearly dependent coefficient is 0.99785, can find out high temperature fracture parameter C ^*there is good variation tendency with crack length a.

By high temperature fracture parameter C ^*relational expression C with crack length a ^*(a) substitution formula (4) calculates creep crack growth rate da/dt.

Be under the service condition of 600 DEG C pressing as 25MPa, temperature, adopt fitting of a polynomial expression formula to carry out matching to da/dt-a curve, as shown in Figure 2.

Fitting of a polynomial expression formula

da/dt＝c ₀+c ₁a+c ₂a ²+c ₃a ³+c ₄a ⁴+c ₅a ⁵

In formula, c ₀, c ₁, c ₂, c ₃, c ₄, c ₅for fitting coefficient.

c ₀＝-4.58799E-10；c ₁＝1.29525E-8；c ₂＝-9.05876E-9；

c ₃＝2.34746E-9；c ₄＝-1.00246E-10；c ₅＝2.02672E-12；

After function curve being solved to zero point of three order derivatives, obtain the turning point under this condition.Calculating at pressure is that 25MPa, temperature are that crack length corresponding under the service condition of 600 DEG C is 2.79mm.So, the life consumption P experiencing after this turning point is 36.14%, and On Creep Crack Growth residual life is 3.83e+04 hour.

Claims (1)

1. a ultra-supercritical boiler heterogenous steel pipe welding joint lifetime estimation method, is characterized in that comprising the following steps:

S1 sets up On Creep Crack Growth model

Use C ^*the expression formula that characterizes field of stresses and strains near crack tip is as follows:

${\mathrm{\σ}}_{\mathrm{ij}}={\mathrm{\σ}}_0{\left(\frac{C^{*}}{{\stackrel{\·}{\mathrm{\ϵ}}}_0{\mathrm{\σ}}_0{I}_{n}r}\right)}^{\frac{1}{n+1}}{\widetilde{\mathrm{\σ}}}_{\mathrm{ij}}(\mathrm{\θ},n)---\left(1\right);$

${\stackrel{\·}{\mathrm{\ϵ}}}_{\mathrm{ij}}={\stackrel{\·}{\mathrm{\ϵ}}}_0{\left(\frac{C^{*}}{{\stackrel{\·}{\mathrm{\ϵ}}}_0{\mathrm{\σ}}_0{I}_{n}r}\right)}^{\frac{n}{n+1}}{\widetilde{\mathrm{\ϵ}}}_{\mathrm{ij}}(\mathrm{\θ},n)---\left(2\right);$

In formula, r is illustrated in crack tip θ angular direction apart from splitting sharp distance; σ ₀it is yield strength; it is the strain rate under corresponding effect of stress; for angle factor, it is the dimensionless function of θ and n; I _nbeing the n dimensionless function of considering stress state, is the function of n;

Based on the stress field of crack tip under hot conditions, the creep crack growth rate of stabilization sub stage utilizes following formula to calculate, i.e. NSW model:

$\frac{\mathrm{da}}{\mathrm{dt}}=\frac{n+1}{{\mathrm{\ϵ}}_f^{*}}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}---\left(3\right);$

In formula, r _cbe crack tip creep loss area size, equate with the average grain size of material;

for multiaxis fracture toughness: the breaking strain ε of multiaxis fracture toughness and single shaft creep _fidentical, breaking strain ε _fdetermine by fracture tension test; The in the situation that of plane strain, be ε _f/ 30;

The stress state of crack tip is taken into account in NSW theoretical prediction model, i.e. NSW-MOD model, expression formula is as follows:

$\frac{\mathrm{da}}{\mathrm{dt}}=\frac{n+1}{{\mathrm{\ϵ}}_f}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}{\frac{\widetilde{\mathrm{\σ}}(\mathrm{\θ},n)}{f(\mathrm{\θ},n)}|}_{\max }---\left(4\right);$

In NSW-MOD model, first material failure occurs obtain peaked position;

The calculating of On Creep Crack Growth Model Parameter

(1) creep strain speed

Material generation creep process is divided into three phases, adopts Norton law to describe the creep behaviour of material for describing this structure of creep of steady-state process, and its expression formula is:

$\stackrel{\·}{\mathrm{\ϵ}}={\mathrm{A\σ}}^n---\left(5\right);$

σ is respectively steady state creep rate of strain and the stress in creep process; A, n is material creep performance parameter;

(2) dimensionless function I _n

I _nbeing the dimensionless function of considering stress state, is the function of n, and the expression formula under plane strain state is:

$I_n=10.3{(0.13+\frac{1}{n})}^{1/2}-\frac{4.6}{n}---\left(6\right);$

Expression formula under plane stress state is:

$I_n=7.2{(0.12+\frac{1}{n})}^{1/2}-\frac{2.9}{n}---\left(7\right);$

(3) multi axial strain factor f (θ, n)

Identical in multi axial strain factor f (θ, n) and creep ductility exhaustion damage constitutive equation, growing up and assembling the stress three axle degree R that depend primarily on material creep intensified index n and material based on creep hole _σ;

Its expression formula of multi axial strain factor f (θ, n) is:

$f(\mathrm{\θ},n)=\frac{{\mathrm{\ϵ}}_f^{*}}{{\mathrm{\ϵ}}_f}=\sinh \left[\frac{2}{3}\left(\frac{n-0.5}{n+0.5}\right)\right]/\sinh \left[2\frac{{\widetilde{\mathrm{\σ}}}_m}{{\widetilde{\mathrm{\σ}}}_e}\left(\frac{n-0.5}{n+0.5}\right)\right]---\left(8\right);$

In formula, $h={\widetilde{\mathrm{\σ}}}_m/{\widetilde{\mathrm{\σ}}}_e;$

Stress three axle degree R _σexpression formula be:

$R_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_m}{{\mathrm{\σ}}_{\mathrm{eq}}}=\frac{\sqrt{2}({\mathrm{\σ}}_1+{\mathrm{\σ}}_2+{\mathrm{\σ}}_3)}{3\sqrt{{({\mathrm{\σ}}_1-{\mathrm{\σ}}_2)}^2+{({\mathrm{\σ}}_2-{\mathrm{\σ}}_3)}^2+{({\mathrm{\σ}}_3-{\mathrm{\σ}}_1)}^2}}---\left(9\right);$

In formula, σ _mfor hydrostatic stress; σ _eqfor equivalent stress;

(4) creep rupture parameter C ^*calculating

Creep rupture parameter C ^*calculate by Finite Element Method, or by obtaining based on Reference Stress method;

Method estimation C based on Reference Stress ^*expression formula as follows:

$C^{*}={\mathrm{\σ}}_{\mathrm{ref}}\·\stackrel{\·}{\mathrm{\ϵ}}\·{\left(\frac{K}{{\mathrm{\σ}}_{\mathrm{ref}}}\right)}^2---\left(10\right);$

In formula, σ _reffor Reference Stress; Stress strength factor K calculates and calculates by theoretical formula, or obtains by numerical evaluation;

Determining of the definition of 3 On Creep Crack Growth turning points and critical crack length

Crackle continue expansion process in, under a certain crack length, cause creep crack growth rate da/dt to change suddenly and accelerate expansion, i.e. the turning point of Crack Extension, is corresponding critical crack length at crack length corresponding to this turning point place;

According to station boiler actual motion condition, through type (4) calculate obtain various different wall temperatures from different in the creep crack growth rate da/dt that depresses, then adopt multinomial model to carry out matching to da/dt-a curve, try to achieve curve break and can obtain the crack length a at turning point place that creep crack growth rate accelerates; Wherein, adopt polynomial regression function to be:

da/dN＝c ₀+c ₁a+c ₂a ²+c ₃a ³+c ₄a ⁴+c ₅a ⁵(11)；

In formula, c ₀, c ₁, c ₂, c ₃, c ₄, c ₅for fitting coefficient;

After three order derivatives of formula (11) solved function curve, try to achieve turning point, then obtain the corresponding crack length a of this turning point;

4 On Creep Crack Growth residual life evaluation

The wall thickness of heating surface tube, much smaller than its axial length, therefore, is one of the most dangerous form containing the heating surface tube of radial cracking; If heating surface tube wall thickness is S, Initial crack length is a ₀; By determining after the crack length a at turning point place, the life consumption P after experience turning point is a/ (S-a ₀); So, the On Creep Crack Growth time t after experience turning point, residual life is:

$t={\∫}_a^S\frac{1}{\frac{n+1}{{\mathrm{\ϵ}}_f}{\left(\frac{C^{*}}{I_n}\right)}^{\frac{n}{n+1}}{\left({\mathrm{Ar}}_c\right)}^{\frac{1}{n+1}}{\frac{\widetilde{\mathrm{\σ}}(\mathrm{\θ},n)}{f(\mathrm{\θ},n)}|}_{\max }}\mathrm{da}---\left(12\right);$

In formula, under integration, be designated as the corresponding crack length a in turning point place, be above designated as-reheater heating surface tube wall thickness S;

S2 obtains the croop property parameter A of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature by creep test, n, set up Creep Equation, and obtain the performance parameter elastic modulus E of Dissimilar Steel Welded Joint mother metal, welding material and heat-affected zone under high temperature; Poisson ratio v, fracture toughness ε _f;

S3 calculates I according to formula (6) or formula (7) _n, and calculate acquisition by Finite Element Method value;

S4 adopts Finite Element Method or theoretical formula to calculate high temperature fracture parameters C ^*, and obtain high temperature fracture parameters C ^*relational expression C with crack length a ^*(a);

S5 is by high temperature fracture mechanics parameter C ^*relational expression C with crack length a ^*(a) after substitution formula (4), obtain creep crack growth rate da/dt;

S6 adopts multinomial model matching da/dt-a curve, and obtaining solved function curve break after the fitting expression of curve is the turning point that creep crack growth rate da/dt accelerates, and to obtain the corresponding crack length a in this turning point place be critical crack length;

It is S that S7 establishes heating surface piping wall thickness, and Initial crack length is a ₀; Life consumption P after experience turning point a is a/ (S-a so ₀);

S8 through type (4) carries out numerical integration between the crack length a at turning point place and pipe thickness S, and formula (12) obtains On Creep Crack Growth residual life t.