CN104122137A - Life-based design method for fatigue strength of ultrahigh-pressure container - Google Patents

Abstract

The invention relates to a life-based design method for the fatigue strength of an ultrahigh-pressure container. The design method comprises the following steps: firstly carrying out primary structure designing; then carrying out an optimal design of self-enhanced treatment according to the principle of minimum shearing stress; then calculating by utilizing finite element software so as to obtain largest local equivalent stress, and comparing with the designed fatigue strength, if the designed fatigue strength is met, calculating the minimum initial fatigue crack length according to a design pressure and a threshold value of fatigue crack propagation of materials; determining the maximum fatigue crack length by utilizing the fracture toughness of the materials and establishing an accurate description equation on the basis of data of a fatigue crack propagation test; and carrying out iterative calculation on the basis, judging whether the fatigue design life is met, if so, finishing the structure design. The design method has the advantages that multiple risk factors in the process of manufacture and operation of the ultrahigh-pressure container are considered and controlled at a design phase, and the fatigue design life is given according to a modern numerical calculation technology; the designing method is safer compared with a conventional elastic-plastic design method and is more accurate and reasonable compared with the existing fracture-mechanics design method.

Description

A kind of ultrahigh pressure vessel fatigue design method based on the life-span

Technical field

The invention belongs to design of pressure vessels field, relate to a kind of ultrahigh pressure vessel fatigue design method based on the life-span.

Background technology

It is industrial that on-stream pressure, the container more than 100MPa calls ultrahigh pressure vessel conventionally, at present for technical fields such as petrochemical complex, synthetic quartz, powder metallurgy, metal forming, Food processings, along with the expansion of people to superhigh pressure technique cognition, its application prospect will be more extensive.Because ultrahigh pressure vessel is very moving (as the pressure of UHV (ultra-high voltage) polyethylene reactor can be up to 350MPa under exacting terms conventionally, temperature can be up to 350 ℃ etc.), and inside is flammable and explosive substance, the catastrophic failures such as often concurrent fire, environmental pollution once lose efficacy, have a strong impact on social economy and people life property safety, therefore, its reliability is most important.

About ultrahigh pressure vessel design aspect, the industrially developed country such as the U.S. and Japan have carried out a large amount of research work, and accumulated rich experience, and promulgated relevant design standard, typically as U.S. ASME VIII-3 " another rules that high pressure vessel is built " and Japanese HPIS C-103 " UHV (ultra-high voltage) cylindrical vessel design pointer ".China is is digesting and assimilating on advanced foreign technology basis at present, has formed TSG R0002-2005 " ultrahigh pressure vessel safety and technical supervision rules ", but not yet set up relevant design standards by independent research.

Ultrahigh pressure vessel pressure and temperature in operational process fluctuates in time, and is subject to the process influences such as start-stop car, often bears fluctuating load effect, and fatigue break is one of its main failure mode.Therefore, U.S. ASME VIII-3 and Japanese HPIS C-103 standard have all stipulated take that plasto-elasticity is as basic fatigue design, for improving, have introduced self-enhancement design fatigue lifetime, have related in addition and take fracturing mechanics as basic Calculation of Fatigue Life.But mainly take, simplify analytical form as main when fatigue design, cannot accurately consider the impact of partial structurtes counter stress distribution etc., the ultrahigh pressure vessel Problem of Failure causing thus at present still happens occasionally; In addition, when carrying out fracture mechanics analysis, also mainly consider simple fatigue crack linear expansion, do not take into account the problems such as nearly threshold expansion that account for larger fatigue lifetime of mark, will cause that design safety nargin is excessive, waste is serious, so urgently develop a kind of more rational method for designing.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, a kind of ultrahigh pressure vessel fatigue design method based on the life-span is provided, taking into account under the prerequisite of manufacture and operation risk, more reasonably provide the fatigue design life-span of ultrahigh pressure vessel.

For achieving the above object, the technical solution adopted in the present invention is:

A ultrahigh pressure vessel fatigue design method based on the life-span, it comprises the following steps:

The military service pressure and temperature requirement of S1, clear and definite ultrahigh pressure vessel, and the fatigue behaviour data of material therefor;

S2, according to elastic-plastic mechanics theory, carry out preliminary structure design;

S3, according to shear stress minimum principle, to completing the ultrahigh pressure vessel of preliminary structure design, carry out self-enhancement and process optimal design;

S4, utilize common finite element software, the project organization of the ultrahigh pressure vessel that completing steps S3 is obtained is carried out stress analysis, obtains the stress distribution situation of ultrahigh pressure vessel structure;

S5, the stress analysis result obtaining in step S4 is converted into equivalent stress, finds out the local equivalent stress value of maximum of ultrahigh pressure vessel structure;

S6, the fatigue behaviour data of the local equivalent stress value of maximum in step S5 and material therefor are compared, when the local equivalent stress value of maximum is greater than the fatigue behaviour data of material therefor, return to step S2, otherwise directly enter step S7;

S7, according to threshold in fatigue crack propagation and the Theory of Fracture Mechanics of the local equivalent stress value of the maximum of step S5, material therefor, calculate minimum initial fatigue crack length computing formula is as follows:

$a_0^{\min }=\frac{1}{\mathrm{\π}}{\left(\frac{{\mathrm{\ΔK}}_{\mathrm{th}}}{Y\·\mathrm{\Δ}{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: for the initial fatigue crack length of minimum, m;

Δ K _thfor the threshold in fatigue crack propagation of material therefor, MPam ^1/2;

the maximum equivalent scope according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

S8, according to material fracture toughness and Theory of Fracture Mechanics, calculate maximum fatigue crack length a _f, computing formula is as follows:

$a_f=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{IC}}}{Y\·{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: a _ffor maximum fatigue crack length, m;

K _iCfor the fracture toughness of material therefor, MPam ^1/2;

the maximum equivalent according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

And set up the accurate equation of describing fatigue crack growth rate based on fatigue crack propagation test data, equation is as follows:

$\mathrm{da}/\mathrm{dN}=c{(\mathrm{\Δ}{K}^2-\mathrm{\Δ}{K}_{\mathrm{th}}^2)}^n$

In formula: da/dN is fatigue crack growth rate, m/cycle;

A is fatigue crack length, m;

N is load cycle number of times, cycle;

Δ K is stress intensity factor range, MPam ^1/2;

Δ K _thfor the threshold in fatigue crack propagation of material therefor, MPam ^1/2;

C and n are fitting coefficient;

S9, according to the maximum fatigue crack length of the initial fatigue crack length of the minimum of step S7, step S8 with describe the equation of fatigue crack growth rate, write the expectation serviceable life that iterative program calculates ultrahigh pressure vessel;

S10, the result of calculation of step S9 and ultrahigh pressure vessel fatigue design life-span are compared, meet and require designed life to enter step S16, otherwise reenter step S2;

S11, complete structural design.

Certainly, in order further to guarantee the quality of production and the operational reliability of ultrahigh pressure vessel, can also introduce Non-Destructive Testing step, now step is as follows:

The military service pressure and temperature requirement of S1, clear and definite ultrahigh pressure vessel, and the fatigue behaviour data of material therefor;

S2, according to elastic-plastic mechanics theory, carry out preliminary structure design;

S3, according to shear stress minimum principle, to completing the ultrahigh pressure vessel of preliminary structure design, carry out self-enhancement and process optimal design;

S4, utilize common finite element software, the project organization of the ultrahigh pressure vessel that completing steps S3 is obtained is carried out stress analysis, obtains the stress distribution situation of ultrahigh pressure vessel structure;

S5, the stress analysis result obtaining in step S4 is converted into equivalent stress, finds out the local equivalent stress value of maximum of ultrahigh pressure vessel structure;

S6, the fatigue behaviour data of the local equivalent stress value of maximum in step S5 and material therefor are compared, when the local equivalent stress value of maximum is greater than the fatigue behaviour data of material therefor, return to step S2, otherwise directly enter step S7;

S6-1, ultrahigh pressure vessel is carried out to Non-Destructive Testing;

S6-2, according to the Non-Destructive Testing result of step S6-1, judge whether containing excessive defect, during without excessive defect, to enter step S7, otherwise enter step S6-3;

S6-3, the excessive defect of step S6-2 is judged whether to meet design requirement, in the time of need carrying out defect repair if do not met design requirement, enter step S6-4, otherwise enter step S6-5;

S6-4, the contained excessive defect of ultrahigh pressure vessel is repaired, reentered afterwards step S7;

S6-5, using excessive defect size as initial fatigue crack length, by step S8 and S9, carry out Calculation of Fatigue Life successively afterwards, when require the designed life that the expectation of ultrahigh pressure vessel does not meet S10 serviceable life, turn back to step S6-4, otherwise enter step S11;

S7, according to threshold in fatigue crack propagation and the Theory of Fracture Mechanics of the local equivalent stress value of the maximum of step S5, material therefor, calculate minimum initial fatigue crack length computing formula is as follows:

$a_0^{\min }=\frac{1}{\mathrm{\π}}{\left(\frac{{\mathrm{\ΔK}}_{\mathrm{th}}}{Y\·\mathrm{\Δ}{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: for the initial fatigue crack length of minimum, m;

Δ K _thfor fatigue of materials Crack Extension threshold value, MPam ^1/2;

the maximum equivalent scope according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

S8, according to material fracture toughness and Theory of Fracture Mechanics, calculate maximum fatigue crack length a _f, computing formula is as follows:

$a_f=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{IC}}}{Y\·{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: a _ffor maximum fatigue crack length, m;

K _iCfor material fracture toughness, MPam ^1/2;

the maximum equivalent according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

And set up the accurate equation of describing fatigue crack growth rate based on fatigue crack propagation test data, equation is as follows:

$\mathrm{da}/\mathrm{dN}=c{(\mathrm{\Δ}{K}^2-\mathrm{\Δ}{K}_{\mathrm{th}}^2)}^n$

In formula: da/dN is fatigue crack growth rate, m/cycle;

A is fatigue crack length, m;

N is load cycle number of times, cycle;

Δ K is stress intensity factor range, MPam ^1/2;

Δ K _thfor fatigue of materials Crack Extension threshold value, MPam ^1/2;

C and n are fitting coefficient.

S9, according to the maximum fatigue crack length of the initial fatigue crack length of the minimum of step S7, step S8 with describe the equation of fatigue crack growth rate, write the expectation serviceable life that iterative program calculates ultrahigh pressure vessel;

S10, the result of calculation of step S9 and ultrahigh pressure vessel fatigue design life-span are compared, meet and require designed life to enter step S11, otherwise reenter step S2;

S11, complete structural design.

While carrying out Non-Destructive Testing, the Interventions Requested of defect are as the criterion with the project of regulation in TSG R0002-2005 " ultrahigh pressure vessel safety and technical supervision rules ", and the standard whether judgement defect exceeds standard is the resolving power (this technology can detect the minimum dimension of defect) of Dynamic Non-Destruction Measurement used.

Beneficial effect of the present invention is:

1), the present invention is on the basis of elastoplasticity fatigue design and self-enhancement design, carry out finite element numerical analysis design, can grasp the stress field feature in ultrahigh pressure vessel manufacture and operational process comprehensively, not only improved the control that changes in process parameters is caused to tired risk, and can avoid resolving design because of tradition end structure influence is considered to the not enough potential risk of bringing.

2), the present invention is by Non-Destructive Testing and fracture mechanics analysis, can control the failure risk of the ultrahigh pressure vessel causing because of processing and manufacturing defect, further increased the reliability of fatigue design.

3), the present invention proposes Non-Destructive Testing not find the ultrahigh pressure vessel of defect, using the minimum crack size of applicable fracturing mechanics as Initial crack length, employing can be described preferably the relational expression of the nearly threshold of fatigue crack and linear expansion behavior and carry out Calculation of Fatigue Life, can obtain more accurate reasonably fatigue life prediction result.

4), the present invention carries out numerical evaluation fatigue lifetime by writing iterative program, be applicable to the stress intensity factor expression formula of various labyrinths, the method that must calculate again fatigue lifetime after loaded down with trivial details integration obtains concrete analytic expression is easier to realize, and more meets the general trend of following design of pressure vessels development.

Accompanying drawing explanation

Fig. 1 is design flow diagram of the present invention.

Fig. 2 is the design flow diagram of the present invention that contains Non-Destructive Testing step.

Fig. 3 is the Fatigue Property Curve (stress ratio R=-1) of AISI4340 alloy steel.

Fig. 4 is the design fatigue curve (stress ratio R=0) of AISI4340 alloy steel.

The finite element analysis result that Fig. 5 (a) UHV (ultra-high voltage) reaction tube axial stress distributes.

The finite element analysis result that Fig. 5 (b) UHV (ultra-high voltage) reaction tube circumference stress distributes.

Fig. 6 is the fatigue crack growth rate curve (stress ratio R=0) of AISI4340 alloy steel.

Fig. 7 is the fatigue crack growth rate curve (stress ratio R=0.1) of AISI4333M4 alloy steel.

Embodiment

Below in conjunction with drawings and Examples, the inventive method is described further.

Embodiment mono-

For explaining the present invention, a certain UHV (ultra-high voltage) reaction tube for the production of Low Density Polyethylene of the petrochemical industry of take is example, introduces whole design process, and provides designed life.

Equipment working pressure is that 245MPa, temperature are 90 ℃.Material adopts AISI4340 alloy pipe, and its yield strength is σ _s=1026MPa, tensile strength is σ _b=1091MPa, the actual measurement Fatigue Property Curve of stress ratio R=-1 (S-N curve) is shown in Fig. 2, life-span is got to safety coefficient 15, counter stress width is got safety coefficient 1.5 and is set up design curve, mean stress converts to the Goodman formula that passes through of design curve, and the design fatigue curve of R=0 is as being shown in Fig. 3.

1), according to technological requirement and material property, carry out preliminary structure design

When only considering that UHV (ultra-high voltage) reaction tube is under on-stream pressure effect, its circumference stress (σ _t), radial stress (σ _t) and axial stress (σ _z) can calculate by following Lam é formula:

${\mathrm{\σ}}_t=\frac{P}{K^2-1}[1+{\left(\frac{r_o}{r}\right)}^2],{\mathrm{\σ}}_r=\frac{P}{K^2-1}[1-{\left(\frac{r_o}{r}\right)}^2],{\mathrm{\σ}}_z\frac{P}{K^2-1}$

In formula: P is working pressure,

K is UHV (ultra-high voltage) reaction tube boss ratio K=r _o/ r _i,

R is any radius, r _ofor external radius, r _ifor inside radius.

Visible σ _t> σ _z> σ _r, and work as r=r _itime, σ _tmaximum.

For shutting down operating mode, from the design fatigue curve of R=0, fatigue limit is 187MPa, and corresponding maximum allowable fatigue stress is 374MPa.For the working pressure of P=245MPa, work as K=2.2, σ _t=372.6MPa, meets fatigue strength requirement.Therefore, primary design internal diameter r _i=20mm, r _o=44mm.

2), according to shear stress minimum principle, carry out self-enhancement optimal design

For internal diameter r _i=20mm, r _othe UHV (ultra-high voltage) reaction tube of=44mm, as elastic-plastic interface radius b=25.12mm, from pressurized energy P _aduring=670MPa, shear stress is minimum, meets following transcendental equation:

$P_A=\frac{{\mathrm{\σ}}_s}{\sqrt{3}}[1-{\left(\frac{b}{r_o}\right)}^2+21\mathrm{nb}]$

Now, self-enhancement rate is about 21.3%.

3), by modeling Analysis, carry out elastoplasticity checking fatigue strength

UHV (ultra-high voltage) reaction tube structure for design is carried out finite element numerical simulation, multianalysis working pressure and self-enhancement processing pressure, and the impact of end interference fit (diameter interference power adopts 0.1mm) counter stress distribution.Axially maximum equivalent alterante stress appears near fit edge, and stress amplitude is 62.2MPa, and mean value is 86.7MPa, sees Fig. 5 (a); Hoop maximum equivalent alterante stress appears near the elastic-plastic interface away from end, stress amplitude 130.9MPa, and mean value 177.5, is shown in Fig. 5 (b).Compare with the design fatigue curve in Fig. 3, all meet as seen the requirement of elastoplasticity fatigue design.

4), based on fracture theory, calculate the fatigue design life-span of UHV (ultra-high voltage) reaction tube

1. adopt AISI4340 alloy pipe to carry out fatigue crack growth rate test, the results are shown in Figure 5.By testing, determine threshold in fatigue crack propagation Δ K _th=23.93MPam ^1/2; According to finite element analysis result, and carry out maximum equivalent range computation by Goodman formula, obtain for shallow surface crack, correction factor Y (Y is the parameter in fracturing mechanics, and Y is an amount relevant with crack shape and load mode) gets 1.122.Bring in the relational expression of step S7, can obtain minimum initial fatigue crack length

2. adopt the fatigue crack growth rate relational expression (describing the equation of fatigue crack growth rate) of step S8 to carry out matching to the data of test acquisition, obtain fitting coefficient c=2.82 * 10 ^-25, n=1.18.

3. carry out the fracture toughness test of AISI4340 alloy pipe, record K _iC=134MPam ^1/2, adopt the maximum fatigue crack length relational expression of step S8 to calculate a _f=10.8mm.

4. write iterative program, using crack length initial value as the initial fatigue crack length of minimum every circulation primary is superimposed with by the fatigue crack growth rate relational expression of S8 and calculates the crackle increment obtaining, and be again brought into stress intensity factor expression formula, calculate next step crack Propagation increment, until accumulated fatigue total length of cracks is while equaling the maximum fatigue crack length of S8, stop calculating output iterations (being fatigue lifetime).

Will a _f=10.8mm, c=2.82 * 10 ^-25, n=1.18 brings iterative program into, and calculating and obtaining fatigue lifetime is 167742 cycles.

If carry out the Calculation of Fatigue Life based on fracturing mechanics according to ASME VIII-3 " another rules that high pressure vessel is built ", minimum initial fatigue crack length is got the Non-Destructive Testing precision 2mm of TSG R0002-2005 " ultrahigh pressure vessel safety and technical supervision rules " regulation, fatigue crack growth rate adopts linear relation (Paris formula), and can obtain fatigue lifetime is only 73405 cycles.And the actual examination survey life-span is 200600 cycles, the Calculation of Fatigue Life method in visible the present invention is more reasonable.

Embodiment bis-

The crack Propagation of take containing the AISI4333M4 alloy steel of excessive defect is example, and the linear Calculation of Fatigue Life method based on fracturing mechanics is more accurate reasonable to further illustrate the inventive method.

1. adopt AISI4333M4 alloy steel to carry out fatigue crack propagation test, the results are shown in Figure 7, fatigue crack expands to fracture from threshold value and has experienced altogether 100600 circulations.

2. for fatigue crack growth rate application linear relation, carry out life prediction, first under log-log coordinate system, matching obtains related coefficient, sets up following Paris relational expression:

da/dN＝1.15×10 ^-29(ΔK) ^2.93

By integration, obtaining fatigue lifetime is only 19956 cycles, as seen far below surveying fatigue lifetime.

3. for the method in fatigue crack growth rate application the present invention, carry out life prediction, adopt the fatigue crack growth rate relational expression of step S10 to carry out matching to the data of test acquisition, obtain fitting coefficient c=3.78 * 10 ^-23, n=1.05, and then by iterative computation, to go out fatigue lifetime be 48023 cycles, although visible bimetry is still conservative fatigue lifetime than actual measurement, the inventive method has obviously been better than linear Calculation of Fatigue Life method.

Claims (1)

1. the ultrahigh pressure vessel fatigue design method based on the life-span, is characterized in that comprising the following steps:

The military service pressure and temperature requirement of S1, clear and definite ultrahigh pressure vessel, and the fatigue behaviour data of material therefor;

S2, according to elastic-plastic mechanics theory, carry out preliminary structure design;

S3, according to shear stress minimum principle, to completing the ultrahigh pressure vessel of preliminary structure design, carry out self-enhancement and process optimal design;

S4, utilize common finite element software, the project organization of the ultrahigh pressure vessel that completing steps S3 is obtained is carried out stress analysis, obtains the stress distribution situation of ultrahigh pressure vessel structure;

S5, the stress analysis result obtaining in step S4 is converted into equivalent stress, finds out the local equivalent stress value of maximum of ultrahigh pressure vessel structure;

S6, the fatigue behaviour data of the local equivalent stress value of maximum in step S5 and material therefor are compared, when the local equivalent stress value of maximum is greater than the fatigue behaviour data of material therefor, return to step S2, otherwise directly enter step S7;

S7, according to threshold in fatigue crack propagation and the Theory of Fracture Mechanics of the local equivalent stress value of the maximum of step S5, material therefor, calculate minimum initial fatigue crack length computing formula is as follows:

$a_0^{\min }=\frac{1}{\mathrm{\π}}{\left(\frac{{\mathrm{\ΔK}}_{\mathrm{th}}}{Y\·\mathrm{\Δ}{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: for the initial fatigue crack length of minimum, m;

Δ K _thfor the threshold in fatigue crack propagation of material therefor, MPam ^1/2;

the maximum equivalent scope according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

S8, according to material fracture toughness and Theory of Fracture Mechanics, calculate maximum fatigue crack length a _f, computing formula is as follows:

$a_f=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{IC}}}{Y\·{\mathrm{\σ}}_{\mathrm{eq}}^{\max }}\right)}^2$

In formula: a _ffor maximum fatigue crack length, m;

K _iCfor the fracture toughness of material therefor, MPam ^1/2;

the maximum equivalent according to the finite element analysis acquisition of step S4, MPa;

Y is correction factor;

And set up the accurate equation of describing fatigue crack growth rate based on fatigue crack propagation test data, equation is as follows:

$\mathrm{da}/\mathrm{dN}=c{(\mathrm{\Δ}{K}^2-\mathrm{\Δ}{K}_{\mathrm{th}}^2)}^n$

In formula: da/dN is fatigue crack growth rate, m/cycle;

A is fatigue crack length, m;

N is load cycle number of times, cycle;

Δ K is stress intensity factor range, MPam ^1/2;

Δ K _thfor the threshold in fatigue crack propagation of material therefor, MPam ^1/2;

C and n are fitting coefficient;

S9, according to the maximum fatigue crack length of the initial fatigue crack length of the minimum of step S7, step S8 with describe the equation of fatigue crack growth rate, write the expectation serviceable life that iterative program calculates ultrahigh pressure vessel;

S10, the result of calculation of step S9 and ultrahigh pressure vessel fatigue design life-span are compared, meet and require designed life to enter step S16, otherwise reenter step S2;

S11, complete structural design.