CN102507895A - Fatigue life estimation method of cast steel joint with obvious defect in cast steel joints - Google Patents

Abstract

The invention relates to a fatigue life estimation method of a cast steel joint with an obvious defect in cast steel joints. The method comprises the following steps of; step 1, determining the original crack size a0 of the cast steel joint; step 2, determining the shape factor f of the original crack of a cast steel joint mould; step 3, determining the final crack size af of the cast steel joint mould; step 4, obtaining the fatigue crack propagation life N of the cast steel mould; and step 5, determining the fatigue life of the cast steel joint. According to the fatigue life estimation method of the cast steel joint with the obvious defect in the cast steel joints, basis is provided for the accurate calculation in a project, the application of the cast steel joint can be greatly promoted, and the appearance and the force of the structure can be improved.

Description

Be used for having in the cast steel node cast steel node fatigue life evaluation method of open defect

Technical field

The present invention provides the fatigue life evaluation method of cast steel node in a kind of civil engineering structure, also can be used for the life estimate of approximate material cast steel tie-point in other field.To the cast steel node under the band open defect situation, to estimating its fatigue lifetime.For open defect is arranged in the node, then be crackle, according to fracturing mechanics method estimation crack propagation life with the equivalence of intranodal casting flaw.

Background technology

Steel-casting is to become molten iron through the iron and steel high temperature melt, is poured into to shift to an earlier date in the ready-made mould, and the cooling back demoulding forms, and cast steel node is a kind of form of expression of steel-casting, is mainly used in the interface of steel construction in the field of civil engineering.Cast steel node adopts the casting technique cast to produce; Because the complicacy of technological process; To occur inevitably loosening, casting flaw such as slag inclusion, bubble, under Fatigue Load, these initial casting flaws have remarkable influence to the load-bearing capacity of cast steel node.Existing nondestructiving detecting means can carry out nondestructive examination to node easily; Site-directed quantitative provides the defect distribution and the size of intranodal; The present invention is divided into cast steel node the band open defect and is not with two kinds of situation of open defect according to result of detection, to estimating its fatigue lifetime.

For the cast steel node that has open defect, this moment materials used S-N (preliminary Fatigue Stress Amplitude life-span) curve to carry out the component fatigue life estimate inapplicable, must adopt other theory, defect influence is taken into account.Theory of Fracture Mechanics has been carried out fine elaboration and sufficient theoretical proof to the material internal crack propagation, and the estimation of fatigue life that is applied to the initial imperfection cast steel node is practicable.Integrated use fracturing mechanics method of the present invention; With all kinds of defective equivalences in the cast steel node is crackle; Through calculating the fitted shapes factor; Thickness according to fracture toughness of materials and place, defective place node is confirmed final crack size, calculates the crack Propagation life-span at last, confirms the fatigue lifetime of cast steel node.

Summary of the invention

Technical matters: the purpose of this invention is to provide a kind of fatigue life evaluation method that is used for having in the cast steel node cast steel node of open defect; Because cast steel node is formed by the casting technique casting; Can produce various casting flaws unavoidably in the production run; Therefore the present invention is directed to has open defect in the node, then carry out life estimate according to the fracturing mechanics method.

Technical scheme: for solving the problems of the technologies described above, the present invention proposes a kind of fatigue life evaluation method that is used for having in the cast steel node cast steel node of open defect, this method comprises the steps:

Step 1: confirm cast steel node initial crack size a ₀:

If the defective in the cast steel node is detected by non-destructive detecting device, and this defective is independent, the original dimension a of the equivalent crackle of defective in the cast steel ₀The same with the size of defective independent in the cast steel;

If defective is detected by non-destructive detecting device, and be intensive, the original dimension a of the equivalent crackle of defective in the cast steel ₀Should be the same with intensive defect distribution area size in the cast steel node;

Step 2: the form factor f that confirms the initial crack of cast steel node model:

Set up the cast steel node model of a plurality of band initial cracks, the crack length in each model is different; Obtain the stress strength factor K under each initial crack length a through the finite element numerical method, the expression formula of K does

$K=f\left(\frac{a}{t}\right)\mathrm{\σ}\sqrt{\mathrm{\π\; a}}$ Formula 9

In the formula: K is a stress intensity factor; A is an initial crack length; T is place, crackle place, the thickness of cast steel node; σ is a stress; F is a form factor, is the function about a;

Obtain the form factor f in the model that initial crack length is a by formula 9,, simulate the expression formula f (a) of form factor f about a according to the f value under the different initial crack length; And then can obtain the expression formula of stress intensity factor range Δ K:

$\mathrm{\ΔK}\left(a\right)=f\·\mathrm{\Δ\σ}\·\sqrt{\mathrm{\π}\·a}$

Wherein Δ σ is the peaked scope of first principal stress;

Step 3: the final crack size a that confirms the cast steel node model _f:

Final crack size a _fFracture toughness according to material is calculated:

$a_c=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{Ic}}}{\mathrm{F\σ}}\right)}^2$ Formula 10

In the formula: a _cBe critical crack size; K _IcBe the cast steel material fracture toughness; F is a form factor, and σ is a stress;

Getting 0.9t is the maximum crack length of allowing appearance, and t is a cracks node wall thickness, then compares critical crack size a _cWith the size of the maximum crack length 0.9t that allows appearance, getting smaller value is final crack length a _f

Initial crack is more and more longer, and when reaching the length of final crackle, cast steel node has just ruptured;

Step 4: the crack Propagation life-span N that obtains the cast steel node model:

Confirm and calculate three variable a by above step ₀, a _fAnd Δ K, the crack Propagation life-span, N was:

$N={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{\Δ\; K}\right)}^m}={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{F\Δ\; \σ}\sqrt{\mathrm{\π\; a}}\right)}^m}$ Formula 11

C, m are respectively the cast steel material constants in the formula; Final crack length a _f, σ is a stress, the original dimension a of the equivalent crackle of defective in the cast steel ₀, f is a form factor, stress intensity factor range Δ K;

Step 5: confirm the fatigue lifetime of cast steel node:

The 4th crack Propagation life-span N that draws of step is the estimation of fatigue life value of cast steel node divided by safety coefficient n, and safety coefficient is chosen according to related specifications according to the significance level of cast steel node.

Preferably, defective described in the step 1 is a pore, or is mingled with.

Beneficial effect:

Cast steel node is aesthetic in appearance, reasonable stress, and it is as new engineering material and engineering structure pattern, and is more and more wider in Application in Civil Engineering.Cast steel node is formed by the casting technique casting, can produce various casting flaws unavoidably in the production run, and the life estimation method of the cast steel node of band defective does not also have at present, has limited the application of cast steel node.It is a kind of with the fatigue life evaluation method of defective by cast steel node that the present invention provides, and for the accurate Calculation in the engineering provides foundation, can promote the application of cast steel node greatly, improves the outward appearance of structure and stressed.

Description of drawings

Fig. 1 is the matched curve figure of f (a).

Embodiment

The present invention will be described below with reference to accompanying drawings.

A kind of fatigue life evaluation method that is used for having in the cast steel node cast steel node of open defect, it is characterized in that: this method comprises the steps:

Step 1: confirm cast steel node initial crack size a ₀:

If the defective in the cast steel node is detected by non-destructive detecting device, and this defective is independent, the original dimension a of the equivalent crackle of defective in the cast steel ₀The same with the size of defective independent in the cast steel;

If defective is detected by non-destructive detecting device, and be intensive, the original dimension a of the equivalent crackle of defective in the cast steel ₀Should be the same with intensive defect distribution area size in the cast steel node;

Step 2: the form factor f that confirms the initial crack of cast steel node model:

Set up the cast steel node model of a plurality of band initial cracks, the crack length in each model is different; Obtain the stress strength factor K under each initial crack length a through the finite element numerical method, the expression formula of K does

$K=f\left(\frac{a}{t}\right)\mathrm{\σ}\sqrt{\mathrm{\π\; a}}$ Formula 9

In the formula: K is a stress intensity factor; A is an initial crack length; T is place, crackle place, the thickness of cast steel node; σ is a stress; F is a form factor, is the function about a;

Obtain the form factor f in the model that initial crack length is a by formula 9,, simulate the expression formula f (a) of form factor f about a according to the f value under the different initial crack length; And then can obtain the expression formula of stress intensity factor range Δ K:

$\mathrm{\ΔK}\left(a\right)=f\·\mathrm{\Δ\σ}\·\sqrt{\mathrm{\π}\·a}$

Wherein Δ σ is the peaked scope of first principal stress;

Step 3: the final crack size a that confirms the cast steel node model _f:

Final crack size a _fFracture toughness according to material is calculated:

$a_c=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{Ic}}}{\mathrm{F\σ}}\right)}^2$ Formula 10

In the formula: a _cBe critical crack size; K _IcBe the cast steel material fracture toughness; F is a form factor, and σ is a stress;

Getting 0.9t is the maximum crack length of allowing appearance, and t is a cracks node wall thickness, then compares critical crack size a _cWith the size of the maximum crack length 0.9t that allows appearance, getting smaller value is final crack length a _f

Initial crack is more and more longer, and when reaching the length of final crackle, cast steel node has just ruptured;

Step 4: the crack Propagation life-span N that obtains the cast steel node model:

Confirm and calculate three variable a by above step ₀, a _fAnd Δ K, the crack Propagation life-span, N was:

$N={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{\Δ\; K}\right)}^m}={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{F\Δ\; \σ}\sqrt{\mathrm{\π\; a}}\right)}^m}$ Formula 11

C, m are respectively the cast steel material constants in the formula; Final crack length a _f, σ is a stress, the original dimension a of the equivalent crackle of defective in the cast steel ₀, f is a form factor, stress intensity factor range Δ K;

Step 5: confirm the fatigue lifetime of cast steel node:

The 4th crack Propagation life-span N that draws of step is the estimation of fatigue life value of cast steel node divided by safety coefficient n, and safety coefficient is chosen according to related specifications according to the significance level of cast steel node.

Defective described in the step 1 is a pore, or is mingled with.

At first cast steel node is carried out nondestructive examination, according to result of detection cast steel node is divided into the band open defect and is not with two kinds of situation of open defect then through nondestructiving detecting means.

Open defect is arranged in the cast steel node

Its calculation procedure is following:

1, confirms initial crack size a ₀:

Because defect kind is a lot, different in the node, there be also having of surface buried in inside, having single also has intensively, and when carrying out life estimate, it work as and quantizes to handle fibrous root according to the scope of all kinds of defectives, big young pathbreaker, and equivalence is quite big or small crackle.The position of at first equivalent crackle should be identical with defective locations, and according to defect shape, equivalent crackle can be divided into surface crack, embed crack and penetrated crack.If defective is bigger, be single, the original dimension a of equivalent crackle ₀Should be suitable with the size of individual defect; If defective is less, be intensive, the original dimension a of equivalent crackle ₀Should be suitable with the defect distribution area size.

2, confirm form factor f:

Set up the cast steel node model of a plurality of band initial cracks, the crack length in each model is different.Through each crack length a of numerical calculations such as finite element _iUnder stress strength factor K _i, K _iExpression formula do

$K=f\left(\frac{a}{t}\right)\mathrm{\σ}\sqrt{\mathrm{\πa}}---\left(9\right)$

In the formula: K is a stress intensity factor; A is a crack length; T is a thickness of slab; σ is a stress; F is a form factor, is the function about a.

Calculating crack length by formula (9) is a _iModel in form factor f _i, according to the f under the different crack lengths _iValue simulates the expression formula f (a) of form factor f about a.And then can obtain the expression formula of stress intensity factor range Δ K:

$\mathrm{\Δ}{K}_I\left(a\right)=f\·\mathrm{\Δ\σ}\·\sqrt{\mathrm{\π}\·a}$

Wherein Δ σ is the peaked scope of first principal stress.

3, confirm final crack size a _f:

Final crack size a _fCan calculate according to the fracture toughness of material:

$a_c=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{Ic}}}{\mathrm{f\σ}}\right)}^2---\left(10\right)$

In the formula: a _cBe critical crack size; K _IcBe fracture toughness of materials; F is a form factor.

Because generally do not allow the existence of penetrated crack in the engineering, get 0.9t (t is a cracks node wall thickness) again, then compare a for allowing the maximum crack length of appearance _cWith the size of 0.9t, getting smaller value is final crack length a _f

4, calculate the crack Propagation life-span:

Confirm and calculate three variable a by above step ₀, a _fAnd Δ K, according to Theory of Fracture Mechanics, the crack Propagation life-span, N was:

$N={\∫}_{a_0}^{a_f}\frac{\mathrm{da}}{C{\left(\mathrm{\ΔK}\right)}^m}={\∫}_{a_0}^{a_f}\frac{\mathrm{da}}{C{\left(\mathrm{f\Δ\σ}\sqrt{\mathrm{\πa}}\right)}^m}---\left(11\right)$

C, m are material constants in the formula.

5, confirming of designed life:

Go on foot the crack Propagation life-span N that calculates is cast steel node divided by safety coefficient n estimation of fatigue life value with the 4th.

The cast steel node that open defect is arranged

The cast steel node that open defect arranged directly Material Used S-N curve is estimated fatigue lifetime, must the utilization Theory of Fracture Mechanics.The crackle initial length is designated as a ₀, the crackle final lengths is designated as a _f, stress intensity factor range is designated as Δ K, and crackle is from a ₀Expand to a _fFatigue lifetime be designated as N, then the calculating formula of life-span N is:

$N={\∫}_{a_0}^{a_f}\frac{\mathrm{da}}{C{\left(\mathrm{\ΔK}\right)}^m}---\left(5\right)$

C, m are material constant.

Solve following formula, need to confirm three variable a ₀, a _fAnd Δ K.

1. confirm initial crack size a ₀:

Because defect kind is a lot, different in the node, there be also having of surface buried in inside, having single also has intensively, and when carrying out life estimate, it work as and quantizes to handle fibrous root according to the scope and big young pathbreaker of all kinds of defectives, and equivalence is quite big or small crackle.The position of at first equivalent crackle should be identical with defective locations, and according to defect shape, equivalent crackle can be divided into surface crack, embed crack and penetrated crack.If defective is bigger, be single, the original dimension a of equivalent crackle ₀Should be suitable with the size of individual defect; If defective is less, be intensive, the original dimension a of equivalent crackle ₀Should be suitable with the defect distribution area size.

2. confirm final crack size a _f:

Final crack size a _fCan calculate according to the fracture toughness of material:

$a_c=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{Ic}}}{\mathrm{f\σ}}\right)}^2---\left(6\right)$

In the formula: a _cBe critical crack size; K _IcBe fracture toughness of materials; F is a form factor.

Because generally do not allow the existence of penetrated crack in the engineering, get 0.9t (t is a cracks node wall thickness) again, then compare a for allowing the maximum crack length of appearance _cWith the size of 0.9t, getting smaller value is final crack length a _f

3. calculating stress strength factor range delta K.

Set up the cast steel node model of a plurality of band initial cracks, the crack length in each model is different.Through each crack length a of numerical calculations such as finite element _iUnder stress strength factor K _i, K _iExpression formula do

$K=f\left(\frac{a}{t}\right)\mathrm{\σ}\sqrt{\mathrm{\πa}}---\left(7\right)$

In the formula: K is a stress intensity factor; A is a crack length; T is a thickness of slab; σ is a stress; F is a form factor, is the function about a.

Calculating crack length by formula (7) is a _iModel in form factor f _i, according to the f under the different crack lengths _iValue simulates the expression formula f (a) (the matched curve figure of f (a) as accompanying drawing 1 shown in) of form factor f about a.And then can obtain the expression formula of stress intensity factor range Δ K:

$\mathrm{\Δ}{K}_I\left(a\right)=f\·\mathrm{\Δ\σ}\·\sqrt{\mathrm{\π}\·a}---\left(8\right)$

Wherein Δ σ is the peaked scope of first principal stress.

The above is merely preferred embodiments of the present invention; Protection scope of the present invention is not exceeded with above-mentioned embodiment; As long as the equivalence that those of ordinary skills do according to disclosed content is modified or changed, all should include in the protection domain of putting down in writing in claims.

Claims (2)

1. fatigue life evaluation method that is used for having in the cast steel node cast steel node of open defect, it is characterized in that: this method comprises the steps:

Step 1: confirm cast steel node initial crack size a ₀:

If the defective in the cast steel node is detected by non-destructive detecting device, and this defective is independent, the original dimension a of the equivalent crackle of defective in the cast steel ₀The same with the size of defective independent in the cast steel;

If defective is detected by non-destructive detecting device, and be intensive, the original dimension a of the equivalent crackle of defective in the cast steel ₀Should be the same with intensive defect distribution area size in the cast steel node;

Step 2: the form factor f that confirms the initial crack of cast steel node model:

Set up the cast steel node model of a plurality of band initial cracks, the crack length in each model is different; Obtain the stress strength factor K under each initial crack length a through the finite element numerical method, the expression formula of K does

$K=f\left(\frac{a}{t}\right)\mathrm{\σ}\sqrt{\mathrm{\π\; a}}$ Formula 9

In the formula: K is a stress intensity factor; A is an initial crack length; T is place, crackle place, the thickness of cast steel node; σ is a stress; F is a form factor, is the function about a;

Obtain the form factor f in the model that initial crack length is a by formula 9,, simulate the expression formula f (a) of form factor f about a according to the f value under the different initial crack length; And then can obtain the expression formula of stress intensity factor range Δ K:

$\mathrm{\ΔK}\left(a\right)=f\·\mathrm{\Δ\σ}\·\sqrt{\mathrm{\π}\·a}$

Wherein Δ σ is the peaked scope of first principal stress;

Step 3: the final crack size a that confirms the cast steel node model _f:

Final crack size a _fFracture toughness according to material is calculated:

$a_c=\frac{1}{\mathrm{\π}}{\left(\frac{K_{\mathrm{Ic}}}{\mathrm{F\σ}}\right)}^2$ Formula 10

In the formula: a _cBe critical crack size; K _IcBe the cast steel material fracture toughness; F is a form factor, and σ is a stress;

Getting 0.9t is the maximum crack length of allowing appearance, and t is a cracks node wall thickness, then compares critical crack size a _cWith the size of the maximum crack length 0.9t that allows appearance, getting smaller value is final crack length a _f

Initial crack is more and more longer, and when reaching the length of final crackle, cast steel node has just ruptured;

Step 4: the crack Propagation life-span N that obtains the cast steel node model:

Confirm and calculate three variable a by above step ₀, a _fAnd Δ K, the crack Propagation life-span, N was:

$N={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{\Δ\; K}\right)}^m}={\∫}_{a_0}^{a_f}\frac{\mathrm{Da}}{C{\left(\mathrm{F\Δ\; \σ}\sqrt{\mathrm{\π\; a}}\right)}^m}$ Formula 11

C, m are respectively the cast steel material constants in the formula; Final crack length a _f, σ is a stress, the original dimension a of the equivalent crackle of defective in the cast steel ₀, f is a form factor, stress intensity factor range Δ K;

Step 5: confirm the fatigue lifetime of cast steel node:

The 4th crack Propagation life-span N that draws of step is the estimation of fatigue life value of cast steel node divided by safety coefficient n, and safety coefficient is chosen according to related specifications according to the significance level of cast steel node.

2. the fatigue life evaluation method that is used for having in the cast steel node cast steel node of open defect according to claim 1, it is characterized in that: defective described in the step 1 is a pore, or is mingled with.

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