CN102176212A - Method for deducing stress intensity factor of butt joint containing I-type center bursts and application - Google Patents

Abstract

The invention relates to a method for deducing a stress intensity factor of a butt joint containing I-type center bursts and application, belonging to the technical field of welding and solving the problems on a solution to the stress intensity factor of the butt joint containing the I-type center bursts by means of work loads, burst dimensions and joint shapes as well as on solutions to critical burst dimensions, critical stress and residual service life of the butt joint containing the I-type center bursts by using a formula in the specifications. The method comprises the following steps of: firstly, solving a stress intensity factor formula for the butt joint containing the I-type center bursts by using an analysis method when the surplus height of the joint is only considered, then solving a stress intensity factor formula by means of a finite element calculation method and a result regression analysis method when the width of a capping bead and the transition arc radius of a weld toe are considered, and further determining the stress intensity factor formula of the butt joint containing the I-type center bursts. By applying the formula, the critical burst dimensions, the critical stress and the residual service life of the butt joint containing the I-type center bursts can be further solved. The method is suitable for conditions of any materials of the butt joint containing the I-type center bursts.

Description

Contain the derivation method and the application of the stress intensity factor of I type centre burst open joint

Technical field

The present invention relates to a kind of derivation method and application of stress intensity factor, be specifically related to the derivation method and the application of the open joint stress intensity factor of the certain reinforcement of a kind of I of containing type central through crack band, belong to welding technology field.

Background technology

Welding is widely used in the structural design as a kind of connection means, general employing grade for matching principle (packing material and strength of parent are suitable) carries out Selection of welding filling material.Because its local fast heating and cooling procedure, make the weld metal zone produce bigger residual tension, be easy to generate defectives such as pore, crackle in addition in the weld seam, subregion crystal grain is thick, these all make the each side load-bearing capacity of weld metal zone be lower than the load-bearing capacity of mother metal, and the stress brittle failure of the easy spot of welded structure.If the increase weld reinforcement, the loaded area of increase weld metal zone can reduce the mean stress of weld metal zone, improves the load-bearing capacity of joint.

If there are defectives such as crackle in the weld metal zone, just should estimate the load-bearing capacity of joint from the fracturing mechanics angle.For having welding crack and the easy welded structure that low stress brittle fracture takes place, reach the fracture toughness K of material when the stress strength factor K of cracks _ICThe time, crackle generation unstable propagation, structural failure.K _ICBe the intrinsic mechanical performance parameter of material, K then through type (1) calculates.

$K=\mathrm{Y\σ}\sqrt{a}---\left(1\right)$

Wherein, Y is a form factor, and it is relevant with mode of the position of the geometric configuration of member, crackle and size, plus load etc., and σ is a working stress, and a is the crack size parameter.

Known work load can be obtained the critical crack size that makes crackle generation unstable propagation according to formula (2).

$a_c={\left(\frac{K_{\mathrm{IC}}}{\mathrm{Y\σ}}\right)}^2---\left(2\right)$

K wherein _ICFracture toughness for material.

Known crack size can be obtained according to formula (3) and make the limit stress of crackle generation unstable propagation, thereby judges whether safety of structure.

${\mathrm{\σ}}_c=\frac{K_{\mathrm{IC}}}{Y\sqrt{a}}---\left(3\right)$

For the structure of bearing cyclic loading, can obtain crack growth rate according to formula (4), and then obtain the remanent fatigue life of structure.

$\frac{\mathrm{da}}{\mathrm{dN}}=A{\left(\mathrm{\ΔK}\right)}^n---\left(4\right)$

The above all needs to know the stress intensity factor of member.The limited wide plate stress intensity factor formula that has only various crackle forms in all fracturing mechanics teaching materials, and the stress intensity factor formula of band reinforcement joint is not appeared in the newspapers.

Importance at the stress intensity factor formula of being with the reinforcement joint contains crackle band reinforcement open joint stress intensity factor formula and application thereof with regard to how to determine, carries out corresponding research work, has realistic meaning.

Summary of the invention

The purpose of this invention is to provide a kind of derivation method and application of stress intensity factor of the I of containing type centre burst open joint, with solve do not provide band reinforcement joint in the prior art and the stress intensity factor formula of open joint when containing I type centre burst and being subjected to tensile load, can't instruct to contain I type central through crack and with the problem of the structural design of the open joint of certain reinforcement.Mentioned " centre burst " of the present invention is meant " central through crack ", and " open joint " is meant " with the open joint of certain reinforcement ".

The present invention has also solved how to find the solution the problem of the stress intensity factor that contains I type centre burst open joint by operating load, crack size and joint geometry, and the critical crack size, limit stress and the joint residual life that how to use this formula to find the solution to contain I type centre burst open joint.

Design concept of the present invention: for the member that has central through crack, increase the loaded area at crack surface place, can reduce the mean stress at crack surface place, and then improve the security of member.The open joint that contains central through crack can increase the loaded area at crack surface place by increasing certain reinforcement, and the load-bearing capacity of joint is increased.When there is certain reinforcement in weld seam, at first must make welding toe have certain transition arc radius r, could guarantee to reduce the factor of stress concentration of welding toe, improve the fatigue strength of joint.In addition, band reinforcement joint also should have enough capping bead half-breadth w and reinforcement height h.Could guarantee the stress equalizing of weld seam region like this.Band reinforcement joint geometry is shown in accompanying drawing (1).Finding the solution of stress intensity factor when containing central through crack and be subjected to tensile load with certain reinforcement joint can obtain by the method that analytical Calculation combines with FEM (finite element) calculation.At first pass through analytical Calculation, only considered the stress intensity factor analytical expression when reinforcement h influences, and then the method by FEM (finite element) calculation, regression Calculation goes out to consider the complete stress intensity factor formula of w and r influence, the stress intensity factor formula when the band reinforcement joint of finally determining to contain central through crack is subjected to tensile load.

Technical scheme of the present invention is:

The derivation method that contains the stress intensity factor of I type centre burst open joint is:

Stress intensity factor formula when step 1, analytical Calculation are only considered h:

Consider that as shown in Figure 2 band reinforcement joint contains the situation of centre burst, by any fracturing mechanics teaching material as can be known, for infinitely great plate, contain central through crack and be subjected to the Westcrgacrd stress function of even tension to be

$Z_I\left(z\right)=\frac{\mathrm{\σz}}{\sqrt{z^2-a^2}}---\left(5\right)$

Wherein: σ is for adding even tension; Z is a complex variable; A is half of centre burst size;

With reference to (5) formula, the stress function that can establish the cracks in body problem of accompanying drawing 2 forms is

$Z_I\left(z\right)=\frac{\mathrm{cz}}{\sqrt{z^2-a^2}}---\left(6\right)$

Wherein c is a undetermined coefficient.

Determine coefficient c by considering whole machine balancing.Because symmetry is got the left side and is assigned to consider then have

${\mathrm{\σ}}_y{|}_{y=0,x>a}=[\mathrm{Re}{Z}_I\left(z\right)-{\mathrm{yI}}_m{Z}_I^{\′}\left(z\right)]{|}_{y=0,x>a}=\frac{\mathrm{cx}}{\sqrt{x^2-a^2}}---\left(7\right)$

By ∑ Y=0, promptly by left-half equilibrium of forces inside and outside the y direction,

${\&Integral;}_a^{t+h}\frac{\mathrm{cx}}{\sqrt{x^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\mathrm{dx}=\mathrm{\&sigma;t}---\left(8\right)$

:

$c=\frac{\mathrm{\&sigma;t}}{\sqrt{{(t+h)}^2-a^2}}---\left(9\right)$

(9) generation is returned (6) formula, and the approximate stress function that can get this problem is

$Z_I\left(z\right)=\frac{\mathrm{\&sigma;tz}}{\sqrt{{(t+h)}^2-a^2}\sqrt{z^2-a^2}}---\left(10\right)$

So, can get stress intensity factor and be

$K_I=\underset{\left|\mathrm{\&xi;}\right|\&RightArrow;0}{\lim }\sqrt{2\mathrm{\&pi;\&xi;}}{Z}_I\left(\mathrm{\&xi;}\right)=\frac{t}{\sqrt{{(t+h)}^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(11\right)$

Wherein ξ=z-a also is a complex variable;

Step 2, definite coefficient of considering w and r influence:

The stress intensity factor formula that formula (11) is determined has only been considered the influence of h, the result of step 1 thinks that w and r have enough big size and make that the factor of stress concentration of crackle place section stress distribution uniform and welding toe is very little, to such an extent as to the band reinforcement joint stress intensity factor that contains centre burst is not had influence.Influence to above-mentioned stress intensity factor when in fact the size of w and r is big inadequately is still bigger.Therefore consider w and r influence the band reinforcement joint stress intensity factor formula that contains centre burst should for

$K_I=f\frac{t}{\sqrt{{(t+h)}^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(12\right)$

Just can determine to contain the band reinforcement joint stress intensity factor formula of centre burst as long as determined coefficient f, by a large amount of FEM (finite element) calculation, and regretional analysis, determine that f is

$f=1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}]---\left(13\right)$

Step 3, determine to contain the stress intensity factor formula of I type centre burst open joint:

The result of integrating step one and step 2 provides the stress intensity factor formula that contains I type centre burst open joint:

$K_I=\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(14\right).$

The stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint critical crack size a of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The fracture toughness K of step 1, measurement weld material _IC

Step 2, with the form parameter of joint: half t substitution formula (13) of capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and thickness of slab is obtained f;

The open joint critical crack size a that contains the certain reinforcement of I type central through crack band is calculated in step 3, foundation _cFormula:

$a_c=\frac{\sqrt{{\left({\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{f}^2\right)}^2+{{4K}_{\mathrm{IC}}}^4{(t+h)}^2}-{\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2{K_{\mathrm{IC}}}^2}---\left(15\right)$

Step 4, the operating load σ substitution formula (15) of the result of step 1 and step 2 and joint, can obtain under this operating load the critical crack size a of joint _c

The stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint critical load σ of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The open joint critical load σ that contains the certain reinforcement of I type central through crack band is calculated in step 1, foundation _cFormula:

${\mathrm{\&sigma;}}_c=\frac{K_{\text{IC}}}{\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\sqrt{\mathrm{\&pi;a}}}---\left(16\right)$

The fracture toughness K of step 2, measurement weld material _IC

Step 3, with the fracture toughness K of weld material _IC, capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and half t of thickness of slab, half a substitution formula (16) of crack size can obtain the open joint critical load σ that contains the certain reinforcement of I type central through crack band _c

The stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint residual life N of the certain reinforcement of I type central through crack band _f

Concrete steps are as follows:

Step 1, obtain the critical crack size a of the open joint crackle unstable propagation that contains the certain reinforcement of I type central through crack band according to claim 2 _c, operating load σ selects maximum stress during calculating;

Step 2, be different situations, can obtain the open joint residual life N that contains the certain reinforcement of I type central through crack band according to formula (20) and formula (21) for n _fA wherein ₀For the initial crack size half, Y is tried to achieve by formula (22); A and n are the intrinsic parameter of material, suppose that Δ σ is a constant;

N ≠ 2 o'clock, $\frac{2}{2-n}(a_c^{1-\frac{n}{2}}-a_0^{1-\frac{n}{2}})=\mathrm{A\&Delta;}{\mathrm{\&sigma;}}^n{Y}^n{N}_f---\left(20\right)$

During n=2, $\ln \frac{a_c}{a_0}=A{\mathrm{\&Delta;\&sigma;}}^2{Y}^2{N}_f---\left(21\right)$

$Y=\mathrm{ft}\sqrt{\frac{\mathrm{\&pi;}}{{(t+h)}^2-a^2}}---\left(22\right)$

Wherein f is obtained by formula (13).

The stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint J integration and the crack tip opening displacement δ of the certain reinforcement of I type central through crack band;

Concrete steps are as follows:

Step 1, obtain the stress strength factor K of the open joint that contains the certain reinforcement of I type central through crack band according to formula (14) _I:

Step 2, can obtain the open joint crack tip opening displacement δ that contains the certain reinforcement of I type central through crack band according to formula (18):

$\mathrm{\&delta;}=\frac{K_I^2}{E^{\&prime;}{\mathrm{\&sigma;}}_S}---\left(18\right)$

In the formula: σ _s---yield strength;

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Step 3, can obtain the open joint J integration that contains the certain reinforcement of I type central through crack band according to formula (19):

$J=\frac{K_I^2}{E^{\&prime;}}---\left(19\right)$

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Stress strength factor K according to the open joint that contains the certain reinforcement of I type central through crack band _I, by J integration and crack tip opening displacement δ respectively with stress strength factor K _ITransforming relationship can obtain J integration and δ.

Useful technique effect of the present invention is:

Fig. 3 is the analog computation of the form factor formula (22) of the given open joint that contains the certain reinforcement of I type central through crack band of this paper and difformity size joint comparable situation as a result.Comparative result shows that for the joint of difformity size, formula that this paper provides and finite element simulation calculation result coincide good.Therefore, the stress intensity factor formula of the open joint that contains the certain reinforcement of I type central through crack band that this paper provides can well instruct the structural design of the open joint that contains the certain reinforcement of I type central through crack band.The present invention is applicable to that any materials (linear elasticity condition) contains the member of the certain reinforcement of I type central through crack band as Fig. 1 form.

Be subjected to the situation of unilateral stretching for the joint that contains I type crackle, when the relative value of plus load and crack size and thickness of slab was known, form factor Y was the decision stress strength factor K _IUnique parameter.And the form factor of this moment is only relevant with the geometric parameter of joint.For joint shown in Figure 2, the variation of joint geometric parameter h, w, r can cause the variation of form factor Y, further causes K _IVariation.Therefore when the relative value of plus load and crack size and thickness of slab is known, only need study joint geometric parameter h, w, r the rule that influences, just can obtain joint geometric parameter h, w, r counter stress intensity factor K form factor Y _IInfluence rule.Form factor Y is more little, and joint is not easy to take place low stress brittle fracture more.

In order to investigate the correctness of formula,, formula result calculated that provides according to this paper and finite element simulation calculation result are compared at different joint geometric parameters.At the open joint that contains central through crack shown in Figure 2, the relative value a/t that chooses crack size and thickness of slab is 0.286.Because when toe of weld arc transition radius r was 8mm, the toe of weld factor of stress concentration was less, can guarantee joint fatigue strength.Therefore selecting r for use is 8mm.By relatively finding to draw to draw a conclusion by this paper formula result of calculation and finite element simulation calculation result (comparing result as shown in Figure 3): stress intensity factor formula that contains I type centre burst open joint that this paper provides and finite element simulation calculation result coincide good, can well instruct the structural design of the open joint that contains the certain reinforcement of I type central through crack band.

Concrete beneficial effect of the present invention shows the following aspects:

1, known work load can be obtained the critical crack size that contains I type centre burst open joint, judges whether safety of joint: when joint bears stretching static load σ, if by observing or method such as Non-Destructive Testing is found to have 2a in the joint ₀Long centre burst (2a ₀Be initial crack length), joint this moment safety whether? can through type (15) calculate the critical crack size a under this operating load _cIf, a ₀＜a _c, then unstable propagation can not take place in crackle, joint safety, a ₀More less than a _cJoint is safe more.

$a_c=\frac{\sqrt{{\left({\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{f}^2\right)}^2+{{4K}_{\mathrm{IC}}}^4{(t+h)}^2}-{\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{{{2K}_{\mathrm{IC}}}^2}---\left(15\right)$

a _c---half of open joint critical crack size;

F can be obtained by formula (13) in the formula.

2, known crack size can be found the solution the critical load that contains I type centre burst open joint: if by observing or method such as Non-Destructive Testing finds to exist in the joint the long centre burst of 2a, but through type (16) is obtained and is made the limit stress σ of this crackle generation unstable propagation _cIf operating load σ＜σ _c, then unstable propagation can not take place in crackle, joint safety, and σ is more less than σ _cJoint is safe more.

${\mathrm{\&sigma;}}_c=\frac{K_{\mathrm{IC}}}{\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-a^2}}\sqrt{\mathrm{\&pi;a}}}---\left(16\right)$

3, when containing I type centre burst open joint and bear cyclic loading, can determine the joint residual life: when joint bears cyclic loading, if there is the long centre burst of 2a in the joint, but through type (15) is obtained the critical dimension that makes crackle generation unstable propagation, the stress intensity factor formula substitution formula (17) of critical dimension that wushu (15) calculates and crackle original dimension and formula (14) is found the solution to obtain by integration and is contained I type centre burst open joint residual life.A in the formula (17) and n are the intrinsic parameter of material.

$\frac{\mathrm{da}}{\mathrm{dN}}=A{\left(\mathrm{\&Delta;K}\right)}^n---\left(17\right)$

4, determine J integration and crack tip opening displacement δ: can change mutually between stress strength factor K, J integration, the crack tip opening displacement δ.The shape of known work stress, crack size, member gets final product through type (14) and obtains and contain the corresponding stress strength factor K of I type centre burst open joint _I, through type (18) and formula (19) can be obtained crack tip opening displacement δ and the J integration of this moment respectively.

$\mathrm{\&delta;}=\frac{K_I^2}{E^{\&prime;}{\mathrm{\&sigma;}}_S}---\left(18\right)$

$J=\frac{K_I^2}{E^{\&prime;}}---\left(19\right)$

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

Description of drawings

Fig. 1 is the open joint shape synoptic diagram (1-mother metal, 2-weld seam) with certain reinforcement; Fig. 2 is open joint shape synoptic diagram (1-mother metal, the 2-weld seam that contains the certain reinforcement of I type central through crack band; The 3-left-half); Fig. 3 is the form factor formula (22) that contains I type centre burst open joint and the finite element simulation calculation of difformity size joint comparison diagram as a result.

Embodiment

Embodiment one: shown in Fig. 1～3, the detailed process of the derivation method of the described I of the containing type of present embodiment centre burst open joint stress intensity factor is:

Stress intensity factor formula when step 1, analytical Calculation are only considered weld reinforcement h:

Contain the situation (as shown in Figure 2) of centre burst based on band reinforcement joint, by any fracturing mechanics teaching material as can be known, for infinitely great plate, when containing central through crack and being subjected to even tension, the Westcrgacrd stress function of this problem is:

$Z_I\left(z\right)=\frac{\mathrm{\&sigma;z}}{\sqrt{z^2-a^2}}---\left(5\right)$

In the formula: σ---working stress;

Z---complex variable;

Half of a---centre burst size;

With reference to (5) formula, can establish the stress function that band reinforcement joint contains the cracks in body problem of central through crack (as shown in Figure 2) form and be:

$Z_I\left(z\right)=\frac{\mathrm{cz}}{\sqrt{z^2-a^2}}---\left(6\right)$

Wherein c is a undetermined coefficient;

Determine undetermined coefficient c by considering the open joint dynamic balance; Because the symmetry of open joint, the left side of getting open joint assign to consider (referring to Fig. 2, left-half 3 is meant what edge process crackle and the cross section vertical with Y-axis intercepted), then have

${\mathrm{\&sigma;}}_y{|}_{y=0,x>a}=[\mathrm{Re}{Z}_I\left(z\right)-{\mathrm{yI}}_m{Z}_I^{\&prime;}\left(z\right)]{|}_{y=0,x>a}=\frac{\mathrm{cx}}{\sqrt{x^2-a^2}}---\left(7\right)$

By ∑ Y=0, promptly pass through left-half equilibrium of forces inside and outside the y direction of open joint,

${\&Integral;}_a^{t+h}\frac{\mathrm{cx}}{\sqrt{x^2-a^2}}\mathrm{dx}=\mathrm{\&sigma;t}---\left(8\right)$

:

$c=\frac{\mathrm{\&sigma;t}}{\sqrt{{(t+h)}^2-a^2}}---\left(9\right)$

(9) generation is returned (6) formula, and the approximate stress function that can get this problem (band reinforcement joint contains the stress function of the cracks in body problem of central through crack form) is:

$Z_I\left(z\right)=\frac{\mathrm{\&sigma;tz}}{\sqrt{{(t+h)}^2-a^2}\sqrt{z^2-a^2}}---\left(10\right)$

So, can get stress intensity factor and be (formula (11) is the stress intensity factor formula when only considering weld reinforcement h):

$K_I=\underset{\left|\mathrm{\&xi;}\right|\&RightArrow;0}{\lim }\sqrt{2\mathrm{\&pi;\&xi;}}{Z}_I\left(\mathrm{\&xi;}\right)=\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(11\right)$

Wherein ξ=z-a also is a complex variable;

Step 2, definite coefficient of considering capping bead half-breadth w and the influence of toe of weld arc transition radius r:

The stress intensity factor formula that formula (11) is determined has only been considered the influence of h, the result of step 1 thinks that w and r have enough big size and make that the factor of stress concentration of crackle place section stress distribution uniform and welding toe is very little, to such an extent as to the band reinforcement joint stress intensity factor that contains central through crack is not had influence; Influence to above-mentioned stress intensity factor when in fact the size of w and r is big inadequately is still bigger; Therefore consider w and r influence the band reinforcement joint stress intensity factor formula that contains central through crack should for:

$K_I=f\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(12\right)$

Just can determine to contain the band reinforcement joint stress intensity factor formula of central through crack as long as determined coefficient f; By a large amount of FEM (finite element) calculation, and regretional analysis, determine that f is:

$f=1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}]---\left(13\right)$

Step 3, determine to contain the stress intensity factor formula of the open joint of the certain reinforcement of I type central through crack band:

The result of integrating step one and step 2 provides the stress intensity factor formula of the open joint that contains the certain reinforcement of I type central through crack band:

$K_I=\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(14\right)$

In the formula:

W---capping bead half-breadth;

R---toe of weld arc transition radius;

H---weld reinforcement;

Half of t---thickness of slab, as shown in Figure 2;

Half of a---centre burst size (or the crack size parameter, be variable); As shown in Figure 2;

σ---working stress (or being called plus load, operating load).

Embodiment two: shown in Fig. 1～3, present embodiment is to utilize the stress intensity factor formula that contains I type centre burst open joint to determine to contain the open joint critical crack size a of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The fracture toughness K of step 1, measurement weld material _IC

Step 2, with the form parameter of joint: half t substitution formula (13) of capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and thickness of slab is obtained f;

The open joint critical crack size a that contains the certain reinforcement of I type central through crack band is calculated in step 3, foundation _cFormula:

$a_c=\frac{\sqrt{{\left({\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{f}^2\right)}^2+{{4K}_{\mathrm{IC}}}^4{(t+h)}^2}-{\mathrm{\&pi;<figure-callout\; id="2"\; label="t"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\mathrm{\&sigma;}}^2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000041893600000021.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{2{K_{\mathrm{IC}}}^2}---\left(15\right)$

Step 4, the operating load σ substitution formula (15) of the result of step 1 and step 2 and joint, can obtain under this operating load the critical crack size a of joint _c

Each form parameter of known joint, cosmetic welding width, weld reinforcement, toe of weld arc transition radius and thickness of slab, working stress can determine to contain I type centre burst open joint critical crack size a _c

Embodiment three: shown in Fig. 1～3, present embodiment is to utilize the stress intensity factor formula of the open joint contain the certain reinforcement of I type central through crack band to determine to contain the open joint critical load σ of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The open joint critical load σ that contains the certain reinforcement of I type central through crack band is calculated in step 1, foundation _cFormula:

${\mathrm{\&sigma;}}_c=\frac{K_{\text{IC}}}{\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-a^2}}\sqrt{\mathrm{\&pi;a}}}---\left(16\right)$

The fracture toughness K of step 2, measurement weld material _IC

Step 3, with the fracture toughness K of weld material _IC, capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and half t of thickness of slab, half a substitution formula (16) of crack size can obtain the open joint critical load σ that contains the certain reinforcement of I type central through crack band _c

Each form parameter of known joint, cosmetic welding width, weld reinforcement, toe of weld arc transition radius and thickness of slab, crack size can determine to contain I type centre burst open joint critical load σ _c

Embodiment four: shown in Fig. 1～3, present embodiment is to utilize the stress intensity factor formula of the open joint contain the certain reinforcement of I type central through crack band to determine to contain the open joint residual life N of the certain reinforcement of I type central through crack band _f

Concrete steps are as follows:

Step 1, obtain the critical crack size a of the open joint crackle unstable propagation that contains the certain reinforcement of I type central through crack band according to claim 2 _c, operating load σ selects maximum stress during calculating;

Step 2, be different situations, can obtain the open joint residual life N that contains the certain reinforcement of I type central through crack band according to formula (20) and formula (21) for n _fA wherein ₀For the initial crack size half, Y is tried to achieve by formula (22); A is the intrinsic parameter of material (A of different materials is different with n, but with regard to same types of material, A and n are definite value, can consult relevant handbook acquisition with crossing) with n, supposes that Δ σ is a constant;

N ≠ 2 o'clock, $\frac{2}{2-n}(a_c^{1-\frac{n}{2}}-a_0^{1-\frac{n}{2}})=\mathrm{A\&Delta;}{\mathrm{\&sigma;}}^n{Y}^n{N}_f---\left(20\right)$

During n=2, $\ln \frac{a_c}{a_0}=A{\mathrm{\&Delta;\&sigma;}}^2{Y}^2{N}_f---\left(21\right)$

$Y=\mathrm{ft}\sqrt{\frac{\mathrm{\&pi;}}{{(t+h)}^2-a^2}}---\left(22\right)$

Wherein f is obtained by formula (13);

Figure (3) is the analog computation of the form factor formula (22) of the given open joint that contains the certain reinforcement of I type central through crack band of this paper and difformity size joint comparable situation as a result.Comparative result shows, for the joint of difformity size, and formula that this paper provides and finite element simulation calculation result coincide good (referring to Fig. 3).Therefore, the formula that this paper provides can well instruct the structural design of the open joint that contains the certain reinforcement of I type central through crack band.

Each form parameter of known joint, cosmetic welding width, weld reinforcement, toe of weld arc transition radius and thickness of slab, crack size, operating load can determine to contain the open joint residual life N of the certain reinforcement of I type central through crack band _f

Embodiment five: shown in Fig. 1～3, present embodiment is to utilize the stress intensity factor formula of the open joint contain the certain reinforcement of I type central through crack band to determine to contain the open joint J integration and the crack tip opening displacement δ of the certain reinforcement of I type central through crack band;

Concrete steps are as follows:

Step 1, obtain the stress strength factor K that contains central through crack band reinforcement joint according to formula (14) _I:

Step 2, can obtain the open joint crack tip opening displacement δ that contains the certain reinforcement of I type central through crack band according to formula (18):

$\mathrm{\&delta;}=\frac{K_I^2}{E^{\&prime;}{\mathrm{\&sigma;}}_S}---\left(18\right)$

In the formula: σ _s---yield strength;

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Step 3, can obtain the open joint J integration that contains the certain reinforcement of I type central through crack band according to formula (19):

$J=\frac{K_I^2}{E^{\&prime;}}---\left(19\right)$

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Stress strength factor K according to the open joint that contains the certain reinforcement of I type central through crack band _I, by J integration and crack tip opening displacement δ respectively with stress strength factor K _ITransforming relationship can obtain J integration and δ.

Claims (5)

1. derivation method that contains the stress intensity factor of I type centre burst open joint, it is characterized in that: the detailed process of described derivation method is:

Stress intensity factor formula when step 1, analytical Calculation are only considered weld reinforcement h:

Westcrgacrd stress function for infinitely great plate, when containing central through crack and being subjected to even tension is:

$Z_I\left(z\right)=\frac{\mathrm{\&sigma;z}}{\sqrt{z^2-a^2}}---\left(5\right)$

In the formula: σ---working stress;

Z---complex variable;

Half of a---centre burst size;

With reference to (5) formula, the stress function the when cracks in body of establishing the open joint form that contains the certain reinforcement of I type central through crack band is stretched loading is:

$Z_I\left(z\right)=\frac{\mathrm{cz}}{\sqrt{z^2-a^2}}---\left(6\right)$

Wherein c is a undetermined coefficient;

By the inside and outside dynamic balance of open joint, determine undetermined coefficient c; Because the symmetry of open joint is got the left side of open joint and is assigned to analyze, and then has

${\mathrm{\&sigma;}}_y{|}_{y=0,x>a}=[\mathrm{Re}{Z}_I\left(z\right)-{\mathrm{yI}}_m{Z}_I^{\&prime;}\left(z\right)]{|}_{y=0,x>a}=\frac{\mathrm{cx}}{\sqrt{x^2-a^2}}---\left(7\right)$

By ∑ Y=0, promptly pass through left-half equilibrium of forces inside and outside the y direction of open joint,

${\&Integral;}_a^{t+h}\frac{\mathrm{cx}}{\sqrt{x^2-a^2}}\mathrm{dx}=\mathrm{\&sigma;t}---\left(8\right)$

:

$c=\frac{\mathrm{\&sigma;t}}{\sqrt{{(t+h)}^2-a^2}}---\left(9\right)$

(9) generation is returned (6) formula, and the approximate stress function the when open joint that can contain the certain reinforcement of I type central through crack band is stretched loading is:

$Z_I\left(z\right)=\frac{\mathrm{\&sigma;tz}}{\sqrt{{(t+h)}^2-a^2}\sqrt{z^2-a^2}}---\left(10\right)$

So, can get stress intensity factor and be (formula (11) is the stress intensity factor formula when only considering weld reinforcement h):

$K_I=\underset{\left|\mathrm{\&xi;}\right|\&RightArrow;0}{\lim }\sqrt{2\mathrm{\&pi;\&xi;}}{Z}_I\left(\mathrm{\&xi;}\right)=\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(11\right)$

Wherein ξ=z-a also is a complex variable;

Step 2, determine to consider the coefficient of capping bead half-breadth w and the influence of toe of weld arc transition radius r: consider w and r influence the open joint that contains the certain reinforcement of I type central through crack band the stress intensity factor formula should for:

$K_I=f\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(12\right)$

Just can determine to contain the stress intensity factor formula of the open joint of the certain reinforcement of I type central through crack band as long as determined coefficient f; By a large amount of FEM (finite element) calculation, and regretional analysis, determine that f is:

$f=1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}]---\left(13\right)$

Step 3, determine to contain the stress intensity factor formula of the open joint of the certain reinforcement of I type central through crack band:

The result of integrating step one and step 2 provides the stress intensity factor formula of the open joint that contains the certain reinforcement of I type central through crack band:

$K_I=\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-a^2}}\mathrm{\&sigma;}\sqrt{\mathrm{\&pi;a}}---\left(14\right)$

In the formula:

W---capping bead half-breadth;

R---toe of weld arc transition radius;

H---weld reinforcement;

Half of t---thickness of slab;

Half of a---centre burst size;

a _c---half of open joint critical crack size;

σ---working stress.

2. described application process that contains the stress intensity factor formula of I type centre burst open joint of claim 1, it is characterized in that: the stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint critical crack size a of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The fracture toughness K of step 1, measurement weld material _IC

Step 2, with the form parameter of joint: half t substitution formula (13) of capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and thickness of slab is obtained f;

The open joint critical crack size a that contains the certain reinforcement of I type central through crack band is calculated in step 3, foundation _cFormula:

$a_c=\frac{\sqrt{{\left({\mathrm{\&pi;t}}^2{\mathrm{\&sigma;}}^2{f}^2\right)}^2+{{4K}_{\mathrm{IC}}}^4{(t+h)}^2}-{\mathrm{\&pi;t}}^2{\mathrm{\&sigma;}}^2{f}^2}{2{K_{\mathrm{IC}}}^2}---\left(15\right)$

Step 4, the operating load σ substitution formula (15) of the result of step 1 and step 2 and joint, can obtain under this operating load the critical crack size a of joint _c

3. described application process that contains the stress intensity factor formula of I type centre burst open joint of claim 1, it is characterized in that: the stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint critical load σ of the certain reinforcement of I type central through crack band _c

Concrete steps are as follows:

The open joint critical load σ that contains the certain reinforcement of I type central through crack band is calculated in step 1, foundation _cFormula:

${\mathrm{\&sigma;}}_c=\frac{K_{\text{IC}}}{\{1+(0.85038+0.84549\frac{h}{h+t})\exp [-\frac{{\left(\frac{w-\sqrt{h(2r-h)}}{t+h}\right)}^{0.17841+0.63191\frac{h}{h+t}}}{0.3+0.6\frac{h}{t}}\left]\right\}\frac{t}{\sqrt{{(t+h)}^2-a^2}}\sqrt{\mathrm{\&pi;a}}}---\left(16\right)$

The fracture toughness K of step 2, measurement weld material _IC

Step 3, with the fracture toughness K of weld material _IC, capping bead half-breadth w, weld reinforcement h, toe of weld arc transition radius r and half t of thickness of slab, half a substitution formula (16) of crack size can obtain the open joint critical load σ that contains the certain reinforcement of I type central through crack band _c

4. described application process that contains the stress intensity factor formula of I type centre burst open joint of claim 1, it is characterized in that: the stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint residual life N of the certain reinforcement of I type central through crack band _f

Concrete steps are as follows:

Step 1, obtain the critical crack size a of the open joint crackle unstable propagation that contains the certain reinforcement of I type central through crack band according to claim 2 _c, operating load σ selects maximum stress during calculating;

Step 2, be different situations, can obtain the open joint residual life N that contains the certain reinforcement of I type central through crack band according to formula (20) and formula (21) for n _fA wherein ₀For the initial crack size half, Y is tried to achieve by formula (22); A and n are the intrinsic parameter of material, suppose that Δ σ is a constant;

N ≠ 2 o'clock, $\frac{2}{2-n}(a_c^{1-\frac{n}{2}}-a_0^{1-\frac{n}{2}})=\mathrm{A\&Delta;}{\mathrm{\&sigma;}}^n{Y}^n{N}_f---\left(20\right)$

During n=2, $\ln \frac{a_c}{a_0}=A{\mathrm{\&Delta;\&sigma;}}^2{Y}^2{N}_f---\left(21\right)$

$Y=\mathrm{ft}\sqrt{\frac{\mathrm{\&pi;}}{{(t+h)}^2-a^2}}---\left(22\right)$

Wherein f is obtained by formula (13).

5. described application process that contains the stress intensity factor formula of I type centre burst open joint of claim 1, it is characterized in that: the stress intensity factor formula of the described I of containing type centre burst open joint is used for determining to contain the open joint J integration and the crack tip opening displacement δ of the certain reinforcement of I type central through crack band;

Concrete steps are as follows:

Step 1, obtain the stress strength factor K of the open joint that contains the certain reinforcement of I type central through crack band according to formula (14) _I:

Step 2, can obtain the open joint crack tip opening displacement δ that contains the certain reinforcement of I type central through crack band according to formula (18):

$\mathrm{\&delta;}=\frac{K_I^2}{E^{\&prime;}{\mathrm{\&sigma;}}_S}---\left(18\right)$

In the formula: σ _s---yield strength;

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Step 3, can obtain the open joint J integration that contains the certain reinforcement of I type central through crack band according to formula (19):

$J=\frac{K_I^2}{E^{\&prime;}}---\left(19\right)$

When open joint is the plane strain stress,

When open joint is the plane stress stress, E '=E

In the formula: μ---Poisson ratio; E---elastic modulus;

Stress strength factor K according to the open joint that contains the certain reinforcement of I type central through crack band _I, by J integration and crack tip opening displacement δ respectively with stress strength factor K _ITransforming relationship can obtain J integration and δ.

Images