CN108375539A - A kind of steel plate build-up welding nickel-base alloy residual stress calculation method - Google Patents
A kind of steel plate build-up welding nickel-base alloy residual stress calculation method Download PDFInfo
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Abstract
The invention discloses a kind of steel plate build-up welding nickel-base alloy residual stress calculation method, the method directly calculates size and the distribution of residual stress according to the essential attribute of the geometric dimension and material of steel plate and overlay cladding.Analytic modell analytical model is established by dynamic balance and equalising torque and interface strain compatibility conditions, calculates the residual stress size and residual stress distribution of the single-layer or multi-layer layer after steel plate and the cooling of built-up welding Ni based alloys.It is calculated according to the analytic modell analytical model, visual result is reliable.This method can calculate the residual stress distribution of steel matrix, while include the residual stress distribution for calculating single layer layer or multilayer layer.And computational methods provided by the invention are not only applicable to nickel alloy cladding, can also be suitable for the residual stress calculation that different steel plate members welds according to the essential attribute of other metal materials.
Description
Technical field
The invention belongs to a kind of remnants for anticorrosive anti-wears steel plate build-up welding components such as petrochemical industry, pressure vessels to answer
Power computational methods and residual stress distribution, and in particular to a kind of steel plate build-up welding nickel-base alloy residual stress calculation method.
Background technology
Residual stress is always to be engaged in the research hotspot of welding specialty personage, the measurement side about welding residual stress
Method also emerges one after another, and computation model is also very much.Mainly there are three component parts for built-up welding residual stress, are interior caused by phase transformation first
Quenching stress caused by stress, the first cooling procedure of molten drop and the common cooling caused thermal stress of layer and matrix.Study table
Bright, these stress all contribute the size of overlay cladding final stress.Layer residual stress may be to lead to layer premature failure
A key factor lose wear-corrosion resistance etc. if layer falls off.Numerous studies show：Built-up welding layer residual stress
It is the driving force of layer cracking or spalling failure.Meanwhile also some researches show that the residual stress sizes of overlay cladding to control welding
The service life of component.
Residual stress test method can substantially be divided into two classes：The mechanical means and lossless physical method damaged.It is common
Test method have X diffraction, curvature method, material remove and boring method.These methods respectively have advantage and disadvantage.X diffraction and curvature method are
Two kinds of lossless detection methods, but surface stress size can only be measured；Material removes and boring method is two kinds and damages detection method, but
The stress distribution of through-thickness can be obtained.If for the popularity used, rear three kinds of methods are also still used for real at present
Test room service stage.But X diffraction methods have been widely applied in Practical Project due to the advantages that light, quick.X spreads out
Shooting method mainly derives the residual stress inside welding by the variation of lattice constant caused by record stress.Past two
In 10 years, this method has been successfully applied in the residual stress analysis of different materials.Material removing method is one and damages
Mechanical means, but distribution situation of the welding internal residual stress with thickness direction can be characterized.In this way, it needs
Paste foil gauge in the other side of matrix.The removal of built-up welding layer surfacing in layer is made using special technique, is often moved
When except certain thickness overlay cladding, the deformation of coating and matrix is recorded by foil gauge.Then the method for using continuity mechanics, passes through
The variation of strain, the residual-stress value of reverse overlay cladding and intrinsic silicon.
Invention content
Goal of the invention：In order to overcome the above-mentioned deficiencies of the prior art, it is residual to provide a kind of steel plate build-up welding nickel-base alloy by the present invention
Residue stress computational methods, this method provide intuitive, reliable, rapid scene and calculate steel plate build-up welding residual stress size and distribution,
Improve the real-time of computational methods and result.
Technical solution：A kind of steel plate build-up welding nickel-base alloy residual stress calculation method, the method include the following steps：
(1) steel plate is subjected to built-up welding postcooling to room temperature, then carries out cutting sampling, the sample cut includes built-up welding
Layer and steel matrix；
(2) according to dynamic balance and equalising torque and interface strain compatibility conditions, the residual stress parsing mould of steel plate is established
Type；
(3) residual stress size and the distribution of sample steel matrix and overlay cladding, including intermediate layer and last weldering are calculated
The residual stress of layer.
Further, the layer of step (1) described built-up welding is one layer or one layer or more.
Further, the interface strain compatibility conditions described in step (2) include temperature strain, ess-strain and bending strain
Three dependent variables.The residual stress calculation formula of steel matrix described in step (2) is as follows：
In above-mentioned formula, Ec：Layer elasticity modulus, Es：Matrix elastic modulus；δc：Layer thickness；δs：Matrix thickness；αc：Weldering
Layer coefficient of thermal expansion；αs：Matrix coefficient of thermal expansion.
Further, the middle layer described in step (3) is the layer of built-up welding when being two layers or two layers or more, removes last
All layers outside layer, the cap weld refer to the layer when the layer of built-up welding is one layer, when the layer of built-up welding is one
Layer or more when last layer.
Further, the layer of the steel plate can be one layer, when the layer of built-up welding is two layers and two layers or more, in
Between layer and cap weld.If when totally 4 layers (n=4) is intermediate layer as n=1, n=2 and n=3 to layer；Work as n=4
When, for cap weld, the calculation formula of in-between layer and cap weld is as follows：The intermediate layer calculation formula of the steel plate is such as
Under：
((j-1)δc≤h≤jδcAnd j ＜ n)；
The cap weld calculation formula of the steel plate is as follows：
((j-1)δc≤h≤jδcAnd j=n)；
In above-mentioned formula, Ec：Layer elasticity modulus, Es：Matrix elastic modulus；δc：Layer thickness；δs：Matrix thickness；αc：Weldering
Layer coefficient of thermal expansion；αs：Matrix coefficient of thermal expansion；Fi：Power suffered by i-th layer of cladding；yi：Neutral axial coordinate after i-th layer of cladding；
h：Matrix and cladding layer thickness；ρi：I-th layer of composite beam radius of curvature；FiAnd FjFor the power suffered by i-th layer and jth layer, wherein i=
J+1, in order to calculate summation formula, using i as transition variable；J is the number of plies；N is total number of plies.When layer is 4 layers altogether, then n=4；
So as j ＜ n, j=1 or j=2 or j=3 is indicated；As j=n, j=4 is indicated.Intermediate layer is the 1st layer, the 2nd layer and the
3 layers, cap weld is the 4th layer.
Advantageous effect：Its significant effect is the present invention compared with prior art, and the parameter involved in the present invention arrived is structure
The geometric parameter of part and the fundamental performance parameter of material, the parameter directly can measure or look into handbook acquisition, therefore this meter in scene
The analytic modell analytical model that calculation method provides, residual stress size and distribution, the result of calculation that can calculate matrix and layer rapidly are straight
It sees reliable.On the other hand, which can not only calculate residual stress size and the distribution of matrix, while can also calculate weldering
The size of layer residual stress and distribution.
Description of the drawings
Fig. 1 be in the present invention built-up welding number of plies to the influence variation diagram of matrix and layer residual stress.
Specific implementation mode
In order to which technical solution disclosed by the invention is described in detail, done with reference to the accompanying drawings of the specification with specific implementation mode
It is further elucidated above.
Steel plate is subjected to built-up welding postcooling to the natural temperature of local environment first, the cutting for then carrying out weld takes
Sample, obtained sample includes the matrix of the layer and steel plate of built-up welding, according to dynamic balance and principle of moment balance and interface strain
Compatibility conditions, the residual stress analytic modell analytical model for establishing steel plate calculate the residual stress size of sample steel matrix and overlay cladding and divide
Cloth.
Assuming that the built-up welding number of plies is n (n >=1), i.e., the built-up welding n-layer layer on matrix, then computational methods and analytic modell analytical model
It is as follows to establish process.
Matrix meets strain coordination condition with layer：εc=εs；Then：
Above formula (1) equal sign left side first item is the temperature strain of layer, equal sign left side Section 2 be layer ess-strain and
Bending strain；First item is the temperature strain of matrix on the right of equal sign, and equal sign the right Section 2 is that matrix stress strain and bending are answered
Become.
Formula (1) obtains after arranging：
According to the relationship of coefficient of thermal expansion and material thickness, elasticity modulus of materials, can obtain：
Formula (3) is substituted into formula (2), arrangement obtains：
In formula (1) (2) (3) and (4), Ec：Layer elasticity modulus, Es：Matrix elastic modulus；δc：Layer thickness；δs：
Matrix thickness；αc：Layer coefficient of thermal expansion；αs：Matrix coefficient of thermal expansion, Fi：Power suffered by i-th layer of cladding；yi：I-th layer of cladding
Neutral axial coordinate afterwards；h：Matrix and cladding layer thickness；ρi：I-th layer of composite beam radius of curvature.
Act on the F above matrix and n-th layer coatingnIt is segmented into two power, i.e. Fn=Fnc+Fns, according to dynamic balance original
Reason can obtain：
According to principle of moment balance, FnCouple forms a moment of couple, i.e.,：
Flecition forms equalising torque：
Combinatorial formula (7) and formula (8), obtain：
It can be calculated according to bending beam theory：
Due to：So：
Because composite beam curvature radius calculation formula is as follows：
Formula (10) is substituted into formula (11), it can be deduced that：
It enables：M=[αc(n-1)δcEc+αsδsEs]·(T0-Ts+n-1)-[(n-1)δcEc+δsEs]αc(T0-Tc)
N=n2δc 2Ec-nδc 2Ec+2nδcδsEs-δcδsEs+δs 2Es
The residual stress calculation formula of final matrix is as follows：
The calculation formula of built-up welding layer middle layer is as follows：
(j-1)δc≤h≤jδcAnd j ＜ n) (14)
The calculation formula of built-up welding layer final layer is as follows：
((j-1)δc≤h≤jδcAnd j=n) (15)
According to above-mentioned calculating step and calculation formula, it is given below and calculates separately 2 layers of (n of built-up welding 1 layer (n=1) and built-up welding
=2) residual stress calculation when is as a result, as shown in the table.
1 matrix of table and weld overlay materials performance and specimen size
Work as αc＞ αsWhen, cladding layer tension, matrix is pressurized.
For 1 layer of layer of built-up welding：
εc=εs
Then：
Flecition forms equalising torque：
Then：
It obtains：It can be counted according to the mechanics of materials
It calculates：
According to theory of mechanics of materials, the E in above-mentioned formula is replaced with the E' in following formula：
Final stress：
For 2 layers of layer of built-up welding：
εc=εs
Then：Since stress is equal on face：
Es+1ε(δc+δs)=Ecεδc+Esεδs, Es+2ε(2δc+δs)=Ecε2δc+Esεδs
Since stress is equal on face：
Es+1αs+1ΔT(δc+δs)=EcαcΔTδc+EsαsΔTδs
Es+2αs+2ΔT(2δc+δs)=EcαcΔT2δc+EsαsΔTδs
So：
Act on the F above matrix and the 1st layer of coating2It is segmented into two power：
F2=F2c+F2s
F2Couple forms a moment of couple：
Flecition forms equalising torque：
Then：
It is calculated：According to material
Expect Mechanics Calculation：
Enable 2 δc=A
According to theory of mechanics of materials, the E in above-mentioned formula is replaced with the E' in following formula：
Final suffered stress is as follows：
Matrix stress：
First layer stress：
Second layer stress：
Result of calculation shows：Residual stress inside intrinsic silicon residual stress and overlay cladding is linearly distributed；It is based on
The present embodiment, intrinsic silicon are compression, are tensile stress inside overlay cladding, compression is maximum wherein at matrix surface, far from table
When face, matrix compression reduces；Tensile stress is maximum at overlay surface, and when far from surface, layer tensile stress reduces.It is specific to calculate
As a result and its influence is detailed as shown in Figure 1, and the size of residual stress and distribution are related with the performance of material.
Claims (6)
1. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method, it is characterised in that：Include the following steps：
(1) steel plate is subjected to built-up welding postcooling to room temperature, then carries out cutting sampling, the sample cut includes the layer of built-up welding
And steel matrix；
(2) according to dynamic balance and equalising torque and interface strain compatibility conditions, the residual stress analytic modell analytical model of steel plate is established；
(3) residual stress size and the distribution of sample steel matrix and overlay cladding are calculated, including intermediate layer and cap weld
Residual stress.
2. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method according to claim 1, it is characterised in that：Step
(1) layer of the built-up welding is one layer or one layer or more.
3. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method according to claim 1, it is characterised in that：Step
(2) the interface strain compatibility conditions described in include three temperature strain, ess-strain and bending strain dependent variables.
4. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method according to claim 1, it is characterised in that：Step
(2) the residual stress calculation formula of the steel matrix of the analytic modell analytical model is as follows：
In formula, Ec：Layer elasticity modulus, Es：Matrix elastic modulus, δc：Layer thickness, δs：Matrix thickness, αc：Layer thermally expands
Coefficient, αs：Matrix coefficient of thermal expansion.
5. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method according to claim 1, it is characterised in that：Step
(3) the intermediate layer described in refer to built-up welding layer be two layers or two layers or more when, all layers in addition to last layer, institute
It refers to the layer when the layer of built-up welding is one layer to state cap weld, or last when the layer of built-up welding is one layer or more
One layer.
6. a kind of steel plate build-up welding nickel-base alloy residual stress calculation method according to claim 5, it is characterised in that：It is described
Intermediate layer and cap weld residual stress calculation formula difference it is as follows：
The intermediate layer calculation formula is：
The cap weld calculation formula is：
In formula, Ec：Layer elasticity modulus,
Es：Matrix elastic modulus, δc：Layer thickness, δs：Matrix thickness, αc：Layer coefficient of thermal expansion, αs：Matrix coefficient of thermal expansion, Fi：
Power suffered by i-th layer of cladding, yi：Neutral axial coordinate, h after i-th layer of cladding：Matrix and cladding layer thickness, ρi：I-th layer of composite beam song
Rate radius, Fi and Fj are respectively i-th layer and the power suffered by jth layer, and as transition parameter, j is the number of plies by wherein i=j+1, i, and n is
Total number of plies.
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| CN110147636A (en) * | 2019-06-03 | 2019-08-20 | 北京航空航天大学 | A kind of hard α that includes based on subregion is mingled with residual stress calculation method around |
| CN112629725A (en) * | 2020-12-04 | 2021-04-09 | 江苏徐工工程机械研究院有限公司 | Method for testing residual stress of piston rod spraying coating |
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