CN110443006A - A method of two phase transition volume ratio of metal material is calculated by measurement area - Google Patents
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Abstract
The invention belongs to physical material fields, more particularly to about a kind of method for calculating two phase transition volume fractions by numerical differentiation on the basis of lever method of metal.By measuring the material data that thermal expansion amount varies with temperature in two-phase transition process, the numerical differentiation curve varied with temperature using lever method export transformed fraction, and by the processing to this numerical differentiation curve, calculate the volume fraction of two phase transition.This method method can solve the computational problem of the phase volume fraction when each phase transition phase transition temperature interval does not overlap or partly overlaps, the Computing Principle of its Computing Principle front method therewith is different, other than calculating operation process (especially from be in harmony operating process) is simple, calculated result theoretically relatively before method it is also more accurate.The method can amplify the volume fraction of each phase when accurately calculating material three-phase or multiphase transformation.
Description
Technical field
The invention belongs to physical material fields, more particularly to one kind about metal is micro- by numerical value on the basis of lever method
It is divided to the method for calculating two phase transition volume ratios.
Background technique
Thermal simulation be one of common method of investigation of materials (bibliography 1:M.Shome, O.P.Gupta,
O.N.Mohanty, Scripta Materialia, 2004,50:1007 and bibliography 2:J.B.Ju, W.Kim, J.Jang,
Materials Science and Engineering:A,2012,546:258).Collected thermal expansion during thermal simulation
Data have very important reference value to the phase change characteristics and process of analysis of material.Collected heat is swollen during thermal simulation
Swollen data are determined for the phase transition temperature, the transition kinetics process for characterizing material, the multiphase phase transformation for calculating material of material
Volume fraction etc..It, also can be different according to the emphasis of analysis to thermal expansion coefficients because of the difference of investigation of materials content.And most of
In the case of, in the continuous cooling process of thermal simulation material, it usually needs the volume fraction for changing each phase is calculated, it is table
Levy an important parameter of material microstructure structure.Thermal simulation is usually calculated by metallographic method and lever method to change in the process
The volume fraction of each phase, can both methods all have some limitations: the operation strategies of metallographic method are wide, but work as each phase constitution
Pattern can not be applied when closely similar；Lever method computational accuracy is high, but when each phase transition undergoes phase transition temperature range overlapping without
Method application.In order to partially solve the computational problem of phase volume fraction, proposed before applicant team a kind of based on numerical differentiation
The method that method determines two phase transition volume ratios, and obtain granted patent (bibliography 3: Huang Jihua, Lei Xuanwei one kind are based on
Numerical differentiation method determines method [P] patent No. of two phase transition volume ratios: ZL201510335105.7), using this method
It can solve the computational problem of the phase volume fraction when each phase transition phase transition temperature interval does not overlap or partly overlaps,
Compensate for the deficiency of lever method.But this method also has shortcoming: operating process (especially from be in harmony operating process) is troublesome,
Also it can increase the error of calculated result while bringing inconvenience to operator to a certain extent.
Summary of the invention
The object of the present invention is to provide a kind of numerical differentiation curves using volume fraction corresponding temperature to calculate two phase transition
The method of volume ratio is counted using the volume of data of the variation of the thermal expansion amount and temperature that are measured in phase transition process
A kind of method calculated, while being also a kind of universal method for calculating phase transition volume fraction that lever rule is amplified out.
To achieve the above object, the method that the present invention uses is: (including the phase transformation in phase transition process using the material of measurement
It is preceding with phase transformation after) the volume of data that varies with temperature of thermal expansion amount thick stick is carried out to thermal expansion amount curve by data conversion
The processing of bar method, obtains the data that volume fraction varies with temperature, and then makes the numerical differentiation of volume fraction corresponding temperature variation
Curve makees straight line or curve by logarithm differential curve, calculates made straight line, curve and numerical differentiation curve and forms closing
The area of figure calculates two-phase volume fraction by area ratio.
The phase transformation of material and the acquisition of thermal expansion amount data occur in certain thermal process, including constant temperature process, at the uniform velocity
Cooling procedure and non-at the uniform velocity cooling procedure.Thermal expansion amount of the material of acquisition after before phase change with temperature or time change a system
Column data needs higher accuracy, and data acquisition temperature interval very little so that the amplitude of variation of thermal expansion amount very
It is small.
The method, which can amplify, accurately calculates material three-phase or multiphase transformation volume fraction.
A method of two phase transition volume ratio of metal material being calculated by measurement area, which is characterized in that in lever
By numerical differentiation on the basis of method, the area of numerical differentiation curve upper ripple caused by two-phase phase transformation respectively, Jin Erji are measured
Two phase transition volume ratio of metal material is calculated, specifically includes the following steps:
Step 1.1) utilizes the corresponding temperature of thermal expansion amount that experimental rig obtains metal material during a or two phase transition
Spend the test data of variation；
Step 1.2) is according to above-mentioned steps 1.1) test data that obtains, using temperature as abscissa, thermal expansion amount is vertical sits
Mark draws out the curve of thermal expansion amount corresponding temperature variation；
Step 1.3) is according to above-mentioned steps 1.2) curve that obtains, the linear change part at curve both ends is extended, then right
This curve carries out lever method processing, obtains the data of overall transformed fraction corresponding temperature variation, carries out to these data
After differential process, and using temperature as abscissa, the data after differential are ordinate, make the variation of transformed fraction corresponding temperature
Numerical differentiation curve；
Step 1.4) is according to above-mentioned steps 1.3) obtain numerical differentiation curve, measure two-phase phase transformation respectively caused by number
It is worth the area of differential curve upper ripple, calculates two phase transition volume ratios.
Further, the temperature interval that data acquisition is carried out in step 1.1) is 100DEG C~10-2K, temperature data precision are
10-1DEG C~10-2K, material heat expansion amount data accuracy are 10-5~10-8m。
Further, the step of lever method in step 1.3) is handled are as follows: the curve point of thermal expansion amount corresponding temperature variation
For 3 parts, the near linear part D of two-phase before phase change1(T), the curve in two-phase phase transition process is approximate straight comprising a part
Line part D2(T) the near linear part D and after two-phase phase transformation3(T)；It will be carried out before phase change with the thermal expansion amount curve after phase transformation
Fitting, obtains straight line D1(T) and D3(T) expression formula；Calculate phase transition temperature section in transformed fraction beTf′≤Ti≤Ts, wherein TiFor the temperature data of thermal modeling test device record, TsFor totality
The start temperature of phase transformation, Tf' for the end temperature of overall phase transformation, D2(Ti) it is the thermal expansion amount that thermal modeling test device records, f
(Ti) it is the data that transformed fraction corresponding temperature changes.The numerical differentiation curve of transformed fraction corresponding temperature variation
Data acquisition method beWherein f (Ti+1) be temperature be Ti+1When
Transformed fraction value, Ti+1For TiNext record temperature.
Further, the numerical differentiation of the transformed fraction corresponding temperature variation obtained according to the step 1.4) is bent
Line judges that two-phase phase transition temperature interval is not overlapped or partially overlaps, according to judgement as a result, calculating two-phase using different methods
Change volume ratio.
Further, when judging result be two-phase phase transition temperature interval be not overlapped when, calculating process the following steps are included:
Step 5.1) is it can be seen that the numerical differentiation curve of transformed fraction corresponding temperature variation shows as two almost
There is no overlapped wave, make horizontal line l by 0 point, surrounds two closed waves with numerical differentiation curve；
The relative area that step 5.2) measures first latter two wave is respectively S1And S2, there is the volume point of the two-phase successively changed
Number is respectivelyWith
Further, when judging result be two-phase phase transition temperature interval partially overlap when, calculating process the following steps are included:
Step 6.1) is it can be seen that the numerical differentiation curve of transformed fraction corresponding temperature variation shows as two mutually
The wave of overlapping respectively corresponds the first phase and the second phase transition；The starting point of first wave and the end point of second wave are right respectively
Answer the start temperature T of the first phase transformations, the second phase transformation end temperature T 'f；It makes corresponding in this curve graph and indulges the level for being designated as 0
Line l, minute mark goes out phase transformation temperature points T on straight line lsWith T 'fCoordinate；
Step 6.2) determines the beginning transition temperature T ' of the second phases, and T ' is marked on straight line lsPoint；
Step 6.3) is with T 'sPoint is used as starting point, connects T 'sPoint a little forms a line segment p on second wave, passes through
The terminal A (A point is located at or not on the numerical differentiation curve of volume fraction) of line segment p makees one perpendicular to the straight of abscissa
Line o, straight line o hand over straight line l in TfPoint makees line segment p about the symmetrical line segment p ' of straight line o, the line segment p ' and transformed fraction
Numerical differentiation curve degree of overlapping be higher than 50%；
Step 6.4) made T 'sIt puts and perpendicular to the straight line o ' intersection number value differential curve of temperature coordinate in A ' point, with A ', Tf
Two o'clock is that Origin And Destination makees curved section q, and the curved section q is dull；
T on the numerical differentiation curve of straight line l, transformed fraction that step 6.5) is determined according to above-mentioned stepssThe part A '
And the figure S that curved section q is surrounded1, determine A ' T ' on the numerical differentiation curve of straight line l, transformed fractionfPart and curve
The figure S that section q is surrounded2, calculate S1And S2Relative area, successively started transformation two phase transition volume ratios be
With
Further, according to curved section q and numerical differentiation curve TsA ' is partially walked about straight line o ' near symmetrical to determine
It is rapid 6.2) in temperature T 'sPosition.
Further, the upper corresponding ordinate value of every bit in the part the AA ' of curved section q, line segment p and numerical value differential curve m
Meet relational expression q+p=m, thereby determines that the curved section q in step 6.4).
The present invention improves a kind of more simple calculation method of operation to solve the deficiency of existing method.This method
The calculating that equally can solve the phase volume fraction when each phase transition phase transition temperature interval does not overlap or partly overlaps is asked
The Computing Principle of topic, Computing Principle front method therewith is different, in addition to calculating operation process (especially from be in harmony operating process) letter
It is single outer, calculated result theoretically relatively before method it is also more accurate.
Detailed description of the invention
When Fig. 1 two-phase phase transition temperature interval is not overlapped, showing for two phase transition volume ratios is calculated on the basis of lever method
It is intended to；
When Fig. 2 two-phase phase transition temperature interval partially overlaps, two phase transition volume ratios are calculated on the basis of lever method
Schematic diagram.
Specific embodiment
Below with reference to embodiment, the invention will be further described:
Embodiment 1
The weld metal material measured by Gleeble material heat expansion under conditions of cooling rate is 12.5 DEG C/s
The volume of data varied with temperature is measured, wherein the relative variation precision thermally expanded reaches 10-6Mm, temperature accuracy reach 10-2
DEG C, temperature interval 10-2K.By being arranged to data:
Step 1: drawing out thermal expansion amount curve, lever method is carried out on this curve and handles to obtain total phase variable volume point
Number data；
Step 2: carrying out differential process to transformed fraction data, the numerical differentiation for drawing out transformed fraction is bent
Line；
Step 3: cross 0 point of one horizontal linear l of work in this numerical differentiation curve graph (marks out first respectively on straight line
The beginning of phase and end temperature TsAnd TfAnd second phase beginning and terminate temperature T 'sWith T 'f), as shown in Figure 1, measurement is bent with this
The relative area S for two waves that line surrounds1And S2, there is the volume fraction of the two-phase successively changed to be respectively
Embodiment 2
The material measured by Gleeble material heat expansion amount under conditions of cooling rate is 12.5 DEG C/s becomes with temperature
The volume of data of change, wherein thermal expansion amount precision reaches 10-6Mm, temperature accuracy reach 10-2℃.By carrying out phase to data
It should arrange, the numerical differentiation curve of obtained volume fraction corresponding temperature variation is as shown in Figure 2.Fig. 2 shows two troughs, point
The phase transition process of two-phase is not corresponded to, the partially phase transition process by being overlapped of the thermal expansion amount numerical differentiation curve AA ' between two troughs
It is contributed.
The horizontal line l for being designated as 0 is indulged step 1: making corresponding on the graph, minute mark goes out first wave on horizontal line l
Starting point TsWith the end point T ' of second wavef, they respectively correspond the temperature that the first phase transformation starts and the second phase transformation terminates temperature
Degree；
Step 2: estimating the beginning transition temperature T ' of the second phase on straight line lsPosition, and mark；
Step 3: with T 'sPoint is used as starting point, connects T 'sPoint a little forms a line segment p on second wave, by line
The terminal A (A point is located at or not on the numerical differentiation curve of volume fraction) of section p makees a straight line perpendicular to abscissa
O, straight line o hand over straight line l in TfPoint makees line segment p about the symmetrical line segment p ' of straight line o, the line segment p ' and transformed fraction
The degree of overlapping of numerical differentiation curve is higher than 50%；
Step 4: making T 'sIt puts and perpendicular to the straight line o ' intersection number value differential curve of temperature coordinate in A ' point, with A ', TfTwo
Point is that Origin And Destination makees curved section q, and the curved section q is dull, while the AA ' of curved section q, line segment p and numerical value differential curve m
The corresponding ordinate value of every bit meets relational expression q+p=m on part.
Step 5: curved section q and numerical differentiation curve TsA ' partially must satisfy about straight line o ' near symmetrical, Ke Yitong
Overregulate T 'sThe position of point is realized, so that it is determined that T 'sThe position of point；
Step 6: measurement is according to T on the straight line l of above-mentioned steps determination, the numerical differentiation curve of transformed fractionsThe portion A '
Point and the area S that is surrounded of curved section q1And A ' T ' on the numerical differentiation curve of straight line l, transformed fractionfPart and curved section
The area S that q is surrounded2, while the two phase transition volume fractions for successively being started transformation are
Claims (8)
1. a kind of method for calculating two phase transition volume ratio of metal material by measurement area, which is characterized in that in lever method
On the basis of by numerical differentiation, measure the area of numerical differentiation curve upper ripple caused by two-phase phase transformation respectively, and then calculate
Two phase transition volume ratio of metal material out, specifically includes the following steps:
Step 1.1) is become using the thermal expansion amount corresponding temperature that experimental rig obtains metal material during a or two phase transition
The test data of change；
Step 1.2) is according to above-mentioned steps 1.1) obtain test data, using temperature as abscissa, thermal expansion amount is ordinate, is drawn
Produce the curve of thermal expansion amount corresponding temperature variation；
Step 1.3) is according to above-mentioned steps 1.2) curve that obtains, the linear change part at curve both ends is extended, then to this song
Line carries out lever method processing, obtains the data of overall transformed fraction corresponding temperature variation, carries out differential to these data
After processing, and using temperature as abscissa, the data after differential are ordinate, make the number of transformed fraction corresponding temperature variation
It is worth differential curve；
Step 1.4) is according to above-mentioned steps 1.3) obtain numerical differentiation curve, measure two-phase phase transformation respectively caused by numerical value it is micro-
The area of component curve upper ripple calculates two phase transition volume ratios.
2. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 1, feature
The temperature interval for being to carry out data acquisition in step 1.1) is 100DEG C~10-2K, temperature data precision are 10-1DEG C~10-2K,
Material heat expansion amount data accuracy is 10-5~10-8m。
3. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 1, feature
It is, the step of the processing of lever method in step 1.3) are as follows: the curve of thermal expansion amount corresponding temperature variation is divided into 3 parts, and two
Mutually near linear part D before phase change1(T), the curve in two-phase phase transition process includes a part of near linear part D2(T) and
Near linear part D after two-phase phase transformation3(T)；It will be fitted before phase change with the thermal expansion amount curve after phase transformation, obtain straight line
D1(T) and D3(T) expression formula；Calculate phase transition temperature section in transformed fraction beTf′
≤Ti≤Ts, wherein TiFor the temperature data of thermal modeling test device record, TsFor the start temperature of overall phase transformation, Tf' it is overall
The end temperature of phase transformation, D2(Ti) it is the thermal expansion amount that thermal modeling test device records, f (Ti) it is that transformed fraction is corresponding
The data of temperature change.The data acquisition method of numerical differentiation curve of transformed fraction corresponding temperature variation isWherein f (Ti+1) be temperature be Ti+1When transformed fraction
Value, Ti+1For TiNext record temperature.
4. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 1, feature
It is, according to the numerical differentiation curve for the transformed fraction corresponding temperature variation that the step 1.4) obtains, judges two-phase phase
Temperature section is not overlapped or partially overlaps, according to judgement as a result, calculating two phase transition volume ratios using different methods.
5. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 4, feature
Be when judging result be two-phase phase transition temperature interval be not overlapped when, calculating process the following steps are included:
Step 5.1) it can be seen that transformed fraction corresponding temperature variation numerical differentiation curve show as two almost without
Overlapped wave makees horizontal line l by 0 point, surrounds two closed waves with numerical differentiation curve；
The relative area that step 5.2) measures first latter two wave is respectively S1And S2, there is the volume fraction point of the two-phase successively changed
It is notWith
6. the method according to claim 4 for calculating two phase transition volume ratio of metal material by measurement area, special
Sign be when judging result be two-phase phase transition temperature interval partially overlap when, calculating process the following steps are included:
Step 6.1) it can be seen that transformed fraction corresponding temperature variation numerical differentiation curve show as two it is overlapped
Wave, respectively correspond the first phase and the second phase transition；The end point of the starting point of first wave and second wave respectively corresponds the
The start temperature T of one phase transformations, the second phase transformation end temperature Tf′；It makes corresponding in this curve graph and indulges the horizontal line l for being designated as 0,
Minute mark goes out phase transformation temperature points T on straight line lsAnd Tf' coordinate；
Step 6.2) determines the beginning transition temperature T of the second phases', and T is marked on straight line ls' point；
Step 6.3) is with Ts' be used as starting point, connect Ts' on second wave a little formed a line segment p, by line segment p
Terminal A make a straight line o perpendicular to abscissa, straight line o hands over straight line l in TfPoint makees line segment p about the symmetrical line of straight line o
The degree of overlapping of the numerical differentiation curve of section p ', the line segment p ' and transformed fraction is higher than 50%；A point is located at or is not located at
On the numerical differentiation curve of volume fraction；
Step 6.4) made Ts' and perpendicular to the straight line o ' intersection number value differential curve of temperature coordinate in A ' point, with A ', TfTwo o'clock
Make curved section q for Origin And Destination, the curved section q is dull；
T on the numerical differentiation curve of straight line l, transformed fraction that step 6.5) is determined according to above-mentioned stepssThe part A ' and curve
The figure S that section q is surrounded1, determine A ' T on the numerical differentiation curve of straight line l, transformed fractionf' part and curved section q are enclosed
At figure S2, calculate S1And S2Relative area, successively started transformation two phase transition volume ratios beWith
7. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 6, feature
It is according to curved section q and numerical differentiation curve TsA ' partially determines temperature T in step 6.2) about straight line o ' near symmetricals′
Position.
8. the method for calculating two phase transition volume ratio of metal material by measurement area according to claim 6, feature
It is, the upper corresponding ordinate value of every bit in the part AA ' of curved section q, line segment p and numerical value differential curve m meet relational expression q+p
=m thereby determines that the curved section q in step 6.4).
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111157567A (en) * | 2020-01-09 | 2020-05-15 | 江西理工大学 | Method for measuring volume ratio of two-phase transformation of low-alloy high-strength steel during continuous cooling |
| CN111157568A (en) * | 2020-01-17 | 2020-05-15 | 江西理工大学 | Method for simply and rapidly measuring volume ratio of two-phase transition of continuous cooling |
| CN111157568B (en) * | 2020-01-17 | 2022-05-31 | 江西理工大学 | Method for simply and rapidly measuring volume ratio of two-phase transition of continuous cooling |
| CN114664393A (en) * | 2022-01-05 | 2022-06-24 | 北京理工大学 | Method for calibrating high-instantaneity solid-state phase change JMAK equation parameters based on thermal expansion |
| CN114896770A (en) * | 2022-04-25 | 2022-08-12 | 江西理工大学 | Low-alloy high-strength steel continuous cooling structure phase volume fraction calculation method |
| CN114896770B (en) * | 2022-04-25 | 2024-05-24 | 江西理工大学 | Method for calculating volume fraction of continuous cooling tissue phase of low-alloy high-strength steel |
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