CN1176371C - Semi-quantitative calculation method for temp gradient at front edge of directional setting interface - Google Patents

Abstract

The present invention relates to a semiquantitative calculation method for the frontal temperature gradient of directional solidification interfaces. The present invention carries out a disposable initial thermal field test on a solidification sample of one kind of material and obtains the characteristic coefficient item A of the material through calculation. As for other solidification test samples of the same material, the present invention directly uses the coefficient item A obtained from the initial test, substitutes a disposable dendrite space lambada 1 and the known draining and pulling speed R, and can obtain the frontal temperature gradient of the solidification interface through calculation. The present invention only uses a small amount of tests, obtains the frontal temperature gradient GL of the directional solidification interface through calculation, avoids the influence of the tests on the solidification process, reflects the fine change of the temperature gradient, and is difficult to realize by tests.

Description

A kind of semi-quantitative calculation method for temp gradient at front edge of directional setting interface

Technical field

The invention belongs to alloy directionally solidified research, specifically a kind of semi-quantitative calculation method for temp gradient at front edge of directional setting interface.

Background technology

In alloy directionally solidified (comprising growth of single crystal) experimental study and technology, one the most key solidifies the thermograde G that parameter is the forward position, freezing interface _L, it produces material impact to the behavior of solidifying and the solidified structure of alloy, until the mechanical property that influences alloy.The freezing interface form is one of most important solidification phenomenon in the directional solidification process, and interface stability is promptly relevant with thermograde, is the result of interface temp gradient at front edge and constitutional supercooling coupling, Wo Andile, triumphant peace Jackson, Qiao Wolute and compare Cha Erma, solute atoms reallocation in the metal solidification process, metallurgical journal, 1953,1,428 (W.A.Tiller, K.A.Jackson, J.W.Rutter and B.Chalmers, The Redistribution During the Solidificationof Metals, Acta Metall, 1953,1,428) and Qiao Wolute and compare Cha Erma, Canada's physics periodical, 1953,31,15 (J.W.Rutter and B.Chalmers, Can.J.Phys., 1953,31,15) in, freezing interface, the plane stability expression formula that Chalmers and co-worker thereof propose is:

G/R＝ΔT/D....................................(1)

G is the freezing interface temp gradient at front edge in the formula, and R is the freezing interface fltting speed, and Δ T is the freezing range (liquidus temperature and solidus temperature are poor) of alloy, and D is the coefficient of diffusion in the liquid phase.When G/R 〉=Δ T/D, the freezing interface keeps planar growth; When G/R＜Δ T/D, the planar interface loss of stability, to born of the same parents' crystalline substance or dendrite development, even and so that wherein a kind of mode is grown, change also appreciable impact tissue topography of G/R.The development of modern directional solidification technique is a sign to improve constantly thermograde just, this shows that thermograde in directional solidification theory and technical critical role, is the problem that solidification theory and technical staff author are concerned about the most.

The direct method that obtains actual solidification processing temperature gradient is an experiment test, but actual solidification experiments does not allow to be provided with temperature element often in order to guarantee the integrality of sample on sample, also just can not realize test.Common all solidification experiments of carrying out in same directed stove quote same thermograde value and there is deviation in the actual temperature gradient, and reason is that experiment material, sample structure and experiment parameter all are variablees, so the solidification processing temperature gradient also is a variate.In addition, computer craze field stimulation technology is the another approach that obtains the solidification processing temperature gradient, but its result usually lacks the adaptability to concrete sample, does not reflect its details.

Summary of the invention

The purpose of this invention is to provide a kind of need not repeat thermal field test solidify sample orientation freezing interface semi-quantitative calculation method for temp gradient at front edge.

Technical scheme of the present invention is: the sample that solidifies to a kind of material is done disposable initial thermal field test, calculates this material character coefficient entry A; With the material solidification test specimen, only need directly quote coefficient entry A and the substitution primary dendritic spacing λ that initial trial obtains to other ₁, reach known drawing velocity R, just can calculate the thermograde in forward position, freezing interface, be specially:

(1) initial thermal field test: solidifying of a kind of material the thermometric galvanic couple is set in the sample, and directional solidification, drawing velocity is 1mm/min～25mm/min, holding temperature is 1450～1800 ℃, measures solidification process thermal analysis data and curve;

(2) determine the alloy A parameter:

1) the sample predetermined cross-section is solidified in intercepting, prepares macroscopical metallographic sample and 10～300 times of metallographs; With the bushing of a known area S, cover on the photo, read a dendrite number n in the described known area S, and get 10 visual fields, get the mean value N of its n value; According to described heat analysis data and curve, calculate the freezing interface temp gradient at front edge G of cross section taken in correspondence _L

2) known area S and a dendrite are counted N substitution formula λ ₁=(4S/3 ^1/2(2N-(12N-3) ^1/2+ 1)) ^1/2Or λ ₁=(2S/3 ^1/2N) ^1/2≈ 1.075 (S/N) ^1/2Try to achieve primary dendritic spacing λ ₁

3) with described primary dendritic spacing λ ₁, the freezing interface temp gradient at front edge G of drawing velocity R when described sample solidifies and cross section taken in correspondence _LSubstitution formula λ ₁=A.G _L ^-0.5.R ^-0.25, try to achieve coefficient A, as constant corresponding to this alloy;

(3) solidify sample for other same material, try to achieve primary dendritic spacing λ according to step (2) ₁, and go into formula λ with known drawing velocity R and coefficient entry A one are contemporary ₁=A.G _L ^-0.5.R ^-0.25, can try to achieve the thermograde G in forward position, freezing interface _L

Described known area S is surrounded by hexagon.

Ultimate principle of the present invention is as follows:

According to plum James McLane work, Chen Shiqing, Chen Rongzhang translates, the directional solidification high-temperature material, Beijing: aircraft industry publishing house, the primary dendritic spacing expression formula that provides in 1989.3,34 one literary compositions:

λ ₁＝A·G _L ^-0.5·R ^-0.25..........(2)

Basis again, Wo Kuzi and De Qiaofeixier solidify the basis, Switzerland, technical papers is published company limited, 1989,83 (W.Kurz, D.J.Fisher, Foundarnentals of Solidification, Switzerland:Trans Tech Publications Ltd, 1989,83.) primary dendritic spacing expression formula:

λ ₁＝4.3(ΔT _oDГ) ^0.25k ^-0.25R ^-0.25G _L ^-0.5......(3)

Learn: thermograde G _LWith primary dendritic spacing λ ₁There is certain functional relation, and (2) formula and (3) formula come down to consistently, and quote (2) formula analysis herein: the A item is the property of alloy material parameter, can be considered as constant for a certain alloy, setting rate R is the actual control that is subjected to the artificial drawing velocity V that sets on technology, in other words $R\≅V,$ And it is known, if so at a certain alloy, as long as thermograde and primary dendritic spacing by a sample of initial testing, substitution (2) formula, then the A value can be asked, as long as record its primary dendritic spacing for other alloy graining sample of the same race, and substitution setting rate V, then can obtain corresponding thermograde.(2) formula is put in order a little, obtains following form:

G _L＝A ²λ ₁ ^-2R ^-0.5…………(4)

The present invention that Here it is is by measuring the solidified structure eigenvalue ₁, come sxemiquantitative calculation sample solidification front thermograde G _LPrinciple, and λ ₁The existing comparatively ripe method of mensuration, take lattice according to Ha Tuoyage ratio and Crouse's SWD, the stable state directional solidification dendrite form of steel, metallurgical transactions, 7A1976,811 (Hatto Jacobiand KlauS Schwerdtfeger, Dendrite for Morphology of Steady State UnidirectionalSolidified Steel, Metall.Trans.A, 7A1976,811) described Jacobi formula:

λ ₁＝(4S/3 ^1/2(2N-(12N-3) ^1/2+1)) ^1/2....(5)

When the N value was big, following formula was reduced to:

${\mathrm{\λ}}_1={(2S/3^{1/2}N)}^{1/2}\≅1.075{(S/N)}^{1/2}...\left(6\right)$

With the test sample product area S of institute with dendrite is counted N substitution (5) or (6) formula is tried to achieve primary dendritic spacing λ ₁And with resulting primary dendritic spacing λ ₁, drawing velocity R when the initial testing sample solidifies and the thermograde G that tests _LSubstitution (2) formula is calculated the coefficient A that tries to achieve corresponding to this alloy, as constant; For other setting test sample, only need said determination primary dendritic spacing λ is pressed in certain cross section ₁Method is tried to achieve λ ₁And with drawing velocity R (4) formula of substitution known coefficient A simultaneously, just try to achieve the thermograde in forward position, freezing interface.Why the present invention is referred to as semi-quantitative method, is because λ ₁Measured value and G _L-λ ₁Relational expression all has statistical.

The present invention has following advantage:

1. the present invention is based on solidification theory, trickle this principle of two information that the thermal field that has used solidified structure to record process of setting truly changes, in conjunction with solidification experiments, sum up and a kind ofly be characterized as clue with solidified structure, measure by sample solidified structure eigenwert, the semi-quantitative analysis computing method of forward position, the freezing interface actual temperature gradient of sample are solidified in acquisition, promptly a kind of sample that solidifies of material is done disposable initial thermal field test, and calculate this material character coefficient entry A, other only need directly quote coefficient entry A and the substitution primary dendritic spacing λ that initial trial obtains with the material solidification test specimen ₁, reach known drawing velocity R, just can calculate the thermograde in forward position, freezing interface, solved the difficult problem that thermograde is difficult to measure.

2. the present invention obtains to solidify sample actual temperature gradient by calculating, and makes the solidification experiments process avoid the additional thermal field of testing element to influence the influence that reaches the behavior of solidifying.

3. because primary dendritic spacing variation and sample and sectional position have good consistance, and the present invention more helps the analysis to different structure sample and different cross section and position thermograde slight change, this is to be difficult to realize in the thermal field test.

4. analytical approach of the present invention is easy, has the semi-quantitative analysis meaning.

Embodiment

Below in conjunction with embodiment the present invention is described in further detail.

Embodiment 1

1. initial thermal field test: solidification experiments equipment is directional solidification furnace.Solidify specimen material for being the alloy of base with Ni, the present embodiment material is the TMS64 single crystal alloy; Sample is the straight rod of 3～50mm diameter pole or the suitable size of other cross sectional shape, and the present embodiment diameter is 16mm; Determine to be provided with 3-20 group thermometric galvanic couple in sample, present embodiment is established 8 groups; Described sample orientation is solidified, and drawing velocity is 1～25mm/min, and present embodiment is 6mm/min, and holding temperature is 1450～1800 ℃, and present embodiment is 1600 ℃; Actual measurement freezing interface temp gradient at front edge is 5.5 ℃/mm;

2. determine the A parameter of described alloy according to test result:

1) the sample xsect is solidified in intercepting, prepares macroscopical metallographic sample, observes solidified structure on microscope, prepares 10～300 times of metallographs, and present embodiment is 30 times of metallographs; Equilateral hexagon bushing with a known area S covers on the photo, present embodiment S=2289mm ², reading the dendrite number n of 10 visual fields in this area, N=14.9 averages;

2) hex area S and a dendrite are counted mean value N substitution formula:

λ ₁＝(4S/3 ^1/2(2N-(12N-3) ^1/2+1)) ^1/2

Or λ ₁=(2S/3 ^1/2N) ^1/2≈ 1.075 (S/N) ^1/2

Try to achieve primary dendritic spacing λ ₁, calculate and the test result demonstration: for the TMS64 alloy, certain cross section primary dendritic spacing λ ₁=0.444mm, corresponding thermograde is 5.5 ℃/mm; With known primary dendritic spacing λ ₁, the drawing velocity R when typical sample solidifies and calculate the freezing interface temp gradient at front edge G of cross section taken in correspondence _LThe substitution formula:

λ ₁＝A.G _L ^-0.5.R ^-0.25

Obtain coefficient A=1.63, as constant corresponding to this alloy.

3. other same material directional solidification laboratory sample thermograde is calculated

For the sample structure size of other same material, solidification equipment can be different with technological parameter, only need to described xsect set by step (2) method try to achieve primary dendritic spacing λ ₁, and with known drawing velocity R and coefficient entry A substitution simultaneously formula:

λ ₁＝A.G _L ^-0.5.R ^-0.25

Promptly try to achieve the thermograde G in forward position, freezing interface _L, formula λ here ₁=A.G _L ^-0.5.R ^-0.25Can make into:

G _L＝A ²λ ₁ ^-2R ^-0.5

Present embodiment is identical to the sample orientation solidification experiments device therefor of other same material, and the solidifying process parameter is also identical, and just sample diameter becomes 6mm, dissects the sample cross section by described step 2, records primary dendritic spacing λ ₁=0.381mm, then Dui Ying thermograde is:

G _L＝A ²λ ₁ ^-2R ^-0.5＝2.66·0.381 ^-2·6 ^-0.5＝7.479℃/mm

Embodiment 2

Technic metal, equipment and to solidify parameter all identical, difference from Example 1 is that sample diameter is decreased to 4mm, and this sample is repeated the step 2 of embodiment 1, tries to achieve primary dendritic spacing λ ₁, with the primary dendritic spacing λ that calculates ₁=0.318mm and known drawing velocity R=6mm/min and A=1.63 generation

G _L＝2.66λ ₁ ^-2R ^-0.5＝2.66*0.318 ^-2*6 ^-0.5＝10.739℃/mm

Computing method of the present invention are applied to the alloy of growing in the dendrite mode.

Claims (2)

1. the sxemiquantitative method of testing of a temp gradient at front edge of directional setting interface is characterized in that: the sample that solidifies to a kind of material is done disposable initial thermal field test, calculates this material character coefficient entry A; With the material solidification test specimen, only need directly quote coefficient entry A and the substitution primary dendritic spacing λ 1 that initial trial obtains to other, reach known drawing velocity R, just can calculate the thermograde in forward position, freezing interface, be specially:

(1) initial thermal field test: solidifying of a kind of material the thermometric galvanic couple is set in the sample, and directional solidification, drawing velocity is 1mm/min～25mm/min, holding temperature is 1450～1800 ℃, measures solidification process thermal analysis data and curve;

(2) determine the alloy A parameter:

1) the sample predetermined cross-section is solidified in intercepting, prepares macroscopical metallographic sample and 10～300 times of metallographs; With the bushing of a known area S, cover on the photo, read a dendrite number n in the described known area S, and get 10 visual fields, get the mean value N of its n value; According to described heat analysis data and curve, the freezing interface temp gradient at front edge G of test cross section taken in correspondence _L

2) known area S and a dendrite are counted N substitution formula λ ₁=(4S/3 ^1/2(2N-(12N-3) ^1/2+ 1)) ^1/2Or λ ₁=(2S/3 ^1/2N) ^1/2≈ 1.075 (S/N) ^1/2Try to achieve primary dendritic spacing λ ₁

3) with described primary dendritic spacing λ ₁, the freezing interface temp gradient at front edge G of drawing velocity R when described sample solidifies and cross section taken in correspondence _LSubstitution formula λ ₁=A.G _L ^-0.5.R ^-0.25, try to achieve coefficient A, as constant corresponding to this alloy;

(3) solidify sample for other same material, try to achieve primary dendritic spacing λ according to step (2) ₁, and go into formula λ with known drawing velocity R and coefficient entry A one are contemporary ₁=A.G _L ^-0.5.R ^-0.25, can try to achieve the thermograde G in forward position, freezing interface _L

2. according to the sxemiquantitative method of testing of the described temp gradient at front edge of directional setting interface of claim 1, it is characterized in that: described known area S is surrounded by hexagon.