CN108844806A - A method of estimation metal material plane strain fracture toughness - Google Patents
A method of estimation metal material plane strain fracture toughness Download PDFInfo
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Abstract
The invention discloses a kind of methods for estimating metal material plane strain fracture toughness, belong to Fracture of Metal Material toughness technical field.This method includes three steps：Small sample fracture toughness tests to obtain experiment value Kq, by Kq 2B and sample thickness B carries out linear fit, K is accurately calculated by straight slopeIC.The plane strain fracture toughness of material can be simply and effectively measured using the present invention, has not only greatly saved experimental cost, and for some since preparation process or its toughness are higher and be unable to measure out accurate KICMaterial (such as amorphous alloy and nano metal material), the method can provide accurate parameter, this is to be provided fundamental basis especially for the damage tolerance design of aviation component how selection is provided a strong basis.
Description
Technical field：
The present invention relates to Fracture of Metal Material toughness technical fields, and in particular to a kind of estimation metal material plane strain is disconnected
Split the method for toughness.
Background technique：
With the development that is constantly progressive of modern science and technology, all trades and professions increasingly improve the mechanical property requirements of structural material,
High-strength and high ductility becomes the direction of structural material development.Especially fracture toughness, in aerospace, nuclear power station and petroleum pipeline etc.
Key areas is all as important indicator [variation of Cao Chun dawn selection criterion and the hair of high damage tolerance titanium alloy for measuring material
Exhibition, Acta Metallurgica Sinica, 2002,38：4-11.].Fracture toughness is the parameter that material resists instable growth of crack ability, theoretical base
Plinth is fracture mechanics.Fracture mechanics starts sex work [Griffith A A, Eng in nineteen twenty-one originating from Griffith
M.VI.The phenomena of rupture and flow in solids[J].Philosophical
Transactions of the Royal Society A,1921,221(582-593):163-198.], his theory is not only
The theoretical strength of brittle solid is obtained, while the relationship of the breaking strength and flaw size to material gives more accurately
Amendment.In 20 middle of century, which is successfully introduced to the field of metal material by Irwin and Orowan, accelerated existing
Development and industrial application [Irwin G R.Fracture dynamics [J] .Fracturing of for Theory of Fracture Mechanics
Metals,1948,152；Orowan E.Fracture and strength of solids[J].Reports on
Progress in Physics,1948,12:183.]。
At present for the test method of material fracture toughness with plane strain fracture toughness KIC, J integral and tri- kinds of CTOD be
It is main.Component needed for the essential industries such as aviation field (such as undercarriage, aircraft beam steel) is all high-strength material,
Easily occurs the case where band crackle brittle failure during the military service of heavy construction component.Compared to J integral and CTOD method, plane
Strain fracture toughness KICIt is more widely applied in the fracture toughness of evaluation high-strength material, especially its measurement method is compared with it
He two kinds it is simpler.In fracture mechanics, KICAffiliated linear elastic fracture mechanics development comparative maturity, and elastic-plastic fracture power
Theory (J integral and CTOD method) also in further explore [Suresh S.Fatigue of Materials,
Cambridge University Press [J] .Cambridge, England, 1998.], develop and not perfect, thus use
KICTo evaluate the fracture toughness of high-strength material with more applicability.Certainly, metal material crack tip there is always plastic zone,
If plastic zone very little (as be much smaller than crack length), by amendment appropriate, then still can using linear elastic fracture mechanics into
Row fracture analysis, so for high-strength material, plane strain fracture toughness KICIt is still its preferred method.
But, the measurement of plane strain fracture toughness also has its limitation, the i.e. standard comparing of fracture toughness numerical value judgement
Harshness, standard sample size have to meet KICThe Effective Judge of test, such as formula (1)：
B in formula (1), a, W are the thickness of sample, width and crack length respectively.KICIt is plane strain fracture toughness, σyIt is
Yield strength.If the size of sample is unsatisfactory for formula (1), the data obtained can only be used as experiment value Kq, cannot function as material
Plane strain fracture toughness.Fig. 1 give fracture toughness experiment value K with sample thickness and variation tendency, KICIt is in thickness
Meet the stationary value under plane strain state, as can be seen from Figure, after sample thickness reaches certain value, experiment value gradually becomes
In stabilization, the at this moment as fracture toughness K of materialIC.Due under requirement of the current industrial development to material high-strength and high ductility, Hen Duocai
The thickness of sample of material is unable to satisfy KICThe dimensional standard of test, and can accomplish for large-sized material for some, institute
Need the load of testing machine again considerably beyond the condition in laboratory.Based under such circumstances, scientific research personnel has done many trials
The plane strain fracture toughness of material is estimated, is such as derived by lab scale quadrat method or by other mechanical properties.
Some scholars have attempted to develop the absorption function (CVN) and plane strain fracture toughness of traditional Xia Shi impact experiment
KICRelationship.Barsom and Rorlfe analyzes a series of steel impact flexibility of varying strengths and the experimental data of fracture toughness
[Rolfe S T,Barsom J M.Fracture and fatigue control in structures:applications
Of fracture mechanics [M] .ASTM International, 1977.], from the experience wherein fitted between the two
Formula, these data can be applicable in the ductile-brittle transiton section of impact flexibility and upper temp section.Teran etc. proposes one kind
Quantitative relationship in welding point about impact flexibility and fracture toughness, the result and reality estimated according to this quantitative relationship
It tests result and coincide fine, their this methods are capable of providing a kind of new thinking to guide the fracture toughness [Ter of assessment material
án G,Capula-Colindres S,Angeles-Herrera D,et al.Estimation of fracture
toughness KIC from Charpy impact test data in T-welded connections repaired
by grinding and wet welding[J].Engineering Fracture Mechanics,2016,153:351-
359.].Although there are quantitative relationships between impact flexibility and fracture toughness, can be adapted for owning there is no a kind of formula
Material.In addition these empirical equation physical significances are indefinite, at present there is no being theoretically proven, so can only conduct
Some materials estimate the empirical relation of fracture toughness.Read et al. has studied influence of the sample thickness to aluminium alloy fracture toughness,
It was found that the result of J integral does not depend on sample thickness, but experimental result also indicates that J product at this time in the case where crackle extension
The value and plane strain fracture toughness K dividedICConsistency [Read D T, Reed R P.Effects of is not had
specimen thickness on fracture toughness of an aluminum alloy[J]
.International Journal of Fracture,1977,13(2):201-213.].Lee et al. is visited according to energy principle
Various sizes of fracture toughness experiment in steel alloy is begged for, they have found the empirical relation formula of share zone and fracture toughness
[Lee B W,Jang J,Kwon D.Evaluation of fracture toughness using small notched
specimens[J].Materials Science and Engineering:A,2002,334(1-2):207-214.]。
Gludovatz et al. has studied the fracture toughness of small sample in amorphous metal, they think the fracture of the small sample in amorphous
Toughness may be also to meet for Unite States Standard ASTM, also indicated that in certain article the fracture toughness of small sample there is point
Dissipate big disadvantage [Gludovatz B, Naleway S E, Ritchie R O, the et al.Size-dependent of property
fracture toughness of bulk metallic glasses[J].Acta Materialia,2014,70:198-
207.].On the whole, how using small sample or other mechanical properties to predict that the plane of material is answered in spite of many scholars
Become in fracture toughness and has done many work, but it is either equal from the method for test or the applicability of theory, their method
There is certain limitation.
Summary of the invention：
For the fracture toughness K of high-strength and high ductility metal material existing in the prior artICIt is difficult to ask by what experiment obtained
Topic, the purpose of the present invention is to provide a kind of method for estimating metal material plane strain fracture toughness, this method can pass through
The plane strain fracture toughness of small size sample simple accurate measurement material under the conditions of small scall yield, avoids selecting larger examination
Sample ruler cun and the test of big load experimental facilities, reduce time cost and monetary cost, to provide accurate power when engineering material selection
Learn performance indicator.
To achieve the above object, the technical solution adopted in the present invention is as follows：
A method of estimation metal material plane strain fracture toughness, this method comprises the following steps：
(1) same material sample with different thickness is selected, plane strain fracture toughness experiment is carried out；
(2) the plane strain fracture toughness K of different-thickness sample is calculatedICExperiment value Kq, then carry out validity and test
Card, the K if meeting Effective Judgeq=KICIf being unsatisfactory for Effective Judge, step (3) are carried out；
(3) thickness of sample B, plane strain fracture toughness K are establishedICWith experiment value KqBetween quantitative relationship, such as formula (8)
It is shown；
In formula (8)：C0For constant；
Using sample thickness B as abscissa, BK in rectangular coordinate systemq 2For ordinate drawing data point, and by each data point
Linear fit is carried out, the slope of gained fitting a straight line is in formula (8)Value, extracted square root and obtain the flat of material
Face strain fracture toughness KIC。
In above-mentioned steps (1), thickness of sample >=2mm.Material sample at least selects two kinds of thickness, and the minimum between each sample is thick
Spend difference >=2mm.(in the case where material preparation condition allows, the difference in thickness of sample is larger as far as possible, such as：Sample thickness B is
4mm, 8mm and 12mm).
In above-mentioned steps (1) and step (2), sample shape, plane strain fracture toughness experiment operating procedure and effectively
Property verification process should be consistent with American Standard ASTM E399-12 or national standard GB/T4161-2007, the measurement of dependent variable needs are adopted
Use strain gauge.
In above-mentioned steps (3), the linearly related degree of fitting a straight line is not less than 0.9.
It Design Mechanism of the invention and has the beneficial effect that：
1, the testing standard for the metal material plane strain fracture toughness being widely recognized as at present is U.S. ASTM E399-12
And China standard GB/T4161-2007.However, two kinds of standards have done stringent regulation to the sample size of material, this
It is required that so that the preparation condition of many high-toughness materials is difficult to meet.Even if specimen size reaches condition, the load of experimental facilities
Also it is difficult to realize.Certainly, for the material fracture toughness test method of higher toughness, there are also J integrals and CTOD method etc., but its
Test method is more complicated cumbersome.And J is integrated with elastic-plastic fracture mechanics theory based on CTOD method still further
In exploration, there is no perfect as linear elastic fracture mechanics theoretical developments.So taking the above method to calculate KICIt is not rigorous
Reliably.Therefore, accurately estimate that the fracture toughness of metal material is particularly important under the conditions of small scall yield using small sample.
The present invention proposes a kind of simple method to predict the plane strain fracture toughness of material, with the sample of different-thickness
Make the experiment Fracture Toughness K of materialq, and by the Fracture Characteristics of sample establish sample thickness and fracture toughness test
Value KqQuantitative relationship, with principle [Qu R T, Zhang Z J, Zhang P, the et al.Generalized of energy balance
energy failure criterion[J].Scientific reports,2016,6:23359.], the flat of material is instead released
Face strain fracture toughness KIC.Its cardinal principle：The fracture of material is made of flat break with cutting, is based on energy principle, crackle is expanded
The gross energy consumed during exhibition is divided into the area Ping Duan and shear zone two parts, and carried out a series of derivation of equation will be broken it is tough
Property experiment value Kq, plane strain fracture toughness KICIt quantitatively links together with sample thickness B.
2, the present invention using small sample (thickness >=2mm) model can be very simple and fast to estimate plane strain fracture tough
Property, estimated value and the experiment value of the model meet fine.The plane of material can be simply and effectively measured by the invention
Strain fracture toughness has not only greatly saved experimental cost, and for some since preparation process or its toughness are higher
And it is unable to measure out accurate KICMaterial (such as amorphous alloy and nano metal material), the method for the present invention can provide accurate ginseng
Amount.
3, the method for the present invention can not only speculate fracture toughness simply by small size sample, and be certain aviations
The fracture toughness measurement at industrial key member position provides new thinking, this is how selection provides a strong basis, especially
It is provided fundamental basis for the damage tolerance design of aviation component.
Detailed description of the invention:
Fig. 1 is variation schematic diagram of the fracture toughness K with plate thickness B.
Fig. 2 is the method schematic diagram that small size sample estimates metal material plane strain fracture toughness.
Fig. 3 is the flat disconnected mixed model figure with shear fracture.
Fig. 4 is to be broken angle with sample thickness in fracture apperance schematic diagram and tempered steel when crackle reaches Instability state
The trend of variation；Wherein：(a) fracture apperance schematic diagram when crackle reaches Instability state；(b) in tempered steel break corner with examination
The tendency chart of sample thickness change.
Fig. 5 is load Fq 2With the data point and cubic polynomial matched curve figure of sample thickness B.
Fig. 6 is the comparison diagram of AISI 4340 steel small sample estimated value and experiment value in embodiment 1.
Fig. 7 is the comparison diagram of 18Ni Maraging steel small sample estimated value and experiment value in embodiment 2.
Specific embodiment：
It is for a more detailed description to the present invention with reference to embodiments.These examples are only to the best embodiment party of the present invention
The description of formula, does not have any restrictions to the scope of the present invention.
One, the present invention is the method for estimation metal material plane strain fracture toughness, and this method comprises the following steps：
(1) sample of two or more thickness is chosen, plane strain fracture toughness experiment is carried out.
(2) experiment value K is calculated according to formula in standardq, validation verification is then carried out, is if meeting validation verification
KICIf being unsatisfactory for Effective Judge, experiment value K only can be used asq.Specimen shape and laboratory operating procedures should be with American Standard ASTM
E399-12 or national standard GB/T4161-2007 are consistent, and the measurement of dependent variable is needed using strain gauge.
(3) with B (sample thickness) for abscissa, Kq 2B is ordinate drawing data point in rectangular coordinate system, and by each number
Strong point carries out linear fit, as shown in Figure 2.As seen from Figure 2, data Kq 2B and sample thickness B has linear well close
System, the square root of institute's fitting a straight line slope is the plane strain fracture toughness K of materialIC.Wherein：The fitting of data should be using special
The data processing software of industry, and linear correlation degree must not be lower than 0.9.
Two, principle based on the present invention：Principle of energy balance
It is well known that the Macroscopic feature of material can be divided into flat disconnected and shear fracture, such as scheme to give in figure shown in (3)
The disconnected mixed model figure with shear fracture is gone out to put down.As can be seen from Figure, the Macroscopic mode of material generally by it is flat disconnected with
The mode of shear fracture mixes.The gross energy of fracture can be divided into the area Ping Duan energy and shear fracture area energy.
Crack propagation will follow energy criteria in fracture toughness experiment, at the steady-state crack propagation stage, energy release
Rate G is equal with the extension drag of crackle, i.e., R-curve is theoretical.Energy consumption needed for it represents crack propagation：Crack tip modeling
Property deformation consumption energy and micropore germinating polymerization grow up consumed energy.However, the presence of triaxiality effect, will so that
Along the energy release rate G at sample center to edge and non-constant.It is otherwise noted that crisp in addition to ideally
Property material, all there is plastic deformations for number metal materials big absolutely, this will form shear fracture region at the edge of sample.
There is document to point out that the part of shear fracture can represent whole CraCk extenslon reslstsnce, i.e. plane strain fracture
Toughness KIC.Plane strain fracture toughness experiment in, the energy proportion of shear fracture generally by increase sample thickness come
Ignore.Have scholar be already indicated above the area Ping Duan and shear fracture region energy should separate computations, so crackle is from starting to extend
Consumed gross energy U can be divided into two parts when to Instability state：The energy U of flat disconnected region consumptionCAnd shear fracture
The energy U of region consumptionS, such as formula (2).
U=UC+US, (2)；
It is inconsistent in the area Ping Duan and the expansion rate in shear fracture area but in crack propagation.This is because part
Energy release rate G is gradually reduced with sample center to surface, and crackle is caused to be faster than shear zone in the spreading rate in the area Ping Duan.It is real
On border, for crackle when the area Ping Duan extends, specimen surface has formd plastically deforming area, and the plastically deforming area of specimen surface exists
The energy in shear fracture region is considered as during crack propagation.According to energy criteria, formula (2) can be expressed as formula
(3)：
Cq·At=CC·AC+GS·AS(3)；
Wherein：Gq、GCAnd GSIt is in the total fracture area of sample, the area Ping Duan and shear zone unit length crack propagation list respectively
Energy consumed by plane product, the area passed through when crack propagation is to Instability state can be used as At, ACAnd ASIt is flat respectively
The area in disconnected area and shear zone.But, shear surface is not parallel to the area Ping Duan surface, since two surfaces are presented nearly 45 °
Angle, it will be assumed that shear surface be 45 ° with flat section angle (share zone is really a curved surface, for simplification on inclined-plane
Calculate here as plane).So shear zone can be used as simple triangle, as shown in Fig. 4 (a), by can be in Fig. 4 (a)
Find out, the energy that when crack propagation consumes consists of two parts：The area Ping Duan and shear fracture area；Wherein：
In formula (4), S is shearing sector width, and da is the distance that crackle begins to expand into Instability state, and m is crackle
The slope of angle between tip and maximum shear width, i.e. fracture angle.Formula (4) is brought into (3), abbreviation obtains formula (5)：
There is very big relationship in the formation of shear zone and Crack Tip Deformation area, firstly, measuring for system is being tempered
The sample fracture angle of different-thickness in steel is such as schemed shown in (4b), by that can determine that fracture angle is and sample is thick in Fig. 4 (b)
Spend unrelated parameter, it was confirmed that m value is constant.When crack propagation is to Instability state, energy release rate has also reached most
Big value, it depends on the distance and allowable stress of crack propagation.So da may be considered a stationary value, (this assumes rear
It is verified in the experimental result in face).Therefore formula (6) are obtained：
According to Theory of Fracture Mechanics, there are quantitative relationships, such as formula between energy release rate G and stress field strength factors K
(7)：
Formula (6) and formula (7) are brought into formula (5), abbreviation obtains formula (8)：
C in formula (8)0It is constant, thus obtains plane strain fracture toughness KIC, experiment value KqWith sample thickness B
Between quantitative relationship, i.e., obtain the plane strain fracture toughness of material using formula (8), be specifically for use in some high tenacity
Material.But it is worth noting that, if the thickness of sample is too small, entire macrofracture will lead to only by shear fracture district's groups
At the area Er Pingduan can disappear, and thus be more than the condition of small scall yield.So the feasibility in order to guarantee this model, choosing
The thickness for selecting sample will guarantee that the area Ping Duan and shear fracture area can be clearly distinguished in the macrofracture having no progeny in it.
All there is parameter B in the right and left of formula (8), then Kq 2Whether the linear relationship of B and B is influenced by B, and one
It is a deeper into verifying to prove sample thickness B on above-mentioned linearly without influence.By plane strain fracture toughness test in formula
(9) it brings into formula (8), simplified formula (10).
F in formula (9)qLoad when being crackle Instability state, f (a/W) is size factor.K at this timeIC, f, D be normal
Number.Formula (10) can be further simplified as formula (11)：
The α and β of formula (11) are constant, by load Fq 2Cubic polynomial fitting is carried out with the data of sample thickness B, such as
Scheme to find its matched curve and formula (11) shown in (5) unanimously, thus demonstrate sample thickness B to linear in formula (8)
Relationship is without influence.
It three, can be using the plane strain fracture toughness of small sample estimation metal material using the present invention
It is tested according to the plane strain fracture toughness of standard, specimen size needed for high-toughness material and testing machine tonnage are difficult
To realize.The plane strain fracture toughness of material is estimated using the present invention, it is possible to reduce the cost of sample processing is reduced simultaneously
The time cost and monetary cost of experiment.Importantly, large-sized material can not be made into because of preparation process for some
Material, can also effectively predict its Fracture Toughness.Table 1 is 4340 steel of undercarriage AISI under different heat treatment technique
Tensile property, fracture toughness and minimum specimen size and loaded load needed for it.The sample for being 500 DEG C with tempering temperature
For, fracture toughness is 127.72MPa m1/2, and minimum sample (three-point bending shape) size of the toughness value can be measured
It is thickness 30mm, width 60mm, length 250mm, and the testing machine tonnage needed for it is at least 100kN.The ginseng of these demands
Number significantly increases the difficulty of experiment.And utilize our small sample (thickness 4-8mm) models can be very simple and fast estimation
Plane strain fracture toughness out, it is fine that confirmatory experiment shows that estimated value meets with experiment value.Can simply have through the invention
The plane strain fracture toughness for measuring material of effect has not only greatly saved experimental cost, and for some due to system
For technique or its toughness are higher and are unable to measure out accurate KICMaterial (such as amorphous alloy and nano metal material), the method
Accurate parameter can be provided, this is how selection provides a strong basis, especially for aviation component
Damage tolerance design is provided fundamental basis.
Conventional tensile property, fracture toughness and its required minimum sample thickness of 1 AISI of table, 4340 steel and load carry
Lotus
Embodiment 1：
The present embodiment is to predict 4340 steel plane strain fracture toughness of AISI using small size sample, and specific step is as follows：
Step 1：The Three Points Bending Specimen for choosing different-thickness (4mm, 6mm, 8mm and 12mm) carries out fracture toughness experiment,
And experiment value K is calculated according to experimental standardq。
Step 2：By formula (8) by Kq 2B and sample thickness B carries out linear fit.
Step 3：K is calculated according to the linear gradient that step 2 is fittedIC, estimated value is as shown in Figure 6 with experiment value.
Embodiment 2：
The present embodiment is to predict 18Ni Maraging steel plane strain fracture toughness, specific steps using small size sample
It is as follows：
Step 1：The Three Points Bending Specimen for choosing different-thickness (4mm, 6mm and 25mm) carries out fracture toughness experiment, and root
Experiment value K is calculated according to experimental standardq。
Step 2：By formula (8) by Kq 2B and sample thickness B carries out linear fit.
Step 3：K is calculated according to the linear gradient that step 2 is fittedIC, estimated value is as shown in Figure 7 with experiment value.
Claims (5)
1. a kind of method for estimating metal material plane strain fracture toughness, it is characterised in that：This method comprises the following steps：
(1) same material sample with different thickness is selected, plane strain fracture toughness experiment is carried out；
(2) the plane strain fracture toughness K of different-thickness sample is calculatedICExperiment value Kq, validation verification is then carried out, such as
Fruit meets Effective Judge, then Kq=KICIf being unsatisfactory for Effective Judge, step (3) are carried out；
(3) thickness of sample B, plane strain fracture toughness K are establishedICWith experiment value KqBetween quantitative relationship, such as formula (8) institute
Show；
In formula (8)：C0For constant；
Using sample thickness B as abscissa, BK in rectangular coordinate systemq 2For ordinate drawing data point, and each data point is carried out
Linear fit, the slope of gained fitting a straight line are K in formula (8)I2CValue, being extracted square root obtains the plane of material and answers
Become fracture toughness KIC。
2. the method for estimation metal material plane strain fracture toughness according to claim 1, it is characterised in that：Step
(1) in, thickness of sample >=2mm.
3. the method for estimation metal material plane strain fracture toughness according to claim 1 or 2, it is characterised in that：Step
Suddenly in (1), the thickness of material sample is at least two kinds, minimum thickness difference >=2mm between each sample.
4. the method for estimation metal material plane strain fracture toughness according to claim 1, it is characterised in that：Step
(1) and in step (2), sample shape, the operating procedure and validation verification process Ying Yumei of plane strain fracture toughness experiment
Mark ASTM E399-12 or national standard GB/T4161-2007 is consistent, and the measurement of dependent variable is needed using strain gauge.
5. the method for estimation metal material plane strain fracture toughness according to claim 1, it is characterised in that：Step
(3) in, the linearly related degree of fitting a straight line is not less than 0.9.
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