CN109900554B - A method of fracture toughness is calculated using indentation method - Google Patents
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Abstract
The invention belongs to fracture toughness test technical fields, provide a kind of method for calculating fracture toughness using indentation method, include the following steps: that (1) obtains material indentation and the relationship between unloading phase depth and load；(2) load displacement curve when being unloaded by material obtains plasticity residual depth, contact depth state parameter；It (3) include radial displacement correction factor and Berkovich pressure head non-axis symmetry modifying factor using finite element software prediction material under pressure head effect；(4) material uniaxial tensile test obtains elasticity modulus of materials and combines finite element software by GTN theory to obtain material critical hole ratio；(5) will be pressed into function be associated with energy to failure and with strain energy density equivalence, thus obtain by critical plasticity residual depth characterize fracture toughness equation.This fracture toughness test method can obtain the elasticity modulus and fracture toughness numerical value of material by the small-scale micro-indentation test of material, quick, low damage.
Description
Technical field
The present invention relates to fracture toughness test technical fields, and in particular to a kind of side that fracture toughness is calculated using indentation method
Method.
Background technique
With the continuous development of aeronautical engineering, reactor engineering, welding technique and petroleum works, to metal material mechanics
The demand of performance test is growing.There are a large amount of in-service equipment, tradition in the industries such as thermoelectricity, nuclear power, metallurgy and petrochemical industry
Sampling test can obtain the more comprehensive performance parameter of in-service equipment and materials, but sampling test generally has destruction, no
Suitable for in-service equipment.Indentation method is not required to sample, and has lossless characteristic, and can accurately and reliably obtain the machine of in-service equipment and materials
Tool performance.Indentation test device volume is relatively small, and the positioning of tested region is easily achieved when test, can be applied to survey
The material (such as weld seam, heat affected area, base material) of scale face performance gradient change.It is disconnected using impression test in view of advantage above
The method for splitting toughness test can quick, the lossless fracture toughness numerical value for obtaining material.
The test function of impression and energy phase needed for crackle crack initiation when impression crack initiation energy (IEF) model thinks to reach critical load
Deng.When having the continuous ball impression test fracture toughness using IEF, because of the geometry of ball, need to be pressed into biggish depth,
It can not be tested in certain functionally gradient material (FGM)s, knee；And Berkovich pressure head is larger in calculating decrement elasticity modulus error, it is existing
Indentation method is simultaneously unreasonable, thus needs to improve.
Summary of the invention
For overcome the deficiencies in the prior art, the present invention provides it is a kind of using indentation method calculate fracture toughness method,
Method by continuously adding unloading using Berkovich pressure head on indentation equipment to measured material, it is corresponding to obtain measured material
Unloading point effective modulus of elasticity and plasticity residual depth according to the indentation function of foundation and energy to failure incidence formula, and then obtain material
The fracture toughness of material, the process for obtaining the fracture toughness numerical value of material is quick, low damage, being capable of effectively save experimental material consumption
Take.
The following technical solution is employed by the present invention:
A method of fracture toughness being calculated using indentation method, is included the following steps:
(1) it is based on indentation test, under constant rate of speed, obtains and is no less than whole load-displacement song under 6 unloading conditions
Line；
(2) fitting of first power function parameter is carried out to the part each unloading curve 30%-70%, it is remaining after being unloaded
It is plastically deformed depth hp, contact depth hcParameter calculates the unloading rigidity at every curve unloading；
It carries out a straight line fitting again to each unloading curve again, obtains the unloading rigidity of each curve；
The unloading rigidity cut-off line match value of first curve, Article 2 start the unloading rigidity for calculating power function fitting
Value is compared with the value of straight line fitting, if the two error judges that power function fitting parameter is effective in 10%；
To effective data point P and hpIt is fitted using following equation:
Wherein, hpFor afterflow depth after unloading, P is loading of pressing in, C1、C2、C3For fitting parameter and meet C2*
C3< 0, and then obtain hpWith the parameters relationship of P；
(3) pressure head process of press in is simulated using finite element, obtains radial displacement correction factor and Berkovich pressure head
Non-axis symmetry modifying factor, to obtain decrement elasticity modulus；
(4) using finite element to process simulation is uniaxially stretched, the critical hole ratio of material is obtained；
(5) by the indentation function and indentation energy to failure incidence formula that propose, fracture toughness is calculated in conjunction with critical hole ratio；
The indentation function and indentation energy to failure incidence formula are as follows:
Wherein GIEFTo be pressed into energy to failure, F (hp) it is hpDepth is pushed down into function, P (hp) it is hpLoad under depth, Ap(hp) be
hpImpression perspective plane area, calculating formula under depth are as follows:
Wherein, γ is radial displacement correction factor, hpFor unloading after afterflow depth,For critical residual plasticity
Deforming depth；
In conjunction with the P and h obtained in step (2)pFitting formula, must be pressed into energy to failure aboutFunction are as follows:
Wherein A, B, C are respectively
Critical residual is plastically deformed depthPass throughWith lnhpRelationship acquires, relationship are as follows:
WhereinFor effective modulus of elasticity, K, b are fitting parameter；
Effective modulus of elasticityCalculation formula are as follows:
Wherein, υ is measured material Poisson's ratio, υiFor pressure head material Poisson's ratio, ErTo reduce elasticity modulus, EiFor pressure head bullet
Property modulus；
InIn E when Critical fracture*Taking corresponding ordinate is critical residual plastic deformation depth
It is pressed into energy to failure and strain energy density is of equal value, equivalence formula are as follows:
Wherein ScrFor critical strain energy density, υ is measured material Poisson's ratio, and SED is strain energy density；
And haveThen fracture toughness finally solves formula are as follows:
Wherein KICFor fracture toughness, E is measured material elasticity modulus.
Preferably, indentation test using constant Berkovich pressure head continuously adds the method for unloading, pressure head in step (1)
No less than 6 equal difference loads, and the unloading after having loaded each time are carried out with the loading speed of 50mN/s, obtain whole load-
Displacement curve.
Preferably, power function parameter fitting formula in step (2) are as follows:
P=B (h-hp)m
Wherein, B, m are fitting parameter, hpFor afterflow depth after unloading, h is pressure head compression distance；
Straight Line Fitting Parameters relationship are as follows:
P=a+S2*h
Wherein, a is fitting parameter, S2For the unloading rigidity in Straight Line Fitting Parameters；
Unloading rigidity S in power function parameter1It is obtained by Oliver-Pharr method, is calculated and obtained by following formula,
S1=Bm (hmax-hp)m-1
Wherein, hmaxFor compression distance maximum in indentation test.
Preferably, reduce the calculation formula of elasticity modulus in step (3) are as follows:
Wherein, ErTo reduce elasticity modulus, β is Berkovich pressure head non-axis symmetry modifying factor, and γ repairs for radial displacement
Positive coefficient, AcTo contact depth area, S is unloading rigidity, and S takes S at first unloading curve2, unloaded in each later
Curve is using the unloading rigidity S in power function parameter1。
The invention has the advantages that:
1, this indentation method calculating fracture toughness method can be by passing through Berkovich to measured material on indentation equipment
Pressure head continuously adds the method for unloading, obtains measured material and corresponds to unloading point effective modulus of elasticity and plasticity residual depth, according to building
The indentation rendered meritorious service and energy to failure incidence formula, and then can get the fracture toughness of material, can more rapidly, low damage obtain the disconnected of material
Ductility values are split, effectively save experimental material expends.
2, the present invention optimizes the fit range of material unloading curve, and by match value and experiment value error analysis,
Guarantee the validity of fitting data.
3, material critical plasticity residual depth is associated with by the present invention by critical hole ratio, and critical hole ratio is drawn by uniaxial
It stretches reality to obtain in conjunction with finite element, avoids the human factor of traditional statistical acquisition, so as to more accurately predict that material is disconnected
Split ductility values.
4, the initial indentation stage elasticity modulus accuracy obtained in calculating process of the present invention significantly improves, and answers with engineering
With value.
Detailed description of the invention
Fig. 1 is the flow chart that indentation method calculates fracture toughness method；
Fig. 2 is that Berkovich pressure head is pressed into material schematic diagram；
Fig. 3 is pressure head radial displacement illustraton of model；
Fig. 4 is the micro-indentation test curve of Al6061 alloy；
Fig. 5 is the micro-indentation test curve of SS302 alloy.
Specific embodiment
The present invention is specifically described with reference to the accompanying drawing:
As shown in Figs. 1-2, a kind of indentation method calculates fracture toughness method, characterized by the following steps:
Step (1) is based on indentation test, under constant rate of speed, obtains and is no less than whole load-position under 6 unloading conditions
Move curve；
Indentation test continuously adds the method for unloading using constant Berkovich pressure head, and pressure head is with the load speed of 50mN/s
Rate carries out no less than 6 equal difference loads, and the unloading after having loaded each time, obtains whole load-displacement curves.
Step (2) carries out the fitting of first power function parameter to each unloading curve, obtains plasticity residual depth, contact
Depth state parameter calculates and unloads rigidity at every curve unloading, then carries out a straight line fitting again to each unloading curve,
The unloading rigidity of each curve is obtained, and obtains hpWith P parameters relationship；
Unloading curve 30%-70% partial fitting, power function parameter fitting formula are chosen in fit procedure are as follows:
P=B (h-hp)m (1)
Wherein, B, m are fitting parameter, hpFor afterflow depth after unloading；
Straight Line Fitting Parameters relationship are as follows:
P=a+S2*h (2)
Wherein, a is fitting parameter, S2For the unloading rigidity in Straight Line Fitting Parameters,
Rigidity S is unloaded in power function parameter1It is obtained by Oliver-Pharr method, is calculated and obtained by following formula,
S1=Bm (hmax-hp)m-1 (3)
Wherein, hmaxFor compression distance maximum in indentation test；The unloading rigidity cut-off line match value of first curve, the
Two unloading rigidity values for starting to calculate power function fitting are compared with the value of straight line fitting, if the two error judges in 10%
Power function fitting parameter is effective；
To effective data point P and hpIt is fitted using following equation:
Wherein, C1、C2、C3For fitting parameter and meet C2*C3< 0.
Step (3), using finite element to pressure head process of press in simulate, obtain radial displacement correction factor and
Berkovich pressure head non-axis symmetry modifying factor, to obtain decrement elasticity modulus；
Pressure head radial displacement model is as shown in Figure 3
Wherein, apart from pressure head center line distance at r* initial markers point A*, r is after being pressed into since initial markers point is by A*
It varies at A apart from pressure head center line distance.
Three-dimensional circular cone pressure head is utilized respectively for the solution of non-axis symmetry modifying factor and three-dimensional Berkovich pressure head is limited
Meta-model simulates nanometer process of press in of the different materials under identical load depth, and calculates the contact stiffness and bullet of unloading curve
Property modulus, wherein contact stiffness ratio obtained by contact stiffness obtained by three-dimensional Berkovich pressure head and three-dimensional circular cone pressure head is as repaired
Positive divisor β.
Reduce elasticity modulus, calculation formula are as follows:
Wherein, ErTo reduce elasticity modulus, β is Berkovich pressure head non-axis symmetry modifying factor, and γ repairs for radial displacement
Positive coefficient, S are that unloading rigidity (namely judge in effective power function parameter unloading rigidity S1), unloading rigidity S passes through Oliver-
Pharr method obtains.
Step (4) obtains the critical hole ratio of material using finite element to process simulation is uniaxially stretched；
It is tough to calculate fracture in conjunction with critical hole ratio by the indentation function and indentation energy to failure incidence formula proposed for step (5)
Property.
It is pressed into function and indentation energy to failure incidence formula is as follows:
Wherein GIEFTo be pressed into energy to failure, F (hp) it is hpDepth is pushed down into function, P (hp) it is hpLoad under depth, Ap(hp) be
hpImpression perspective plane area, calculating formula under depth are as follows:
Wherein, γ is radial displacement correction factor, hpAfterflow depth after unloading,For the change of critical residual plasticity
Shape depth.In conjunction with acquisition P (h in step (2)p) fitting formula, can must be pressed into energy to failure aboutFunction are as follows:
Wherein A, B, C are respectively
Critical residual is plastically deformed depthPass throughWith lnhpRelationship acquires, relationship are as follows:
WhereinFor effective modulus of elasticity, K, b are fitting parameter,
Effective modulus of elasticityCalculation formula are as follows:
Wherein, υ is measured material Poisson's ratio, υiFor pressure head material Poisson's ratio, EiFor pressure head elasticity modulus
InIn E when Critical fracture*Taking corresponding ordinate is critical residual plastic deformation depth
Damaging hole theory according to metal toughness has following formula:
Wherein, D is damage ratio,For effective modulus of elasticity, E is measured material elasticity modulus.
Wherein, f is the hole ratio of metal toughness damage,
Have in metal critical breaking state:
f*=fF (14)
Wherein, fFFor in step (4) by test and finite element optimization critical hole ratio
It is pressed into energy to failure and strain energy density is of equal value, equivalence formula are as follows:
Wherein ScrFor critical strain energy density, υ is material Poisson's ratio, and SED is strain energy density.
And have
Then fracture toughness finally solves formula are as follows:
Wherein KICFor fracture toughness, E is elasticity modulus of materials.
Calculate Al6061 alloy and SS302 alloy fracture toughness.Fig. 4 is the micro-indentation test curve of Al6061 alloy,
Fig. 5 is the micro-indentation test curve of SS302 alloy.The parameter in model mentioned in the present invention is obtained by test data fitting,
Each fitting parameter of Al6061, γ=1.1, β=1.049, f in fit procedure*=0.045, E*=58.3583GPa,GIEF=5.495mJ/m2, can be calculatedIt is obtained with routine experimentDeviation be 3% be less than current method 15%；Each fitting parameter of SS302 in fit procedure, γ=
1.02, β=1.034, f*=0.195, E*=109.195GPa,GIEF=5.750mJ/m2, can be calculatedIt is obtained with routine experimentDeviation be 3%, less than current method
15%, and can compared with conventional method more rapidly, lossless acquisition material fracture toughness data.
1 distinct methods of table, which calculate, obtains Al6061 alloy effective modulus of elasticity and elasticity modulus error analysis
2 distinct methods of table, which calculate, obtains SS302 alloy effective modulus of elasticity and elasticity modulus error analysis
During initial loading, material does not start to damage, and the effective modulus of elasticity after calculating should be with practical routine
Mechanical test acquired value is close, with experiment progress due to damage generation, effective modulus of elasticity should further decline with
Routine experiment acquired value, from table 1 in table 2 it can be seen that measure effective modulus of elasticity precision obviously high for original state in the present invention
In the method for Sina Amiri, the method for the present invention can predict elastic modulus change development trend very well, therefore proposed by the present invention
Method can rationally determine the Critical fracture state of material, obtain the not damaged elasticity modulus of material and Fracture Toughness.
3 distinct methods of table, which calculate, obtains fracture toughness error analysis
The result of table 3 reflects that fracture toughness computation model proposed by the invention can be reasonably under different materials
Acquisition Fracture Toughness, therefore, fracture toughness test method proposed by the present invention can accurately calculate the elasticity modulus of material with
Fracture Toughness.
Certainly, the above description is not a limitation of the present invention, and the present invention is also not limited to the example above, this technology neck
The variations, modifications, additions or substitutions that the technical staff in domain is made within the essential scope of the present invention also should belong to of the invention
Protection scope.
Claims (4)
1. a kind of method for calculating fracture toughness using indentation method, which comprises the steps of:
(1) it is based on indentation test, under constant rate of speed, obtains and is no less than whole load-displacement curves under 6 unloading conditions；
(2) fitting of first power function parameter, residual plastic after being unloaded are carried out to the part each unloading curve 30%-70%
Deforming depth hp, contact depth hcParameter calculates the unloading rigidity at every curve unloading；
It carries out a straight line fitting again to each unloading curve again, obtains the unloading rigidity of each curve；
The unloading rigidity cut-off line match value of first curve, Article 2 start by power function fitting calculate unloading rigidity value with
The value of straight line fitting compares, if the two error judges that power function fitting parameter is effective in 10%；
To effective data point P and hpIt is fitted using following equation:
Wherein, hpFor afterflow depth after unloading, P is loading of pressing in, C1、C2、C3For fitting parameter and meet C2*C3<
0, and then obtain hpWith the parameters relationship of P；
(3) pressure head process of press in is simulated using finite element, obtains radial displacement correction factor and the non-axis of Berkovich pressure head
The symmetry correction factor, to obtain decrement elasticity modulus；
(4) using finite element to process simulation is uniaxially stretched, the critical hole ratio of material is obtained；
(5) by the indentation function and indentation energy to failure incidence formula that propose, fracture toughness is calculated in conjunction with critical hole ratio；
The indentation function and indentation energy to failure incidence formula are as follows:
Wherein GIEFTo be pressed into energy to failure, F (hp) it is hpDepth is pushed down into function, P (hp) it is hpLoad under depth, Ap(hp) it is hpDepth
Lower impression perspective plane area, calculating formula are as follows:
Wherein, γ is radial displacement correction factor, hpFor unloading after afterflow depth,For critical residual plastic deformation
Depth；
In conjunction with the P and h obtained in step (2)pFitting formula, must be pressed into energy to failure aboutFunction are as follows:
Wherein A, B, C are respectively
Critical residual is plastically deformed depthPass throughWith ln hpRelationship acquires, relationship are as follows:
WhereinFor effective modulus of elasticity, K, b are fitting parameter；
Effective modulus of elasticityCalculation formula are as follows:
Wherein, υ is measured material Poisson's ratio, υiFor pressure head material Poisson's ratio, ErTo reduce elasticity modulus, EiFor pressure head springform
Amount；
InIn E when Critical fracture*Taking corresponding ordinate is critical residual plastic deformation depth
It is pressed into energy to failure and strain energy density is of equal value, equivalence formula are as follows:
Wherein ScrFor critical strain energy density, υ is measured material Poisson's ratio, and SED is strain energy density；
And haveThen fracture toughness finally solves formula are as follows:
Wherein KICFor fracture toughness, E is measured material elasticity modulus.
2. a kind of method for calculating fracture toughness using indentation method according to claim 1, which is characterized in that step (1)
Middle indentation test continuously adds the method for unloading using constant Berkovich pressure head, and pressure head is carried out with the loading speed of 50mN/s
No less than 6 equal difference loads, and the unloading after having loaded each time, obtain whole load-displacement curves.
3. a kind of method for calculating fracture toughness using indentation method according to claim 1, which is characterized in that step (2)
Middle power function parameter fitting formula are as follows:
P=B (h-hp)m
Wherein, B, m are fitting parameter, hpFor afterflow depth after unloading, h is pressure head compression distance；
Straight Line Fitting Parameters relationship are as follows:
P=a+S2*h
Wherein, a is fitting parameter, S2For the unloading rigidity in Straight Line Fitting Parameters；
Unloading rigidity S in power function parameter1It is obtained by Oliver-Pharr method, is calculated and obtained by following formula,
S1=Bm (hmax-hp)m-1
Wherein, hmaxFor compression distance maximum in indentation test.
4. a kind of method for calculating fracture toughness using indentation method according to claim 3, which is characterized in that step (3)
The calculation formula of middle decrement elasticity modulus are as follows:
Wherein, ErTo reduce elasticity modulus, β is Berkovich pressure head non-axis symmetry modifying factor, and γ is radial displacement amendment system
Number, AcTo contact depth area, S is unloading rigidity, and S takes S at first unloading curve2, in each unloading curve later
Using the unloading rigidity S in power function parameter1。
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| CN111351710A (en) * | 2020-03-24 | 2020-06-30 | 中国电子科技集团公司第三十八研究所 | Method for measuring Poisson's ratio of viscoelastic material |
| CN111964824B (en) * | 2020-08-19 | 2021-11-09 | 中国石油大学(华东) | Method for testing residual stress based on indentation energy difference |
| CN113466038B (en) * | 2021-06-21 | 2022-05-20 | 长江存储科技有限责任公司 | Detection sample for fracture toughness and detection method thereof |
| CN114935516A (en) * | 2022-04-28 | 2022-08-23 | 中国石油大学(华东) | Method for testing tensile property of metal material by adopting ball indentation method |
| CN115235888B (en) * | 2022-07-06 | 2023-06-13 | 中国人民解放军国防科技大学 | Material elastic property in-situ local touch pressure measurement method and measurement system |
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| US5602329A (en) * | 1995-08-09 | 1997-02-11 | Massachusetts Institute Of Technology | Method and apparatus for measuring fracture toughness of a material |
| KR100302400B1 (en) * | 1998-12-21 | 2001-11-02 | 이구택 | Method for evaluating weldability of welded thick plate with ease |
| CN100501368C (en) * | 2006-11-01 | 2009-06-17 | 北京科技大学 | Apparatus for testing transformation temperature between toughness and brittleness, rupture toughness at different temperature and rigidity |
| CN103091185B (en) * | 2011-10-31 | 2014-11-19 | 湘潭大学 | Process for characterizing elastoplasticity of metal material through indentation method |
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| WO2016045024A1 (en) * | 2014-09-25 | 2016-03-31 | 华东理工大学 | Method for measuring and determining fracture toughness of structural material in high-temperature environment |
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Effective date of registration: 20230420 Address after: Luo she Zhen Dou men Cun, Huishan District, Wuxi City, Jiangsu Province, 214000 Patentee after: Jiangsu Jiayian Technology Co.,Ltd. Address before: 266580 No. 66 Changjiang West Road, Huangdao economic and Technological Development Zone, Qingdao, Shandong Patentee before: CHINA University OF PETROLEUM (EAST CHINA) |
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