CN109030259A - A method of repeatedly plus unloading spherical indenter indentation obtains material simple stress-strain stress relation - Google Patents
A method of repeatedly plus unloading spherical indenter indentation obtains material simple stress-strain stress relation Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/40—Investigating hardness or rebound hardness
- G01N3/42—Investigating hardness or rebound hardness by performing impressions under a steady load by indentors, e.g. sphere, pyramid
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
- G01N2203/0005—Repeated or cyclic
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0014—Type of force applied
- G01N2203/0016—Tensile or compressive
- G01N2203/0019—Compressive
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0076—Hardness, compressibility or resistance to crushing
- G01N2203/0078—Hardness, compressibility or resistance to crushing using indentation
- G01N2203/008—Residual indentation measurement
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Abstract
The present invention relates to the testing fields of in-service structural timber simple stress-strain stress relation, especially a kind of that unloading spherical indenter indentation is added to obtain material simple stress-strain stress relation method repeatedly.Hard material spherical indenter is used first, is added unloading manner repeatedly so that n times are quasi-static, is pressed into measured material smooth surface, obtains continuous loading of pressing in P- compression distance h curve, the plastic zone radius r on remaining impression pit periphery is then measured after the completion of indentation testp, and the stress σ-strain stress scatter plot similar with uniaxial mechanical property test result is drawn out with the method for the present invention processing data.It is sex-limited dependent on the occasion of the office of tested material ranges caused by specific constitutive relation that the present invention overcomes existing spherical indenter indentation test technologies, and it needs to summarize the experience by a large amount of finite element modelling results or experimental result in existing spherical indenter indentation test technology, the deficiencies of time-consuming and laborious and fitting result unreliable, be conducive to the popularization and application of spherical indenter indentation test technology.
Description
One, technical field
The present invention relates to the testing fields of in-service structural timber simple stress-strain stress relation, especially one kind repeatedly
Unloading spherical indenter indentation is added to obtain material simple stress-strain stress relation method.
Two, background technique
Simple stress-strain stress relation is the basis of determining material yield strength, tensile strength and fracture toughness, for in-service
The structural intergrity assessment of zero component of engineering has vital effect.Tradition is uniaxially stretched or the uniaxial mechanics of uniaxial compression
Performance acquisition methods need to carry out destructive sampling according to standard size, thus can not be suitable for in-service engineering structure comprehensively.
In addition, requirement of the tradition single shaft mechanical property test for specimen size also limits them in such as weld metal zone and heat affected area
Etc. local materials mechanical property assessment on application.
Spherical indenter indentation test is used for the measurement of material Brinell hardness and B scale Rockwell hardness before this.1992,
G.Pharr et al. has delivered entitled " On the at periodical " Journal of materials research " on the 3rd phase
generality of the relationship among contact stiffness,contact area,and
The paper of elastic modulus during indentation " proposes pressure using spherical indenter indentation test in text
Enter the unloading gradient method that load p-compression distance h curve unloading slope obtains young modulus of material E.Since then, spherical indenter pressure
Enter the acquisition that test is gradually applied to bill of materials axis mechanical property.It is spherical although spherical indenter indentation test is easy to implement
Pressure head underlying materials are but in simple uniaxial stressed state, therefore spherical indenter pressure unlike in uniaxial mechanical property test
Enter test and bill of materials axis mechanical property is mainly obtained by empirical formula method, the numerical method based on finite element modelling and semi analytical method
Energy.
1997, T.Byun et al. was in periodical " International Journal of Pressure Vessels and
Piping " entitled " Measurement of through-the-thickness variations of has been delivered on the 3rd phase
mechanical properties in SA508Gr.3pressure vessel steels using ball
Indentation test technique's " obtains material simple stress-strain stress relation indentation test based on empirical equation
Method.This method is by the inclusion of the spherical indenter indentation test for adding unloading repeatedly, and using being based on, the materials such as annealed copper and carbon steel are total
Characterization strain-characterization of knot answers the bingham's plasticity strain stress of force evaluating formula calculating materialpTrus stress σtRelationship, such as formula (1) and formula
(2)；
In formula, D and dPThe respectively diameter projected of spherical indenter diameter and remaining impression pit, ψ is constraint factor, and can
To be calculated by formula (3)；
In formula,Develop parameter for plastic zone and is calculated by formula (4)；
In formula, EiFor the Young's modulus of spherical indenter.For adding unloading circulation to require each time in empirical formula method
Assuming that a ψ (generally taking 1.12), this ψ value is brought into and calculates σ in formula (2)t, and the σ that will be obtainedtValue brings formula (4) and formula (3) into
Whether middle calculating ψ meets hypothesis before this.If meet it is assumed that if ε at this timep-σtThe bingham's plasticity of the as circulation strain-is really answered
Power repeats above-mentioned calculating process after otherwise changing ψ value.Add the spherical indenter indentation test of unloading repeatedly comprising n times for one,
Empirical formula method can calculate N group εp-σtValue.However, in this method characterize strain-characterization stress estimation formula from
For the summary of experience of the power-law hardening materials such as carbon steel, annealed copper, other materials are applied to, when being especially non-power-law hardening material, are lacked
It weary theoretical foundation and is difficult to ensure precision of prediction.
2005, H.Lee et al. was in periodical " Journal of the Mechanics and Physics of
Solids " entitled " A numerical approach to spherical indentation has been delivered on the 9th phase
Techniques for material property evaluation " based on finite element modelling spherical indenter process of press in
With material simple stress-strain stress relation indentation test acquisition methods of numerical analysis.This method is based on a large amount of finite element modelling,
It proposes as shown in formula (5), formula (6) for power-law hardening material with loading of pressing in-compression distance curve computational representation strain-table
Levy the complicated numerical relation of stress；
In formula, ε0With proportional limit strain and the work hardening index that n is respectively in power hardening constitutive relation.Above-mentioned two formula
Middle factor betaijkAnd γijkDetermine and need a large amount of finite element modellings and numerical analysis.However, the impression obtained by multistage recurrence
Comprising numerous parameters for needing to demarcate by finite element result in governing equation, the presence of these parameters causes this to pass through numerical value
The impression governing equation that method obtains is often extremely unstable, and the requirement to spherical indenter indentation test result precision is very high, limitation
This method at the scene changes the application in test.In addition, the multistage regression equation obtained by finite element modelling and numerical analysis
Lack physical significance, analysis result is largely dependent upon the reliability of finite element modelling result, and test material is confined to
Power-law hardening material used in finite element modelling, for the Ovshinsky for being usually expressed as obvious linear strain-hardening widely applied in engineering
Body stainless steel material and material with yield point elongation, measuring accuracy are difficult to ensure.
It is ON105675420, name that China State Intellectual Property Office Patent Office, which disclosed publication No. on 06 15th, 2016,
The referred to as patent application of " spheroidal indentation prediction material simple stress-strain stress relation measuring method ", the patent such as are based at the efficiency
Amount is theoretical, proposes for power-law hardening material through loading of pressing in-compression distance curve associated material parameter method.In the party
In method, loading of pressing in-compression distance relationship can be fitted with formula (7)；
P=Chm (7)
In formula, P is loading of pressing in；C is load curvature；M loads index；Relationship between C and m and material parameter can use formula
(8) it indicates；
In formula, v* is characterized energy density, factor alpha1、α2、α3And α4It needs to be pressed by finite element modelling spherical indenter
Journey obtains.However, this method also needs the ginseng undetermined being pressed into calibration equation formula (8) by finite element modelling spherical indenter
Number, therefore estimation precision is largely dependent upon the reliability of finite element modelling result.And test material is confined to power hardening
Material is difficult to ensure for the measuring accuracy of non-power-law hardening material.
Three, summary of the invention
The purpose of the present invention is overcoming the shortcomings of the prior art only to be directed to certain a kind of material or a certain constitutive relation,
It provides one kind repeatedly plus unloading spherical indenter indentation obtains material simple stress-strain stress relation method.
The technical solution of the present invention is as follows: adding unloading manner, pressure repeatedly using hard material spherical indenter with n times are quasi-static
Enter measured material smooth surface, continuous loading of pressing in P- compression distance h curve is obtained, after the completion of spherical indenter indentation test
Measure the plastic zone radius r on remaining impression pit peripheryp, material simple stress-strain stress relation is then obtained using the following method；Its
Method and step is as follows:
1, the proportional limit σ of material is calculated0With proportional strain limit ε0, the proportional limit σ of material is calculated according to formula (9)0With
Proportional strain limit ε0；
In formula, E is the Young's modulus of tested material, can be obtained by the unloading Slope Method of Pharr-Oliver；Pmax
For the maximum loading of pressing in indentation test；rpFor the plastic zone radius on remaining impression pit periphery.
2, fitting unloading slope S(i)With remaining depth of cupIt is bent to loading of pressing in P- compression distance h according to formula (10)
The unloading curve section of line is fitted, and obtains the remaining depth of cup of i-th indentation circulationWith unloading slope S(i)；
3, the impression for calculating i-th indentation circulation springs back depthThe pressure of i-th indentation circulation is calculated according to formula (11)
Trace springs back depth
In formula,For the maximum depth of cup of i-th indentation circulation.
4, remaining pit radius of curvature is calculatedRemaining pit radius of curvature is calculated according to formula (12)
In formula, R is spherical indenter radius.
5, the elastic work that external force is done in i-th indentation circulation is calculatedAnd plastic work doneRespectively according to formula (13) and
Formula (14) calculates the elastic work that external force is done in i-th indentation circulationAnd plastic work done
In formula,WithRespectively represent loading of pressing in-indentation when i-th indentation CYCLIC LOADING and unloading
Depth curve.
6, the equivalent stress of i-th indentation circulation is calculatedAccording to formula (15) calculate i-th indentation circulation etc. effects
Power
In formula,For the maximum loading of pressing in of i-th indentation circulation；Remaining pit for i-th indentation circulation is bent
Rate radius；A is contact radius,EindAnd vindSpherical indenter young modulus of material and Poisson's ratio respectively.
7, the equivalent strain incresment of i-th indentation circulation is calculatedAccording to formula (16) calculate i-th indentation circulation etc.
Imitate strain increment
In formula,WithThe respectively plastic work done that external force is done in i-th and (i-1)-th indentation circulation；WithThe respectively maximum loading of pressing in of i-th and (i-1)-th indentation circulation；WithRespectively i-th and (i-1)-th time
It is pressed into the equivalent stress of circulation.
8, the equivalent strain of i-th indentation circulation is calculatedThe equivalent strain of i-th indentation circulation is calculated according to formula (17)
In formula,The equivalent strain of circulation is pressed into for (i-1)-th time,For i-th indentation circulation etc.
Imitate strain increment.
9, the proportional limit σ sought by step 10-ε0, the equivalent stress sought respectively by step 6 and step 8With it is equivalent
StrainStress σ-strain stress the scatter plot similar with uniaxial mechanical property test result can be drawn out.
Method of the invention overcomes existing spherical indenter indentation test technology dependent on caused by specific constitutive relation
The occasion of the office of tested material ranges is sex-limited, also overcomes and needs in existing spherical indenter indentation test technology by largely having
The deficiencies of time-consuming and laborious and fitting result unreliable caused by first analog result or experimental result summary of experience is limited, is conducive to
The universal and application of spherical indenter indentation test technology.This method is suitable for being difficult to according to conventional one-axis Mechanics Performance Testing requirement
The occasion being sampled, especially for bridge, naval vessel, boiler, pressure vessel, pressure pipeline etc. there are material property deterioration,
And as weld metal zone and heat affected area material one kind need to discuss local material single shaft mechanical property difference.
Four, Detailed description of the invention:
Fig. 1 is spherical indenter process of press in schematic diagram in the method for the present invention；
Fig. 2 is 15CrMoR steel curved beam surface topography photo before the method for the present invention indentation is tested；
Fig. 3 is the method for the present invention 15 times repeatedly plus 15CrMoR steel ball shape pressure head loading of pressing in-indentation of unloading indentation circulation
Depth curve figure；
Fig. 4 is 15CrMoR steel curved beam surface topography photo after indentation test；
Fig. 5 is reflection 15CrMoR steel impression plastic zone radius r after indentation testpDigital picture speckle pattern；
Fig. 6 is the external work schematic diagram in i-th spherical indenter indentation circulation；
Fig. 7 is the stress-strain result figure that 15CrMoR steel is obtained using method of the invention,
Fig. 8 is engineering stress-engineering strain result figure that 15CrMoR steel is obtained using method of the invention.
Appended drawing reference:
1, loading of pressing in 2, spherical indenter 3, sample 4, speckle 5, specimen surface 6, telltale mark point 7, residual pressure
Trace pit 8, plastic strain cloud atlas 9, elastic work 10, plastic work done 11, conventional one-axis stress strain curve 12, the technology of the present invention side
The data point 13 of case acquisition, yield strength Rp0.214, tensile strength Rm
Five, specific embodiment
The method of the present invention is described in further detail with reference to the accompanying drawing.
Embodiment: 15CrMoR steel simple stress-strain stress relation is obtained using the method for the present invention.
Preliminary preparation: as shown in Figure 1, the tungsten-carbide ball indenter 2 using radius 0.38mm is acted in loading of pressing in 1
Under to 40mm long × 10mm wide × 10mm thickness sample 3 carry out indentation test.
Firstly, then covering a slice width degree in specimen surface less than 0.32 μm to surface roughness with sand paper polishing sample 3
Surface for the pad pasting of 0.7-0.8mm, then after sample pad pasting is 10-20 μm with white dumb light paint even application a layer thickness
The carbon powder particle that diameter is about 2 μm is then uniformly sprayed on dumb light lacquer coat surface by coating, will be covered in after waiting 5-10 minutes
The pad pasting of specimen surface is thrown off, and sample metal surface is exposed.
Secondly, sample being placed under 50 times of amplification factor of stereomicroscope and being obtained after telltale mark is done in metal surface
As shown in Fig. 2, preceding 15CrMoR steel curved beam surface topography is tested in the indentation comprising speckle 4, specimen surface 5 and telltale mark point 6.
Again, 15 spherical indenter indentation tests for adding unloading repeatedly are unfolded in the specimen surface 5 for obtaining speckle distribution, the
The maximum compression distance of 15 circulations is the 24% of spherical indenter radius R, and circulation is all offloaded to the circulation maximum load every time
40%, continuous loading of pressing in P- compression distance h curve as shown in Figure 3 is obtained by load transducer and displacement sensor.
4th, the sample for completing indentation test is replaced under 50 times of amplification factor of stereomicroscope, obtains such as Fig. 4
It is shown, 15CrMoR steel curved beam after the indentation test comprising speckle 4, specimen surface 5, telltale mark point 6 and remaining impression pit 7
Surface topography.
5th, using commercialized digital speckle processing software handle indentation test before and after speckle distribution map, obtain as
Shown in Fig. 5, comprising speckle 4, specimen surface 5, telltale mark point 6, remaining impression pit 7 and plastic strain cloud atlas 8 residual pressure
Trace pit periphery plastic strain distribution map, and therefrom read the plastic zone radius r on remaining impression pit peripheryp。
Then, material simple stress-strain stress relation is obtained with method of the invention:
1. calculating the proportional limit σ of 15CrMoR steel0With proportional strain limit ε0, the ratio pole of material is calculated according to formula (9)
Limit σ0(MPa) and proportional strain limit ε0；
In formula, E is to obtain Young's modulus known to 15CrMoR steel or by the unloading Slope Method of Pharr-Oliver,
MPa；For the maximum loading of pressing in of the 15th load in indentation test, N；rpFor the plastic zone half on remaining impression pit periphery
Diameter, mm.
2. fitting unloading slope S(i)With remaining depth of cupThe remaining depth of cup that i-th adds unloading to recycleWith unloading slope S(i)(N/mm) according to formula (10) to the i-th of the compression distance h curve of loading of pressing in P- shown in Fig. 3
The unloading part in unloading circulation is added to be obtained with linear function fit；
In formula, P is loading of pressing in, N；H is compression distance, mm.
3. the impression for calculating i-th indentation circulation springs back depthAccording to formula (11), the pressure of i-th indentation circulation is calculated
Trace springs back depth
In formula,WithThe respectively remaining depth of cup of i-th indentation circulation and maximum depth of cup, mm.
4. calculating remaining pit radius of curvatureThe remaining pit curvature half of i-th indentation circulation is calculated according to formula (12)
Diameter
In formula,WithThe respectively remaining depth of cup of i-th indentation circulation and maximum depth of cup, mm；R is
The spherical indenter radius known, mm.
5, the elastic work that external force is done in i-th indentation circulation is calculatedAnd plastic work doneAccording to formula (13) and formula
(14), the elastic work that external force is done in i-th indentation circulation as shown in FIG. 6 is calculatedAnd plastic work done
In formula,WithLoading of pressing in-compression distance when respectively representing the CYCLIC LOADING and unloading is bent
Line；H is compression distance, mm；WithThe respectively remaining depth of cup of i-th indentation circulation and maximum depth of cup, mm.
6, the equivalent stress of i-th indentation circulation is calculatedAccording to formula (15), the equivalent stress of the i-th indentation circulation is calculated
In formula,The elastic work done by external force in i-th indentation circulation, Nmm；For i-th indentation circulation
Maximum loading of pressing in, N；WithRespectively the maximum depth of cup of i-th indentation circulation and impression spring back depth, mm；
For the remaining pit radius of curvature of i-th indentation circulation, mm；A is contact radius,H is indentation displacement, mm；
σ0For the proportional limit of 15CrMoR steel, MPa；E is the Young's modulus of 15CrMoR steel, MPa；EindFor tungsten-carbide ball indenter material
Expect Young's modulus, Eind=710GPa, MPa；vindFor tungsten-carbide ball indenter material Poisson's ratio, vind=0.23.
7, the equivalent strain incresment of i-th indentation circulation is calculatedAccording to formula (16), the equivalent of i-th circulation is calculated
Plastic strain increment
In formula,WithThe respectively plastic work done that external force is done in i-th and (i-1)-th indentation circulation, Nmm；WithThe respectively maximum loading of pressing in of i-th and (i-1)-th indentation circulation, N；WithRespectively i-th and
The equivalent stress of (i-1)-th indentation circulation, MPa；σ0For the proportional limit of 15CrMoR steel, MPa；E is the Young of 15CrMoR steel
Modulus, MPa.
8, the equivalent strain of i-th indentation circulation is calculatedAccording to formula (17), calculate i-th indentation circulation etc. effects
Become
In formula,For the equivalent strain of (i-1)-th indentation circulation；ε0For the material proportion limit；It is i-th
The equivalent strain incresment of secondary indentation circulation.
9, the proportional limit σ sought by step 10-ε0, the equivalent stress sought respectively by step 6 and step 8With etc.
Effect becomesEfficacy-equivalent strain the scatter plot similar with uniaxial mechanical property test result can be drawn out.Fig. 7 is
The 15CrMoR steel equivalent stress-equivalent strain data point obtained using technical solution of the present invention and uniaxial mechanical property test knot
Fruit comparison.
It can be equally used for after simple function is fitted using equivalent stress-equivalent strain data point that this method obtains
Determine the yield strength R of sample materialp0.2With tensile strength Rm.According to formula (18), it is fitted what technical solution of the present invention obtained
15CrMoR steel equivalent stress-equivalent strain data point.
In formula, E is the Young's modulus of 15CrMoR steel；σ0(MPa) and ε0The respectively material proportion pole of stress-strain expression
Limit；σeq(MPa) and εeqRespectively equivalent stress-equivalent strain；WithRespectively first spherical indenter pressure
Enter equivalent stress-equivalent strain data point of cycle calculations；EpFor strength factor, MPa；N is work hardening index.
According to formula (19) and formula (20), engineering strain ε is calculatedengWith engineering stress σeng(MPa)。
In formula, e is natural constant；σeq(MPa) and εeqRespectively equivalent stress-equivalent strain.
Fig. 8 is the 15CrMoR steel engineering stress-engineering strain curve obtained using technical solution of the present invention, wherein sample
Material yield strength Rp0.213 are defined as equivalent plastic strain εpEngineering stress value when=0.2%, MPa, sample material are anti-
Tensile strength Rm14 are defined as engineering stress σeng-εengMaximum engineering stress value on curve, MPa.Destructiveness is uniaxially stretched examination
Test the 15CrMoR steel yield strength R of acquisitionp0.213 and tensile strength Rm14 be respectively 434MPa and 541MPa, using the present invention
The 15CrMoR steel yield strength R that method obtainsp0.213 and tensile strength Rm14 be respectively 417MPa and 509MPa, with destructiveness
Uniaxial tensile test result is compared, the 15CrMoR steel yield strength R that the method for the present invention obtainsp0.213 and tensile strength Rm14 miss
Difference is respectively -3.92% and -5.91%, can satisfy engineer application requirement.
Claims (1)
1. a kind of add unloading spherical indenter indentation to obtain material simple stress-strain stress relation method repeatedly, using hard material
Spherical indenter adds unloading manner so that n times are quasi-static repeatedly, is pressed into measured material smooth surface, obtains continuous loading of pressing in P-
Compression distance h curve, which is characterized in that the plastic zone on remaining impression pit periphery is measured after the completion of spherical indenter indentation test
Radius rp, material simple stress-strain stress relation is then obtained using the following method, and method and step is as follows:
[1], the proportional limit σ of material is calculated0With proportional strain limit ε0, the proportional limit σ of material is calculated according to formula (9)0With than
Example strain limit ε0；
In formula, E is the Young's modulus of tested material, can be obtained by the unloading Slope Method of Pharr-Oliver；PmaxFor pressure
Enter the maximum loading of pressing in test；rpFor the plastic zone radius on remaining impression pit periphery；
[2], fitting unloading slope S(i)With remaining depth of cupAccording to formula (10), to loading of pressing in P- compression distance h curve
Unloading curve section be fitted, obtain i-th indentation circulation remaining depth of cupWith unloading slope S(i)；
[3], the impression for calculating i-th indentation circulation springs back depthIt is returned according to the impression that formula (11) calculate i-th indentation circulation
Play depth
In formula,For the maximum depth of cup of i-th indentation circulation；
[4], remaining pit radius of curvature is calculatedRemaining pit radius of curvature is calculated according to formula (12)
In formula, R is spherical indenter radius；
[5], the elastic work W that external force is done in i-th indentation circulation is calculatede (i)And plastic work doneRespectively according to formula (13) and formula
(14) the elastic work W that external force is done in i-th indentation circulation is calculatede (i)And plastic work done
In formula,WithRespectively represent loading of pressing in-compression distance when i-th indentation CYCLIC LOADING and unloading
Curve；
[6], the equivalent stress of i-th indentation circulation is calculatedThe equivalent stress of i-th indentation circulation is calculated according to formula (15)
In formula,For the maximum loading of pressing in of i-th indentation circulation；For the remaining pit curvature half of i-th indentation circulation
Diameter；A is contact radius,EindAnd vindSpherical indenter young modulus of material and Poisson's ratio respectively；
[7], the equivalent strain incresment of i-th indentation circulation is calculatedThe equivalent of i-th indentation circulation is calculated according to formula (16)
Strain increment
In formula,WithThe respectively plastic work done that external force is done in i-th and (i-1)-th indentation circulation；WithPoint
Not Wei i-th and (i-1)-th time indentation circulation maximum loading of pressing in；WithRespectively i-th and (i-1)-th indentation circulation
Equivalent stress；
[8], the equivalent strain of i-th indentation circulation is calculatedThe equivalent strain of i-th indentation circulation is calculated according to formula (17)
In formula,The equivalent strain of circulation is pressed into for (i-1)-th time, For the equivalent strain of i-th indentation circulation
Increment；
[9], the proportional limit σ sought by step 10-ε0, the equivalent stress sought respectively by step 6 and step 8With etc. effects
BecomeStress σ-strain stress the scatter plot similar with uniaxial mechanical property test result can be drawn out.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111458243A (en) * | 2020-03-26 | 2020-07-28 | 舟山市质量技术监督检测研究院 | Experimental method for measuring metal mechanical property by using indentation instrument |
| CN114295504A (en) * | 2021-11-30 | 2022-04-08 | 浙江省计量科学研究院 | Ball indentation hardness measurement method |
| CN114459931A (en) * | 2022-01-11 | 2022-05-10 | 东南大学 | Method for acquiring uniaxial stress-strain relation of material by cylindrical pressing |
| TWI767264B (en) * | 2020-06-24 | 2022-06-11 | 財團法人工業技術研究院 | Compression state measuring method and compression state measuring system |
| CN115235888A (en) * | 2022-07-06 | 2022-10-25 | 中国人民解放军国防科技大学 | In-situ local contact pressure measurement method and system for elastic property of material |
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| CN114459931A (en) * | 2022-01-11 | 2022-05-10 | 东南大学 | Method for acquiring uniaxial stress-strain relation of material by cylindrical pressing |
| CN114459931B (en) * | 2022-01-11 | 2023-09-29 | 东南大学 | Method for acquiring uniaxial stress-strain relation of material by cylindrical pressing |
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