CN104077444B - Analysis method of indentation data - Google Patents
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- CN104077444B CN104077444B CN201410302066.6A CN201410302066A CN104077444B CN 104077444 B CN104077444 B CN 104077444B CN 201410302066 A CN201410302066 A CN 201410302066A CN 104077444 B CN104077444 B CN 104077444B
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- 238000007373 indentation Methods 0.000 title claims abstract description 51
- 238000004458 analytical method Methods 0.000 title abstract description 9
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- 239000000463 material Substances 0.000 claims abstract description 29
- 238000002474 experimental method Methods 0.000 claims abstract description 17
- 238000012897 Levenberg–Marquardt algorithm Methods 0.000 claims abstract description 9
- 238000012360 testing method Methods 0.000 claims description 38
- 238000007405 data analysis Methods 0.000 claims description 12
- 238000004088 simulation Methods 0.000 claims description 10
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Abstract
The invention relates to an analysis method of indentation data. The core of the method is based on the numerical optimation of a Levenberg-Marquardt algorithm, an optimized target function is a difference between the indentation data obtained by finite element modelling and experiment indentation data, and an optimized parameter is a mechanical parameter of a tested material to be obtained. A plurality of loading and unloading schemes and constitutive models of materials can be defined in the finite element model, therefore, the analysis method of the data is very strong in universality.
Description
Technical field
The present invention relates to indentation data analysis method.
Background technology
Used as a kind of most simple method, creasing method is probably the Mechanics Performance Testing side of mankind's application earliest
Method.According to the size of the difficulty or ease or the residual area of indentation for producing impression, people are defined various hardness numbers and are supported with assessment material
The ability of anti-permanent deformation, most common of which is penetration hardness, i.e., the pressure head for being determined shape with certain load is pressed into quilt
Measure and monitor the growth of standing timber material, the soft or hard degree of the material is assessed according to the size of embedding area residual deformation.Protected according to pressure head, load and load
The difference of time is held, penetration hardness there are the polytypes such as Brinell hardness, Rockwell hardness, Vickers hardness and microhardness.
Hardness test is simple, data favorable repeatability.However, hardness simply weighs material opposing plastic deformation ability
A kind of overall target, lack clear and definite conversion relation between the constitutive parameter such as elastic modelling quantity, the yield strength of it and material, this
Result in hardness test to be difficult to obtain directly application in the sign of material constitutive relation.With accurate measurement and control technology
Development, the one kind that has been born the seventies and eighties in last century is derived from micro-hardness testing but precision is higher and can continuously record pressure
Enter the method for testing of power and compression distance, i.e. instrumentation press-in (instrumented indentation) method or depth sensitive
Impression (depth-sensing indentation) method.Because spatial resolution is high, (indenter size can be as small as micro-/ nano
Level), instrumentation method of press-fitting kind is particularly suitable for the Mechanics Performance Testing of small dimensional material, film and coating material system.Jing
Cross the fast development of nearly two, 30 years, the method is widely used to each of mechanical measurement and material deformation mechanism research
Aspect, has expanded the range of application of creasing method significantly.
Because process of press in is related to the 3 D deformation of complexity, impression test is such without image of Buddha uniaxial tension or uniaxial compression,
The constitutive parameters such as elastic modelling quantity, yield strength can be directly obtained from empirical curve.To impression test, due to constitutive parameter and survey
Lack simple corresponding relation between examination data, it usually needs experimental data is analyzed using suitable model and method,
Required constitutive parameter could be obtained from test data, this process is referred to as the back analysis (reverse of indentation data
analysis)。
At present business-like instrumentation press-fit equipment is generally using the work of expensive capacitance distance measuring sensor and electromagnetic type
Dynamic device.To realize the loading of high frequency, generally also using complicated measurement and control technology.This causes instrumentation press-fit equipment
Cost remains high, and seriously constrains this simple structure, purposes are various, spatial resolution is high equipment in industrial detection
Using.The still main application experiment room research of current press-fit equipment.In addition, constitutive parameter to be measured is different, the pressure of employing
Trace testing scheme and indentation data inverse analysis method also tend to difference.Due to impression the complex nature of the problem, one kind is there is presently no
More general indentation data inverse analysis method, people generally require that suitable data are selected or developed according to the characteristics of detected materials
Analysis method, this undoubtedly also limit application of the instrumentation method of press-fitting in commercial measurement.
The content of the invention
It is an object of the invention to propose a kind of indentation data analysis method, it is not general that it can solve traditional analysis method
Problem.
In order to achieve the above object, the technical solution adopted in the present invention is as follows：
A kind of indentation data analysis method, it is comprised the following steps：
Step 1, the FEM model for setting up impression test process, wherein, the mechanics parameter of measured material is defined as variable；
Step 2, given initial mechanics parameter is input into the FEM model, and the FEM model is entered
Row is calculated, and obtains simulating indentation data；
Step 3, call it is described simulation indentation data and read experiment indentation data, using the calculating simulation impression of formula one
Difference between data and experiment indentation data；
(formula one)
Wherein, F (Pk) for object function return value；P0For the initial value of mechanics parameter, PkTo correct the mechanics after k time
Parameter；N is to test the data amount check that indentation data is included；fexp(ti) it is equal to t for the loading momentiWhen experiment impression test knot
Really；fcal(Pk,ti) it is equal to t for the loading momentiWhen simulation impression test result；
Step 4, object function is optimized using Levenberg-Marquardt algorithms, when determining F (Pk) be less than
During predetermined threshold value, P is exportedkAs final optimum results.
Preferably, the step 4 specifically includes following sub-step：
A () is by P0As the initial parameter of Levenberg-Marquardt algorithms；
B () calculates sensitivity matrix or Jacobian matrixes using finite difference method
(c) solving equation (ATA+λI)gk=-ATF(Pk), obtain correction gk, wherein I is unit matrix, and λ is non-negative
Scalar parameter；
D () calculates Pk+1=Pk+gk, and judge that object function, whether less than predetermined threshold value, if so, then exports PkAs final
Optimum results, if it is not, then repeat step a is to step d.
Preferably, the FEM model is axial symmetry FEM model.
The present invention has the advantages that：
Using the reverse analysis method of indentation data, it is adaptable to any loading scheme and material type, it is to avoid press-in test
Be not suitable for measuring the problem of material with complex.
Description of the drawings
Fig. 1 is the algorithm flow chart of the indentation data analysis method of present pre-ferred embodiments；
Fig. 2 is experiment indentation data curve；
Fig. 3 is the FEM model that the present invention sets up；
Fig. 4 is the load-deformation curve that the present invention is obtained.
Specific embodiment
Below, with reference to accompanying drawing and specific embodiment, the present invention is described further.
With reference to shown in Fig. 1, a kind of indentation data analysis method, it is comprised the following steps：
Step 1, the FEM model for setting up impression test process, wherein, the mechanics parameter of measured material is defined as variable.
The FEM model includes the material model selected according to the type of measured material.
In view of analyze pressing-in force-compression distance data when, the circular cone of the pyramid indenter available equivalents such as Berkovich
Shape pressure head replaces, therefore the present embodiment adopts axial symmetry FEM model.Spherical indenter is defined as rigid 1/4 circular arc, circular cone
Shape pressure head is defined as rigid straight line.To Berkovich pressure heads, the equivalent inclination angle of straight line is 65.03 °, to Vicker pressure heads, directly
The equivalent inclination angle of line is 70.32 °.Pressure head and a control point couple, and its motion is driven by the power or displacement being applied on the control point
It is dynamic.Sample identity is rectangular area, and its length and width size is all higher than 10 times of indenter size.Have in the region segmentation near pressure head
The first grid of limit, unit size is not more than the 1/20 of pressure head-sample contact radius in divided area.The upper surface of pressure head and sample it
Between definition contact.In the FEM model, mechanics parameter to be asked such as Young's modulus, yield strength, hardenability value, servo-actuated strong
Change parameter and wait the mechanics parameter definition asked for convenience of the parameter replaced.In addition, the boundary condition or load of the FEM model
It is equivalent with actual test loading procedure, if controlling compression distance with pressing-in force during test, defined in FEM model
The pressing-in force course of equivalent, if controlled as drive control amount using compression distance during test, defined in FEM model
The displacement boundary conditions of equivalent.Finally, the FEM model is saved as into a data text for being available for finite element solving device to call
Part.
Step 2, given initial mechanics parameter is input into the FEM model, and the FEM model is entered
Row is calculated, and obtains simulating indentation data.
When implementing, initial mechanics parameter is artificially given according to the type of measured material, initial mechanics parameter is
Number more than 0, it is also possible to estimated according to measured material, within the scope of the empirical value of the measured material, gives
Initial mechanics parameter have no effect on result of calculation, only can affect calculating speed.Given initial mechanics parameter is incoming
FEM model into step 1, replaces the variable in the FEM model and then is calculated, m- press-in when being output as
Force curve or compression distance-press-in force curve (simulating indentation data).The flow definition of this step is that impression test simulates letter
Number.
From the angle description that software is performed, process is then as follows：When impression test analog function is performed, search first with data
Rope and replacement function, are analyzed to the FEM model defined in step 1, using in incoming mechanics parameter replacement step 1
Corresponding mechanics parameter in FEM model, and the FEM model after replacement is saved as into new FEM model.Then root
According to the command format of finite element solving device, finite element solving device is called to solve newly-generated FEM model.Calculate
Cheng Hou, preserves in the form of a file result of calculation m- press-in force data or depth-press-in force data immediately.
Step 3, call it is described simulation indentation data and read experiment indentation data, the experiment indentation data is by impression
Test equipment is tested measured material and obtained, m- pressing-in force curve or compression distance-press-in force curve when can be,
Using the difference between the calculating simulation indentation data of formula one and experiment indentation data；
(formula one)
Wherein, F (Pk) for object function return value；P0For the initial value of mechanics parameter, (as artificial given is initial
Value), PkTo correct the mechanics parameter after k time；N is the data amount check included on the curve for test indentation data；fexp(ti) it is to add
The moment is carried equal to tiWhen experiment impression test result (testing indentation data)；fcal(Pk,ti) it is equal to t for the loading momentiWhen
Simulation impression test result (simulating indentation data).If tiIt is not equal to output in step 2 and sometime, then utilizes slotting
Value method obtains tiThe calculating impression test result at moment.
Step 4, object function is optimized using Levenberg-Marquardt algorithms, when determining F (Pk) be less than
Predetermined threshold value (such as 10-3) when, export PkAs final optimum results.
Preferably, the step 4 specifically includes following sub-step：
A () is by P0As the initial parameter of Levenberg-Marquardt algorithms；
B () calculates sensitivity matrix or Jacobian matrixes using finite difference methodWherein F
(Pk) for the object function defined in step 3；
(c) solving equation (ATA+λI)gk=-ATF(Pk), obtain correction gk, wherein I be unit matrix, T representing matrixs
Transposition, λ for non-negative scalar parameter, if the iterative step causes object function to reduce, increase should λ, otherwise reduce；
D () calculates Pk+1=Pk+gk, and judge that object function, whether less than predetermined threshold value, if so, then exports PkAs final
Optimum results, if it is not, then repeat step a is to step d.
In order to improve optimization precision, the given initial mechanical parameter that 3-5 groups are different can be selected, according to step 4, difference
The mechanics parameter of optimization is obtained, then the mechanics parameter of the multigroup optimization to obtaining is counted, each mechanics ginseng is tried to achieve respectively
Several mean value and standard deviation, if 10% (or the ratio of sets itself) of standard deviation more than mean value, then it is assumed that mechanics is joined
Number is not unique, needs to improve testing scheme and be estimated improved testing scheme repeat step 1-4.
For the ease of the understanding to the present embodiment, illustrate with reference to specific case.
Q350 steel is tested by impression test equipment, is obtained 3 groups of indentation curves for typically measuring and (is tested
Indentation data), as shown in Figure 2.
Using the indentation data analysis method of the present embodiment, the data shown in Fig. 2 are analyzed, calculate measured material
Young's modulus, yield strength and strain hardening exponent.
(1) FEM model of impression test process is set up.
A diameter of 1mm of pressure head, local cypher is carried out to pressure head-sample contacting area, and the size of minimum unit is
0.01mm.It is assumed that material follows Holloman models, i.e., its stress-strain relation is：
Wherein E be Young's modulus, σ0For yield strength, n is strain hardening exponent.In FEM model file, definition
These three mechanical quantities be interchangeable parameter, i.e., _ E, _ S0, _ n.Linear loading-unloading, load time 10s, discharge time 10s
With the time consistency adopted during test.Bit andits control is loaded, and exports pressing-in force-time result.
(2) define impression test analog function double*VirturalIndentation (double E, double S0,
Double n), wherein E, S0 and n are respectively Young's modulus, yield strength and strain hardening exponent.Using the search work(of character string
Can, obtain " _ E ", " _ S0 ", position of " _ n " three variable names in FEM model file, and using the replacement work(of character string
These three parameters can respectively be replaced with the initial value of E, S0 and n, the model file after replacement is saved as into new model text
Part, such as newIndent.comm.Calling system order system (" waster-m512newIndent.comm ") carries out finite element
Calculate, wherein waster is finite element solving device name, and it is 512M that-m512 specifies maximum memory.After the completion of calculating, from destination file
Middle reading pressing-in force-time data, is returned in the form of array.
(3) optimization object function double ObjectiveFun (double E, double S0, double n) are defined.
The optimization object function (flow process) first calls impression analog function VirturalIndentation, and (E, S0 n) obtain corresponding mould
Intend indentation data.Then experiment indentation data is read, according to the data point number that experiment indentation data is included, is counted using formula one
The difference between simulation indentation data and experiment indentation data is calculated, and is returned.
(4) object function ObjectiveFun is optimized using Levenberg-Marquardt algorithms, threshold value is
10-5。
According to the characteristic of Q345 steel, three groups of mechanics parameter valuations are have chosen as the initial value of optimization, be to confirm mechanics ginseng
Several uniqueness, there is larger deviation between initial value and representative value：
After optimization, the elastic-plastic mechanical parameter of acquisition is：
Can be determined that three mechanics parameters can be uniquely identified.
Corresponding load-deformation curve is as shown in Figure 4.
In general, the present embodiment is related to a kind of indentation data analysis method, and the core of the method is to be based on
The numerical optimization of Levenberg-Marquardt algorithms, the object function of optimization is the impression number obtained by finite element modelling
According to and difference between experiment indentation data, Optimal Parameters are measured material mechanics parameter to be asked.Due to can be in finite element
Various plus-unloading scheme and material constitutive model defined in model, therefore notebook data analysis method has very strong versatility.
Compared to the prior art, advantage of this embodiment is that：
(1) technology maturation, stability are high：Dynamometry, range finding and the control technology that the present embodiment is adopted is mature technology (i.e.
Traditional impression test equipment can be adopted), have the advantages that cost is controllable, good operating stability；
(2) applicable material type is wide：Suitable for the test of the various engineering material such as metal, plastics, ceramics；
(3) can determine whether the uniqueness of result.
For a person skilled in the art, technical scheme that can be as described above and design, make other each
Plant corresponding change and deform, and all these changes and deforms the protection model that should all belong to the claims in the present invention
Within enclosing.
Claims (2)
1. a kind of indentation data analysis method, it is characterised in that comprise the following steps：
Step 1, the FEM model for setting up impression test process, wherein, the mechanics parameter of measured material is defined as variable；
Step 2, given initial mechanics parameter is input into the FEM model, and the FEM model is counted
Calculate, obtain simulating indentation data；
Step 3, call it is described simulation indentation data and read experiment indentation data, using the calculating simulation indentation data of formula one
With the difference between experiment indentation data；
Wherein, F (Pk) for object function return value；P0For the initial value of mechanics parameter, PkTo correct the mechanics parameter after k time；
N is to test the data amount check that indentation data is included；fexp(ti) it is equal to t for the loading momentiWhen experiment impression test result；fcal
(Pk, ti) it is equal to t for the loading momentiWhen simulation impression test result；
Step 4, object function is optimized using Levenberg-Marquardt algorithms, when determining F (Pk) less than default
During threshold value, P is exportedkAs final optimum results；The step 4 specifically includes following sub-step：
A () is by P0As the initial parameter of Levenberg-Marquardt algorithms；
B () calculates sensitivity matrix or Jacobi an matrixes using finite difference method
(c) solving equation (ATA+λI)gk=-ATF(Pk), obtain correction gk, wherein I is unit matrix, and λ is the scalar of non-negative
Parameter；
D () calculates Pk+1=Pk+gk, and judge that object function, whether less than predetermined threshold value, if so, then exports PkAs final excellent
Change result, if it is not, then repeat step a is to step d.
2. indentation data analysis method as claimed in claim 1, it is characterised in that the FEM model is that axial symmetry is limited
Meta-model.
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| A general inverse analysis method for identifying multiple parameters from indentation measurements;zhang C 等;《中国力学大会》;20131231;第112页第1栏第3段 * |
| 纳米压痕过程的三维有限元数值试验研究;李敏 等;《力学学报》;20030531;第35卷(第3期);第257-264页 * |
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