CN110631906A - DIC technology-based material parameter acquisition method - Google Patents

DIC technology-based material parameter acquisition method Download PDF

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CN110631906A
CN110631906A CN201910868262.2A CN201910868262A CN110631906A CN 110631906 A CN110631906 A CN 110631906A CN 201910868262 A CN201910868262 A CN 201910868262A CN 110631906 A CN110631906 A CN 110631906A
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simplex
value
parameters
dic
load displacement
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许杨剑
单庆鹏
阮洪势
马天杰
徐学聪
朱佳文
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Zhejiang University of Technology ZJUT
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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
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    • G01N3/068—Special adaptations of indicating or recording means with optical indicating or recording means
    • 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
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • 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
    • G01N2203/0017—Tensile
    • 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
    • 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
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/0641—Indicating or recording means; Sensing means using optical, X-ray, ultraviolet, infrared or similar detectors
    • G01N2203/0647—Image analysis
    • 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
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/067—Parameter measured for estimating the property
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Abstract

Performing a unilateral notch tensile experiment based on a material parameter acquisition method of DIC technology, spraying speckles on the surface of a sample, performing data acquisition by adopting DIC digital image measuring equipment in the experimental process, obtaining a load displacement curve of the material from a testing machine, obtaining three-dimensional size information from the DIC and establishing a finite element model; correcting a load displacement curve and a target load displacement response curve of the experimental machine; and obtaining load displacement information and evaluating. The invention combines the digital image correlation method and the finite element method, and can reasonably and accurately acquire the material parameters of the sample. The invention has wide applicability and can be used for metal materials and most non-metal materials. The invention can greatly reduce the experiment times and shorten the time so as to reduce the material cost.

Description

DIC technology-based material parameter acquisition method
Technical Field
The invention relates to a metal material measuring method, in particular to a material parameter obtaining method based on DIC technology.
Background
The traditional metal material parameter measuring method is to obtain a load displacement curve in a gauge length section through a uniaxial tension experiment on a material sample, and then convert the curve into a material performance curve. The traditional method requires additional processing of a batch of standard tensile test samples when the fatigue test samples are manufactured, and the manufacturing and processing process requirements of the tensile test samples are high. Moreover, when the material parameters are calculated by the traditional method, the default sample deforms uniformly in the gauge length section in the stretching process, and in fact, no matter a rod-shaped tensile sample or a plate-shaped tensile sample, because the sample generates more or less fine defects in the processing process, or residual stress exists on the surface of the sample, the deformation of all parts in the gauge length section in the stretching process is not completely consistent. During the stretching process, the parts with microscopic fine defects are deformed more greatly, while the remaining parts without defects are deformed much less, in which case the calculated material parameters are not accurate enough.
Traditional tensile experiment is on the testing machine, because there are phenomenons such as crossbeam elastic deformation and clearance in the testing machine operation process, consequently will have some inevitable experimental error to produce certain influence to the experimental result, lead to this displacement measurement value to have great error.
Disclosure of Invention
In view of the above problems, a method for obtaining material parameters by DIC technology is provided, which can more reasonably obtain material parameters of metals.
The invention adopts the following technical scheme:
the method for acquiring the material parameters based on the DIC technology comprises the following steps:
the method comprises the following steps of firstly, carrying out a unilateral notch tensile experiment, spraying speckles on the surface of a sample, carrying out data acquisition on the experiment process by adopting DIC digital image measuring equipment, obtaining a load displacement curve of a material from a testing machine, and obtaining three-dimensional size information from DIC;
step two, establishing a finite element model according to the three-dimensional size information, selecting a region to divide a grid, and carrying out grid refinement at a stress strain concentration position;
extracting the relation between time and displacement at the node of the corresponding node from the DIC according to the position and the number of the grid nodes at the boundary of the finite element model; correcting a load displacement curve of the experiment machine according to the relation between the time and the displacement at the node to obtain a more accurate load displacement response curve, and interpolating to obtain a target load displacement response curve;
assigning the boundary condition to a finite element model, inputting initial material parameters, namely elastic modulus and yield strength stress value, calling finite element software to carry out operation, and extracting a simulation result after the operation is finished to finally obtain load displacement information;
step five, substituting the simulated load displacement information obtained in the step four and the target load displacement response curve obtained in the step three into an evaluation function:
Figure BDA0002201097560000021
p is an input quantity, i.e. an initial material parameter;
si (P) represents the simulated load value calculated to the step i under the P material parameter;
mi is the load of the target load displacement response curve in the step i;
n is the number of the middle points of the target load displacement response curve;
performing qualitative evaluation on the result, if the evaluation requirement is met, ending the inversion process, if the evaluation requirement is not met, updating the initial material value through an N-M algorithm, and returning to the fourth step;
recording n parameters to be inverted as x1,x2,…,x3. A point in the n-dimensional space is taken as a set of parameters and is marked as X0Then, a positive number delta (constructed polyhedron radius) and a unit vector e are selectediConstructing a simplex of n +1 vertices, i.e.
Figure BDA0002201097560000022
S0＝[λ0,λ1,…,λn]For simplex, S for each simplex0And establishing a simplex function phi as an objective function, and enabling the simplex function phi to correspond to each group of parameters.
N-M Algorithm optimization from initial simplex S0＝[λ0,λ1,…,λn]Initially, the simplex function is used to obtain the objective function value of each group of parameters and sort them to select the effect worst value phi (lambda)l)＝min0≤i≤n(φi) Calculating the mean value after removing the worst value
Figure BDA0002201097560000023
And then, obtaining a better value by operations of reflection, expansion, retraction, outward retraction and the like, replacing the just mentioned worst value, reconstructing the simplex, and continuously repeating the steps until the difference between each parameter in the simplex and the function value corresponding to each parameter reaches a set threshold value, thus obtaining a final optimal solution which is regarded as convergence. The specific optimizing process is as follows:
s1 reflection step: let the simplex obtained in the kth iteration be
Figure BDA0002201097560000031
Respectively calculating the objective functions corresponding to each group of parameters
Figure BDA0002201097560000032
i is 0,1, … n. Calculated according to the following empirical formula
Figure BDA0002201097560000033
Reflection point of
Figure BDA0002201097560000034
Where ρ is the reflection coefficient. If it is
Figure BDA0002201097560000035
By reflection, if phi (lambda) is obtainedr)<φ(λh) I.e. the ratio of
Figure BDA0002201097560000036
Better point
Figure BDA0002201097560000037
Convenient to use
Figure BDA0002201097560000038
Is replaced by
Figure BDA0002201097560000039
And the other groups of parameters are unchanged, a new simplex is formed and the step (5) is carried out;
s2 expanding step: by reflection, if
Figure BDA00022010975600000310
Then followsCan be still further. Thus calculating
Figure BDA00022010975600000312
Is called as
Figure BDA00022010975600000313
The expansion point of (1). If still have
Figure BDA00022010975600000314
Then it is proceeded withReplacement of
Figure BDA00022010975600000316
Otherwise, it is calculated by
Figure BDA00022010975600000317
Replacement of
Figure BDA00022010975600000318
Forming a new simplex and then turning to the step (5);
s3 shrinkage step: if it is
Figure BDA00022010975600000319
Then the reflection point is explained
Figure BDA00022010975600000320
Is not better than the original simplex, so the shrinkage can be handled in two categories: the first case, if
Figure BDA00022010975600000321
Then the reflection point is worse than all the points of the original simplex and is discarded
Figure BDA00022010975600000322
Shrinkage vector
Figure BDA00022010975600000323
The expression is as follows:
Figure BDA00022010975600000324
Figure BDA00022010975600000325
will be provided with
Figure BDA00022010975600000326
Replacement of
Figure BDA00022010975600000327
The shrinkage point of (c) is regarded as the neck-in, cc is the shrinkage factor. After shrinkage, judgment is made
Figure BDA00022010975600000328
Whether or not this is true. If yes, abandoning the contraction point, turning to the operation step (4), otherwise, turning to the step
Figure BDA00022010975600000329
By replacement withForming a new simplex and going to the judging step (5). In the second case, if
Figure BDA00022010975600000331
Figure BDA00022010975600000332
If not, the vector quantity
Figure BDA00022010975600000333
And performing contraction, namely outward contraction, wherein the calculation formula is as follows:
Figure BDA00022010975600000334
need to judge the shrinkage point after shrinkage
Figure BDA00022010975600000335
Whether to compare reflection pointsAlso poor, i.e. formula
Figure BDA00022010975600000337
Whether or not this is true. If yes, deleting the contraction point and turning to the step (4); if not, turning to the step (5);
s4 edge shrinking step: if the original simplex cannot be solved better in all the ways, the optimal value in the original simplex is obtainedThe difference between each set of parameters and the average value is reduced by half without change, and a new simplex is formed.
And S5, step judgment. Judgment of
Figure BDA00022010975600000339
And | λi-λj|<Whether zeta (i ≠ j) is satisfied, if yes, the algorithm is terminated, and the optimal result is lambda*(ii) a Otherwise, the next iteration is carried out again.
The DIC digital image measuring apparatus includes: hardware devices and software devices. The hardware device includes: a pair of lenses of Schneider Xenoplan1.4/23 in Germany and a pair of GRAS-20S4/MCCCD digital cameras of PointGrey in Canada, the camera parameters are as follows: resolution 1624 × 1224 pixels, 8bits grey, 30Hz transmission rate, camera stand, level, spotlight, calibration board, PC computer configured to: kurui i5-4570, memory 4GB, PCIE-FIW64 image acquisition card, camera PC transmission interface for IEEE-1394b interface. The software devices are Vic-3DSnap and Vic-3 DANalysis.
The tester is an Instron8872 type electrohydraulic servo tester. The testing machine is suitable for dynamic or static tests of various materials and components, and is used for carrying out tensile tests on a single-side notch copper sheet sample to obtain load displacement information of the tests.
When the finite element model is built by utilizing the three-dimensional size information, the finite element model can be built by combining the Saint-Vinan principle, wherein the Saint-Vinan principle is that if the surface force on a small part of the boundary of an object is converted into the surface force which is distributed differently but is static equivalent, the stress distribution at the near part is obviously changed, and the influence at the far part is negligible.
Wherein the N-M algorithm is a classical local optimization algorithm for processing the unconstrained optimization problem. Firstly, constructing a convex polyhedron with n +1 vertexes in an n-dimensional space, calculating function values of all the vertexes and sequencing; and then, through operations such as reflection, expansion, retraction, outward retraction and the like, new values are obtained again to replace the worst points and form a new polyhedron, so that a better local optimal solution can be obtained through a repeated iterative process.
The invention provides a material parameter identification method based on a Nelder-Mead algorithm by combining a digital image correlation method and a finite element method, and the material parameters of the sample can be more reasonably and accurately acquired. The invention has wide applicability and can be used for metal materials and most non-metal materials. The invention can greatly reduce the experiment times and shorten the time so as to reduce the material cost.
Drawings
FIG. 1 is a schematic flow chart of a material parameter obtaining method based on DIC technology according to the present invention.
FIG. 2 is a design drawing of a sample of example 1 of the present invention.
FIG. 3 is a DIC experiment of the present invention.
Fig. 4 is a schematic diagram of the speckle effect of the sample spray coating of the invention.
FIG. 5 is a schematic diagram of a finite element model of the present invention.
FIG. 6 is a schematic diagram of the present invention DIC and finite element matching.
FIG. 7 is a diagram of selected nodes of the DIC of the present invention.
FIG. 8 is a finite element boundary condition diagram of the present invention.
FIG. 9 is a graph of an interpolation target of the present invention.
Fig. 10 is a graph of the target of the present invention.
FIG. 11 is a schematic diagram of the inversion analysis process of the present invention.
FIG. 12 is a graph of the convergence trend of the inversion analysis of the present invention.
FIG. 13 is a fluctuation chart of the evaluation value of the present invention.
Labeled as: 2 experiment machine, 3 lighting lamp, 4 lens and camera, 5 DIC host computer, 6 tensile sample.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The material parameter acquisition method based on DIC technology comprises the following steps:
step one, carrying out a unilateral notch stretching experiment, wherein the material is red copper T2, the length of a gauge length is 20mm, the thickness is 5mm, the width is 16mm, and the radius of a notch is 3mm as seen in the enlarged view of the notch on the right side. Tensile experiments were performed on an Instron model 8872 electro-hydraulic servo tester. In the experimental process, a digital image correlation method is adopted to observe and measure the gap area, the English name of the digital image correlation method is DIC for short, and the DIC system comprises: hardware devices and software devices. The hardware device includes: a pair of lenses of Schneider Xenoplan1.4/23 in Germany, a pair of GRAS-20S4/MCCCD digital cameras of PointGrey in Canada, a camera frame, a level meter, a spotlight, a calibration board and a PC computer, wherein the camera parameters are as follows: 1624 × 1224 pixels in resolution, 8bits in gray, 30Hz transmission rate, computer configured: kurui i5-4570, memory 4GB, PCIE-FIW64 image acquisition card, camera PC transmission interface for IEEE-1394b interface. The software devices are Vic-3DSnap and Vic-3 DANalysis. DIC system is experimental measuring equipment, and non-contact full field strain optics measuring equipment can realize full field surface strain and measure, is applied to scientific research education field.
Speckle needs to be sprayed on the surface of the sample before the experiment, and the effect is shown in the figure. And clamping the speckle sample on a tensile testing machine, and calibrating the camera by using a calibration plate after the DIC system is arranged. At this time, the preparation work is completed, and the experimental machine and the DIC system are started at the same time.
And obtaining data output by the experimental machine and the three-dimensional size information of the initial sample in the DIC after the experiment is finished. Wherein the output data comprises: time, displacement, load information.
And step two, establishing a finite element model according to the three-dimensional information obtained in the step one and the Saint-Wein principle. Finite element models are built in ABAQUS, ABAQUS is a powerful engineering simulation set of finite element software that solves problems ranging from relatively simple linear analysis to many complex non-linear problems. In order to facilitate the operation and the application of boundary conditions, the middle area of the finite element model is intercepted by 60mm for analysis, in order to facilitate the efficient and accurate operation, the grid division at the stress concentration position is dense, and the grids of other areas are sparse. As shown in fig. 5, the left diagram is a finite element size diagram, in which the mesh encryption area is enlarged and the mesh shape is as shown in the right diagram.
And step three, matching the finite element model with the DIC calculation area, matching the characteristic points on the speckle sample with the characteristic nodes on the finite element model, finding the positions of 18 nodes at the upper and lower boundaries of the finite element model on the DIC calculation area, as shown in the leftmost diagram in FIG. 6, deriving a time displacement correlation curve of each node from the DIC, wherein due to limitation of a DIC system, information at the edges cannot be obtained, as shown in FIG. 7, and extrapolating the information of the nodes at the upper and lower boundaries by utilizing cubic Spline interpolation Spline in the MATLAB according to the information of other nodes. And (3) carrying out mean value processing on the time displacement relation curve at the node 9 of the upper boundary, and obtaining a time displacement relation curve of the lower boundary by adopting the same method for the lower boundary, wherein the time displacement relation curve is the position of each characteristic point of the upper boundary and the lower boundary at different moments. And (3) subtracting the time displacement relation curve of the upper boundary from the time displacement curve of the lower boundary to obtain a time displacement curve of the whole sample, wherein the difference means the motion state of the upper boundary relative to the lower boundary.
Because the phenomenon such as crossbeam elastic deformation and clearance exist among the testing machine operation process, consequently will have some inevitable experimental error to produce certain influence to the experimental result, lead to this displacement measurement value to have great error. To reduce the effect of error, many experiments have used strain control, in which extensometers are used. The extensometer is usually in a contact type, and often can not be fixed on a sample because of slipping, the sensor can be damaged by sample breakage, the measurement range is small, and the like, and the extensometer is rarely used in a tensile experiment. DIC is used as a virtual extensometer, and the virtual extensometer can dynamically measure strain, displacement and the like in real time to correct displacement values of experimental curves to obtain accurate load displacement curves. The specific correction process is as follows: the testing machine directly derives time, displacement and load data, and the number of the displacement columns is directly deleted due to the problem of the displacement in the testing machine. The time and the displacement on the testing machine correspond to each other, but the inaccurate displacement requires the accurate corresponding displacement, and the displacement is obtained from the DIC. And interpolating the whole sample time displacement curve extracted from the DIC to obtain the displacement of the testing machine in time, and covering the obtained displacement with the displacement of the original testing machine. Taking a load displacement curve with the corrected displacement within 0.9mm, dividing the curve into 200 equal parts, interpolating to obtain the load corresponding to the displacement of the 200 points, and taking the load displacement curve obtained by interpolation as a target value in the fourth step to obtain a target load displacement response curve
And step four, obtaining time displacement curves of nodes of the upper and lower boundaries through the step three, applying the curves to the nodes corresponding to the finite element model boundaries to serve as the time and displacement relation of the nodes, and generating the inp document. The time-displacement relationship, i.e. the boundary condition, is usually used to describe the stability of the boundary of the study object and is used as the initial condition solving force. The curve imposed on the boundary nodes is interpolated where the curve is divided into 200 equal parts with a total displacement of 0.9mm of stretch. The generated inp document is a file format that defines finite element model data and historical data, which can be used for ABAQUS calculations.
Inputting material parameters including elastic model E and stress value sigma in MATLAB (mathematical model laboratory) of MathWorks corporation0、σ1、σ2、σ3. The strain values corresponding to the stress values are written in inp, which are 0, 0.01, 0.02, 0.08, respectively. As shown in table one.
Watch 1
Figure BDA0002201097560000071
Step five: the MATLAB was used to input material parameters into the inp document and ABAQUS was called for the unbounded operation. As the script interface of the ABAQUS is a Python language basis, and Python can be automatically post-processed and accesses an output database, after the operation is finished, a load displacement curve on the boundary of the finite element model is extracted by using Python to obtain a simulation value. The analog value is compared with the target value, and the patent uses the comparison as an evaluation function to carry out the suitability evaluation. The evaluation function is:
Figure BDA0002201097560000072
wherein P is a set of material parameters: E. sigma0、σ1、σ2、σ3，SiAnd MiRespectively represent the simulation result and the experimental target value at i. Can be understood as SiAnd MiThe displacement is the load of simulation and experiment when i is the displacement, and the value number of i is 200. And when the evaluation value is smaller than a certain value or is not reduced any more, finishing the inversion. If not, substituting the initial simplicity into the N-M algorithm to carry out iterative calculation until the convergence criterion is met, terminating the inversion analysis, and finally setting the parameters as shown in the table 2. The inversion flow chart, the inversion analysis convergence trend chart and the evaluation value fluctuation chart are shown in the attached drawings.
TABLE 2
Figure BDA0002201097560000073
Figure BDA0002201097560000081
The N-M algorithm is a classical local optimization algorithm for processing an unconstrained optimization problem. Firstly, constructing a convex polyhedron with n +1 vertexes in an n-dimensional space, calculating function values of all the vertexes and sequencing; and then, through operations such as reflection, expansion, retraction, outward retraction and the like, new values are obtained again to replace the worst points and form a new polyhedron, so that a better local optimal solution can be obtained through a repeated iterative process. In this patent, 5 parameters to be inverted are recorded as x1、x2、x3、x4、x5. A point in the 5-dimensional space is taken as a set of parameters and is marked as X0Then selecting positive number delta and unit vector e for constructing radius of polyhedroniTo construct a simplex of 6 vertices thereof, i.e.
Figure BDA0002201097560000082
S0＝[λ0,λ1,λ2,λ3,λ4,λ5]For simplex, S for each simplex0And establishing a simplex function phi as an objective function, and enabling the simplex function phi to correspond to each group of parameters. N-M Algorithm optimization from initial simplex S0＝[λ0,λ1,λ2,λ3,λ4，λ5]Initially, the simplex function is used to obtain the objective function value of each group of parameters and sort them to select the effect worst value phi (lambda)l)＝min0≤i≤5(φi) Calculating the mean value after removing the worst value
Figure BDA0002201097560000083
Then using reflection, expansion, retraction and external retraction to obtain better value, replacing the just-mentioned worst value, reconstructing simplex and repeatingAnd in the steps, until the difference between each parameter in the simplex and the function value corresponding to each parameter reaches the set threshold value, the final optimal solution is obtained and is regarded as convergence. The specific optimizing process is as follows:
s1: and (5) a reflecting step. Let the simplex obtained in the kth iteration be S0＝[λ0,λ1,λ2,λ3,λ4,λ5]Respectively calculating the objective function corresponding to each group of parameters
Figure BDA0002201097560000084
i is 0,1,2,3,4, 5. Calculated according to the following empirical formula
Figure BDA0002201097560000085
Reflection point of
Figure BDA0002201097560000086
Where ρ is the reflection coefficient. If it is
Figure BDA0002201097560000087
By reflection, if phi (lambda) is obtainedr)<φ(λh) I.e. the ratio of
Figure BDA0002201097560000088
Better point
Figure BDA0002201097560000089
Convenient to use
Figure BDA00022010975600000810
Is replaced by
Figure BDA00022010975600000811
And the other groups of parameters are unchanged, a new simplex is formed and the step (5) is carried out.
S2: and (5) an expansion step. By reflection, if
Figure BDA00022010975600000812
Then follows
Figure BDA00022010975600000813
Can be still further. Thus calculating
Figure BDA00022010975600000814
Is called asThe expansion point of (1). If still have
Figure BDA0002201097560000091
Then it is proceeded with
Figure BDA0002201097560000092
Replacement of
Figure BDA0002201097560000093
Otherwise, it is calculated byReplacement of
Figure BDA0002201097560000095
A new simplex is constructed and then it goes to step (5).
S3: and (5) a contraction step. If it is
Figure BDA0002201097560000096
Then the reflection point is explained
Figure BDA0002201097560000097
Is not better than the original simplex, so the shrinkage can be handled in two categories: the first case, if
Figure BDA0002201097560000098
Then the reflection point is worse than all the points of the original simplex and is discarded
Figure BDA0002201097560000099
Shrinkage vector
Figure BDA00022010975600000910
The expression is as follows:
Figure BDA00022010975600000911
Figure BDA00022010975600000912
will be provided with
Figure BDA00022010975600000913
Replacement of
Figure BDA00022010975600000914
The shrinkage point of (c) is regarded as the neck-in, cc is the shrinkage factor. After shrinkage, judgment is made
Figure BDA00022010975600000915
Whether or not this is true. If yes, abandoning the contraction point, turning to the operation step (4), otherwise, turning to the stepBy replacement with
Figure BDA00022010975600000917
Forming a new simplex and going to the judging step (5). In the second case, if
Figure BDA00022010975600000918
If not, the vector quantityContracting is regarded as outward contraction, and the calculation formula is
Figure BDA00022010975600000920
Need to judge the shrinkage point after shrinkage
Figure BDA00022010975600000921
Whether to compare reflection points
Figure BDA00022010975600000922
Also poor, i.e. formula
Figure BDA00022010975600000923
Whether or not this is true. If yes, deleting the contraction point and turning to the step (4); if not, go to step (5).
S4: and (5) edge shrinking. If the original simplex cannot be solved better in all the ways, the optimal value in the original simplex is obtained
Figure BDA00022010975600000924
The difference between each set of parameters and the average value is reduced by half without change, and a new simplex is formed.
S5: and a step of judgment. Judgment ofAnd | λi-λj|<Whether zeta (i ≠ j) is satisfied, if yes, the algorithm is terminated, and the optimal result is lambda*(ii) a Otherwise, the next iteration is carried out again.
The whole inversion analysis process automatically operates and finally obtains an inversion analysis result, the operation is simple and convenient, and the inversion analysis result is reliable.

Claims (1)

1. The method for acquiring the material parameters based on the DIC technology is characterized by comprising the following steps of:
the method comprises the following steps of firstly, carrying out a unilateral notch tensile experiment, spraying speckles on the surface of a sample, carrying out data acquisition on the experiment process by adopting DIC digital image measuring equipment, obtaining a load displacement curve of a material from a testing machine, and obtaining three-dimensional size information from DIC;
step two, establishing a finite element model according to the three-dimensional size information, selecting a region to divide a grid, and carrying out grid refinement at a stress strain concentration position;
extracting the relation between time and displacement at the node of the corresponding node from the DIC according to the position and the number of the grid nodes at the boundary of the finite element model; correcting a load displacement curve of the experiment machine according to the relation between the time and the displacement at the node to obtain a more accurate load displacement response curve, and interpolating to obtain a target load displacement response curve;
assigning the boundary condition to a finite element model, inputting initial material parameters, namely elastic modulus and yield strength stress value, calling finite element software to carry out operation, and extracting a simulation result after the operation is finished to finally obtain load displacement information;
step five, substituting the simulated load displacement information obtained in the step four and the target load displacement response curve obtained in the step three into an evaluation function:
Figure FDA0002201097550000011
p is an input quantity, i.e. an initial material parameter;
si (P) represents the simulated load value calculated to the step i under the P material parameter;
mi is the load of the target load displacement response curve in the step i;
n is the number of the middle points of the target load displacement response curve;
performing qualitative evaluation on the result, if the evaluation requirement is met, ending the inversion process, if the evaluation requirement is not met, updating the initial material value through an N-M algorithm, and returning to the fourth step;
recording n parameters to be inverted as x1,x2,…,x3. A point in the n-dimensional space is taken as a set of parameters and is marked as X0Then, a positive number delta (constructed polyhedron radius) and a unit vector e are selectediConstructing a simplex of n +1 vertices, i.e.
S0＝[λ0,λ1,…,λn]For simplex, S for each simplex0And establishing a simplex function phi as an objective function, and enabling the simplex function phi to correspond to each group of parameters.
N-M Algorithm optimization from initial simplex S0＝[λ0,λ1,…,λn]Initially, the simplex function is used to obtain the objective function value of each group of parameters and sort them to select the effect worst value phi (lambda)l)＝min0≤i≤n(φi) Calculating after removing the worst valueMean value of
Figure FDA0002201097550000022
And then, obtaining a better value by operations of reflection, expansion, retraction, outward retraction and the like, replacing the just mentioned worst value, reconstructing the simplex, and continuously repeating the steps until the difference between each parameter in the simplex and the function value corresponding to each parameter reaches a set threshold value, thus obtaining a final optimal solution which is regarded as convergence. The specific optimizing process is as follows:
s1 reflection step: let the simplex obtained in the kth iteration beRespectively calculating the objective functions corresponding to each group of parameters
Figure FDA0002201097550000024
Calculated according to the following empirical formula
Figure FDA0002201097550000025
Reflection point of
Figure FDA0002201097550000026
Where ρ is the reflection coefficient. If it is
Figure FDA0002201097550000027
By reflection, if phi (lambda) is obtainedr)<φ(λh) I.e. the ratio of
Figure FDA0002201097550000028
Better point
Figure FDA0002201097550000029
Convenient to use
Figure FDA00022010975500000210
Is replaced by
Figure FDA00022010975500000211
And the other groups of parameters are unchanged, a new simplex is formed and the step (5) is carried out;
s2 expanding step: by reflection, ifThen follows
Figure FDA00022010975500000213
Can be still further. Thus calculating
Figure FDA00022010975500000214
Figure FDA00022010975500000215
Is called as
Figure FDA00022010975500000216
The expansion point of (1). If still have
Figure FDA00022010975500000217
Then it is proceeded withReplacement of
Figure FDA00022010975500000219
Otherwise, it is calculated by
Figure FDA00022010975500000220
Replacement of
Figure FDA00022010975500000221
Forming a new simplex and then turning to the step (5);
s3 shrinkage step: if it is
Figure FDA00022010975500000222
Then the reflection point is explained
Figure FDA00022010975500000223
Is not better than the original simplex, so the shrinkage can be handled in two categories: the first case, if
Figure FDA00022010975500000224
Then the reflection point is worse than all the points of the original simplex and is discarded
Figure FDA00022010975500000225
Shrinkage vector
Figure FDA00022010975500000226
The expression is as follows:
Figure FDA00022010975500000227
Figure FDA00022010975500000228
will be provided with
Figure FDA00022010975500000229
Replacement of
Figure FDA00022010975500000230
The shrinkage point of (c) is regarded as the neck-in, cc is the shrinkage factor. After shrinkage, judgment is made
Figure FDA00022010975500000231
Whether or not this is true. If yes, abandoning the contraction point, turning to the operation step (4), otherwise, turning to the stepBy replacement with
Figure FDA00022010975500000233
Forming a new simplex and going to the judging step (5). In the second case, if
Figure FDA00022010975500000234
Figure FDA0002201097550000031
If not, the vector quantity
Figure FDA0002201097550000032
And performing contraction, namely outward contraction, wherein the calculation formula is as follows:
Figure FDA0002201097550000033
need to judge the shrinkage point after shrinkage
Figure FDA0002201097550000034
Whether to compare reflection points
Figure FDA0002201097550000035
Also poor, i.e. formula
Figure FDA0002201097550000036
Whether or not this is true. If yes, deleting the contraction point and turning to the step (4); if not, turning to the step (5);
s4 edge shrinking step: if the original simplex cannot be solved better in all the ways, the optimal value in the original simplex is obtained
Figure FDA0002201097550000037
The difference between each set of parameters and the average value is reduced by half without change, and a new simplex is formed.
And S5, step judgment. Judgment ofAnd | λi-λj|<Whether zeta (i ≠ j) is satisfied, if yes, the algorithm is terminated, and the optimal result is lambda*(ii) a Otherwise, the next iteration is carried out again.
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