CN110220781A - A kind of plate anisotropy constitutive parameter scaling method and system - Google Patents
A kind of plate anisotropy constitutive parameter scaling method and system Download PDFInfo
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Abstract
The present invention discloses a kind of plate anisotropy constitutive parameter scaling method and system, is related to materials processing technology field, mainly carries out the bulging along rolling direction and vertical rolling direction to plate including the use of capsule-type expanding die, obtains two groups of force-stroke experimental datas;Stretch section and plasticity section material parameter just are set, is substituted into capsule-type bulging prediction model, two groups of force-stroke analogue datas are obtained;Combined optimization is carried out by optimization aim of the least residual quadratic sum of force-stroke experimental data and force-stroke analogue data, obtains elasticity modulus optimal value, yield stress optimal value, anisotropic parameters optimal value.Method or system provided by the invention have the function of precisely to demarcate material parameter on line, and high-efficient, at low cost.
Description
Technical field
The present invention relates to materials processing technology fields, more particularly to a kind of plate anisotropy constitutive parameter scaling method
And system.
Background technique
Stamping plate is in apparent anisotropy after rolling, and demarcates material anisotropy parameter to adding
Work technique is most important.Generally before processing, can be to utilize one directional tensile test to demarcate material parameter under line, but needed before testing
Corresponding test specimen is made according to national standards, is not only wasted time, but also increases processing cost;Secondly, one directional tensile test is only
Uniform one section of the material parameter of changes in material can be measured, after constriction and constriction occur for material, experimental data just can not be accurate
Calibrating parameters.
Summary of the invention
The object of the present invention is to provide a kind of plate anisotropy constitutive parameter scaling method and system, have on line precisely
Material parameter function is demarcated, and high-efficient, at low cost.
To achieve the above object, the present invention provides following schemes:
A kind of plate anisotropy constitutive parameter scaling method, comprising:
Bulging experiment is carried out to plate using capsule-type expanding die, obtains two groups of experimental datas;Wherein, the capsule-type
Expanding die includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, and the capsule-type bulging punch-pin is two four/
The punch-pin that one sphere is formed by connecting by semicylinder, the blank holder is located at below the capsule-type bulging punch-pin, described
Bulging cavity plate is located at below the blank holder, and the head of the capsule-type bulging punch-pin is connect with pressure plare, the pressure plare
It is connect with press machine, the pressure coil is connect by four springs with the pressure plare, installation position on the lateral column of the press machine
The middle part of displacement sensor, the capsule-type bulging punch-pin is connect with pressure sensor;The experimental data includes along plate rolling
Direction force-stroke experimental data and vertical plate rolling direction force-stroke experimental data;
It determines plate initial parameter value, and the plate initial parameter value is input to established capsule-type bulging and is predicted
In model, two groups of analogue datas are obtained;Wherein, at the beginning of the plate initial parameter value includes elasticity modulus initial value, yield stress
Initial value, anisotropic parameters initial value;The capsule-type bulging prediction model is constructed according to the capsule-type expanding die;
The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data;
Using interpolation algorithm, on the basis of the analogue data, equally spaced interpolation is carried out to the experimental data, is obtained
Multi-group data set;The data acquisition system includes with the experiment new data under one stroke;The experiment new data includes along plate
Rolling direction tests power, vertical plate rolling direction tests power;
According to the experiment new data under the same one stroke in all data acquisition systems, elastic limit value is calculated;
According to the elastic limit value, all experiment new datas and all analogue datas are divided, are obtained
To the first data group and the second data group;First data group includes the analogue data and reality that force-stroke is less than elastic limit value
Test new data;Second data group includes the analogue data and experiment new data that force-stroke is greater than elastic limit value;
According to established first optimization object function and first data group, elasticity modulus optimal value is calculated;It is described
First optimization object function is under same one stroke, along plate rolling direction analog force and along plate rolling direction experiment power
0.5 times of least residual quadratic sum is the objective function that optimization aim is established, or under same one stroke, is rolled with vertical plate
0.5 times of mesh established for optimization aim of the least residual quadratic sum of direction analog force processed and vertical plate rolling direction experiment power
Scalar functions;
According to established second optimization object function and second data group, calculate yield stress optimal value, respectively to
Anisotropic parameter optimal value;Second optimization object function is under same one stroke, along plate rolling direction analog force and edge
0.5 times of the least residual quadratic sum of power is tested in plate rolling direction, with vertical plate rolling direction analog force and vertical plate
Rolling direction tests the objective function that 0.5 times of superposition value of the least residual quadratic sum of power is established for optimization aim.
Optionally, the determining plate initial parameter value, and the plate initial parameter value is input to established glue
In bellows bulging prediction models, two groups of analogue datas are obtained, are specifically included:
In finite element method (FEM) software, plate grid cell shape is set as hexahedron, and take advanced algorithm, by plate
It is to be completely fixed that periphery, which applies boundary condition, obtains the INP file of capsule-type bulging prediction model;
The plate initial parameter value is input in the capsule-type bulging prediction model, then according to the INP text
The simulation of the bulging of part and the capsule-type bulging prediction model, obtains two groups of analogue datas;The analogue data includes along plate
Material rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data.
Optionally, the experiment new data under the same one stroke according in all data acquisition systems calculates elastic pole
Limit value specifically includes:
Force-stroke is retrieved using window technique according to the experiment new data under the same one stroke in all data acquisition systems
Inflection point;The force-stroke inflection point is elastic limit value.
Optionally, described according to established first optimization object function and first data group, calculate elasticity modulus
Optimal value specifically includes:
The first second approximation objective function is converted by established first optimization object function;
According to first data group, using truncation conjugate gradient method, optimization calculates the first second approximation target letter
Several minimum values, and then obtain elasticity modulus optimal value.
Optionally, described according to established second optimization object function and second data group, calculate yield stress
Optimal value, anisotropic parameters optimal value, specifically include:
Second secondary approximate objective function is converted by established second optimization object function;
According to second data group, using truncation conjugate gradient method, optimization calculates the second secondary approximate target letter
Several minimum values, and then obtain yield stress optimal value, anisotropic parameters optimal value.
A kind of plate anisotropy constitutive parameter calibration system, comprising:
Experimental data obtains module, for carrying out bulging experiment to plate using capsule-type expanding die, obtains two groups of realities
Test data;Wherein, the capsule-type expanding die includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, the capsule
Formula bulging punch-pin is the punch-pin that two a quarter spheres are formed by connecting by semicylinder, and the blank holder is located at the capsule
Below formula bulging punch-pin, the bulging cavity plate is located at below the blank holder, the head of the capsule-type bulging punch-pin with
Pressure plare connection, the pressure plare are connect with press machine, and the pressure coil is connect by four springs with the pressure plare, described
Displacement sensor is installed, the middle part of the capsule-type bulging punch-pin is connect with pressure sensor on the lateral column of press machine;The reality
Testing data includes along plate rolling direction force-stroke experimental data and vertical plate rolling direction force-stroke experimental data;
Analogue data obtains module, is input to for determining plate initial parameter value, and by the plate initial parameter value
In established capsule-type bulging prediction model, two groups of analogue datas are obtained;Wherein, the plate initial parameter value includes elasticity
Modulus initial value, yield stress initial value, anisotropic parameters initial value;The capsule-type bulging prediction model is according to
The building of capsule-type expanding die;The analogue data includes rolling along plate rolling direction force-stroke analogue data and vertical plate
Force-stroke analogue data in direction processed;
Data acquisition system obtains module, for utilizing interpolation algorithm, on the basis of the analogue data, to the experimental data
Equally spaced interpolation is carried out, multi-group data set is obtained;The data acquisition system includes with the experiment new data under one stroke;It is described
Experiment new data includes along plate rolling direction experiment power, vertical plate rolling direction experiment power;
Elastic limit value computing module, for newly being counted according to the experiment under the same one stroke in all data acquisition systems
According to calculating elastic limit value;
Data division module is used for according to the elastic limit value, to all experiment new datas and all moulds
Quasi- data are divided, and the first data group and the second data group are obtained;First data group includes that force-stroke is less than elastic pole
The analogue data and experiment new data of limit value;Second data group include force-stroke be greater than elastic limit value analogue data and
Test new data;
Elasticity modulus optimization module, for according to established first optimization object function and first data group, meter
Calculate elasticity modulus optimal value;First optimization object function be under same one stroke, with along plate rolling direction analog force and
Along 0.5 times of objective function established for optimization aim of the least residual quadratic sum of plate rolling direction experiment power, or
With under one stroke, the least residual quadratic sum of power is tested with vertical plate rolling direction analog force and vertical plate rolling direction
0.5 times of objective function established for optimization aim;
Yield stress, anisotropic parameters optimization module, for according to established second optimization object function and described
Second data group calculates yield stress optimal value, anisotropic parameters optimal value;Second optimization object function is same
Under stroke, with 0.5 times of the least residual quadratic sum along plate rolling direction analog force and along plate rolling direction experiment power, with
0.5 times of superposition value of the least residual quadratic sum of vertical plate rolling direction analog force and vertical plate rolling direction experiment power
The objective function established for optimization aim.
Optionally, the analogue data obtains module, specifically includes:
INP file obtaining unit, in finite element method (FEM) software, plate grid cell shape to be set as hexahedron,
And advanced algorithm is taken, it is to be completely fixed that blank perimeter, which is applied boundary condition, obtains the INP text of capsule-type bulging prediction model
Part;
Analogue data acquiring unit, for the plate initial parameter value to be input to the capsule-type bulging prediction model
In, it is then simulated according to the bulging of the INP file and the capsule-type bulging prediction model, obtains two groups of analogue datas;
The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data.
Optionally, the elastic limit value computing module, specifically includes:
Elastic limit value computing unit, for newly being counted according to the experiment under the same one stroke in all data acquisition systems
According to, utilize window technique, retrieve force-stroke inflection point;The force-stroke inflection point is elastic limit value.
Optionally, the elasticity modulus optimization module, specifically includes:
First conversion unit, for converting the first second approximation target letter for established first optimization object function
Number;
Elasticity modulus optimizes unit, for according to first data group, using truncation conjugate gradient method, optimization to calculate institute
The minimum value of the first second approximation objective function is stated, and then obtains elasticity modulus optimal value.
Optionally, the yield stress, anisotropic parameters optimization module, specifically include:
Second conversion unit, for converting second secondary approximate target letter for established second optimization object function
Number;
Yield stress, anisotropic parameters optimize unit, are used for according to second data group, using truncation conjugate gradient
Method, optimization calculate the minimum value of the second secondary approximate objective function, and then obtain yield stress optimal value, anisotropy ginseng
Number optimal value.
The specific embodiment provided according to the present invention, the invention discloses following technical effects:
Capsule-type expanding die is embedded on the plate to be processed by the present invention, and on-line monitoring plate mechanical property may be implemented
It can fluctuation.When plate generating material performance change, the scaling method or calibration system provided through the invention obtains each
On-line machining control is realized in the mutation of anisotropy parameter.For obtaining sheet mechanical property parametric procedure online, the present invention is to test
On the basis of normal data, combined optimization goes out one group and includes the comprehensive performance material along plate rolling direction and vertical plate rolling direction
Expect parameter, improves the parameter scope of application and precision.
In addition, the present invention directly intercepts rectangular coupon from plate different direction, need to mark according to country before overcoming experiment
Standard makes corresponding test specimen bring, and time-consuming, problem at high cost.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the flow diagram of plate of embodiment of the present invention anisotropy constitutive parameter scaling method;
Fig. 2 is the structural schematic diagram of plate of embodiment of the present invention anisotropy constitutive parameter calibration system;
Fig. 3 is capsule-type of embodiment of the present invention expanding die schematic diagram.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Embodiment one
As shown in Figure 1, a kind of plate anisotropy constitutive parameter scaling method provided in this embodiment, including it is following
Step.
Step 101: bulging experiment being carried out to plate using capsule-type expanding die, obtains two groups of experimental datas;Wherein, institute
Stating capsule-type expanding die includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, and the capsule-type bulging punch-pin is two
The punch-pin that a a quarter sphere is formed by connecting by semicylinder, the blank holder are located under the capsule-type bulging punch-pin
Face, the bulging cavity plate are located at below the blank holder, and the head of the capsule-type bulging punch-pin is connect with pressure plare, described
Pressure plare is connect with press machine, and the pressure coil is connect by four springs with the pressure plare, on the lateral column of the press machine
Displacement sensor is installed, the middle part of the capsule-type bulging punch-pin is connect with pressure sensor;The experimental data includes along plate
Material rolling direction force-stroke experimental data and vertical plate rolling direction force-stroke experimental data.
Step 102: determining plate initial parameter value, and the plate initial parameter value is input to established capsule-type
In bulging prediction model, two groups of analogue datas are obtained;Wherein, the plate initial parameter value includes elasticity modulus initial value, bends
Take stress initial value, anisotropic parameters initial value;The capsule-type bulging prediction model is according to the capsule-type bulging die
Tool building;The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke
Analogue data.It specifically includes:
In finite element method (FEM) software, plate grid cell shape is set as hexahedron, and take advanced algorithm, by plate
It is to be completely fixed that periphery, which applies boundary condition, obtains the INP file of capsule-type bulging prediction model.
The plate initial parameter value is input in the capsule-type bulging prediction model, then according to the INP text
The simulation of the bulging of part and the capsule-type bulging prediction model, obtains two groups of analogue datas;The analogue data includes along plate
Material rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data.The analogue data includes same
Under stroke along plate rolling direction analog force and vertical plate rolling direction analog force.
Step 103: utilizing interpolation algorithm, on the basis of the analogue data, the experimental data is carried out equally spaced
Interpolation obtains multi-group data set;The data acquisition system includes with the experiment new data under one stroke;The experiment new data packets
It includes along plate rolling direction experiment power, vertical plate rolling direction experiment power.
Step 104: according to the experiment new data under the same one stroke in all data acquisition systems, calculating elastic limit
Value;It specifically includes:
Force-stroke is retrieved using window technique according to the experiment new data under the same one stroke in all data acquisition systems
Inflection point;The force-stroke inflection point is elastic limit value.
Step 105: according to the elastic limit value, all experiment new datas and all analogue datas being carried out
It divides, obtains the first data group and the second data group;First data group includes the simulation that force-stroke is less than elastic limit value
Data and experiment new data;Second data group includes the analogue data and the new number of experiment that force-stroke is greater than elastic limit value
According to.
Step 106: according to established first optimization object function and first data group, calculating elasticity modulus optimization
Value;First optimization object function is under same one stroke, along plate rolling direction analog force and along plate rolling direction
The objective function that 0.5 times of the least residual quadratic sum of power is established for optimization aim is tested, or under same one stroke, to hang down
0.5 times of the least residual quadratic sum of straight panel material rolling direction analog force and vertical plate rolling direction experiment power is optimization aim
The objective function of foundation;It specifically includes:
The first second approximation objective function is converted by established first optimization object function.
According to first data group, using truncation conjugate gradient method, optimization calculates the first second approximation target letter
Several minimum values, and then obtain elasticity modulus optimal value.
Step 107: according to established second optimization object function and second data group, calculating yield stress optimization
Value, anisotropic parameters optimal value;Second optimization object function is under same one stroke, to simulate along plate rolling direction
Power and along 0.5 times of least residual quadratic sum of plate rolling direction experiment power, with vertical plate rolling direction analog force and vertical
Straight panel material rolling direction tests the objective function that 0.5 times of superposition value of the least residual quadratic sum of power is established for optimization aim;
It specifically includes:
Second secondary approximate objective function is converted by established second optimization object function.
According to second data group, using truncation conjugate gradient method, optimization calculates the second secondary approximate target letter
Several minimum values, and then obtain yield stress optimal value, anisotropic parameters optimal value.
Embodiment two
As shown in Fig. 2, a kind of plate anisotropy constitutive parameter calibration system provided in this embodiment includes:
Experimental data obtains module 201, for carrying out bulging experiment to plate using capsule-type expanding die, obtains two groups
Experimental data;Wherein, the capsule-type expanding die includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, the glue
Bellows bulging punch-pin is the punch-pin that two a quarter spheres are formed by connecting by semicylinder, and the blank holder is located at the glue
Below bellows bulging punch-pin, the bulging cavity plate is located at below the blank holder, the head of the capsule-type bulging punch-pin
It is connect with pressure plare, the pressure plare is connect with press machine, and the pressure coil is connect by four springs with the pressure plare, institute
It states and displacement sensor is installed on the lateral column of press machine, the middle part of the capsule-type bulging punch-pin is connect with pressure sensor;It is described
Experimental data includes along plate rolling direction force-stroke experimental data and vertical plate rolling direction force-stroke experimental data.
Analogue data obtains module 202, inputs for determining plate initial parameter value, and by the plate initial parameter value
Into established capsule-type bulging prediction model, two groups of analogue datas are obtained;Wherein, the plate initial parameter value includes bullet
Property modulus initial value, yield stress initial value, anisotropic parameters initial value;The capsule-type bulging prediction model is according to institute
State the building of capsule-type expanding die;The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate
Rolling direction force-stroke analogue data.
Data acquisition system obtains module 203, for utilizing interpolation algorithm, on the basis of analogue data, to the experimental data
Equally spaced interpolation is carried out, multi-group data set is obtained;The data acquisition system includes with the experiment new data under one stroke;It is described
Experiment new data includes along plate rolling direction experiment power, vertical plate rolling direction experiment power.
Elastic limit value computing module 204, for new according to the experiment under the same one stroke in all data acquisition systems
Data calculate elastic limit value.
Data division module 205, for according to the elastic limit value, to all experiment new datas and all described
Analogue data is divided, and the first data group and the second data group are obtained;First data group includes that force-stroke is less than elasticity
The analogue data and experiment new data of limiting value;Second data group includes the analogue data that force-stroke is greater than elastic limit value
With experiment new data.
Elasticity modulus optimization module 206 is used for according to established first optimization object function and first data group,
Calculate elasticity modulus optimal value;First optimization object function is under same one stroke, along plate rolling direction analog force
With 0.5 times of the least residual quadratic sum objective function established for optimization aim along plate rolling direction experiment power, either
Under same one stroke, with the least residual quadratic sum of vertical plate rolling direction analog force and vertical plate rolling direction experiment power
0.5 times for optimization aim establish objective function.
Yield stress, anisotropic parameters optimization module 207, for according to established second optimization object function and institute
The second data group is stated, yield stress optimal value, anisotropic parameters optimal value are calculated;Second optimization object function is same
Under one stroke, with 0.5 times of the least residual quadratic sum along plate rolling direction analog force and along plate rolling direction experiment power,
Being superimposed for 0.5 times of the least residual quadratic sum of power is tested with vertical plate rolling direction analog force and vertical plate rolling direction
Value is the objective function that optimization aim is established.
The analogue data obtains module 202, specifically includes:
INP file obtaining unit, in finite element method (FEM) software, plate grid cell shape to be set as hexahedron,
And advanced algorithm is taken, it is to be completely fixed that blank perimeter, which is applied boundary condition, obtains the INP text of capsule-type bulging prediction model
Part.
Analogue data acquiring unit, for the plate initial parameter value to be input to the capsule-type bulging prediction model
In, it is then simulated according to the bulging of the INP file and the capsule-type bulging prediction model, obtains two groups of analogue datas;
The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data.
The elastic limit value computing module 204, specifically includes:
Elastic limit value computing unit, for newly being counted according to the experiment under the same one stroke in all data acquisition systems
According to, utilize window technique, retrieve force-stroke inflection point;The force-stroke inflection point is elastic limit value.
The elasticity modulus optimization module 206, specifically includes:
First conversion unit, for converting the first second approximation target letter for established first optimization object function
Number.
Elasticity modulus optimizes unit, for according to first data group, using truncation conjugate gradient method, optimization to calculate institute
The minimum value of the first second approximation objective function is stated, and then obtains elasticity modulus optimal value.
The yield stress, anisotropic parameters optimization module 207, specifically include:
Second conversion unit, for converting second secondary approximate target letter for established second optimization object function
Number.
Isotropism parameter and intra-face anisotropy parameter optimization unit outside yield stress, face, for according to described the
Two data groups, using truncation conjugate gradient method, optimization calculates the minimum value of the second secondary approximate objective function, and then obtains
Yield stress optimal value, anisotropic parameters optimal value.
Embodiment three
The scaling method for present embodiments providing a kind of plate anisotropy constitutive parameter, specifically includes following step
Suddenly.
Step 1: the use of capsule-type expanding die and experimental data obtain.
Traditional bulb bulging punch-pin, the anisotropy for plate along rolling direction different angle can not be distinguished clearly
It opens, so a kind of special expanding die is present embodiments provided, as shown in figure 3, plate different direction can be distinguished clearly
Material data.
Capsule-type expanding die consists of three parts, respectively capsule-type bulging punch-pin, blank holder and bulging cavity plate.Glue
Bellows bulging punch-pin is the punch-pin that two a quarter spheres are formed by connecting by semicylinder.Wherein, semicylinder section is straight
Diameter is equal to hemispherical diameter, at least more than 2 times hemispherical diameters of semicylinder cross-sectional length.The head of capsule-type bulging punch-pin is connected
Onto pressure plare, centre is connected with pressure sensor, and pressure plare is connected on press machine, when press machine work, pressure sensing
Device real-time detection capsule-type bulging punch-pin load data;Blank holder is the rectangular-shaped piece of thickness 10mm, and central hollow cross section is slightly larger than
Capsule-type bulging punch-pin cross section when capsule-type bulging punch-pin passes through, keeps the gap 1mm.Blank holder passes through four spring connections
Onto pressure plare, as capsule-type bulging punch-pin pushes, spring provides pressure-pad-force;Bulging cavity plate is the rectangular-shaped piece of high 15mm, in
Between hollow cross-section be equal to capsule-type bulging punch-pin cross section, radius of corner 2mm.
Displacement sensor is installed on the press machine lateral column of connection capsule-type bulging punch-pin, is applied when to capsule-type bulging punch-pin
When plus-pressure, displacement sensor pushes record run-length data, the load of combination pressure sensor record with capsule-type bulging punch-pin
Lotus data, to draw out bulging force-stroke experimental data.
By above-mentioned capsule-type expanding die, for two pieces of tests along plate rolling direction and vertical plate rolling direction
Material obtains two groups of experimental datas, draws Pi r0-hi r0And Pi r90-hi r90Empirical curve, wherein Pi r0-hi r0For along plate rolling side
To force-stroke experimental data, Pi r90-hi r90For vertical plate rolling direction force-stroke experimental data, i=1,2 ..., me, meFor
Maximum experiment run-length data index value.
Step 2: the foundation of capsule-type bulging prediction model.
Capsule-type bulging prediction model provided in this embodiment is identical with capsule-type expanding die, capsule-type bulging prediction
Model consists of three parts, respectively capsule-type bulging punch-pin, blank holder and bulging cavity plate.Capsule-type punch-pin is by two parts group
At it is D that both sides, which take same diameter,sHemisphere, centre be diameter Ds, length be greater than 2DsCylinder connection, shape be similar to capsule;
Blank holder cross section is passed through similar to runway, the enough capsule-type bulging punch-pin in intermediate region;Bulging cavity plate cross section is similar to flanging
Circle, the enough capsule-type bulging punch-pin indentations in intermediate region, the fillet of bulging cavity plate is Rc。
It is calculated since capsule-type bulging prediction model is axisymmetric, while to reduce ABAQUS (finite element method (FEM) software)
Amount takes a quarter of capsule-type bulging prediction model to carry out model analysis, in the upper table of a quarter capsule-type bulging punch-pin
Face makes reference a little.Plate grid cell shape is set as hexahedron in ABAQUS, takes advanced algorithm, and blank perimeter is applied side
Boundary's condition is to be completely fixed.After the completion of processing, the initial INP file of capsule-type bulging prediction model is obtained, then, carries out bulging
Simulation, exports the reaction force data of reference point, meanwhile, the time independent variable of output is multiplied into capsule-type bulging punch travel, when
Between variable be changed into stroke variable, obtain force-stroke analogue data.
Step 3: the calibration of elasticity modulus of materials E, main to be realized by following components:
(1) Hill48 yield criterion is proposed on the basis of Mises yield criterion, six anisotropy ginseng of addition
Number, equation are as follows:
Wherein, L0~N0It is constant coefficient Deng six values to generally acknowledge material anisotropy constant;At the beginning of material anisotropy parameter
Initial value is L0、M0、F0、G0、H0、N0, elasticity modulus initial value is E0, yield stress initial value is σs0, will be at the beginning of anisotropic parameters
Capsule-type bulging prediction model is written in initial value, and pre-treatment obtains the INP file of ABAQUS, by capsule-type bulging prediction model mould
It is quasi-, two groups of analogue datas, draw out when being set at the beginning of parameter along rolling direction force-strokeSimulation curve and hang down
Straight rolling direction force-strokeSimulation curve, wherein i=1,2 ..., mint, i is simulation run-length data index value,
mintFor maximum analog run-length data index value, k is Optimized Iterative number, wherein k=1,2 ....
(2) not corresponding in view of experimental data and analogue data can use interpolation algorithm and carry out to experimental data etc.
The interpolation at interval.With analog force run-length dataOn the basis of middle run-length data, wherein i=
1,2,...,mint, mintFor maximum analog run-length data index value,After the kth suboptimization iteration along plate rolling direction
I-th of simulation stroke value,The simulation force value of stroke is simulated for i-th after the kth suboptimization iteration along plate rolling direction,For i-th of simulation stroke value after kth suboptimization iteration in vertical plate rolling direction,For vertical plate rolling direction
The simulation force value of i-th of simulation stroke after upper kth suboptimization iteration, wherein k=1,2 ....To experiment run-length dataCarry out interpolation, wherein i=1,2 ..., me, meRun-length data index value is tested for maximum,
For i-th of experiment stroke value, P along plate rolling directioni r0For the experiment power of i-th of experiment stroke along plate rolling direction
Value,For i-th of experiment stroke value in vertical plate rolling direction,It goes for i-th of experiment in vertical plate rolling direction
The experiment force value of journey.And then to obtain interpolation experimental dataWherein, i=1,2 ..., mint,For i-th of experiment stroke interpolation, P along plate rolling directioni ir0For i-th of experiment interpolation row along plate rolling direction
The experiment power interpolation of journey,For i-th of experiment stroke interpolation, P in vertical plate rolling directioni ir90For vertical plate rolling side
The experiment power interpolation of upward i-th of experiment interpolation stroke.
(3) by the analysis to the new experimental data of interpolation, it is known that when force-stroke is less than elastic limitWhen, mechanical model
It is only related to elasticity modulus of materials E, therefore only optimize elasticity modulus numerical value, and testing two groups of analysis of experimental data of acquisition to bulging can
Know, plate elastic modulus E then can set elasticity modulus to along the first of rolling direction equal along rolling direction and vertical rolling direction
E0It optimizes.Specifically: force-stroke inflection point abscissa value is retrieved using window techniqueThat is elastic limitInflection pointIt
Preceding optimization elasticity modulus of materials E.
(4) with power Pi ir0With0.5 times of least residual quadratic sum be optimization aim, establish along plate rolling direction
Optimization object function Ge0(Xek)。
(5) to optimization object function Ge0(Xek) second approximation is carried out, by optimization object function Ge0(Xek) optimization problem turn
The minimum value for solving second approximation objective function is turned to, and then solves the elasticity modulus of materials E of optimization1。
Wherein, step (2) specifically includes: interpolation is carried out to the experiment force data for obtaining two groups, on the basis of analogue data,
Interpolation goes out the power P along plate rolling direction at equal intervalsi ir0, vertical plate rolling direction Pi ir90.Wherein, i=1,2 ...,
mint。
Wherein,For j-th of the experiment power after rolling direction interpolation, Pi r0For i-th of the experiment power along rolling direction,For i-th of experiment stroke along rolling direction,Stroke is simulated along rolling direction for i-th in kth time iteration optimization
Incremental value, the power after interpolationSimilar to formula (2).
Step (3) specifically includes: retrieving force-stroke inflection point by window techniqueInflection pointOnly optimize elasticity modulus before
E。
Wherein,For along the i-th slope of plate direction force run-length data, w is the width of window.
Step (4) specifically includes: in conjunction with optimization algorithm, withAnd Pi ir00.5 times of least residual quadratic sum be optimization
Target optimizes along rolling direction objective function Ge0(Xek), Xek=[E]T。
ae≤Xek≤be(7);
Wherein, the dimension of independent variable X is 1, Ge0(Xek) be Optimal Parameters elastic modulus E interpolation trip objective value, ae、be
To optimize elasticity modulus objective function independent variable range, mintRun-length data index value is tested for maximum,For along plate rolling
On direction after kth suboptimization iteration i-th simulation stroke simulation force value, Pi ir0For i-th of interpolation after rolling direction interpolation
The interpolation of stroke tests power.
Step (5) specifically includes: to optimization object function Ge0(Xek) second approximation is carried out, independent variable X quadratic interpolation is obtained
To new sampling point Yej, updated by data repeatedly, at the kth iteration, obtain approximate function Qe0(Yej):
Qe0(Yej)=Ge0(Yej), j=1,2 ..., m (8);
Wherein, l is Optimal Parameters number, is herein 1, YejNew sampling point after interpolation for Optimal Parameters elasticity modulus.
Therefore, by optimization object function Ge0(Xek) it is converted into the minimum value for solving second approximation objective function;It will be for
Optimization object function Ge0(Xek) optimization problem be converted into minimum approximate function:
Wherein, d is the vector step-length of each iteration, ΔkFor confidence region radius at the kth iteration.
The direction of search and step-length for calculating each iteration by truncation conjugate gradient method are until confidence region radius reaches minimum
Setting accuracy, optimization elasticity modulus of materials E1。
Step 4: yield stress and anisotropic parameters calibration, main to be realized by following components:
(1) elastic limit strokeData later advanced optimize other anisotropic parameters using Optimized model,
Change optimization object function, while considering plate along the anisotropy of rolling direction and vertical rolling direction, by both direction
Power residual sum of squares (RSS) is overlapped, and realizes combined optimization, obtains the optimization aim letter along rolling direction and vertical rolling direction
Number Gp0_90(Xpk), wherein Xpk=[σs,L,M,N,F,G,H]T。
(2) to optimization object function Gp0_90(Xpk) second approximation is carried out, second approximation target letter is converted by parameter optimization
Number minimum value solves.
In conjunction with optimization algorithm, with powerAnd Pi ir0Least residual quadratic sum 0.5 times and powerAnd Pi ir90Most
0.5 times of superposition value of small residual sum of squares (RSS) is optimization aim, establishes optimization object function Gp0_90(Xpk)。
ap≤Xpk≤bp(12);
Wherein, Gp0_90(Xpk) it is the interpolation trip objective value for optimizing other parameters, ap、bpFor the objective function of Optimal Parameters
Independent variable value range, the independent variable X of kth time iterationpk=[σs,L,M,N,F,G,H]T。
To optimization object function Gp0_90(Xpk) second approximation is carried out, new sampling point Y is obtained to independent variable X quadratic interpolationpj,
It is updated by data repeatedly, at the kth iteration, there is approximate function:
Qp0_90(Ypj)=Gp0_90(Ypj), j=1,2 ..., m (13);
Wherein, l is Optimal Parameters number, is herein 7, therefore, by optimization object function Gp0_90(Xpk) it is converted into solution two
The minimum value of secondary approximate objective function.
The direction of search and step-length for calculating each iteration using truncation conjugate gradient method are until confidence region radius reaches minimum
Setting accuracy, and then yield value of stress σ is set to firsts0, anisotropic parameters L0、M0、F0、G0、H0、N0Combined optimization is carried out, it can be with
Obtain yield stress optimal value σs1, anisotropic parameters optimal value L1、M1、F1、G1、H1、N1。
Example IV
Plate anisotropy constitutive parameter scaling method provided in this embodiment includes following steps.
Step S1: carrying out bulging experiment, obtains optimization aim force stroke curve.
Step S2: just setting optimization material parameter, obtains force-stroke analogue data.Take anisotropic parameters L0=1.5, M0=
1.5、F0=1.0, G0=1.0, H0=1.0, N0=1.5, E0=200000MPa, yield stress σs0=250MPa.Pass through utilization
Bulging this structure INP file of above-mentioned initial value write-in ABAQUS bulging simulation is submitted task by the subprogram that FORTRAN writes,
Analogue data is obtained, draws out two groups in these first setting parameters along rolling direction and vertical rolling direction Analog force run-length data.
Step S3: an interpolation is carried out to the curve data that step S1, S2 is found out, on the basis of simulating stroke at equal intervalsInterpolation goes out a common run-length dataSince analogue data stroke incremental step is consistent, institute
With consistent with vertical rolling direction simulation run-length data along rolling direction, and then Slope Method is utilized, interpolation is solved in strokeUnder the power P along rolling direction and vertical rolling directioni ir0WithThe experiment force-stroke data for arranging newly
Wherein,For j-th of the experiment power after rolling direction interpolation, Pi r0For i-th of experiment along rolling direction
Power,For i-th of experiment stroke along rolling direction,It simulates and goes along rolling direction for i-th in kth time iteration optimization
Journey incremental value, the power after interpolationSimilar to formula (15).
Step S4: by the analysis to experimental data, it is known that work as strokeLess than inflection pointWhen, bulging is processed on edge
Plate rolling direction and vertical plate rolling direction have common elasticity modulus of materials E, and elasticity modulus of materials E, utilize window
Method retrieves inflection point
Wherein,For along the i-th slope of plate direction force run-length data, w is the width of window.
In conjunction with optimization algorithm, with powerAnd Pi ir00.5 times of least residual quadratic sum be optimization aim, optimization is along rolling
Objective function G in direction processede0(Xek)。
ae≤Xek≤be(20);
Wherein, Ge0(Xek) be Optimal Parameters elastic modulus E interpolation trip objective value, ae、beTo optimize elasticity modulus mesh
Scalar functions independent variable range, mintRun-length data index value is tested for maximum,For the kth suboptimization along plate rolling direction
The simulation force value of i-th of simulation stroke, P after iterationi ir0It is tested for i-th of interpolation along rolling direction interpolation interpolation stroke
Power.
To optimization object function Ge0(Xek) second approximation is carried out, new sampling point Y is obtained to independent variable X quadratic interpolationej, lead to
Data update is crossed repeatedly, at the kth iteration, obtains approximate function Qe0(Yej):
Qe0(Yej)=Ge0(Yej), j=1,2 ..., m (21);
Wherein, l is Optimal Parameters number, is herein 1, YejNew sampling point after interpolation for Optimal Parameters elasticity modulus.
Therefore, by optimization object function Ge0(Xek) it is converted into the minimum value for solving second approximation objective function;It will be for
Optimization object function Ge0(Xek) optimization problem be converted into minimum approximate function:
Wherein, d is the vector step-length of each iteration, ΔkFor confidence region radius at the kth iteration.
The direction of search and step-length for calculating each iteration by truncation conjugate gradient method are until confidence region radius reaches minimum
Setting accuracy, optimization elasticity modulus of materials E1。
Step S5: work as strokeGreater than inflection pointWhen, by 0.5 timesAnd Pi ir0Residual sum of squares (RSS) with 0.5 times
'sAnd Pi ir90Residual sum superposition, using superposition value as optimization aim, combined optimization other materials parameter, with Optimization Solution
Elastic modulus E1Step is similar, and it is jointly right along rolling direction and vertical rolling direction that difference is to consider when solving other parameters
The influence of parameter realizes combined optimization anisotropic parameters, by the elastic modulus E of optimization1, initial value anisotropic parameters
L0=1.5, M0=1.5, F0=1.0, G0=1.0, H0=1.0, N0=1.5, yield stress σs0=250MPa write-in utilizes
ABAQUS this structure INP file that FORTRAN subprogram is write, by submitting operation to obtain new force-stroke data, in conjunction with optimization
Algorithm establishes optimization object function Gp0_90(Xpk)。
ap≤Xpk≤bp(25);
Wherein, Gp0_90(Xpk) it is the interpolation trip objective value for optimizing other parameters, ap, bpFor the objective function of Optimal Parameters
Independent variable value range, the independent variable X of kth time iterationpk=[σ, L, M, N, F, G, H]T。
To optimization object function Gp0_90(Xpk) second approximation is carried out, new sampling point Y is obtained to independent variable X quadratic interpolationpj,
It is updated by data repeatedly, at the kth iteration, there is approximate function:
Qp0_90(Ypj)=Gp0_90(Ypj), i=1,2 ..., m (26);
Wherein, l is Optimal Parameters number, is herein 7, therefore, by optimization object function Gp0_90(Xpk) it is converted into solution two
The minimum value of secondary approximate objective function.
The direction of search and step-length for calculating each iteration by truncation conjugate gradient method are until confidence region radius reaches minimum
Setting accuracy, thus optimization yield stress σs1, anisotropic parameters L1、M1、F1、G1、H1、N1。
Embodiment five
It takes long 50mm, wide 30mm to machine with a thickness of the aluminum alloy plate materials of 1mm through bulging test, obtains experiment force-stroke
Curve, by empirical value elastic modulus E0=200000MPa, yield stress σs0=250MPa, anisotropic parameters L0=1.5, M0=
1.5、F0=1.0, G0=1.0, H0=1.0, N0=1.5, it substitutes into calibration algorithm provided by the above embodiment, to test Lixing
Journey curve is target, optimizes material parameter, the elastic modulus E after can must optimizing1=200000MPa, yield stress σs1=
265MPa, anisotropic parameters L1=1.0, M1=1.0, F1=1.000, G1=1.040, H1=1.248, N1=1.078.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other
The difference of embodiment, the same or similar parts in each embodiment may refer to each other.For system disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is said referring to method part
It is bright.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention;At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not
It is interpreted as limitation of the present invention.
Claims (10)
1. a kind of plate anisotropy constitutive parameter scaling method, which is characterized in that the plate anisotropy constitutive parameter mark
The method of determining includes:
Bulging experiment is carried out to plate using capsule-type expanding die, obtains two groups of experimental datas;Wherein, the capsule-type bulging
Mold includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, and the capsule-type bulging punch-pin is two a quarter balls
The punch-pin that body is formed by connecting by semicylinder, the blank holder are located at below the capsule-type bulging punch-pin, the bulging
Cavity plate is located at below the blank holder, and the head of the capsule-type bulging punch-pin is connect with pressure plare, the pressure plare and pressure
The connection of power machine, the pressure coil are connect by four springs with the pressure plare, and installation displacement passes on the lateral column of the press machine
The middle part of sensor, the capsule-type bulging punch-pin is connect with pressure sensor;The experimental data includes along plate rolling direction
Force-stroke experimental data and vertical plate rolling direction force-stroke experimental data;
It determines plate initial parameter value, and the plate initial parameter value is input to established capsule-type bulging prediction model
In, obtain two groups of analogue datas;Wherein, the plate initial parameter value include elasticity modulus initial value, yield stress initial value,
Anisotropic parameters initial value;The capsule-type bulging prediction model is constructed according to the capsule-type expanding die;It is described
Analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data;
Using interpolation algorithm, on the basis of the analogue data, equally spaced interpolation is carried out to the experimental data, obtains multiple groups
Data acquisition system;The data acquisition system includes with the experiment new data under one stroke;The experiment new data includes along plate rolling
Power is tested in direction, vertical plate rolling direction tests power;
According to the experiment new data under the same one stroke in all data acquisition systems, elastic limit value is calculated;
According to the elastic limit value, all experiment new datas and all analogue datas are divided, obtain
One data group and the second data group;First data group includes that force-stroke is less than the analogue data of elastic limit value and tests new
Data;Second data group includes the analogue data and experiment new data that force-stroke is greater than elastic limit value;
According to established first optimization object function and first data group, elasticity modulus optimal value is calculated;Described first
Optimization object function is under same one stroke, along plate rolling direction analog force and along the minimum of plate rolling direction experiment power
0.5 times of residual sum of squares (RSS) is the objective function that optimization aim is established, or under same one stroke, with vertical plate rolling side
To 0.5 times of target letter established for optimization aim of analog force and the least residual quadratic sum of vertical plate rolling direction experiment power
Number;
According to established second optimization object function and second data group, yield stress optimal value, anisotropy are calculated
Parameter optimization value;Second optimization object function is under same one stroke, along plate rolling direction analog force and along plate
Rolling direction tests 0.5 times of the least residual quadratic sum of power, with vertical plate rolling direction analog force and vertical plate rolling
Test the objective function that 0.5 times of superposition value of the least residual quadratic sum of power is established for optimization aim in direction.
2. plate anisotropy constitutive parameter scaling method according to claim 1, which is characterized in that the determining plate ginseng
Number initial value, and the plate initial parameter value is input in established capsule-type bulging prediction model, obtain two groups of moulds
Quasi- data, specifically include:
In finite element method (FEM) software, plate grid cell shape is set as hexahedron, and take advanced algorithm, by blank perimeter
Applying boundary condition is to be completely fixed, and obtains the INP file of capsule-type bulging prediction model;
The plate initial parameter value is input in the capsule-type bulging prediction model, then according to the INP file with
And the bulging simulation of the capsule-type bulging prediction model, obtain two groups of analogue datas;The analogue data includes rolling along plate
Force-stroke analogue data in direction processed and vertical plate rolling direction force-stroke analogue data.
3. plate anisotropy constitutive parameter scaling method according to claim 1, which is characterized in that described according to all institutes
The experiment new data under the same one stroke in data acquisition system is stated, elastic limit value is calculated, specifically includes:
Force-stroke inflection point is retrieved using window technique according to the experiment new data under the same one stroke in all data acquisition systems;
The force-stroke inflection point is elastic limit value.
4. plate anisotropy constitutive parameter scaling method according to claim 1, which is characterized in that the basis has been established
The first optimization object function and first data group, calculate elasticity modulus optimal value, specifically include:
The first second approximation objective function is converted by established first optimization object function;
According to first data group, using truncation conjugate gradient method, optimization calculates the first second approximation objective function
Minimum value, and then obtain elasticity modulus optimal value.
5. plate anisotropy constitutive parameter scaling method according to claim 1, which is characterized in that the basis has been established
The second optimization object function and second data group, calculate yield stress optimal value, anisotropic parameters optimal value, specifically
Include:
Second secondary approximate objective function is converted by established second optimization object function;
According to second data group, using truncation conjugate gradient method, optimization calculates the second secondary approximate objective function
Minimum value, and then obtain yield stress optimal value, anisotropic parameters optimal value.
6. a kind of plate anisotropy constitutive parameter calibration system, which is characterized in that the plate anisotropy constitutive parameter mark
Determining system includes:
Experimental data obtains module, for carrying out bulging experiment to plate using capsule-type expanding die, obtains two groups of experiment numbers
According to;Wherein, the capsule-type expanding die includes capsule-type bulging punch-pin, blank holder and bulging cavity plate, and the capsule-type is swollen
Shape punch-pin is the punch-pin that two a quarter spheres are formed by connecting by semicylinder, and it is swollen that the blank holder is located at the capsule-type
Below shape punch-pin, the bulging cavity plate is located at below the blank holder, the head of the capsule-type bulging punch-pin and pressure
Plate connection, the pressure plare are connect with press machine, and the pressure coil is connect by four springs with the pressure plare, the pressure
Displacement sensor is installed, the middle part of the capsule-type bulging punch-pin is connect with pressure sensor on the lateral column of machine;The experiment number
According to including along plate rolling direction force-stroke experimental data and vertical plate rolling direction force-stroke experimental data;
Analogue data obtains module, for determining plate initial parameter value, and the plate initial parameter value is input to built
In vertical capsule-type bulging prediction model, two groups of analogue datas are obtained;Wherein, the plate initial parameter value includes elasticity modulus
Initial value, yield stress initial value, anisotropic parameters initial value;The capsule-type bulging prediction model is according to the capsule
The building of formula expanding die;The analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling side
To force-stroke analogue data;
Data acquisition system obtains module, for utilizing interpolation algorithm, on the basis of the analogue data, carries out to the experimental data
Equally spaced interpolation obtains multi-group data set;The data acquisition system includes with the experiment new data under one stroke;The experiment
New data includes along plate rolling direction experiment power, vertical plate rolling direction experiment power;
Elastic limit value computing module, for according to the experiment new data under the same one stroke in all data acquisition systems, meter
Calculate elastic limit value;
Data division module is used for according to the elastic limit value, to all experiment new datas and all simulation numbers
According to being divided, the first data group and the second data group are obtained;First data group includes that force-stroke is less than elastic limit value
Analogue data and experiment new data;Second data group includes the analogue data and experiment that force-stroke is greater than elastic limit value
New data;
Elasticity modulus optimization module, for calculating bullet according to established first optimization object function and first data group
Property modulus optimal value;First optimization object function is under same one stroke, along plate rolling direction analog force and along plate
Material rolling direction tests the objective function that 0.5 times of the least residual quadratic sum of power is established for optimization aim, or same
Under stroke, the 0.5 of the least residual quadratic sum of power is tested with vertical plate rolling direction analog force and vertical plate rolling direction
The objective function established again for optimization aim;
Yield stress, anisotropic parameters optimization module, for according to established second optimization object function and described second
Data group calculates yield stress optimal value, anisotropic parameters optimal value;Second optimization object function is in same one stroke
Under, it is and vertical with along plate rolling direction analog force and along 0.5 times of least residual quadratic sum of plate rolling direction experiment power
0.5 times of superposition value of the least residual quadratic sum of plate rolling direction analog force and vertical plate rolling direction experiment power is excellent
Change the objective function that target is established.
7. plate anisotropy constitutive parameter calibration system according to claim 6, which is characterized in that the analogue data obtains
Modulus block, specifically includes:
INP file obtaining unit, for plate grid cell shape being set as hexahedron, and adopt in finite element method (FEM) software
Advanced algorithm is taken, it is to be completely fixed that blank perimeter, which is applied boundary condition, obtains the INP file of capsule-type bulging prediction model;
Analogue data acquiring unit, for the plate initial parameter value to be input in the capsule-type bulging prediction model,
Then it is simulated according to the bulging of the INP file and the capsule-type bulging prediction model, obtains two groups of analogue datas;It is described
Analogue data includes along plate rolling direction force-stroke analogue data and vertical plate rolling direction force-stroke analogue data.
8. plate anisotropy constitutive parameter calibration system according to claim 6, which is characterized in that the elastic limit value
Computing module specifically includes:
Elastic limit value computing unit, for according to the experiment new data under the same one stroke in all data acquisition systems, benefit
With window technique, force-stroke inflection point is retrieved;The force-stroke inflection point is elastic limit value.
9. plate anisotropy constitutive parameter calibration system according to claim 6, which is characterized in that the elasticity modulus is excellent
Change module, specifically include:
First conversion unit, for converting the first second approximation objective function for established first optimization object function;
Elasticity modulus optimizes unit, and for according to first data group, using truncation conjugate gradient method, optimization calculates described the
The minimum value of one second approximation objective function, and then obtain elasticity modulus optimal value.
10. plate anisotropy constitutive parameter calibration system according to claim 6, which is characterized in that the yield stress,
Anisotropic parameters optimization module, specifically includes:
Second conversion unit, for converting second secondary approximate objective function for established second optimization object function;
Yield stress, anisotropic parameters optimize unit, for according to second data group, using truncation conjugate gradient method,
Optimization calculates the minimum value of the second secondary approximate objective function, and then obtains yield stress optimal value, anisotropic parameters
Optimal value.
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