CN110750926A - Particle swarm algorithm-based high-speed tensile curve processing and predicting method - Google Patents
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Abstract
The invention relates to a particle swarm algorithm-based high-speed tensile curve processing and predicting method, which comprises the following steps: step S1: inputting original data of high-speed stretching under a plurality of different strain rates; step S2: extracting experimental data before a necking section, carrying out homogenization treatment and converting the experimental data into a true stress-plastic strain curve; step S3: determining the upper and lower limit ranges of data extrapolation based on the stress-strain curve; step S4: selecting a material constitutive equation related to the strain rate; step S5: optimizing parameters in a material constitutive equation by using a particle swarm algorithm; step S6: based on an optimized material constitutive equation, deducing engineering stress-strain curves under different strain rates by adopting a finite element reverse method; step S7: outputting parameters in the related constitutive equation; step S8: and predicting a stress-strain curve under any strain rate based on the parameters of the material constitutive model. Compared with the prior art, the method has the advantages of high authenticity, high goodness of fit and the like.
Description
Technical Field
The invention relates to the technical field of data processing, in particular to a particle swarm algorithm-based high-speed tensile curve processing and predicting method.
Background
During the collision of the automobile, the strain rate of the automobile body material can reach 500s-1Even higher, for increasingly stringent vehicle safety design, collision simulation is an effective means, but the simulation accuracy depends on whether the parameter input of the material model is accurate or not. Therefore, the characterization of materials under dynamic load, especially the simulation and prediction of the mechanical behavior of materials under medium and high strain rates, has been a hot spot and a difficult point of industry attention.
The strain rate related model can be divided into a physical model and a phenomenological model, and compared with the physical model, the phenomenological model has the advantages of easy calibration, convenient use of finite elements and the like, so the phenomenological model is more favored in practical application. The core thought is as follows: firstly, aiming at strain rate effect items in a rate-related structure, selecting a group of flow stresses under certain plastic strain to carry out fitting calibration, and obtaining rate-related model parameters; and then, calibrating a hardening criterion, namely assuming a hardening criterion, simulating an actual stretching experiment process by adopting a finite element method to obtain an engineering stress-strain or force-displacement curve, comparing the engineering stress-strain or force-displacement curve with an experiment result, and repeatedly optimizing parameters in a material constitutive so as to enable the simulated and experimental curves to be as close as possible, thereby finally obtaining all parameters related to the rate in the constitutive.
However, the prior art has the following problems that:
1. when the strain rate effect item is calibrated, only a small part of test data is used for fitting and calibrating the constitutive model, most data information is lost, and the precision of parameter calibration is influenced.
2. Aiming at the calibration of a hardening standard model, a phenomenological theory is required to be used for carrying out calibration analysis on data under each strain rate one by one, the obtained model parameters are different under each strain rate curve, and the crossing of stress-strain curves under different strain rates cannot be prevented, so that the use of collision simulation is difficult.
3. The prior art cannot fully utilize test data under different strain rates, uniform model parameters in a rate-related structure cannot be obtained, further, a stress-strain curve under a strain rate cannot be effectively predicted, and the existing calibration method is low in efficiency and difficult to guarantee precision.
Disclosure of Invention
The present invention aims to overcome the above-mentioned drawbacks of the prior art and provide a method for processing and predicting a high-speed tensile curve based on a particle swarm algorithm.
The purpose of the invention can be realized by the following technical scheme:
a high-speed tensile curve processing and predicting method based on a particle swarm algorithm specifically comprises the following steps:
step S1: inputting original data of high-speed stretching under a plurality of different strain rates;
step S2: extracting experimental data before a necking section, carrying out partial homogenization treatment on the extracted experimental data and converting the experimental data into a true stress-plastic strain curve;
step S3: determining the upper and lower limit ranges of data extrapolation after necking based on the stress-strain curve under any strain rate;
step S4: selecting a material constitutive equation related to the strain rate;
step S5: optimizing parameters in a material constitutive equation by using a particle swarm algorithm based on experimental data before necking and an upper and lower limit range defined after necking;
step S6: based on an optimized material constitutive equation, an engineering stress-strain curve or a force-displacement curve under different strain rates is deduced by adopting a finite element reverse method;
step S7: comparing experimental and simulation data under different strain rates, if the error meets the requirement, outputting all parameters in a related constitutive equation, if the difference is larger, adjusting a necked data fitting point in an upper limit and a lower limit range, applying a particle swarm algorithm to re-optimize the parameters of the material constitutive equation, and repeatedly circulating until the error meets the requirement;
step S8: and predicting a stress-strain curve under any strain rate based on the finally determined parameters of the material constitutive model.
True stress σ in the step S2TAnd plastic strain epsilonPCalculated by the following formula:
σT＝σ(1+ε)
εP＝ln(1+ε)-σT/E
wherein, sigma is engineering stress, epsilon is engineering strain, and E is Young modulus.
The lower limit in step S3 is a flat push of a tensile point, which is a coordinate point after which the slope of the curve is 0.
The slope tan θ of the upper limit in the step S3 satisfies the following formula:
wherein epsilonbThe plastic strain corresponds to the tensile strength.
The constitutive equation of the material related to the strain rate in the step S4 includes strain εPAnd strain rate
Exponential function, power function or logarithmic function relationship.
The calculation formulas of the particle velocity v [ i ] and the position present [ i ] corresponding to the particle group algorithm in the step S5 are as follows:
v[i]＝w*v[i]+c1*rand()*(pbest[i]-present[i])+c2*rand()*(gbest[i]-present[i])
present[i]＝present[i]+v[i]
wherein w is an inertial weight, c1 is a first learning factor, c2 is a second learning factor, pbest [ i ] is an individual optimum, and gbest [ i ] is a global optimum.
The fitness function fitness calculation formula of the particle group algorithm in step S5 is as follows:
wherein,
and
respectively is a stress value and an actual measurement value obtained by calculation according to a material constitutive equation.
The finite element reverse method in step S6 is to establish a finite element model according to the actual sample size of the high-speed tensile test and simulate the test process.
The adjustment of the upper and lower limit ranges in said step S7 is based on the true stress-plastic strain curve.
Compared with the prior art, the invention has the following beneficial effects:
1. the method fully utilizes experimental data under different strain rates, obtains a material constitutive equation related to the strain rate after parameter optimization based on a particle swarm algorithm and a finite element reverse calibration technology, and calculates true stress-plastic strain extension according to the material constitutive equation to obtain data with high authenticity.
2. The invention uses the finite element reverse method to deduce the engineering stress-strain curve or force-displacement curve under different strain rates, is convenient for the application of related finite element software, has high goodness of fit of experimental and simulation results, and can effectively predict the stress-strain curve under any strain rate.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic representation of the upper and lower limits of a predicted true stress-plastic strain curve after necking in accordance with the present invention;
FIG. 3 is a schematic diagram of a true stress-plastic strain curve obtained by particle swarm optimization in the first embodiment;
FIG. 4 is a schematic diagram of an engineering stress-strain curve obtained by a finite element inverse calibration technique according to the first embodiment;
FIG. 5 is a graph illustrating the prediction of true stress-plastic strain curves at different strain rates according to one embodiment;
FIG. 6 is a graph showing a comparison of predicted engineering stress-strain curves and measured curves at strain rates of 1/s and 200/s for one example;
FIG. 7 is a diagram illustrating a true stress-plastic strain curve obtained by the example group algorithm optimization in the second embodiment;
FIG. 8 is a schematic diagram of an engineering stress-strain curve obtained by a reverse finite element calibration technique according to the second embodiment;
FIG. 9 is a graph showing the prediction of true stress-plastic strain curves at different strain rates for the second example;
FIG. 10 is a graphical comparison of predicted engineering stress-strain curves and measured curves at strain rates of 100/s and 1000/s for example two.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, a method for processing and predicting a high-speed tensile curve based on a particle swarm algorithm specifically includes the following steps:
step S1: inputting original data of high-speed stretching under a plurality of different strain rates;
step S2: extracting experimental data before a necking section, carrying out partial homogenization treatment on the extracted experimental data and converting the experimental data into a true stress-plastic strain curve;
step S3: determining the upper and lower limit ranges of data extrapolation after necking based on the stress-strain curve under any strain rate;
step S4: selecting a material constitutive equation related to the strain rate;
step S5: optimizing parameters in a material constitutive equation by using a particle swarm algorithm based on experimental data before necking and an upper and lower limit range defined after necking;
step S6: based on an optimized material constitutive equation, an engineering stress-strain curve or a force-displacement curve under different strain rates is deduced by adopting a finite element reverse method;
step S7: comparing experimental and simulation data under different strain rates, if the error meets the requirement, outputting all parameters in a related constitutive equation, if the difference is larger, adjusting a necked data fitting point in an upper limit and a lower limit range, applying a particle swarm algorithm to re-optimize the parameters of the material constitutive equation, and repeatedly circulating until the error meets the requirement;
step S8: and predicting a stress-strain curve under any strain rate based on the finally determined parameters of the material constitutive model.
Example one
Performing high-speed tensile test on the DP780 steel plate by using high-speed tensile test equipment, and respectively measuring that the strain rates are 10-3Engineering stress-strain curves at/s, 10/s, 500/s.
The formula true stress sigma is obtained by the following calculationTAnd plastic strain epsilonPConverting the engineering stress-strain curve into a true stress-plastic strain curve:
σT＝σ(1+ε)
εP＝ln(1+ε)-σT/E
wherein, sigma is engineering stress, epsilon is engineering strain, and E is Young modulus.
Based on strain rate 10-3The data under/s, the upper and lower limit adjustment ranges of the true stress-plastic strain curve after the prediction of necking are shown in figure 2, the slope is calculated to be between 0 and 457.32 according to a formula, and the specific formula is as follows:
wherein epsilonbThe plastic strain corresponds to the tensile strength.
Selected strain rate 10-3The material constitutive equation in terms of/s is based on the data and strain rate before all necking points 10-3The lower limit of the true stress-plastic strain curve under/s, namely the slope is 0, parameters in the related material constitutive are optimized by adopting a particle swarm optimization, the number of particle swarms is set to be 500, and the speed v [ i ] of the particles]And position present [ i ]]The calculation formula is as follows:
v[i]＝w*v[i]+c1*rand()*(pbest[i]-present[i])+c2*rand()*(gbest[i]-present[i])
present[i]＝present[i]+v[i]
the inertia weight w is 0.7368, the first learning factor c1 is 1.5926, the second learning factor c2 is 1.2962, pbest [ i ] is individually optimal, and gbest [ i ] is globally optimal.
The fitness function fitness calculation formula is as follows:
wherein,
and
respectively is a stress value and an actual measurement value obtained by calculation according to a material constitutive equation.
The particle swarm optimization is realized by Matlab programming, so that the optimized constitutive parameters of the material can be obtained, and the true stress-plastic strain curve obtained by optimization is shown in FIG. 3.
Establishing a finite element model for a high-speed stretching practical test, inputting the material constitutive after the particle swarm optimization, obtaining engineering stress-strain curves under different strain rates through a finite element reverse technology, comparing a simulation result with an actually measured curve, and if the difference between the simulation result and the actually measured curve is larger, comparing 10-3Adjusting a true stress-plastic strain curve after a necking point under the strain rate/s to the upper limit direction, then optimizing material constitutive parameters by using a particle swarm algorithm, and repeatedly and circularly calculating until the simulated engineering stress-strain curve under different strain rates is closer to an actual measurement value, so that the optimal rate-related material constitutive equation can be finally obtained, wherein the method specifically comprises the following steps:
the engineering stress-strain curve obtained by the finite element reverse calibration technology is shown in fig. 4, and the coincidence degree of the engineering stress-strain curve and the actually measured curve is high.
As shown in FIG. 5, based on the material constitutive, true stress and plastic strain curves with strain rates of 1/s and 200/s are calculated, and an engineering stress-strain curve obtained by finite element inversion technology is shown in FIG. 6, which is better in consistency than an actually measured curve.
Example two
The B280VK steel plate is subjected to high-speed tensile test through high-speed tensile test equipment, and the strain rate is respectively measured to be 10-3Engineering stress-strain curves at/s, 10/s, 500/s.
The formula true stress sigma is obtained by the following calculationTAnd plastic strain epsilonPConverting the engineering stress-strain curve into a true stress-plastic strain curve:
σT＝σ(1+ε)
εP＝ln(1+ε)-σT/E
wherein, sigma is engineering stress, epsilon is engineering strain, and E is Young modulus.
Based on strain rate 10-3The data under/s, the upper and lower limit adjustment ranges of the true stress-plastic strain curve after the prediction of necking are shown in figure 2, the slope is calculated to be between 0 and 517.96 according to a formula, and the specific formula is as follows:
wherein epsilonbThe plastic strain corresponds to the tensile strength.
Selected strain rate 10-3The material constitutive equation related to/s is based on the data before all necking points and the lower limit of a true stress-plastic strain curve under the strain rate of 10 < -3 >/s, namely the slope is 0, parameters in the material constitutive equation are optimized by adopting a particle swarm optimization, the number of particle swarms is set to be 500, and the speed v [ i ] of particles]And position present [ i ]]The calculation formula is as follows:
v[i]＝w*v[i]+c1*rand()*(pbest[i]-present[i])+c2*rand()*(gbest[i]-present[i])
present[i]＝present[i]+v[i]
the inertia weight w is 0.6127, the first learning factor c1 is 1.3748, the second learning factor c2 is 1.4784, pbest [ i ] is individually optimal, and gbest [ i ] is globally optimal.
The fitness function fitness calculation formula is as follows:
wherein,
and
respectively is a stress value and an actual measurement value obtained by calculation according to a material constitutive equation.
The particle swarm optimization is realized by Matlab programming, so that the optimized constitutive parameters of the material can be obtained, and the true stress-plastic strain curve obtained by optimization is shown in FIG. 7.
The reverse finite element calibration process is the same as that of the first embodiment, and the obtained constitutive equation is as follows:
the engineering stress-strain curve obtained by the finite element reverse calibration technology is shown in fig. 8, and the coincidence degree of the engineering stress-strain curve and the actually measured curve is high.
As shown in FIG. 9, based on the material constitution, the true stress and plastic strain curves of the strain rate of 100/s and 1000/s are calculated, and the engineering stress-strain curve obtained by finite element inversion technique is shown in FIG. 10, which is better in consistency than the measured curve.
The foregoing is a preferred embodiment of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should be considered as the protection scope of the present invention.
Claims (9)
1. A high-speed tensile curve processing and predicting method based on a particle swarm algorithm is characterized by comprising the following steps:
step S1: inputting original data of high-speed stretching under a plurality of different strain rates;
step S2: extracting experimental data before a necking section, carrying out partial homogenization treatment on the extracted experimental data and converting the experimental data into a true stress-plastic strain curve;
step S3: determining the upper and lower limit ranges of data extrapolation after necking based on the stress-strain curve under any strain rate;
step S4: selecting a material constitutive equation related to the strain rate;
step S5: optimizing parameters in a material constitutive equation by using a particle swarm algorithm based on the extracted experimental data before necking and the upper and lower limit ranges defined after necking;
step S6: based on an optimized material constitutive equation, an engineering stress-strain curve or a force-displacement curve under different strain rates is deduced by adopting a finite element reverse method;
step S7: comparing experimental and simulation data under different strain rates, if the error meets the requirement, outputting all parameters in a related constitutive equation, if the difference is larger, adjusting a necked data fitting point in an upper limit and a lower limit range, applying a particle swarm algorithm to re-optimize the parameters of the material constitutive equation, and repeatedly circulating until the error meets the requirement;
step S8: and predicting a stress-strain curve under any strain rate based on the finally determined parameters of the material constitutive model.
2. The method for processing and predicting the high-speed tensile curve based on the particle swarm optimization algorithm according to claim 1, wherein the true stress σ in the step S2 isTAnd plastic strain epsilonPCalculated by the following formula:
σT＝σ(1+ε)
εP＝ln(1+ε)-σT/E
wherein, sigma is engineering stress, epsilon is engineering strain, and E is Young modulus.
3. The method for processing and predicting the high-speed tensile curve based on the particle swarm optimization of claim 1, wherein the lower limit in the step S3 is a flat push of a tensile point, and the tensile point is a coordinate point after the flat push of the tensile point, where the slope of the curve is 0.
4. The method for processing and predicting the high-speed stretching curve based on the particle swarm optimization algorithm, according to claim 1, wherein the slope tan θ of the upper limit in the step S3 satisfies the following formula:
wherein epsilonbThe plastic strain corresponds to the tensile strength.
5. The method for processing and predicting the high-speed tensile curve based on the particle swarm optimization algorithm according to claim 1, wherein the material constitutive equation related to the strain rate in the step S4 includes strain εPAnd strain rate
Exponential function, power function or logarithmic function relationship.
6. The method for processing and predicting the high-speed stretching curve based on the particle swarm optimization algorithm according to claim 1, wherein the particle velocity vi and the position present i corresponding to the particle swarm optimization algorithm in the step S5 are calculated as follows:
v[i]＝w*v[i]+c1*rand()*(pbest[i]-present[i])+c2*rand()*(gbest[i]-present[i])
present[i]＝present[i]+v[i]
wherein w is an inertial weight, c1 is a first learning factor, c2 is a second learning factor, pbest [ i ] is an individual optimum, and gbest [ i ] is a global optimum.
7. The method for processing and predicting the high-speed tensile curve based on the particle swarm algorithm according to claim 1, wherein the fitness function fitness calculation formula of the particle swarm algorithm in the step S5 is as follows:
wherein,
and
respectively is a stress value and an actual measurement value obtained by calculation according to a material constitutive equation.
8. The method for processing and predicting the high-speed tensile curve based on the particle swarm optimization algorithm according to claim 1, wherein the finite element inverse method in the step S6 is to create a finite element model according to the actual sample size of the high-speed tensile test and simulate the test process.
9. The method for processing and predicting the high-speed tensile curve based on the particle swarm optimization algorithm according to claim 1, wherein the adjustment of the upper and lower limit ranges in the step S7 is based on the true stress-plastic strain curve.
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