CN105910886B - The application of the Browman of aluminium alloy stress-strain relation this structure Optimized models - Google Patents
The application of the Browman of aluminium alloy stress-strain relation this structure Optimized models Download PDFInfo
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Abstract
The present invention relates to a kind of this structure of Browman Optimized model of aluminium alloy stress-strain relation and its applications, in conjunction with aluminium alloy stress-strain tester data, strength factor, strain hardening exponent and strain-rate-sensitivity exponent are calculated using least square method, so that it is determined that stress-strain relation based on Browman this structure Optimized models, predicts aluminium alloy capability.Compared with prior art, the precision of prediction higher of this structure of Browman Optimized model of the present invention more can accurately disclose rule of the aluminium alloy stress with strain variation.
Description
Technical field
The present invention relates to aluminium alloy capability Predicting Techniques, more particularly, to a kind of aluminium alloy stress-strain relation
This structure of Browman Optimized model and its application.
Background technology
Aluminium alloy is automobile, the light-weighted preferred material in Aeronautics and Astronautics field, using very extensive.On spacecraft,
Aluminium alloy is the ideal material of main fuel tank, combustion adjuvant case；Aboard, aluminium alloy is mainly used for structural material, such as covers
Skin, siding and undercarriage leg etc..Aluminium alloy be also solve communications include high-speed railway, subway transports and automobile visitor,
The breach of the defeated equal lightweight problems of shipping.Aluminium alloy is to pass through to the dynamic response of kinetic parameter during thermoplasticity processing
Constitutive relation is reflected, and constitutive relation is also the foundation of finite element analysis and formulates the basis of forming technology, wherein stress
The research for straining constitutive relation has more important meaning to improving Mechanical Properties of Aluminum Alloys.Currently, many scholars close aluminium
The constitutive model of golden material stress strain is studied, such as Hollomon, Ludwik, Browman model, wherein
Browman models are to apply a kind of relatively broad and ripe constitutive model, but precision of prediction still needs to be further improved.
Invention content
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of aluminium alloy stress to answer
This structure of the Browman of change relationship Optimized model and its application.
The purpose of the present invention can be achieved through the following technical solutions：
Currently, the Browman constitutive models for mostly using following form describe the stress-strain relation of aluminium alloy.
In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is strain hardening exponent, and m is strain
Rate sensitivity index.
In order to preferably study crystallized ability when aluminium alloy high temperature, the precision of prediction of aluminium alloy constitutive model is improved, and
Theoretical foundation and technical support are provided for aluminium lightweight.
A kind of Browman this structure Optimized models of aluminium alloy stress-strain relation, in conjunction with hyperbolic sine function and aluminium alloy
Stress-strain relation is used and is optimized to Browman constitutive models with drag
In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is strain hardening exponent, and m is strain
Rate sensitivity index；
And determine strain hardening exponent, strain-rate-sensitivity exponent and strength factor.
The strain hardening exponent n determination process is as follows：
In one timing of strain rate, formula (1) is deformed into
σ=K1(sinhε)n (2)
In formula, K1For constant；
Logarithm is taken to obtain simultaneously on formula (2) both sides
Ln σ=lnK1+nln(sinhε) (3)
Strain hardening exponent n is an important parameter of gauge sheet metal deformation strengthening ability, and evaluation plate stamping is drawn
Stretch the actual parameter of formability；Strain hardening exponent n is obtained by finding out the slope of ln σ and lnsinh (ε) relation curve；Therefore
N values are obtained by carrying out linear fit to formula (3), and expression formula is written as
In formula, A is the influence coefficient of strain rate, and B is influence relationships of the temperature T to n values；B useable linear relational expressions are retouched
State the relationship between temperature
B=a+bT (5)
In formula, a and b are undetermined constant.
The strain-rate-sensitivity exponent m determination process is as follows：
When strain remains unchanged, formula (1) can transform to
In formula, K2For constant, logarithm is taken to obtain formula (6)
By formula (7) it is found that strain hardening and strain-rate sensitivity Coefficient m be curve ln σ withSlope, therefore by rightLinear fit is carried out to acquire；M variation with temperature relationships are expressed as
M=d1+d2T (8)
In formula, d1、d2It is undetermined constant.
The strength factor K determination process is as follows：
K values are related with deformation temperature, are written as
K=e1+e2T (10)
In formula, e1、e2It is undetermined constant.
A kind of application of Browman this structure Optimized models of aluminium alloy stress-strain relation, in conjunction with aluminium alloy ess-strain
Test data calculates strength factor, strain hardening exponent and strain-rate-sensitivity exponent using least square method, so that it is determined that
Stress-strain relation based on Browman this structure Optimized models, predicts aluminium alloy capability.
Compared with prior art, the characteristics of present invention combination hyperbolic sine function is with aluminium alloy stress-strain diagram is established
Browman this structure Optimized models, and the Optimized model is predicted applied to 6016H18 Mechanical Properties of Aluminum Alloys, it is determined that it answers
Become hardenability value, strain-rate-sensitivity exponent and strength factor, has obtained the aluminium alloy and be based on Browman this structure Optimized models
Stress-strain relation；Verified, the precision of prediction higher of Browman this structure Optimized models more can accurately disclose aluminium conjunction
Golden stress with strain variation rule.
Description of the drawings
Fig. 1 is that strain rate of the present invention is 0.001s-1When ln σ-ln (sinh ε) fitting a straight line figure；
Fig. 2 is variation relation figure of the n values of the present invention with strain rate and temperature；
Fig. 3 is that strain rate of the present invention is 0.1s-1When B value variation with temperature relational graphs；
When Fig. 4 is aluminum alloy T=450 DEG C 6016H18 of the present inventionQuadratic fit curve figure；
Fig. 5 is that 6016H18 aluminium alloys existWhen K values and temperature relation figure；
Fig. 6 is that strain rate is 0.1s-1When 6016H18 aluminium alloy stress match value and test value comparison diagram.
Specific implementation mode
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 describes, it is clear that described embodiment is a part of the embodiment of the present invention, rather than whole embodiments.Based on this hair
Embodiment in bright, the every other reality that those of ordinary skill in the art are obtained without making creative work
Example is applied, the scope of protection of the invention should be all belonged to.
To verify the precision of prediction for Browman this structure Optimized models that the present invention obtains, below by the Optimized model application
In the stress prediction of 6016H18 aluminium alloys.
The n values known to formula (3) are the slope of ln σ and ln (sinh ε) relation curve, select 6016H18 aluminium alloys five
Stress test value under kind temperature, five kinds of strain rates takes a little since stress-strain diagram the part of generation strain hardening
(σi,εi), until close to peak stress, with strain rateIn the case of for test data point (σi,εi) as schemed
Shown in 1.Therefore, (ln σ can be calculatedi,ln(sinhεi)), and linear regression is carried out to it, show that the slope of straight line is n values,
Fitting a straight line between ln σ and ln (sinh ε) is plotted in Fig. 1 together.
By Fig. 1 it is not difficult to find that the two is substantially linear, to test data (the ln σ under other strain ratesi,ln
(sinhεi)) linear regression fit is carried out, the n values under different temperatures, differently strained rate can be obtained, be as a result listed in table 1.
Table 1
Convolution (4), by n value of the 6016H18 aluminium alloys obtained under different temperatures and differently strained rate into line
Property return, be as a result plotted in Fig. 2.
By Fig. 2 it is not difficult to find that n values are substantially linear with the variation of strain rate, and strains different at each temperature
There are deviations between the slope of curve that rate group obtains when being fitted.Relationship between n values and temperature, base are indicated using formula (4)
It is drawn under different temperatures in formula (4)The relationship of curve, it is the value of A to take the average value 0.008446 of slope, with this
To improve the precision of prediction of Browman this structure Optimized models.N values in the A values found out and table 1 are substituted into formula (4) i.e. respectively
The B values at five kinds of temperature and five kinds of strain rates can be acquired.Convolution (5), is 0.1s with strain rate-1For, make B values and temperature
The relationship between T is spent, it is found that B values variation with temperature is also substantially in a linear relationship, linear regression is carried out to it, as a result such as Fig. 3
It is shown.Equally, the linear fit equation that B values and temperature under other four kinds of strain rates can be obtained, respectively takes slope and intercept
Average value, you can obtain the approximate fits relationship of B values and temperature, as
B=-3.23 × 10-4T+0.22351 (11)
Therefore, the A=0.008446 acquired and formula (11) are substituted into formula (4), n values and strain rate and temperature can be obtained
Approximate relation, as
In determining Browman this structure Optimized models after the relational expression of n, it is thus necessary to determine that strain hardening and strain-rate sensitivity refers in formula (8)
Relationship between number m and temperature.Strain for 0.25 when (uniform plastic deformation section), take five kinds of temperature of 6016H18 aluminium alloys,
Stress-strain tester data under five kinds of strain rates draw the logarithmic curve under this strainUsing two
Order polynomial is fitted it, can be obtained m values under relevant temperature by seeking differential to curve, to take temperature be 450 DEG C,
For ess-strain rate value when strain is 0.25, it is fitted using quadratic polynomial, fitting result such as Fig. 4 institutes
Show.
Equally, the Sensitivity Index m at a temperature of other four kinds can also be acquired by the above method.Relationship between m and temperature
Useable linear equation (8) indicates, by linear fit can determine under different temperatures and differently strained rate m values and temperature it
Between linear relation, for improve Browman this structure Optimized models precision of prediction, here to the slope in linear fit equation
With intercept averaged, to obtain the linear fit equation of m values and temperature, as
M=0.06414+1.91 × 10-4T (13)
The final step for establishing the Browman of 6016H18 aluminium alloys this structure Optimized models is to determine the value of strength factor K.
The n and m that are found out by above-mentioned two step are substituted into equationIn, 6016H18 aluminium alloys can be obtained
K values under different temperatures and differently strained rate carry out linear regression analysis to K values, withFor, as a result it is plotted in
Fig. 5.
As shown in Figure 5,6016H18 aluminium alloys existWhen K values and temperature it is in a linear relationship, useable linear equation is close
Like relationship between the two is expressed, the line of relationship between K values and temperature under other strain rates is can determine using identical method
Property equation, the slope in linear equation is averaged with intercept, you can obtain the relational expression between K values and temperature, i.e., respectively
Have
K=136.975-0.18787T (14)
By analyzing calculating above, the expression formula of coefficient n, m, K in Browman this structure Optimized models are finally obtained, has been incited somebody to action
Formula (12), formula (13) and formula (14) substitute into formula (1) and obtain the Browman of 6016H18 aluminium alloy ess-strains this structure optimization moulds
Type has
In conjunction with 6016H18 aluminium alloys strain rate be 0.1s-1When stress-strain tester data, be respectively adopted
Browman constitutive models and Browman this structure Optimized models are predicted, and are compared with test value, as a result such as Fig. 6 institutes
Show.By in Fig. 6 it is not difficult to find that no matter at a temperature of which kind of, this structure of Browman Optimized model and tradition Browman constitutive models
It is more nearly test value compared to predicted value, more can accurately describe the stress-strain relation of 6016H18 aluminium alloys.In addition, logical
The predicted value for crossing two kinds of constitutive models when comparison strain is 0.25 finds that the average relative error of Browman constitutive models is
21.01%, and the average relative error of Browman this structure Optimized models is 3.18%, this further illustrates that this structure of Browman is excellent
Changing model has higher precision of prediction.Therefore, this structure of Browman Optimized model that the present invention obtains can be researcher in aluminium
A kind of more accurate prediction model is provided in terms of alloy property prediction.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can readily occur in various equivalent modifications or replace
It changes, these modifications or substitutions should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with right
It is required that protection domain subject to.
Claims (4)
1. a kind of application of Browman this structure Optimized models of aluminium alloy stress-strain relation, which is characterized in that in conjunction with aluminium alloy
Stress-strain tester data calculate strength factor, strain hardening exponent and strain-rate-sensitivity exponent using least square method,
So that it is determined that stress-strain relation based on Browman this structure Optimized models, predicts aluminium alloy capability,
The Browman of aluminium alloy stress-strain relation this structure Optimized models, are answered in conjunction with hyperbolic sine function and aluminium alloy
Stress-strain relationship is used and is optimized to Browman constitutive models with drag
In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is strain hardening exponent, and m is strain rate
Sensitivity Index；
And determine strain hardening exponent, strain-rate-sensitivity exponent and strength factor.
2. application according to claim 1, which is characterized in that the strain hardening exponent n determination process is as follows：
In one timing of strain rate, formula (1) is deformed into
σ=K1(sinhε)n (2)
In formula, K1For constant；
Logarithm is taken to obtain simultaneously on formula (2) both sides
Ln σ=lnK1+nln(sinhε) (3)
Strain hardening exponent n is obtained by finding out the slope of ln σ and lnsinh (ε) relation curve；Therefore n values pass through to formula (3)
It carries out linear fit to obtain, expression formula is written as
In formula, A is the influence coefficient of strain rate, and B is influence relationships of the temperature T to n values；B useable linear relational expressions describe with
Relationship between temperature
B=a+bT (5)
In formula, a and b are undetermined constant.
3. application according to claim 1, which is characterized in that the strain-rate-sensitivity exponent m determination process is as follows：
When strain remains unchanged, formula (1) can transform to
In formula, K2For constant, logarithm is taken to obtain formula (6)
By formula (7) it is found that strain hardening and strain-rate sensitivity Coefficient m be curve ln σ withSlope, therefore by rightLinear fit is carried out to acquire；M variation with temperature relationships are expressed as
M=d1+d2T (8)
In formula, d1、d2It is undetermined constant.
4. application according to claim 1, which is characterized in that the strength factor K determination process is as follows：
K values are related with deformation temperature, are written as
K=e1+e2T (10)
In formula, e1、e2It is undetermined constant.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2000031139A1 (en) * | 1998-11-25 | 2000-06-02 | University Of Bristol | Peptide inhibitor of browman-birk type |
| WO2013042600A1 (en) * | 2011-09-19 | 2013-03-28 | 日本電気株式会社 | Stress-strain relation simulation method, stress-strain relation simulation system, and stress-strain relation simulation program which use chaboche model |
| CN105181435A (en) * | 2015-10-15 | 2015-12-23 | 中国石油大学(华东) | Method of establishing elastic-plastic mechanical constitutive model made of rock material |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2000031139A1 (en) * | 1998-11-25 | 2000-06-02 | University Of Bristol | Peptide inhibitor of browman-birk type |
| WO2013042600A1 (en) * | 2011-09-19 | 2013-03-28 | 日本電気株式会社 | Stress-strain relation simulation method, stress-strain relation simulation system, and stress-strain relation simulation program which use chaboche model |
| CN105181435A (en) * | 2015-10-15 | 2015-12-23 | 中国石油大学(华东) | Method of establishing elastic-plastic mechanical constitutive model made of rock material |
Non-Patent Citations (1)
| Title |
|---|
| 基于Sellars－Tegart方程和 BP 神经网络的6016铝合金稳态应力的预测;张建平;《锻压技术》;20160131;第41卷(第1期);116-120 * |
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