CN105910886A - Browman constitutive optimization model of aluminum alloy stress-strain relation and application of Browman constitutive optimization model - Google Patents

Abstract

The invention relates to a Browman constitutive optimization model of an aluminum ally stress-strain relation and application of the Browman constitutive optimization model. Combined with aluminum alloy stress-strain experimental data, a strength coefficient, a strain hardening index and a strain rate sensitivity index are calculated according to a least square method, a stress-strain relational expression based on the Browman constitutive optimization model is determined, and aluminum alloy performance is predicated. Compared with the prior art, the Browman constitutive optimization model has the advantages of high prediction accuracy and capability of accurately revealing the rule that the stress of aluminum alloy changes along with strain.

Description

Browman this structure Optimized model of aluminium alloy stress-strain relation and application thereof

Technical field

The present invention relates to aluminium alloy capability Predicting Technique, especially relate to a kind of aluminium alloy stress-strain relation Browman this structure Optimized model and application thereof.

Background technology

Aluminium alloy is automobile, the light-weighted preferred material in Aeronautics and Astronautics field, and its application is quite varied.In space flight On device, aluminium alloy is main fuel tank, the ideal material of combustion adjuvant case；Aboard, aluminium alloy is mainly used in Structural material, such as eyelid covering, wallboard and undercarriage leg etc..Aluminium alloy also be solve communications include high-speed railway, The breach of the lightweight problems such as subway transports and automobile visitor, shipping is defeated.Aluminium alloy is in the thermoplasticity course of processing In the dynamic response of kinetic parameter is embodied by constitutive relation, constitutive relation is also finite element analysis Foundation and the basis of formulation forming technology, wherein, the research of stress-strain Constitutive Relationship is to improving aluminium alloy mechanical property Can have the most important meaning.At present, the constitutive model of aluminum alloy materials ess-strain is carried out by a lot of scholars Research, such as Hollomon, Ludwik, Browman model etc., wherein, Browman model is to apply more Extensive and ripe a kind of constitutive model, but precision of prediction still awaits improving further.

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and a kind of aluminium alloy stress is provided Browman this structure Optimized model of strain stress relation and application thereof.

The purpose of the present invention can be achieved through the following technical solutions:

At present, the Browman constitutive models using following form describe the stress-strain relation of aluminium alloy more.

$\mathrm{\σ}={\mathrm{K\ϵ}}^n{\stackrel{\·}{\mathrm{\ϵ}}}^m---\left(0\right)$

In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is strain hardening exponent, m For strain-rate-sensitivity exponent.

In order to preferably study crystallized ability during aluminium alloy high temperature, improve the precision of prediction of aluminium alloy constitutive model, And provide theoretical foundation and technical support for aluminum lightweight.

Browman this structure Optimized model of a kind of aluminium alloy stress-strain relation, in conjunction with hyperbolic sine function and aluminum Alloy stress strain stress relation, uses and is optimized Browman constitutive model with drag

$\mathrm{\σ}=K{\left(\sinh \mathrm{\ϵ}\right)}^n{\left(\sinh \stackrel{\·}{\mathrm{\ϵ}}\right)}^m---\left(1\right)$

In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is that strain hardening refers to Number, m is strain-rate-sensitivity exponent；

And determine strain hardening exponent, strain-rate-sensitivity exponent and strength factor.

Described strain hardening exponent n determines that process is as follows:

In strain rate one timing, formula (1) is deformed into

σ=K₁(sinhε)ⁿ (2)

In formula, K₁For constant；

Are taken the logarithm in formula (2) both sides simultaneously

Ln σ=lnK₁+nln(sinhε) (3)

Strain hardening exponent n is an important parameter of gauge sheet metal deformation strengthening ability, is also to evaluate plate stamping The actual parameter of stretch forming；Strain hardening exponent n is by obtaining the slope of ln σ Yu lnsinh (ε) relation curve Obtain；Therefore n value obtains by formula (3) is carried out linear fit, and its expression formula is written as

$n=Alog\stackrel{\·}{\mathrm{\ϵ}}+B---\left(4\right)$

In formula, A is the coefficient that affects of strain rate, and B is that temperature T affects relation to n value；B useable linear relation Formula describes the relation between temperature

B=a+bT (5)

In formula, a and b is undetermined constant.

Described strain-rate-sensitivity exponent m determines that process is as follows:

When strain keeps constant, formula (1) can transform to

$\mathrm{\σ}=K_2{\[\sinh \left(\stackrel{\·}{\mathrm{\ϵ}}\right)\]}^m---\left(6\right)$

In formula, K₂For constant, formula (6) is taken the logarithm

$ln\mathrm{\σ}={\mathrm{lnK}}_2+m\ln \sinh \left(\stackrel{\·}{\mathrm{\ϵ}}\right)---\left(7\right)$

From formula (7), strain hardening and strain-rate sensitivity Coefficient m be curve ln σ withSlope, therefore By rightCarry out linear fit to try to achieve；M variation with temperature relational representation is

M=d₁+d₂T (8)

In formula, d₁、d₂It is undetermined constant.

Described strength factor K determines that process is as follows:

K value is relevant with deformation temperature, is written as

K=e₁+e₂T (10)

In formula, e₁、e₂It is undetermined constant.

The application of Browman this structure Optimized model of a kind of aluminium alloy stress-strain relation, in conjunction with aluminium alloy stress Strain-gauge test data, use method of least square to calculate strength factor, strain hardening exponent and strain hardening and strain-rate sensitivity and refer to Number, so that it is determined that stress-strain relation of based on Browman this structure Optimized model, enters aluminium alloy capability Row prediction.

Compared with prior art, the present invention combines the feature of hyperbolic sine function and aluminium alloy stress-strain diagram, Establish Browman this structure Optimized model, and this Optimized model is applied to 6016H18 Mechanical Properties of Aluminum Alloys Prediction, it is determined that strain hardening exponent, strain-rate-sensitivity exponent and strength factor, obtained this aluminium alloy based on The stress-strain relation of Browman this structure Optimized model；Empirical tests, Browman this structure Optimized model pre- Survey precision higher, more can disclose the aluminium alloy stress rule with strain variation exactly.

Accompanying drawing explanation

Fig. 1 be strain rate of the present invention be 0.001s^-1Time ln σ-ln (sinh ε) fitting a straight line figure；

Fig. 2 is the n value of the present invention variation relation figure with strain rate and temperature；

Fig. 3 be strain rate of the present invention be 0.1s^-1Time B value variation with temperature graph of a relation；

When Fig. 4 is 6016H18 aluminum alloy T=450 DEG C of the present inventionQuadratic fit curve figure；

Fig. 5 is that 6016H18 aluminium alloy existsTime K value and temperature relation figure；

Fig. 6 be strain rate be 0.1s^-1Time 6016H18 aluminium alloy stress match value and test value comparison diagram.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, It is fully described by, it is clear that described embodiment is a part of embodiment of the present invention rather than whole embodiment. Based on the embodiment in the present invention, those of ordinary skill in the art are obtained on the premise of not making creative work The every other embodiment obtained, all should belong to the scope of protection of the invention.

The precision of prediction of Browman this structure Optimized model obtained for the checking present invention, below by this Optimized model It is applied in the stress prediction of 6016H18 aluminium alloy.

Understood n value by formula (3) and be the slope of ln σ Yu ln (sinh ε) relation curve, select 6016H18 aluminum to close Stress test value under Jin Wu kind temperature, five kinds of strain rates, starts to produce strain hardening from stress-strain diagram Part starts to take point (σ_i,ε_i), until close to peak stress, with strain rateExamination as a example by the case of Test data point (σ_i,ε_i) as shown in Figure 1.Therefore, (ln σ can be calculated_i,ln(sinhε_i)), and it is linearly returned Returning, show that the slope of straight line is n value, the fitting a straight line between ln σ and ln (sinh ε) is plotted in Fig. 1 in the lump.

By Fig. 1 it is seen that, the two is the most linear, to the test data under other strain rate (lnσ_i,ln(sinhε_i)) carry out linear regression fit, the n value under available different temperatures, differently strained speed, knot Fruit is listed in table 1.

Table 1

Convolution (4), enters the 6016H18 aluminium alloy drawn n value under different temperatures and differently strained speed Line linearity returns, and result is plotted in Fig. 2.

By Fig. 2 it is seen that, n value is basic and strain rate be changing into linear relationship, and the most different Deviation is there is between the slope of curve drawn during strain rate group matching.Employing formula (4) represents n value and temperature Between relation, draw under different temperatures based on formula (4)The relation of curve, takes the meansigma methods of slope 0.008446 value being A, improves the precision of prediction of Browman this structure Optimized model with this.The A that will obtain Value substitutes into, with the n value in table 1, the B value can tried to achieve in formula (4) under five kinds of temperature and five kinds of strain rates respectively. Convolution (5), with strain rate as 0.1s^-1As a example by, make the relation between B value and temperature T, find B value with The change of temperature is the most linear, and it is carried out linear regression, and result is as shown in Figure 3.Equally, can obtain Under other four kinds of strain rates, B value and the linear fit equation of temperature, average to slope and intercept respectively, The approximate fits relation of B value and temperature can be drawn, be

B=-3.23 × 10^-4T+0.22351 (11)

Therefore, the A=0.008446 that try to achieve and formula (11) are substituted into formula (4), available n value and strain rate and The approximate relation of temperature, is

$n=0.008446log\stackrel{\·}{\mathrm{\ϵ}}-3.23\×{10}^{-4}T+0.22351---\left(12\right)$

In determining Browman this structure Optimized model after the relational expression of n, it is thus necessary to determine that strain rate in formula (8) Relation between Sensitivity Index m and temperature.When strain is 0.25 (uniform plastic deformation section), take 6016H18 Stress-strain tester data under five kinds of temperature of aluminium alloy, five kinds of strain rates, draw the loaarithmic curve under this strainUsing quadratic polynomial that it is fitted, i.e. can get phase by curve being asked for differential M value at a temperature of Ying, takes temperature and is 450 DEG C, as a example by strain is ess-strain rate value when 0.25, uses two It is fitted by order polynomial, and fitting result is as shown in Figure 4.

Equally, the Sensitivity Index m at a temperature of other four kinds also can be tried to achieve by said method.Between m and temperature Relation useable linear equation (8) represents, can determine that m under different temperatures and differently strained speed by linear fit Linear relation between value and temperature, for improving the precision of prediction of Browman this structure Optimized model, the most right Slope in linear fit equation and intercept averaged, to obtain the linear fit equation of m value and temperature, i.e. For

M=0.06414+1.91 × 10^-4T (13)

Set up the final step of Browman this structure Optimized model of 6016H18 aluminium alloy for determining strength factor K Value.N and m obtained by above-mentioned two steps is substituted into equationIn, available 6016H18 aluminium alloy K value under different temperatures and differently strained speed, carries out linear regression analysis to K value, WithAs a example by, result is plotted in Fig. 5.

As shown in Figure 5,6016H18 aluminium alloy existsTime K value linear with temperature, useable linear Equation approximate expression relation therebetween, uses identical method to can determine that K value and temperature under other strain rate Between the linear equation of relation, the slope in linear equation is averaged respectively with intercept, i.e. can get K value with Relational expression between temperature, i.e. has

K=136.975-0.18787T (14)

By above analytical calculation, coefficient n, m, K in Browman this structure Optimized model are finally given Expression formula, formula (12), formula (13) and formula (14) substitution formula (1) are obtained 6016H18 aluminium alloy should Browman this structure Optimized model of stress-strain, i.e. has

$\begin{array}{c}\mathrm{\σ}=(136.975-0.18787T){\[\sinh \left(\mathrm{\ϵ}\right)\]}^{0.008446log\stackrel{\·}{\mathrm{\ϵ}}-3.23\×{10}^{-4}T+0.22351}\\ {\[\sinh \left(\stackrel{\·}{\mathrm{\ϵ}}\right)\]}^{0.06414+1.91\×{10}^{-4}T}\end{array}---\left(15\right)$

It is 0.1s in conjunction with 6016H18 aluminium alloy in strain rate^-1Time stress-strain tester data, be respectively adopted Browman constitutive model and Browman this structure Optimized model are predicted, and contrast with test value, knot Fruit is as shown in Figure 6.By in Fig. 6 it is seen that, no matter at a temperature of which kind of, Browman this structure Optimized model Predictive value is all more nearly test value compared with traditional B rowman constitutive model, more can describe 6016H18 exactly The stress-strain relation of aluminium alloy.Additionally, the predictive value of two kinds of constitutive models is sent out when being 0.25 by contrast strain Existing, the average relative error of Browman constitutive model is 21.01%, and Browman this structure Optimized model is flat All relative erroies are 3.18%, and this further illustrates Browman this structure Optimized model and has higher precision of prediction. Therefore, Browman this structure Optimized model that the present invention obtains can be that research worker is in terms of aluminium alloy capability prediction The most accurate forecast model of one is provided.

The above, the only detailed description of the invention of the present invention, but protection scope of the present invention is not limited thereto, Any those familiar with the art, in the technical scope that the invention discloses, can readily occur in various equivalence Amendment or replacement, these amendment or replace all should contain within protection scope of the present invention.Therefore, the present invention Protection domain should be as the criterion with scope of the claims.

Claims (5)

1. Browman this structure Optimized model of an aluminium alloy stress-strain relation, it is characterised in that combine double Bent SIN function and aluminium alloy stress-strain relation, use and be optimized Browman constitutive model with drag

$\mathrm{\σ}=K{\left(\sinh \mathrm{\ϵ}\right)}^n{\left(\sinh \stackrel{\·}{\mathrm{\ϵ}}\right)}^m---\left(1\right)$

In formula, σ is stress, and ε is strain,For strain rate, K is strength factor, and n is that strain hardening refers to Number, m is strain-rate-sensitivity exponent；

And determine strain hardening exponent, strain-rate-sensitivity exponent and strength factor.

Browman this structure Optimized model of a kind of aluminium alloy stress-strain relation the most according to claim 1, It is characterized in that, described strain hardening exponent n determines that process is as follows:

In strain rate one timing, formula (1) is deformed into

σ=K₁(sinhε)ⁿ (2)

In formula, K₁For constant；

Are taken the logarithm in formula (2) both sides simultaneously

Ln σ=lnK₁+n ln(sinhε) (3)

Strain hardening exponent n obtains by obtaining the slope of ln σ and ln sinh (ε) relation curve；Therefore n value is passed through Formula (3) being carried out linear fit obtain, its expression formula is written as

$n=Alog\stackrel{\·}{\mathrm{\ϵ}}+B---\left(4\right)$

In formula, A is the coefficient that affects of strain rate, and B is that temperature T affects relation to n value；B useable linear relation Formula describes the relation between temperature

B=a+bT (5)

In formula, a and b is undetermined constant.

Browman this structure Optimized model of a kind of aluminium alloy stress-strain relation the most according to claim 1, It is characterized in that, described strain-rate-sensitivity exponent m determines that process is as follows:

When strain keeps constant, formula (1) can transform to

$\mathrm{\σ}=K_2{\[\sinh \left(\stackrel{\·}{\mathrm{\ϵ}}\right)\]}^m---\left(6\right)$

In formula, K₂For constant, formula (6) is taken the logarithm

$ln\mathrm{\σ}={\mathrm{lnK}}_2+m\ln \sinh \left(\stackrel{\·}{\mathrm{\ϵ}}\right)---\left(7\right)$

From formula (7), strain hardening and strain-rate sensitivity Coefficient m be curve ln σ withSlope, therefore By rightCarry out linear fit to try to achieve；M variation with temperature relational representation is

M=d₁+d₂T (8)

In formula, d₁、d₂It is undetermined constant.

Browman this structure Optimized model of a kind of aluminium alloy stress-strain relation the most according to claim 1, It is characterized in that, described strength factor K determines that process is as follows:

K value is relevant with deformation temperature, is written as

K=e₁+e₂T (10)

In formula, e₁、e₂It is undetermined constant.

5. Browman this structure Optimized model of the aluminium alloy stress-strain relation described in a claim 1 should With, it is characterised in that combine aluminium alloy stress-strain tester data, use method of least square calculate strength factor, Strain hardening exponent and strain-rate-sensitivity exponent, so that it is determined that based on Browman this structure Optimized model should Stress-strain relationship formula, is predicted aluminium alloy capability.