CN104156590B - A kind of method for building up of Mg-based nanocomposite thixotroping Plastic Forming constitutive model - Google Patents
A kind of method for building up of Mg-based nanocomposite thixotroping Plastic Forming constitutive model Download PDFInfo
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Abstract
A kind of method for building up of Mg-based nanocomposite thixotroping Plastic Forming constitutive model, the data of gained are tested according to the thixotroping Plastic Forming of Mg-based nanocomposite first, obtain stress σ, strain stress, strain rateTemperature T, liquid fraction fL, enhancing phase nano particle volume fraction fpBetween non-linear relation, while consider that its constitutive model is expressed by following formula because nano particle can cause Orowan enhancing mechanism to influence the yield strength of composite: <mrow> <mi>σ</mi> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>+</mo> <msub> <mi>bf</mi> <mi>p</mi> </msub> <mo>+</mo> <msubsup> <mi>cf</mi> <mi>p</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mi>d</mi> <mo>/</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>·</mo> <msup> <mi>ϵ</mi> <mi>n</mi> </msup> <mo>·</mo> <msup> <mover> <mi>ϵ</mi> <mo>·</mo> </mover> <mi>m</mi> </msup> <mo>·</mo> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>βf</mi> <mi>L</mi> </msub> <mo>]</mo> </mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> </msup> <mo>·</mo> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>α</mi> <mover> <mi>ϵ</mi> <mo>·</mo> </mover> <mo>)</mo> </mrow> <mi>m</mi> </msup> <msub> <mi>f</mi> <mi>p</mi> </msub> <mo>]</mo> </mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> </msup> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mi>λf</mi> <mi>p</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>3</mn> </mrow> </msubsup> <mo>]</mo> </mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> </msup> <mo>;</mo> </mrow> With reference to thixotroping Plastic Forming experimental data, pass through the parameter being calculated in constitutive relation model.The present invention can accurately reproduce ess-strain in thixotroping plastic forming process and change, accurate material constitutive model is provided for numerical simulation, the analog result accuracy of acquisition is high, thixotroping Plastic Forming characteristic for analyzing Mg-based nanocomposite, Optimize the forming scheme technological parameter have great importance.
Description
Technical field
The invention belongs to metal-base composites molding field, and in particular to a kind of Mg-based nanocomposite thixotroping plasticity
Shape the method for building up of constitutive model.
Technical background
The constitutive relation of material refers to the mathematical modeling of material property, as newton law of viscosity, Hooke's law etc. belong to power
Constitutive relation in terms of.The constitutive relation of semi-solid-state metal thixotroping Plastic Forming, i.e., semi-solid material is in thixotroping Plastic Forming
During true stress value with the factors such as deformation temperature, liquid-solid one after another, logarithmic strain and strain rate variation relation.It
It is the important prerequisite of Semi-Solid Metals Forming numerical simulation, while exploitation to semi-solid-state metal thixotropic forming technology and should
With also there is important directive significance.
At present, conventional constitutive relation model has following two：Count constitutive relation and phenomenological constitutive relation.Count this structure
Relation is then built upon in the micromechanism of atom and molecular model description, and the microstructure for laying particular emphasis on description deformation process is drilled
Become, this model has certain limitation, because it is difficult to accurately describing the micromechanism of material；And what phenomenological constitutive relation referred to
It is that stress, strain and strain rate established with mathematical statistics method or artificial neural network etc. can macroscopical thing determined
Relation between reason amount, wherein not being related to relevant atomic and molecular structure etc. micromechanism, although this carries certain experience
Property, but it is very practical.So the practicality more relatively easy than statistical relationship of phenomenological constitutive relation, answering more conducively on Practical Project
With.
From learning for prior art report, substantial amounts of research focuses primarily upon matrix alloy in heat distortion temperature and semisolid
The research of the constitutive relation of temperature range.In the last few years, developed and a kind of prepared nano-particle reinforcement using high-energy ultrasonic and answer
The method of condensation material, because nano particle diameter is small, surface energy is high, is easy to reunite, acoustic cavitation caused by high-energy ultrasonic vibration and
Acoustic streaming effect can improve the wetting of reinforcement in the base simultaneously with scattered within the extremely short time, and to solution alloy without dirt
Dye, is a kind of ideal method for preparing metal-base nanometer composite material.But there is presently no on establishing Metal Substrate
The report of the method for nano composite material thixotroping Plastic Forming constitutive model.Due to thixotroping plastic forming process, deformation ratio is larger,
The precision of numerical simulation will be had a strong impact on using the constitutive model of inaccuracy.It is therefore proposed that a kind of Mg-based nanocomposite touches
Become the method for building up of Plastic Forming constitutive model, the development and application to thixotroping plastic forming technology has important guidance meaning
Justice.
The content of the invention
It is an object of the invention to provide a kind of method for building up of Mg-based nanocomposite thixotroping Plastic Forming constitutive model,
Reliable foundation is provided for Mg-based nanocomposite thixotropic forming numerical simulation.
The purpose of the present invention is achieved through the following technical solutions.
1) data of gained are tested according to the thixotroping Plastic Forming of Mg-based nanocomposite, stress σ, strain stress is obtained, answers
Variable RateTemperature T, liquid fraction fL, enhancing phase nano particle volume fraction fpBetween nonlinear relation：
In formula：σ is stress；ε is strain；For strain rate；T is temperature；fLFor liquid fraction；fpTo strengthen phase nano particle
Volume fraction；a,b,c,d,a1And a2For constant term；N is strain hardening exponent；M is strain-rate-sensitivity exponent；β is geometry
Parameter；α is correction factor.
2) on the basis of above-mentioned relation formula, consider to cause Orowan enhancing mechanism to surrender by force composite by nano particle
The influence of degree, therefore, Mg-based nanocomposite thixotropic forming constitutive model are expressed as：
In formula：a3For constant；fOroanStrengthen the related enhancer of mechanism for Orowan, be expressed as：
In formula：B is Bai Song vectors；
Dp is enhancing phase nano-particle diameter；
Gm is modulus of shearing；
σSFor the yield strength of matrix material；
Fp is enhancing phase nano particle volume fraction.
Formula (2) can be reduced to：
In formula：λ is material coefficient；
fpTo strengthen phase nano particle volume fraction；
dpTo strengthen nano-particle diameter.
3) it can thus be concluded that Mg-based nanocomposite thixotroping Plastic Forming constitutive model：
4) to each parametric solution in the constitutive model of gained：Wushu (4) both sides are taken the logarithm, and are carried out non-linear regression and are converted into
Linear regression processing, after in thixotroping Plastic Forming experimental data generation of the Mg-based nanocomposite under semisolid, is entered in formula, and
Its correction factor α values are constantly corrected, to causeIn m values withIn m it is consistent.
5) model is verified：Constitutive model is calculated into stress-strain curves with experiment true stress-strain curve structure to enter
Row is relatively verified.
Composite of the present invention is Mg-based nanocomposite prepared by high-energy ultrasonic method.
A kind of constitutive model for Mg-based nanocomposite thixotroping Plastic Forming that the present invention establishes can accurately reproduce
Ess-strain changes in thixotroping plastic forming process, and accurate material constitutive model, the simulation knot of acquisition are provided for numerical simulation
Fruit accuracy is high, and the thixotroping Plastic Forming characteristic for analyzing Mg-based nanocomposite, Optimize the forming scheme technological parameter has weight
Want meaning.
Brief description of the drawings
Fig. 1 be nano SiC of the present invention strengthen Mg-6Al-Zn composites test true stress-logarithmic strain curve with it is more
First nonlinear regression calculates (constitutive equation calculated curve) results contrast.
Embodiment
The present invention will be described further by following examples.
The present embodiment is to strengthen Mg-6Al-Zn composites in semisolid condition by the nano SiC for preparing ultrasonic method
Under with different strain rate (0.1S-1, 0.5S-1, 5S-1, 10S-1), temperature (535 DEG C, 545 DEG C, 555 DEG C, 565 DEG C), enhancing
Phase content (0.5wt.%, 1wt.%, 2wt.%) carries out thixotroping Plastic Forming experiment, and gained laboratory data generation is entered in formula,
And its correction factor α values are constantly corrected, to causeIn m values withIn m it is consistent.The model table
It is clear up to formula, it is easy to practical engineering application.
Strengthen the data of the thixotroping Plastic Forming experiment gained of Mg-6Al-Zn composites according to nano SiC, find stress
σ, strain stress, strain rateTemperature T, liquid fraction fL, enhancing phase nano particle volume fraction fpBetween exist it is following non-linear
Relation：
In formula：σ is stress；ε is strain；For strain rate；T is temperature；fLFor liquid fraction；fpTo strengthen phase nanometer
The volume fraction of grain；a,b,c,d,a1And a2For constant term；N is strain hardening exponent；M is strain-rate-sensitivity exponent；β is several
What parameter；α is correction factor；fpTo strengthen the volume fraction of phase SiC nano particles.
Wherein fLCalculated and obtained by Sheil formula：
In formula：TMFor the fusing point of simple metal, 650 DEG C (923K)；TLFor the liquidus temperature of alloy, 620 DEG C (893K)；K is
Equilibrium distribution coefficient, K=0.36.
The enhancing particle that the present invention uses is nano-scale particle, it is contemplated that causes Orowan to strengthen mechanism pair by nano particle
The yield strength of composite influences, and therefore, nano Mg base composite material thixotropic forming constitutive model can be expressed as：
In formula：a3For constant；fOroanStrengthen the related enhancer of mechanism for orowan.
Wherein：
In formula：B is Bai Song vectors；dpTo strengthen phase nano-particle diameter；GmFor modulus of shearing；σSFor bending for matrix material
Take intensity；fpTo strengthen phase nano particle volume fraction.
Formula (3) can be reduced to：
In formula：λ is material coefficient；fpTo strengthen phase nano particle volume fraction；dpTo strengthen phase nano-particle diameter.
Therefore, nano SiC enhancing Mg-6Al-Zn composite thixotropic forming constitutive models are deformed into：
In embodiment the volume fraction of additional nano SiC granule (average diameter 100nm) used be 0.27%,
0.54%th, 1.12% (being converted respectively by corresponding mass fraction), due to fpInherently very little, just smaller after square, institute
To neglect here, formula (5) is deformed into：
Formula (6) both sides are taken the logarithm, nonlinear regression is converted into linear regression processing, obtained：
Order：
X7=ln (1+ λ fp 1/3)A0=a, A1=b, A2=c, A3=n, A4=m, A5=a1,A6=a2,A7=a3
Therefore, the available mathematical modeling of formula (7) represents：
Y=A0+A1X1+A2X2+A3X3+A4X4+A5X5+A6X6+A7X7 (8)
In formula：α is correction factor.
Regression analysis calculates the calculating that regression coefficient and statistical testing figure are carried out using mathematical statistics software, utilizes amendment
Factor alpha is to the continuous amendment of operation result, so that X6In m values and A4In m it is consistent.By correcting repeatedly, α=58 are finally taken.Cause
This, the constitutive relation of acquisition is as follows：
Y=-5.768+14.158X1+3674.674X2-0.353X3+0.245X4+6.076X5-1.663X6+17.834X7 (9)
Formula (7) and (8) are reversely derived, and substitutes into formula (9) and produces nano SiC enhancing Mg-6Al-Zn composite woods
Expect thixotroping Plastic Forming constitutive equation：
Model is verified：It is compound that Mg-6Al-Zn is strengthened to the nano SiC that the mass fractions of SiC containing nanometer silicon carbide are 1wt.%
The true stress and strain curve and constitutive equation calculated curve Comparative result of material thixotroping Plastic Forming experiment, such as specification Fig. 1
Shown, its strain rate is 0.1S-1, strain temperature is 535 DEG C.It was found that result of calculation is coincide well with experimental result, it is believed that
The constitutive equation model that the present invention is established has higher precision of prediction and practical significance.
Claims (1)
- A kind of 1. method for building up of Mg-based nanocomposite thixotroping Plastic Forming constitutive model, it is characterized in that according to the following steps：1) data of gained are tested according to the thixotroping Plastic Forming of Mg-based nanocomposite, obtain stress σ, strain stress, judgement of speed change Rate temperature T, liquid fraction fL, enhancing phase nano particle volume fraction fpBetween nonlinear relation：In formula：σ is stress；ε is strain；For strain rate；T is temperature；fLFor liquid fraction；fpTo strengthen the body of phase nano particle Fraction；A, b, c, d, a1And a2For constant term；N is strain hardening exponent；M is strain-rate-sensitivity exponent；β is geometric parameter； α is correction factor；2) on the basis of above-mentioned relation formula, consider to cause Orowan to strengthen mechanism to composite yield strength by nano particle Influence, therefore, Mg-based nanocomposite thixotropic forming constitutive model is expressed as：In formula：A3 is constant；fOrowanStrengthen the related enhancer of mechanism for Orowan, be expressed as：In formula：B is Bai Song vectors；Dp is enhancing phase nano-particle diameter；Gm is modulus of shearing；σSIt is strong for the surrender of matrix material Degree；Fp is enhancing phase nano particle volume fraction；Formula (2) can be reduced to：In formula：λ is material coefficient；Fp is enhancing phase nano particle volume fraction；Dp is enhancing nano-particle diameter；3) it can thus be concluded that Mg-based nanocomposite thixotroping Plastic Forming constitutive model：4) formula (4) both sides are taken the logarithm, carries out non-linear regression and be converted into linear regression processing, Mg-based nanocomposite is existed After thixotroping Plastic Forming experimental data generation under semisolid enters in formula, and its correction factor α values are constantly corrected, to causeIn m values withIn m it is consistent；Model is verified：Constitutive model calculating load-deformation curve is tested compared with testing true stress and strain curve structure Card.
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Non-Patent Citations (4)
| Title |
|---|
| "Consideration of Orowan strengthening effect in particulate-reinforced metal matrix nanocomposites:A model for predicting their yield strength";Z.Zhang et al;《Scripta Materialia》;20060118;第54卷(第7期);摘要，第2.3节 * |
| "SiC_p/AZ61复合材料触变塑性成形本构关系及数值模拟研究";王建金;《中国优秀硕士学位论文全文数据库-工程科技I辑》;20081115;第2008年卷(第11期);摘要，第1.2节,第4.4.1-4.4.3节 * |
| "纳米SiC颗粒增强2024铝基复合材料的力学性能研究";田晓风 等;《稀有金属》;20050831;第29卷(第4期);第2.3节 * |
| "纳米颗粒分布对镁基复合材料强化机制的影响";何广进 等;《复合材料学报》;20130430;第30卷(第2期);105-110 * |
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