CN107413870A - One kind simulation magnesium alloy equal channel angular pressing technology optimization method - Google Patents

One kind simulation magnesium alloy equal channel angular pressing technology optimization method Download PDF

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CN107413870A
CN107413870A CN201710716740.9A CN201710716740A CN107413870A CN 107413870 A CN107413870 A CN 107413870A CN 201710716740 A CN201710716740 A CN 201710716740A CN 107413870 A CN107413870 A CN 107413870A
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mrow
msub
msup
mfrac
particle
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CN107413870B (en
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牛晓峰
许春香
王晨晨
王涵
王宝健
宋振亮
阎佩雯
梁伟
陈福振
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KANG MEI TECHNOLOGY DEVELOPMENT CO., LTD.
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Taiyuan University of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21C—MANUFACTURE OF METAL SHEETS, WIRE, RODS, TUBES OR PROFILES, OTHERWISE THAN BY ROLLING; AUXILIARY OPERATIONS USED IN CONNECTION WITH METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL
    • B21C23/00—Extruding metal; Impact extrusion
    • B21C23/001—Extruding metal; Impact extrusion to improve the material properties, e.g. lateral extrusion
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

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Abstract

The present invention relates to one kind to simulate magnesium alloy equal channel angular pressing technology optimization method, it is the numerical simulation study carried out for magnesium alloy compressional deformation, the crack initiation and propagation in magnesium alloy equal channel angular pressing can effectively be simulated, caused crackle in magnesium alloy equal channel angular pressing can preferably be predicted, demonstrate the correctness for building the calculation procedure prediction Equal Channel Angular Pressing crack initiation and propagation containing damage forecast, the method can be predicted to fracture of the metal material in equal channel angular pressing, and theoretical foundation is provided for process optimization.

Description

One kind simulation magnesium alloy equal channel angular pressing technology optimization method
Technical field
The present invention relates to one kind to simulate magnesium alloy equal channel angular pressing technology optimization method, and it is excellent to belong to magnesium alloy Equal Channel Angular Pressing Chemical industry skill and the technical field of application.
Background technology
Equal Channel Angular Pressing is to produce intense plastic strain by the mould of two equal cross-sectional passages and do not change rapidoprint A kind of technique of cross-sectional geometry, crimp repeatedly can be carried out to reach best fine grain effect, to improve deformation The mechanical property of material.
Deformation workpiece is easily broken in equal channel angular pressing, based on Smoothed Particle Hydrodynamics Method, obtains workpiece at isometrical angle The regularity of distribution of stress, strain and damage in extrusion process, the fracture for deforming workpiece is predicted, because its mesh free is special Property can avoid FInite Element that mesh distortion problem occurs during material plasticity deformation simulative, excellent with channel angular angular pressing technology Change and theoretical foundation is provided, this technology is also in scientific research.
The content of the invention
Goal of the invention
The purpose of the present invention is the characteristics of being directed to Equal Channel Angular Pressing, and answering in equal channel angular pressing is calculated by simulating Power, strain and damage, the fracture to magnesium alloy miter angle extruding deforming process are predicted, and are that equal channel angular pressing technique is excellent Change and theoretical foundation is provided.
Technical scheme
The present invention is to plastic deformation and the method for damage development emulation based on Smoothed Particle Hydrodynamics Method, is equal channel angular pressing Process optimization provides theoretical foundation, comprises the following steps that：
(1) mould and extruding test specimen are prepared
1. prepare ECAP Die
ECAP Die makes of chrome-molybdenum steel；The vertical die cavity of mold cavity point, horizontal die cavity, vertical die cavity and horizontal die cavity Between angle be 90 °；
Vertical die cavity and horizontal die cavity are rectangle mold cavity, vertical cavity dimension and horizontal cavity dimension be the ㎜ of 10 ㎜ × 10 × 87 ㎜, mold cavity surface roughness are Ra0.08-0.16 μm；
2. prepare Equal Channel Angular Pressing test specimen
Equal Channel Angular Pressing material for test is magnesium alloy, and size is the ㎜ of the ㎜ of 8 ㎜ × 8 × 66.5；
(2) forecast model is built
1. foundation and the particlized of three-dimensional entity model
3D solid is established with modeling software；By mould, test specimen and the discrete initial bit for being particle, determining particle of pressure ram Put；Mould particle is solid wall boundary particle, and pressure ram particle is moving boundary particle, and border is handled using force method is repelled；
2. the setting of basic parameter
Extrusion speed is 0.005 meter per second, and time step Δ t is 0.000001 second, and smooth length h is 0.000375 meter；
3. particle search simultaneously matches
Any particle i and other all particles distance are calculated, if particle i and particle j distance is less than or equal to 2 times During smooth length, then it is assumed that particle j is in particle i support region, it is believed that particle j has an impact to particle i, travels through in addition to particle i All particles after complete pairing；
4. the accumulating injuring value and yield strength of calculation testing piece particle
1) pressure is calculated
In formula, P represents pressure value, and ρ represents density, ρ0Value 1780kg/m3, c0The meter per second of value 4300,It is calculated as follows It is shown：
WhereinFor the rate of change of the density of i particles,For summation of the j particles to i particle influences, m in support regionj For the quality of j particles, vijFor i particles and the speed difference of j particles, alpha, β, γ denotation coordination direction, with index method table Show the superposition of equation, WijFor smooth function,For smooth function gradient；
2) total stresstensor and acceleration are calculated
σαβ=-P δαβ+ταβ Ⅲ
σ is total stresstensor, and P is pressure, and τ is deviatoric stress；δ represents Dirac function, and when α is identical with β values, δ is 1, on the contrary δ is 0；
Wherein pressure P is tried to achieve by formula I,For deviatoric stress rate, deviatoric stress adds deviatoric stress rate and time step equal to deviatoric stress Product, deviatoric stress rateIt can be tried to achieve by following formula：
In formula：G is modulus of shearing；ε is strain rate tensor, strain rate tensor calculation expression such as following table：
In formula：ρjRepresent particle j density；Total stresstensor can obtain by formula I-V, and then calculate the acceleration of particle, It is as follows：
For the acceleration of i particles, mjFor the quality of j particles, σiWith σjThe respectively total stress of i particles and j particles Amount,WithRespectively square of i particles and j particle densities, WijFor smooth function,For smooth function gradient；
3) accumulating injuring value and yield strength are calculated
Shown in the yield strength Y of material is calculated as follows：
In formula, Y is yield strength, DsFor accumulating injuring value,For equivalent plastic strain rate, εpFor equivalent plastic strain value, Equivalent plastic strain value is equal to the product that equivalent plastic strain value adds equivalent plastic strain rate and time step,Should for reference Variability, it is set to 1 meter per second；A is initial yield stress, and B is metal material strain hardening parameter, and C represents metal material strain rate effect The coefficient answered, m is material thermal softening coefficient, for magnesium alloy, A 172MPa, B 360MPa, n 0.456, C 0.092, m For 0.95；T*Calculation expression it is as follows：
T in formulaiRepresent the temperature of i particles, TmFor the fusing point of magnesium alloy, room temperature TrFor 25 DEG C；
Equivalent plastic strain rateExpression formula it is as follows：
In formula, x denotation coordination x directions, y denotation coordination y directions, z denotation coordination z directions；ε is strain rate tensor；
DsFor accumulating injuring value, if damage threshold DscFor 1, work as DsMore than DscWhen, it is broken, accumulating injuring value is equal to tired Product impairment value and damage increment and；IfFor damage increment,Shown in being calculated as follows：
In formula, εdIf value is 0.000001, εfExpression formula is：
In formula, impairment parameter D1、D2And D3The stress hardening of material, D are described4The strain rate effect of material, D are described5Description Material thermal softening；For magnesium alloy, D1For 0.0205, D2For -1.782, D3For -0.421, D4For 0.012, D5For 0.0,For 1 Meter per second；η is pressure P and equivalent stress σeqRatio, equivalent stress σeqCalculation expression it is as follows：
4) judge whether particle accumulation impairment value reaches threshold value
If the D of particlesMore than or equal to Dsc, then it is assumed that it is broken at the particle；Conversely, deviatoric stress is modified, Its innovation representation is as follows：
In formula, Y is yield strength, and τ is deviatoric stress, σeqFor equivalent stress；
5. time integral
One time step terminates rear, it is necessary to be updated to the density, speed and position of particle；Wherein particle is next The density that the density that the density at moment is equal to current time is obtained plus II formula changes with time the product of rate and time step； The acceleration and the product of time step that particle obtains in the speed of subsequent time equal to the speed at current time plus VI formula；By The position at current time, the speed at current time, acceleration and time step try to achieve the position of subsequent time；
Programming is carried out by development platform of VC++, calculation procedure is as follows：
(3) analog result
Simulation calculates stress, strain and the damage in equal channel angular pressing, the results showed that, in equal channel angular pressing In, surface of test piece crack initiation at mould inside lock, and be along cutting the reason for extended along shear surface, cause this result The Large strain of section is concentrated；
(4) Equal Channel Angular Pressing
Parameter is input on numerical control extruder, numerical control extruder carries out Equal Channel Angular Pressing according to instruction, is obtained after extruding There is the cracking of sheet in the upper surface of test specimen, and is extended along shear surface, and experimental result is consistent with analog result；
Conclusion：In equal channel angular pressing, test specimen upper surface crack initiation at mould inside lock, and along shearing Face extends, and the reason for causing this result is the Large strain concentration along shear surface, and analog result is consistent with experimental result, by right The fracture of magnesium alloy miter angle extruding deforming process is predicted, and theoretical foundation is provided for process optimization.
Beneficial effect
The present invention is the numerical simulation study to magnesium alloy Equal Channel Angular Pressing damage development, can effectively simulate magnesium alloy and exist Crack initiation and propagation in equal channel angular pressing, by being contrasted with experimental result, demonstrate this patent and build containing damage The correctness of the calculation procedure prediction Equal Channel Angular Pressing crack initiation and propagation of prediction；The method can also exist to other metal materials Fracture in equal channel angular pressing is predicted, and theoretical foundation is provided for process optimization.
Brief description of the drawings
Fig. 1, magnesium alloy Equal Channel Angular Pressing state diagram
Fig. 2, magnesium alloy Equal Channel Angular Pressing simulation result and experimental result comparison diagram
Shown in figure, list of numerals is as follows：
1st, ECAP Die, 2, perpendicular passage, 3, transverse passage-way, 4, discharging opening, 5, mould vertical position, 6, mould it is parallel Position, 7, magnesium alloy test specimen, 8, pressure ram, 9, contiguous block.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described：
Shown in Fig. 1, magnesium alloy Equal Channel Angular Pressing state diagram, each portion position, annexation correctly will be operated sequentially.
ECAP Die 1 is L-shaped, is made up of vertical position 5 with parallel position 6, vertical position 5 and parallel position 6 Between angle be 90 °；It is made up of, erects between passage 2 and transverse passage-way 3 perpendicular passage 2, transverse passage-way 3 inside ECAP Die 1 Angle also be 90 °；Magnesium alloy test specimen 7 is put in perpendicular passage 2, is fastened on the top of magnesium alloy test specimen 7 by pressure ram 8, is extruded The top of bar 8 is provided with contiguous block 9, contiguous block 9 and the pressure motor connection on extruder top；The right part of transverse passage-way 3 is discharging opening 4.
It is analog result and experimental result comparison diagram after Equal Channel Angular Pressing, wherein (a) figure is analog result shown in Fig. 2 Figure, (b) figure is experimental result picture, and the cracking of sheet occurs in the upper surface of (a) figure magnesium alloy test specimen, and expands along shear surface Exhibition, analog result are consistent with experimental result.

Claims (2)

1. one kind simulation magnesium alloy equal channel angular pressing technology optimization method, it is characterised in that：It is to plasticity based on Smoothed Particle Hydrodynamics Method Deformation and the emulation mode of damage development, applied to the process optimization of magnesium alloy equal channel angular pressing, are comprised the following steps that：
(1) mould and extruding test specimen are prepared
1. prepare ECAP Die
ECAP Die makes of chrome-molybdenum steel；The vertical die cavity of mold cavity point, horizontal die cavity, between vertical die cavity and horizontal die cavity Angle is 90 °；
Vertical die cavity and horizontal die cavity are rectangle mold cavity, and vertical cavity dimension and horizontal cavity dimension are ㎜ × 87 of 10 ㎜ × 10 ㎜, mold cavity surface roughness are Ra0.08-0.16 μm；
2. prepare Equal Channel Angular Pressing test specimen
Equal Channel Angular Pressing material for test is magnesium alloy, and size is the ㎜ of the ㎜ of 8 ㎜ × 8 × 66.5；
(2) forecast model is built
1. foundation and the particlized of three-dimensional entity model
3D solid is established with modeling software；By mould, test specimen and the discrete initial position for being particle, determining particle of pressure ram； Mould particle is solid wall boundary particle, and pressure ram particle is moving boundary particle, and border is handled using force method is repelled；
2. the setting of basic parameter
Extrusion speed is 0.005 meter per second, and time step Δ t is 0.000001 second, and smooth length h is 0.000375 meter；
3. particle search simultaneously matches
Any particle i and other all particles distance are calculated, if particle i and particle j distance is smooth less than or equal to 2 times During length, then it is assumed that particle j is in particle i support region, it is believed that particle j has an impact to particle i, travels through the institute in addition to particle i Pairing is completed after having particle；
4. the accumulating injuring value and yield strength of calculation testing piece particle
1) pressure is calculated
<mrow> <mi>P</mi> <mo>=</mo> <msubsup> <mi>c</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>-</mo> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>I</mi> </mrow>
In formula, P represents pressure value, and ρ represents density, ρ0Value 1780kg/m3, c0The meter per second of value 4300,It is calculated as follows institute Show：
<mrow> <mfrac> <mrow> <msub> <mi>d&amp;rho;</mi> <mi>i</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>&amp;beta;</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&amp;beta;</mi> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>I</mi> <mi>I</mi> </mrow>
WhereinFor the rate of change of the density of i particles,For summation of the j particles to i particle influences, m in support regionjFor j grains The quality of son, vijFor i particles and the speed difference of j particles, alpha, β, γ denotation coordination direction, equation is represented with index method Superposition, WijFor smooth function,For smooth function gradient；
2) total stresstensor and acceleration are calculated
σαβ=-P δαβ+ταβ Ⅲ
σ is total stresstensor, and P is pressure, and τ is deviatoric stress；δ represents Dirac function, when α is identical with β values, δ 1, instead δ be 0；
Wherein pressure P is tried to achieve by formula I,For deviatoric stress rate, deviatoric stress is equal to deviatoric stress multiplying plus deviatoric stress rate and time step Product, deviatoric stress rateIt can be tried to achieve by following formula：
<mrow> <msup> <mover> <mi>&amp;tau;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msup> <mo>=</mo> <mi>G</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msup> <mo>-</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <msup> <mi>&amp;delta;</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msup> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>&amp;gamma;</mi> <mi>&amp;gamma;</mi> </mrow> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>I</mi> <mi>V</mi> </mrow>
In formula：G is modulus of shearing；ε is strain rate tensor, strain rate tensor calculation expression such as following table：
<mrow> <msubsup> <mi>&amp;epsiv;</mi> <mi>i</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <mfrac> <msub> <mi>m</mi> <mi>j</mi> </msub> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>&amp;alpha;</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&amp;beta;</mi> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>m</mi> <mi>j</mi> </msub> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>&amp;beta;</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&amp;alpha;</mi> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>V</mi> </mrow>
In formula：ρjRepresent particle j density；Total stresstensor can obtain by formula I-V, and then calculate the acceleration of particle, it is as follows It is shown：
<mrow> <mfrac> <mrow> <msubsup> <mi>dv</mi> <mi>i</mi> <mi>&amp;alpha;</mi> </msubsup> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msubsup> <msubsup> <mi>&amp;rho;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>j</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msubsup> <msubsup> <mi>&amp;rho;</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&amp;beta;</mi> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>V</mi> <mi>I</mi> </mrow>
For the acceleration of i particles, mjFor the quality of j particles, σiWith σjThe respectively total stresstensor of i particles and j particles, WithRespectively square of i particles and j particle densities, WijFor smooth function,For smooth function gradient；
3) accumulating injuring value and yield strength are calculated
Shown in the yield strength Y of material is calculated as follows：
<mrow> <mi>Y</mi> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mo>&amp;lsqb;</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>&amp;epsiv;</mi> <mi>p</mi> <mi>n</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>&amp;times;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>+</mo> <mi>C</mi> <mi>ln</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> </mrow> <mo>)</mo> <mfrac> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>p</mi> </msub> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>T</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mi>m</mi> </msup> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>V</mi> <mi>I</mi> <mi>I</mi> </mrow>
In formula, Y is yield strength, DsFor accumulating injuring value,For equivalent plastic strain rate, εpIt is equivalent for equivalent plastic strain value Plastic strain value is equal to the product that equivalent plastic strain value adds equivalent plastic strain rate and time step,For with reference to strain Rate, it is set to 1 meter per second；A is initial yield stress, and B is metal material strain hardening parameter, and C represents metal material strain rate effect Coefficient, m is material thermal softening coefficient, and for magnesium alloy, A 172MPa, B 360MPa, n 0.456, C 0.092, m are 0.95；T*Calculation expression it is as follows：
<mrow> <msup> <mi>T</mi> <mo>*</mo> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&lt;</mo> <msub> <mi>T</mi> <mi>m</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;GreaterEqual;</mo> <msub> <mi>T</mi> <mi>m</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>V</mi> <mi>I</mi> <mi>I</mi> <mi>I</mi> </mrow>
T in formulaiRepresent the temperature of i particles, TmFor the fusing point of magnesium alloy, room temperature TrFor 25 DEG C；
Equivalent plastic strain rateExpression formula it is as follows：
<mrow> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>p</mi> </msub> <mo>=</mo> <msqrt> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;epsiv;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>I</mi> <mi>X</mi> </mrow>
In formula, x denotation coordination x directions, y denotation coordination y directions, z denotation coordination z directions；ε is strain rate tensor；
DsFor accumulating injuring value, if damage threshold DscFor 1, work as DsMore than DscWhen, it is broken, accumulating injuring value, which is equal to accumulation, to be damaged Wound value and damage increment and；IfFor damage increment,Shown in being calculated as follows：
<mrow> <msub> <mover> <mi>D</mi> <mo>&amp;OverBar;</mo> </mover> <mi>s</mi> </msub> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>p</mi> </msub> <mrow> <msub> <mi>&amp;epsiv;</mi> <mi>f</mi> </msub> <mo>-</mo> <msub> <mi>&amp;epsiv;</mi> <mi>d</mi> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;epsiv;</mi> <mi>p</mi> </msub> <mo>&gt;</mo> <msub> <mi>&amp;epsiv;</mi> <mi>d</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;epsiv;</mi> <mi>p</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>&amp;epsiv;</mi> <mi>d</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>X</mi> </mrow> </mrow> </mrow>
In formula, εdIf value is 0.000001, εfExpression formula is：
<mrow> <msub> <mi>&amp;epsiv;</mi> <mi>f</mi> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>D</mi> <mn>2</mn> </msub> <msup> <mi>e</mi> <mrow> <msub> <mi>D</mi> <mn>3</mn> </msub> <mi>&amp;eta;</mi> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>D</mi> <mn>4</mn> </msub> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>p</mi> </msub> <msub> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>D</mi> <mn>5</mn> </msub> <msup> <mi>T</mi> <mo>*</mo> </msup> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>X</mi> <mi>I</mi> </mrow>
In formula, impairment parameter D1、D2And D3The stress hardening of material, D are described4The strain rate effect of material, D are described5Material is described Thermal softening；For magnesium alloy, D1For 0.0205, D2For -1.782, D3For -0.421, D4For 0.012, D5For 0.0,For 1 meter/ Second；η is pressure P and equivalent stress σeqRatio, equivalent stress σeqCalculation expression it is as follows：
<mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>&amp;tau;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>X</mi> <mi>I</mi> <mi>I</mi> </mrow>
4) judge whether particle accumulation impairment value reaches threshold value
If the D of particlesMore than or equal to Dsc, then it is assumed that it is broken at the particle；Conversely, being modified to deviatoric stress, it is repaiied Positive expression formula is as follows：
<mrow> <msup> <mi>&amp;tau;</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>&amp;tau;</mi> <mrow> <mi>&amp;alpha;</mi> <mi>&amp;beta;</mi> </mrow> </msup> <mfrac> <mi>Y</mi> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mi>X</mi> <mi>I</mi> <mi>I</mi> <mi>I</mi> </mrow>
In formula, Y is yield strength, and τ is deviatoric stress, σeqFor equivalent stress；
5. time integral
One time step terminates rear, it is necessary to be updated to the density, speed and position of particle；Wherein particle is in subsequent time Density be equal to the density that the density at current time is obtained plus II formula and change with time the product of rate and time step；Particle The acceleration and the product of time step obtained in the speed of subsequent time equal to the speed at current time plus VI formula；By current The position at moment, the speed at current time, acceleration and time step try to achieve the position of subsequent time；
Programming is carried out by development platform of VC++；
(3) analog result
Simulation calculates stress, strain and the damage in equal channel angular pressing, the results showed that, in equal channel angular pressing, Surface of test piece crack initiation at mould inside lock, and be along shearing the reason for extended along shear surface, cause this result The Large strain in face is concentrated；
(4) Equal Channel Angular Pressing
Parameter is input on numerical control extruder, numerical control extruder carries out Equal Channel Angular Pressing according to instruction, and test specimen is obtained after extruding Upper surface there is the cracking of sheet, and extended along shear surface, experimental result is consistent with analog result；
Conclusion：In equal channel angular pressing, test specimen upper surface crack initiation at mould inside lock, and expand along shear surface The reason for opening up, causing this result is the Large strain concentration along shear surface, and experimental result is consistent with analog result, by being closed to magnesium The fracture of golden miter angle extruding deforming process is predicted, and theoretical foundation is provided for process optimization.
A kind of 2. simulation magnesium alloy equal channel angular pressing technology optimization method according to claim 1, it is characterised in that：
Described ECAP Die (1) is L-shaped, is made up of vertical position (5) with parallel position (6), vertical position (5) with Angle between parallel position (6) is 90 °；ECAP Die (1) is internal to be made up of perpendicular passage (2), transverse passage-way (3), is erected Angle between passage (2) and transverse passage-way (3) is also 90 °；Magnesium alloy test specimen (7) is put in perpendicular passage (2), is tried in magnesium alloy Part (7) top is fastened by pressure ram (8), and pressure ram (8) top is provided with contiguous block (9), contiguous block (9) and the pressure on extruder top Force motor connects；Transverse passage-way (3) right part is discharging opening (4).
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