CN101912890A - Method for establishing constitutive relation model of material during extrusion deformation of pipe - Google Patents

Abstract

The invention discloses a method for establishing a constitutive relation model of a material during extrusion deformation of a pipe, which is characterized by comprising the following process steps: (1) preparing an extrusion blank and related auxiliary materials; (2) testing an extrusion stress-strain rate curve by using an extrusion device through extrusion experiments; (3) drawing curves shown in the description; and (4) calculating the constitutive relation model suitable for the extrusion deformation of the pipe. The method has the advantage that the established pipe extrusion molding constitutive relation model is more suitable for calculating values or determining related process parameters during extrusion molding of the pipe.

Description

A kind of method for establishing constitutive relation model of material during extrusion deformation of pipe

Technical field

The method for building up of material constitutive relational model when the invention belongs to the tubing extrusion molding goes for the constitutive relation model of different materials when the tubing extrusion molding and sets up.

Background technology

Set up accurately the materials hot deformation constitutive relation model for analysis of material deformation behaviour and forming property, it is significant to optimize the design of plastic forming process and mould.

The material constitutive relational model is that plastic history numerical simulation and mould design indispensable basic theory model, and the computational accuracy of material constitutive relational model and form directly influence result of calculation and computational speed.From document, the method for building up about the materials hot deformation constitutive relation model is according to Arrhenius type equation form at present, adopts mathematical statistic method to set up to thermal simulation experiment or hot-stretch experimental data.Deformable body during thermal simulation experiment or hot-stretch experiment is a free compression or the deformation process that freely stretches, all be to be subjected to unidirectional external force effect, and its not to be subjected on the force direction all be Free Surface, if the material constitutive relational model that adopts thermal simulation experiment or hot-stretch experimental data to set up is applied in the extrusion process used for forming, because deformation condition differences such as stress state, certainly lead to the error of calculation, and then influence simulation precision.Because the stress difference when stress during crimp and thermal simulation experiment or hot-stretch experiment is obvious, three of deformable body directions all are the compression chord effects during crimp, and the deformable body during thermal simulation experiment or hot-stretch experiment all is to be subjected to uniaxial pressure or the effect of simple tension power, and all is Free Surface on other direction.Therefore in order to set up material during extrusion deformation of pipe constitutive relation model accurately, patent of the present invention has been proposed, experimental data during promptly according to extrusion deformation of pipe, according to Arrhenius type equation form, the material constitutive relational model when adopting mathematical statistic method foundation to be suitable for extrusion deformation of pipe to experimental data.

Summary of the invention

The purpose of patent of the present invention is exactly the stress-strain speed relation during according to the tubing extrusion molding, and a kind of method of the constitutive relation model when determining to be applicable to extrusion deformation of pipe is provided.

The pressurizing unit that the present invention adopts, comprise extrusion axis, recipient, extrusion die plate, the extrusion die plate of recipient bottom is provided with Extruding die, extrusion axis is plugged in the top of recipient, and extrusion die plate is provided with extrusion billet, is respectively arranged with graphite pads and dummy block on the end face of extrusion billet, be provided with a pressure ram in the recipient, pressure ram passes extrusion billet, graphite pads and dummy block respectively, and the upper end of pressure ram is connected with extrusion axis, and the lower end of pressure ram is connected with Extruding die.

A kind of method for establishing constitutive relation model of material during extrusion deformation of pipe is characterized in that comprising following processing step: (1) prepares extrusion billet, relevant auxiliary material; (2) with pressurizing unit by record extrusion stress-strain rate curve by extrusion experiment; (3) draw

With

Curve;

(4) by calculating the constitutive relation model when being applicable to extrusion deformation of pipe.

Computational methods:

The high temperature deformation of metal is a hot activation process, and its deformation temperature, strain rate are to the available Arrhenius The Representation Equation of the influence of flow stress:

$\stackrel{\·}{\mathrm{\ϵ}}=A{\left[\sinh \left(\mathrm{\α\σ}\right)\right]}^n\exp (-\frac{Q}{\mathrm{RT}})---\left(1\right)$

Formula (1) can obtain after simplifying:

In the formula: A ₁=A α ⁿ, A ₂=A/2 ⁿ,

, strain rate (S ^-1); Q, deformation activation energy (J/mol), relevant with material; σ, unit extrusion stress (MPa); N, stress exponent; T, absolute temperature K; R, gas constant, its value is 8.314J/ (molK); A, the constant relevant with material.

Under temperature-resistant condition, Q, R, T, A all are constants, can determine n and α value according to formula (3), that is:

$n=\frac{\∂\ln \stackrel{\·}{\mathrm{\ϵ}}}{\∂\ln \mathrm{\σ}}\mathrm{and\α}=\frac{1}{n}\frac{\∂\ln \stackrel{\·}{\mathrm{\ϵ}}}{\∂\mathrm{\σ}}---\left(3\right)$

Under the condition of variations in temperature, Q changes with variation of temperature, R, and α, n, A all are constants, can obtain calculating formula (4) and the formula (5) of Q and A according to formula (2).

$Q=\mathrm{Rn}\frac{\∂\left\{\ln \right[\sinh \left(\mathrm{\α\σ}\right)\left]\right\}}{\∂(1/T)}--\left(4\right)$

$A=\stackrel{\·}{\mathrm{\ϵ}}{\left[\sinh \left(\mathrm{\α\σ}\right)\right]}^{-n}\exp \left(\frac{Q}{\mathrm{RT}}\right)---\left(5\right)$

Stress-strain speed numerical value during according to extrusion deformation of pipe can be determined n, α, and Q, the A value, the material constitutive relational model just can be set up like this.At definite n, α, Q, during the A value, the extrusion stress σ of unit in the formula (1) to (5) also can get peak stress, calculates fairly simple like this.Record peak stress σ _pValue after, draw

With

Curve, just can determine n, α, Q, the A value, thick in the substitution formula (1), the material constitutive relational model in the time of just can determining to be suitable for extrusion deformation of pipe.

The principle of patent of the present invention:

The principle of patent of the present invention is that material is in extrusion process used for forming, hot compression deformation force rule when the Changing Pattern of its extruding force is tested to the cylinder hot Compression Simulation is similar, the constitutive relation model when the stress-strain speed numerical value when therefore adopting crimp is determined to be applicable to extrusion deformation of pipe be feasible also be rational.In addition, the deformation temperature during crimp is also regulated easily, and the relation of average strain rate and extrusion speed is seen formula (7).

$\stackrel{\·}{\mathrm{\ϵ}}=\frac{G-1}{H}{\stackrel{\·}{u}}_o---\left(6\right)$

$H=\frac{(D-d)}{2}\tan (90-\mathrm{\α})---\left(7\right)$

In the formula,

, average strain rate, 1/s;

, extrusion speed, mm/s; G,, extrusion ratio; H, taper matrix height, mm; α is a die awl half-angle, degree D, extrusion billet external diameter, mm; D, extrude tubes external diameter, mm.

As long as change extrusion speed, the average strain rate in the time of just can obtaining different crimp.Therefore, according to extrusion experiment, extrusion stress in the time of just can obtaining different temperatures and differently strained speed and temperature, strain rate relation curve.According to these experimental datas, and formula (3)-(5), just can determine the n in the formula (1), α, Q, A value.Thereby, material constitutive relational model in the time of just can obtaining the tubing extrusion molding.

The advantage of patent of the present invention:

Numerical computations when the tubing extrusion molding constitutive relation model of setting up is more suitable for the tubing extrusion molding or relevant technological parameter are determined and the mould design.

Description of drawings

Fig. 1 is the structural representation of pressurizing unit of the present invention.

The specific embodiment:

Embodiment one:

The pressurizing unit that the present invention adopts, comprise extrusion axis 1, recipient 2, extrusion die plate 8, the extrusion die plate 8 of recipient 2 bottoms is provided with Extruding die 7, extrusion axis 1 is plugged in the top of recipient 2, extrusion die plate 8 is provided with extrusion billet 6, be respectively arranged with graphite pads 4 and dummy block 3 on the end face of extrusion billet 6, be provided with a pressure ram 5 in the recipient 2, pressure ram passes extrusion billet 6, graphite pads 4 and dummy block 3 respectively, the upper end of pressure ram 5 is connected with extrusion axis 1, and the lower end of pressure ram 5 is connected with Extruding die 7.

A kind of method for establishing constitutive relation model of material during extrusion deformation of pipe comprises following processing step:

(1) selected ZK60 magnesium alloy pipe is an extrusion billet.

(2) select extrusion equipment: the 1000kN forcing press.Extrusion process parameters: temperature is respectively 270 ℃, and 300 ℃, 330 ℃.Extrusion speed is respectively (mm/s) 1.00mm/s, 2.00mm/s, 4.00mm/s.Corresponding average strain rate is respectively (1/s) 1.29,2.56,5.15.

(3) numerical value of the unit's of recording extrusion stress-strain rate sees Table 1.

(4) draw

With

Curve.

(5) according to formula (3)-(5), obtain n, α, Q, the A value is respectively n=9.45, α=0.00278, Q=169388, A=4.729 * 10 ¹⁴

(6) with n, α, Q, the constitutive relation model when promptly obtaining the crimp of ZK60 magnesium alloy pipe in the A value substitution formula (1):

$\stackrel{\·}{\mathrm{\ϵ}}=4.729{\left[\sinh \left(0.00278\mathrm{\σ}\right)\right]}^{9.45}\exp \left(\frac{169388}{\mathrm{RT}}\right)---\left(8\right)$

Extrusion pressure (MPa) when table 1 records extruding

Claims (2)

1. a method for establishing constitutive relation model of material during extrusion deformation of pipe is characterized in that comprising following processing step: (1) preparation extrusion billet, relevant auxiliary material; (2) with pressurizing unit by record extrusion stress-strain rate curve by extrusion experiment; (3) draw

With

Curve; (4) by calculating the constitutive relation model when being applicable to extrusion deformation of pipe.

2. a kind of method for establishing constitutive relation model of material during extrusion deformation of pipe according to claim 1, it is characterized in that described pressurizing unit, comprise extrusion axis, recipient, extrusion die plate, the extrusion die plate of recipient bottom is provided with Extruding die, extrusion axis is plugged in the top of recipient, extrusion die plate is provided with extrusion billet, be respectively arranged with graphite pads and dummy block on the end face of extrusion billet, be provided with a pressure ram in the recipient, pressure ram passes extrusion billet respectively, graphite pads and dummy block, the upper end of pressure ram is connected with extrusion axis, and the lower end of pressure ram is connected with Extruding die.

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