简介概要

Constitutive equation and hot processing maps of Al-5Ti-1B master alloy

来源期刊：Rare Metals2018年第8期

论文作者：Fu-Wei Kang Jie Zhou Zhi-Wei Wang Xue-Min Zhang Yi-Cheng Feng Er-Jun Guo

文章页码：668 - 674

摘要：The isothermal compression tests of Al-5 Ti-1 B master alloy were conducted on the thermal mechanical simulator Gleeble-1500 D at the deformation temperature range of 300-450 ℃,the strain rate range of 0.01-10.00 s^-1,and the engineering strain of 50 %.The effects of deformation temperatures and strain rates on the flow stress were analyzed by the true stress-true strain curves.The result indicates that the flow stress increases with the increase of strain rate,while it decreases with the increase of temperature.The hot deformation activation energy of Al-5 Ti-1 B master alloy is calculated to be250.9 kJ·mol^-1,and the constitutive equation is established as ε= 1.97×10¹⁹[sinh（0.015σ）]^11.14exp（-250.9/RT）,and the validity of this constitutive equation is verified.Based on dynamic material model（DMM） criterion,the hot processing map of Al-5 Ti-1 B master alloy is obtained.The optimum hot extrusion conditions are determined as deformation temperature of 400 ℃ and strain rate of1.00 s^-1,and the flow instability only appears at the temperature range of 300-340 ℃ at the base of the hot processing map.

稀有金属(英文版) 2018,37(08),668-674

Constitutive equation and hot processing maps of Al-5Ti-1B master alloy

Fu-Wei Kang Jie Zhou Zhi-Wei Wang Xue-Min Zhang Yi-Cheng Feng Er-Jun Guo

School of Materials Science and Engineering,Harbin University of Science and Technology

Harbin Dong An Engine Group Corporation Ltd.,Aviation Industry Corporation of China

作者简介：*Fu-Wei Kang e-mail:fuwei_kang@163.com;

收稿日期：5 December 2013

基金：financially supported by the Natural Science Foundation of Heilongjiang Province(No.E201107);

Constitutive equation and hot processing maps of Al-5Ti-1B master alloy

Fu-Wei Kang Jie Zhou Zhi-Wei Wang Xue-Min Zhang Yi-Cheng Feng Er-Jun Guo

School of Materials Science and Engineering,Harbin University of Science and Technology

Harbin Dong An Engine Group Corporation Ltd.,Aviation Industry Corporation of China

Abstract：

The isothermal compression tests of Al-5 Ti-1 B master alloy were conducted on the thermal mechanical simulator Gleeble-1500 D at the deformation temperature range of 300-450 ℃,the strain rate range of 0.01-10.00 s^-1,and the engineering strain of 50 %.The effects of deformation temperatures and strain rates on the flow stress were analyzed by the true stress-true strain curves.The result indicates that the flow stress increases with the increase of strain rate,while it decreases with the increase of temperature.The hot deformation activation energy of Al-5 Ti-1 B master alloy is calculated to be250.9 kJ·mol^-1,and the constitutive equation is established as ε= 1.97×10¹⁹[sinh(0.015σ)]^11.14exp(-250.9/RT),and the validity of this constitutive equation is verified.Based on dynamic material model(DMM) criterion,the hot processing map of Al-5 Ti-1 B master alloy is obtained.The optimum hot extrusion conditions are determined as deformation temperature of 400 ℃ and strain rate of1.00 s^-1,and the flow instability only appears at the temperature range of 300-340 ℃ at the base of the hot processing map.

Keyword：

Al-5Ti-1B master alloy; Flow stress; Constitutive equation; Hot processing map;

Received： 5 December 2013

1 Introduction

It is well known that the size of aluminum alloy grains depends on the state of the melt before casting.It is now a common practice to add grain refiners to molten Al before casting to produce fine-grained structure in the solidified ingots or cast products.There are many benefits from the use of grain refiners in aluminum alloy castings,including improving mechanical properties,reducing susceptibility of hot cracking and porosity,increasing fluidity and homogeneity,and improving surface finishing for alloys used in rolled or extruded form ^[1,2,3,4] .In the grain refinements of aluminum alloys,commercial ternary AlTi-B master alloys are widely used to refine some aluminum and aluminum alloys because of their good grain-refining performance.Usually,to improve the refining efficiency,AlTi-B master alloys are extruded to rods with diameter of9.5 mm,and fed into molten Al.However,there are few systematic data on deformation behavior of Al-Ti-B alloy over the ranges of temperature and strain rate encountered during hot working,often leading to surface cracks,or even fracture for the rod.

The objective of this paper is to optimize the hot extrusion parameters by conducting isothermal compression tests,analyzing flow stresses,and establishing the constitutive equation and hot processing map of Al-5Ti-1B master alloy.

2 Experimental

2.1 Materials

Al-5Ti-lB master alloys were prepared in induction furnace with the addition of inorganic salts—K₂TiF₆ and KBF₄ to molten aluminum.The dimensions of indigenous Al-5Ti-1B master alloy ingot were 60 mm in diameter and200 mm in height,and the chemical compositions of the ingot are shown in Table 1.It can be seen that the proportion of Ti and B elements is almost 5:1.

2.2 Hot compression test

Cylindrical specimens with diameter of 8 mm and height of 12 mm were machined from the ingot.The isothermal compression tests were performed on the thermal mechanical simulator (Gleeble-1500D) at temperatures of300,350,400,and 450℃,strain rates of 0.01,0.10,1.00,and 10.00 s^-1,and engineering strain of 50%.Graphite foils were pasted as the lubricant at both surfaces of specimens in order to reduce the frictional force between specimens and the compression dies.Thermocouples were welded on the surface of compression specimens to measure temperature.The specimens were preheated at different deformation temperatures at heating rate of10℃·s^-1,then soaked for 2 min,and finally,deformed up to total strain of 0.5.After the compression process,compressed specimens should be put instantly into water for quenching.

2.3 Hot extrusion test

The hot extrusion tests were performed on extruding machine at deformation temperature of 400℃and strain rate of 1.00 s^-1.This optimal hot extrusion condition was determined on the basis of the hot processing map.The Al-5Ti-1B master alloy cast ingots were extruded to rods with diameter of 9.5 mm.

Post-extruded specimens were sectioned parallel to the extrusion axis and prepared for metallographic examination,and the metallographic examination was carried out on Olympus GX71-6230A optical microscope (OM).

3 Results and discussion

3.1 True stress-true strain curves

Typical true stress-true strain curves of Al-5Ti-1B alloy obtained during hot compression at various deformation conditions are shown in Fig.1.It can be seen that the flow stress increases with the decrease of deformation temperature and the increase of strain rate.This demonstrates that Al-5Ti-1B alloy is not only the temperature-sensitive material but also the strain rate-sensitive material.In the initial deformation stage,the flow stress rises sharply because of the work hardening,until a peak stress appears at a certain strain,and then the work hardening and the dynamic softening begin to reach a balance,and the flow stress remains constant or decreases tardily with the strain increasing.However,at high strain rate (10.00 s^-1),the curves exhibit continuous oscillation,and this phenomenon can be illustrated in terms of dynamic recrystallization or flow instability [ 5, 6, 7] .

下载原图

Table 1 Chemical compositions of Al-5Ti-1B master alloy (wt%)

3.2 Constitutive equation

As an important model of plastic processing,constitutive equation is universally used to relate the dynamic response of flow stress to thermodynamic parameters,such as deformation temperature,strain rate,and true strain [ 8] .In general,the Arrhenius-type equations are used to describe the relationship between flow stress,strain rate,and temperature.There are three forms of mathematical expression as follows [ 9, 10, 11] :

whereσis the flow stress which is often taken as the peak flow stress (MPa),εis the strain rate (s^-1),T is the absolute temperature (K),Q is the deformation activation energy(kJ·mol^-1),R is the ideal gas constant (kJ-mol^-1·K^-1),and A₁,A₂,A₃,n₁,n,andβare all constants independent of temperature,α=β/n₁.Expression forms of Eqs.(1)-(3)are known as the exponential equation,power function equations,and hyperbolic sine equation,which are usually,respectively,suitable for higher flow stress,lower flow stress,and both the cases in the hot deformation process.

Supposing that Q is a constant at a given temperature,taking natural logarithms of Eqs.(1)-(3),they can be described as follows:

According to the experimental data,a linear relationship between and lnσwith a linear slope n₁ is shown in Fig.2,and a linear relationship between andσwith a linear slopeβis shown in Fig.3.The average values of n₁andβare calculated asβ=0.226,n₁=14.62,andα=β/n₁=0.015.

Fig.1 True stress-strain curves of Al-5Ti-1B master alloy at various strain rates and deformation temperatures:a 0.01 s^-1,b 10.00 s^-1,c 350℃,and d 400℃

Fig.2 Relationships between

and lnσ

Numerous experimental results indicate that Eq.(3) can describe metal’s routine hot deformation process very well [ 9] .Besides,the Zener-Hollomon parameter (Z) can be used to describe and model the interaction between temperature and strain rate during the hot deformation of materials: [ 12, 13] :

When the strain rate is constant,the value of activation energy (Q) will remain invariant at a certain temperature range.Based on Eq.(7),the relationship between stress and temperature can be expressed as follows:

A linear relationship between and lnsinh(ασ) is shown in Fig.4 and a linear relationship between lnsinh(ασ) and 10³T^-1 is shown in Fig.5.

The deformation activation energy could be calculated based on the following equation:

Fig.3 Relationships between

andσ

Fig.4 Relationships between

and lnsinh (ασ)

where and stand for theslopes of straight line (namely n) and lnsinh(ασ)-10³T^-1 straight line.The average slope values are calculated to be 11.14 and 15.27,respectively,and A can be derived to be 1.97×10¹⁹.Meanwhile,activation energy (Q) can be calculated to be 250.9 kJ·mol^-1 based on Eq.(9).The constitutive equation of Al-5Ti-1B alloy during hot deformation compression can be obtained as follows:

In order to verify the validity of this constitutive equation,comparison of peak stress values obtained in experiment and calculation at different deformation conditions is shown in Fig.6.It can be seen from Fig.6 that except one point(circled part),the errors between experimental and theoretical values are within 9%.Therefore,this constitutive equation can accurately describe the flow stress behavior during the hot compression deformation of Al-5Ti-1B master alloy.

Fig.5 Relationships between lnsinh (ασ) and 10³ T^-1

Fig.6 Comparison of peak stress in theory and by calculation at different deformation conditions

3.3 Hot processing map

In recent years,processing maps have been used for optimizing the metal-working parameters and controlling the microstructure [ 14] .These maps are developed on the basis of the dynamic material model (DMM),the application of which to bulk metal working was discussed by Gegel et al. [ 15] .

DMM regards metal-working process as a system,which includes power source (hydraulic pressure energy),power storage (tool),and power consumption (work piece).The total dissipated power absorbed by the work piece(P) can be regarded as the sum of two complementary terms of G and J.The former (G) contains the power dissipated by plastic work,while the latter (J) is the energy or work consumed by dynamic microstructural mechanisms.The total dissipated power therefore can be given by [ 16, 17] :

The relationship between J and G is given by

The ratio m is the strain rate sensitivity parameter,and its values are obtained from the slopes of curves.The dynamic constitutive equation can be given as follows:

It can be obtained from Eq.(13) that

When the material is at an ideal linear dissipation state(m=1),J reaches its maximum value:

The efficiency of power dissipation (η) can be therefore defined as follows:

This parameterηvaries with deformation temperatures and strain rates [ 18] ,and the values can be determined according to Eq.(16).The power dissipation map can be developed based on the values ofηunder different conditions,as Fig.7 shows.Contour numbers represent the percentage efficiency of dissipation;the domain characterized by the maximumηmay ensure the best processing performance region.

Fig.7 Power dissipation map of Al-5Ti-1B alloy

On the basis of DMM and the extreme principles of irreversible thermodynamic as applied to large plastic flow [ 19] ,an instability criterion for predicting the onset of flow instability was developed by Prasad and Seshacharyulu [ 20] as follows:

So the material instability condition is:

The instability parameterξvaries with deformation temperatures and strain rates.The instability map can be developed based on the values ofξunder different conditions,as Fig.8 shows.The unstable regions are characterized by negative values ofξ.The instability map can be superimposed on the power-dissipation map to obtain a hot processing map.The hot processing map of Al-5Ti-1B alloy at the engineering strain of 50%is shown in Fig.9.The contour numbers represent the percentage efficiency of dissipation,and the shaded regions correspond to the flow instability.It can be seen from the map that the efficiency of power dissipation increases with temperature increasing gradually,which reaches the highest value of 16%at about 1.00 s^-1 and400℃.Over the whole range of test parameters,flow instability is observed at low-temperature conditions and only appears at temperatures in the range of 300-340°C.

Fig.8 Instability map of Al-5Ti-1B alloy

Fig.9 Hot processing map of Al-5Ti-1B alloy

Fig.10 Macro-image of Al-5Ti-1B alloy extruded rods

Fig.11 OM images of Al-5Ti-1B alloy:a before extrusion and b after extrusion

Figure 10 shows the macro-images of Al-5Ti-1B master alloy rods (Φ9.5 mm) extruded under the processing conditions obtained from the processing map.It can be seen that the surface is smooth with no crack or other defects.Figure 11 shows the OM images of Al-5Ti-1B alloy before and after extrusion.It can be seen that after extrusion,the grains are crushed to be finer and distribute linearly along the extrusion direction.

4 Conclusion

Under the condition of the strain rate range of 0.01-10.00 s^-1,the deformation temperature range of 300-450℃and the engineering strain of 50%during hot compression deformation of Al-5Ti-1B master alloy,it could be concluded as follows.The flow stress increases with the deformation temperature decreasing and the strain rate increasing.The hyperbolic sine equation can accurately describe the flow stress behavior.The deformation activation energy (Q) is 250.9 kJ.mol^-1.The hot deformation constitutive equation is expressed as follows: =1.97×10¹⁹[sinh(0.015σ)]^11.14exp(-250.9/RT) According to the processing map,the flow instability only appears at the temperature range of 300-340℃.The optimum hot processing parameters are strain rate of 1.00 s^-1 and deformation temperature of 400℃,at which the efficiency of power dissipation reaches the highest value of 16%.The Al-5Ti-1B master alloy rods with smooth surface and finer grain are extruded based on the optimum parameters.