F.Dobe?, P.Dymá?ek

CEITEC IPM, Institute of Physics of Materials CAS, ?i?kova 22, 616 62 Brno, Czech Republic

Abstract Creep tests were conducted in uniaxial compression to evaluate the creep behavior of magnesium-aluminum-strontium alloy at temperatures from 373 to 673K.Stress dependencies of the creep rate over the whole interval of temperatures and stresses can be well described phenomenologically by the Garofalo sine hyperbolic equation modifie by the inclusion of a threshold stress.The threshold stress increases with decreasing temperature.Creep data normalized by a diffusion coefficien and shear modulus clearly reveal the existence of two different regions.Possible mechanisms by which plastic deformation takes place have been identifie in both regions.The critical stress at which dislocations break away from the cloud of foreign atoms agrees well with the value determined by data normalization.At low stresses, a value of the stress exponent of n～=3 is consistent with the model of deformation that takes place through dislocation glide controlled by dragging of solute atoms.At high stresses, the multiple regression yields the activation energy which agrees with that for prismatic glide.

Keywords: Dislocations; Diffusion; Mechanical properties; Creep.

1.Introduction

Magnesium-based alloys have been extensively developed for use as structural materials in the automotive, aircraft and aerospace industries [1-3].Automotive powertrain components (e.g., transmission cases and engine blocks) require materials that are resistant to the creep deformation that occurs as a result of long-term exposure to loading at elevated temperatures.To meet this requirement, it is necessary to carefully select alloy compositions that have acceptable mechanical properties and conform to high-productivity operations(i.e.die casting).Prospective creep-resistant alloys are based on ternary additions of Si, rare earth elements, Ca and Sr to Mg-Al binary alloys [4-8].Several creep-resistant alloys based on Sr additions to the Mg-Al system were developed by Pekguleryuz et al.at the beginning of new millennium[9-12].

The available creep investigations of these alloys are described in detail in the review paper by Pekguleryuz and Celikin [13].The elevated temperature creep of the alloys has received considerable attention, but the reported experimental data focused mainly on a limited temperature range 423-473K[10,11,14-16]with sporadic excursions to lower(408K[17], 398K [18,19]) or higher temperatures (523K [20]).To understand the creep mechanisms, this work aims to carry out an experimental investigation using a broader range of temperatures and stresses.

2.Experimental procedure

The AJ62 magnesium alloy (nominal compositions in wt.%: 6Al-2Sr-balance Mg) used in this study was prepared by the squeeze-casting technique.Chemical analysis was performed using glow discharge optical emission spectroscopy and energy-dispersive X-ray spectroscopy.Fig.1 shows an optical micrograph of the as cast alloy.The primary solidifie Mg dendrites are surrounded by interdendritic ternary phase.Its chemical composition corresponds to Mg9Al3Sr.The results of constant strain-rate testing of the same experimental heat can be found in previous paper [21].

Fig.1.Light optical microscope image of microstructure of the as-received alloy AJ62.

The creep tests were performed in uniaxial compression on samples with a gauge length of 12mm and a diameter of 6mm.The compression testing allows studying creep deformation not affected by the onset of fracture processes.On the other hand, this mode of testing does not make it possible to study superplasticity or fracture-related phenomena[22,23].The test arrangement, which uses specifi compression cage (reversible grips), also does not allow rapid cooling of the specimen under stress.Effective observation of the microstructure after creep is, therefore, limited.The tests were performed under a constant load in a protective atmosphere of dry purifie argon at temperatures ranging from 373 to 673K.The test temperature was held constant within ± 1K for each individual test.Changes in specimen length were measured using a linear variable displacement transducer.The samples were subjected to stepwise loading, where the load was changed after the steady-state creep rate was established for a given load.

Examples of the time dependence of true compressive strain [24],

wherelandl0are the instantaneous specimen height and the initial specimen height, respectively, are given in Fig.2.The terminal values of the true stress [24],

whereFiis the force applied in theith step andS0is the initial cross-section area,and of the creep rate(i.e.,true compressive strain rate)

were evaluated for each step.The tests were conducted until the strain reached a value ofε=0.15.The stress dependence of the creep rate ˙εat a single temperature was usually obtained from two or more tests.The results of the described stepwise procedure were verifie in several cases by a comparison with results obtained from a conventional single-stress compressive test.Differences in the creep rates obtained by means of both techniques were negligible in all cases.

Fig.2.Example of creep curve at 623K.Note a compressed time axis on the right-hand side of the figure

3.Results

The stress dependencies of the creep rate ˙εat temperatures used in the experiments are shown in Fig.3 in double logarithmic coordinates.Analysis of these dependencies in a broad temperature interval showed that they can be well described by the sine hyperbolic equation [25] modifie by the inclusion (addition) of a threshold stress,σth,

whereA, Bandnare stress-independent parameters.Optimal values of these parameters and of the threshold stress were found by nonlinear regression with the criterion of the least squares of relative deviations.

The value of the stress exponentnis close to 3 and the integer valuen=3 is used for the computation of the regression curves drawn in the Fig.3.The computed values of parametersAandBand of the threshold stressσthare given in Figs.4, 5 and 6 as a function of temperature (reciprocal temperature, respectively).ParameterAincreases with increasing temperature.The Arrhenius type of dependence can be formally applied for this parameter (cf.Fig.4)

whereRis the universal gas constant (R=8.314J/mole) andTis the absolute temperature in K.The activation energyQis equal to 41kJ/mole at low temperatures (T≤523K) and 330kJ/mole at high temperatures (T≥523K).ParameterBranges from 0.01 to 0.06MPa and is likely only slightly dependent on temperature (Fig.5).The threshold stressσthdecreases with increasing temperature (Fig.6).To demonstrate that its temperature dependence is stronger than that of the shear modulusG, the threshold stress is normalized to the shear modulus.The values of the threshold stress are of the same order as those observed previously in a Mg-4Al-1Ca(AX41) alloy but substantially less than that in the magnesium alloys strengthened by Saffi fibre [26,27].They are also close to the value of 30MPa reported for the AJ62 alloy at 423K determined by a different technique [19].

Fig.3.Dependence of the creep rate on applied stress at different temperatures.

Fig.4.Dependence of parameter A on reciprocal temperature.

Fig.5.Temperature dependence of the parameter B.

4.Discussion

In Fig.7, the creep rates normalized byDGb/(kT), whereDis the lattice diffusion coefficientGis the shear modulus,bis the length of the Burgers vector andkis the Boltzmann constant, are plotted against the applied stressesσnormalized by the shear modulusG.For normalization, the values of material constants for pure magnesium were used[28]:D=0.0001 · exp[?135000/(RT)] m2s?1,G=16.6 ·[1?0.00053 · (T?300)] GPa andb=0.32nm.A simple visual inspection of the normalized data clearly reveals the existence of two different regions: the border is at approximately 0.0035σ/G.It is convenient to examine these regions separately.

4.1.Low stress region

The creep results at low normalized stresses suggest that the stress exponent is close to ～3 and the creep rate can be described by a Dorn type equation

whereA1is the material constant.The threshold stressσthcan then be estimated using the linear extrapolation technique(e.g.[29]) based on plotting ˙ε1/3versus applied stressσ(Fig.8).The procedure results in a simple linear function,

Fig.6.Temperature dependence of the threshold stress normalized to the shear modulus.

Fig.7.Relationship between normalized minimum creep rate and normalized stress.

Fig.8.Relationship between ε1/3 and applied stress in double linear coordinates.

Fig.9.Dependence of slope a (Fig.8) on reciprocal temperature.

whereais the temperature-dependent parameter and the threshold stress is given by

The apparent activation energy of creep at constant effective stressσ?σthcan be estimated as

The dependence of the parameteraon the reciprocal temperature is given in Fig.9.Mean value ofQCis equal to 123kJ/mol.Nevertheless, it is evident that the activation energy decreases with decreasing temperature: from 148 to 105kJ/mol.

The activation enthalpyΔHof the diffusion coefficienD,D=D0?exp(?ΔH/RT), which controls the creep process is then

The last two terms on the right-hand side have only negligible influenc on the value of the activation enthalpyΔH:they increase the apparent activation energy by 1 to 2kJ/mol in the studied temperature range.The creep results with a stress exponent ofn≈3 at the lowest stresses are consistent with the model of deformation that takes place through dislocation glide controlled by dragging of solute atoms.The diffusion coefficien can be taken as that of chemical interdiffusivity suggested either by Darken[30] or by Fuentes-Samaniego et al.[31,32]

whereD?AandD?Bare the tracer diffusion coefficient for the A and B atoms in the AB alloy, respectively;xAandxBare the atomic fractions of A and B in the alloy, respectively; andFAis the activity coefficien for the A atoms.The respective activation enthalpies are [33]

where

The microprobe analysis indicated negligible amount of strontium in the matrix (～0.06 at.%), which agrees with the previous investigations [19].Consequently, only the diffusion coefficient of Mg and Al were included in the estimations of activation energiesQDandQF-S.The same measurement revealed aluminum content of ～2.5 at.% in the matrix.The diffusion of aluminum in magnesium can be best approximated asD=0.000574?exp(?152310/(RT)) (m2/s) [34].The contribution of the temperature dependence of the thermodynamic factor was neglected.The results of calculations of the activation energies of diffusion that control dislocation glide are given in Fig.10.The energy from the Fuentes-Samaniego et al.proposal is weakly dependent on the concentration of aluminum and temperature.

4.2.High-stress region

With increasing effective stress, the solute atoms can no longer hinder the dislocation motion.At a critical stress, the dislocation breaks away from the cloud of foreign atoms and moves in a different mode characterized by a high stress power dependence.The critical stress depends on the concentration of solute atomscand the binding energy between the solute atom and the dislocation, which is proportional to the absolute value of the difference in volume between the solute and solvent atomsΔV[35]

whereM=3.06 is the Taylor factor andν=0.34 is the Poisson ratio.TakingΔV=8.2×10?30m3andb=3.2×10?10m,we obtain a normalized breakaway stressσB/Gfrom 3 to 5×10?3, which is in very good agreement with the above suggested division of normalized creep data in Fig.7.The temperature dependence of the breakaway stresses is evident from the dashed line added to Fig.3.

Fig.10.Temperature dependence of calculated activation energies according to Darken [30] and Fuentes-Samaniego et al.[31,32].

Above the breakaway stresses, the stress powernincreases to 7.7.It is more convenient to describe the creep rate at these stresses by means of the exponential function

whereU0is the Gibbs free enthalpy necessary for overcoming a short range obstacle without the stress,A?is the activation area andA2is material constant.The multiple regression of the high-stress data yields the activation energyU0equal to 111kJ/mol.This is in fairly good agreement with the activation energy for prismatic glide (1.2eV=115.8kJ/mol) predicted by Caillard and Martin [36] and compatible with the values for creep in magnesium at intermediate temperatures quoted by Couret and Caillard [37].Additionally, the estimated activation areas (9.5b2- 16b2) correspond to those reported by Caillard and Martin (9b2at room temperature).

5.Conclusions

The creep of Mg-Al-Sr alloy was studied in the temperature range from 373K to 673K.The alloy was prepared by the squeeze-casting technique.The following conclusions regarding the creep resistance can be drawn:

·Stress dependences of the creep rate over the whole interval of temperatures and stresses can be well described phenomenologically by the Garofalo sine hyperbolic equation modifie by the addition of a threshold stress.

·Temperature dependence of the creep rate at lower stresses is characterized by an activation energy that decreases with decreasing temperature: from 148 to 105kJ/mol.Analysis of the creep rate at higher stresses yields the activation energy equal to 111kJ/mol.

·Creep data normalized by the diffusion coefficien and shear modulus clearly reveal the existence of two different regions.

·At low stresses, the value of the stress exponent ofn～=3 is consistent with the model of deformation that takes place through dislocation glide controlled by dragging of solute atoms.

·At high stresses, multiple regression yields the activation energy,which agrees with that for prismatic glide predicted by Caillard and Martin.

Acknowledgements

This research has been financiall supported by the Ministry of Education, Youth and Sports of the Czech Republic under the project CEITEC 2020 (LQ1601).