Materials Science and Engineering A324 (2002) 141–144

Hardening and softening in deformed magnesium alloys

K. Mathis, Z. Trojanova *, P. LukacDepartment of Metal Physics, Charles Uni�ersity, Ke Karlo�u 5, 121 16 Praha 2, Czech Republic

Abstract

The deformation behaviour of three commercial magnesium alloys AZ91, AS21 and AE42 has been investigated in a widetemperature range. Specimens were deformed in tension and in compression in the temperature range of 300–573 K at constantbut various strain rates. The form of the stress–strain curves is very sensitive to the test temperature and the strain rate. Thedeformation behaviour of the specimens can be attributed to the occurrence of hardening and softening during straining. In orderto identify hardening and softening processes, the stress dependence of the strain-hardening coefficient was evaluated. Differentmodels describing hardening and softening were used to analyse the observed behaviour. The model proposed by Lukac and Balıkcan describe the experimental data in the temperature range of 373–473 K. The analysis shows that conservative slip ofdislocations is the main recovery process. The yield stress analysis reveals an asymmetry of values obtained in tensile andcompression tests. © 2002 Elsevier Science B.V. All rights reserved.

Keywords: Magnesium alloys; Tensile and compression tests; Work-hardening; Recovery

www.elsevier.com/locate/msea

1. Introduction

Excellent specific mechanical properties of magne-sium alloys, comparable with steel, and low weightpredestine these materials for applications in the auto-mobile and aircraft industry. The mechanical propertiesof magnesium alloys are in the focus of investigations.However, the deformation behaviour of magnesiumalloys has not been investigated in detail in the view ofthe evolution of the dislocation structure.

In ductile crystalline materials the flow stress � de-pends on the average dislocation density � as ����.The dislocation structure can change during deforma-tion. A part of the moving dislocations stored at grainboundaries and at the obstacles contributes to harden-ing. On the other hand, dislocations may annihilate andhence contribute to softening. A strong decrease in thework hardening rate �= (��/��)�� ,T (where � is the trueplastic strain and T, temperature) with increasing stress�, caused by dynamic recovery due to conservative slipand/or climb of dislocations. Formulating an evolutionequation for the dislocation density leads to a model

equation that describes the stress dependence of thework hardening rate. The aim of this work is to investi-gate the deformation behaviour of magnesium alloysAZ91, AE42 and AS21. The experimental data, elabo-rated according to Kral and Lukac [1] and Lukac [2],will be compared with predictions of models of Malygin[3] and Lukac and Balık [4].

2. Experimental procedure

Three different magnesium alloys: AE42 and AS21supplied by Norsk Hydro Ltd. and AZ91 from theTechnical University at Clausthal were prepared by diecasting. The chemical composition of the materials isgiven in Table 1.

Cylindrical specimens of AE42 and AS21 with alength of 9.95 and 8.95 mm in diameter, and with agauge length of 69.2 and 6.25 mm in diameter wereused for compression and for tensile tests, respectively.Specimens of AZ91 for compression tests had a rectan-gular cross section of 4.95×4.98 mm2 and were 9.95mm long. For tensile tests cylindrical specimens (27.2mm gauge length, 4.95 mm diameter) were used. Speci-mens were deformed in an INSTRON machine at aconstant cross-head speed giving an initial strain rate of

* Corresponding author. Tel.: +420-2-21911357; fax: +420-2-21911490.

E-mail address: ztrojan@met.mff.cuni.cz (Z. Trojanova).

0921-5093/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0 9 21 -5093 (01 )01296 -5

K. Mathis et al. / Materials Science and Engineering A324 (2002) 141–144142

Table 1Chemical composition of the specimens

wt.% Al wt.% Zn wt.% Mn wt.% Si wt.% Fe wt.% Cu wt.% Ni wt.% RE ppm Be

AZ91 8.6 0.80 0.19 0.01 0.0014 0.0015 0.0008 – 6– 0.14 – 0.00104.0 –AE42 – 2.3 –0.046 0.21 0.94 0.0010 0.0010 0.0010AS21 –2.4 4

8.3×10−5 s−1 in the temperature region from roomtemperature to 300°C in compression and to 200°C intension.

3. Experimental results and discussion

Fig. 1 shows the true stress– true strain curves ofAZ91 obtained in compression at various temperatures.The yield stress decreases rapidly with increasing tem-perature. This decrease is connected with the thermallyactivated motion of dislocations. The activity of anon-basal (probably pyramidal) slip system cannot beexcluded at higher temperatures.

The stress dependence of the work hardening coeffi-cient � for specimens of AE42 (tension) and AS21(compression) for various temperatures is shown inFigs. 2 and 3. The values of � were computed bynumerical derivation of the experimental stress–straincurves. The results for �(�) may be compared with thepredictions of models describing the deformation be-haviour of crystalline materials.

3.1. Simulation models

Malygin [3] took into account processes of multipli-cation of dislocations at both impenetrable obstaclesand forest dislocations, and dislocation annihilationdue to conservative slip in a homogeneous material.The evolution equation in this case has the followingform:

��

��=

1bs

+�f�1/2−�a�, (1)

where s is the particle spacing or grain size, �f, thecoefficient of the dislocation multiplication intensitydue to interaction with forest dislocations and �a, thecoefficient of the dislocation annihilation intensity dueto conservative slip. Finally, he obtained the followingequation that is suitable for an analysis of the experi-mental work hardening curve of polycrystals:

�=��

��=A/(�−�y)+B−C(�−�y). (2)

The yield stress �y corresponds to the beginning ofplastic deformation and comprises all contributionsfrom the various hardening mechanisms.

At intermediate temperatures (about 0.4 Tm, whereTm is the melting temperature) there are deviationsfrom the predictions of the Malygin model [3], whichindicates the presence of some other recovery process inaddition to conservative slip. Lukac and Balık [4] as-sumed dislocation climb to be this additional processand derived the kinetic equation in the following form:

��

��=

1bs

+�f�1/2−

cLcs

b−

Dcb2�c

�kBT�� ��3/2, (3)

Fig. 1. Deformation curves of AZ91 in compression for varioustemperatures.

Fig. 2. Fitting of work hardening-true stress curves for AE42, tensiletest.

K. Mathis et al. / Materials Science and Engineering A324 (2002) 141–144 143

Fig. 3. Fitting of work hardening-true stress curves for AS21, com-pression test.

Fig. 4. Depending of maximal flow stress on the temperature, AS21-tensile test.

where Lcs is the dislocation segment length recovered byone conservative slip event, c, the areal density of therecovery sites in a slip plane, �c, a fraction of thedislocations which can be annihilated by climb of dislo-cations with jogs, �, a parameter which gives the rela-tion between dislocation climb distance w and theaverage dislocations spacing 1/�� in the form w=�/��, �, the shear stress, kB, Boltzmann’s constant andDc, an abbreviation which includes the diffusion coeffi-cient and the stacking fault energy and �� , the shearstrain rate. The stress dependence of the work harden-ing rate for polycrystals can thus be written in thefollowing form:

�=A/(�−�y)+B−C(�−�y)−D(�−�y)3. (4)

Parameter A is connected with the interaction ofdislocations with the non-dislocation obstacles.Parameter B relates to the work hardening due to theinteraction with forest dislocations. Both parameters Aand B should not depend on temperature. The parame-ter C relates to recovery due to conservative slip andincreases with increasing temperature, as can be ex-pected because the thermally activated character ofconservative slip. The parameter D connected withclimb of dislocations should also increase with increas-ing temperature.

The theoretical models were fitted to �(�) curves bymeans of the Table Curve program. Results are intro-duced in Table 2.

The Lukac and Balık model [4] was found to describethe experimental curves in the intermediate temperaturerange best, as can be seen from Figs. 2 and 3. Thefitting parameters were analysed with the followingresults:

3.1.1. AE42 and AS21 – tensile testBoth parameters A and B are independent of temper-

ature in accordance with the prediction of the model.The comparison of the temperature dependence ofparameter C with the temperature variation of themaximum flow stress (Figs. 4 and 5 and Table 2) is veryimportant.

Dynamical recovery processes, including conservativeslip, compensate the hardening processes. It can beassumed that the maximum flow stress �max is a charac-teristics of the conservative slip process. Then the max-imum flow stress should decrease with temperature asthe stress necessary for conservative slip. The tempera-ture dependence of the maximum stress can then beexpressed in the form:

ln� �max

�0max

�= −K(�sf,�� )T, (5)

Table 2Parameters of the Lukac and Balık model for the specimens AS21, tensile test

20°C 50°C 100°C 150°CAS21 200°C

7758�370 8507�332A (MPa2) 3625�103 –5629�193B (MPa) –509�141067�10946�301035�42

−11.51�0.98 −6.48�0.62C 4.55�0.22 5.61�0.33 –D×103 (MPa−2) 2�0.09 1�0.04 0.6�0.01 0.7�0.04 –

129�0.08 119�0.05 101�0.12�y (MPa) –137�0.0070.96 0.99Correlation 0.9960.94 –

K. Mathis et al. / Materials Science and Engineering A324 (2002) 141–144144

Fig. 5. Depending of parameter C on the temperature, AS21-tensiletest.

takes place ([6]), which was not included in the abovementioned models.

4. Conclusions

The deformation behaviour of magnesium alloysstudied in this work can be described as a sum ofhardening and softening processes. The temperaturedependence of the yield stress is due to thermallyactivated motion of dislocations. The analysis of thestress dependence of the work hardening coefficientgives the following results.

(1) The Lukac and Balık [4] model describes theexperimental curves of AE42 and AS21 magnesiumalloys satisfactorily in the intermediate temperaturerange.

(2) The main recovery mechanisms during plasticdeformation of AE42 and AS21 alloys are conservativeslip and climb of dislocations with jogs (from 373 K to473 K).

(3) The Malygin model is suitable for describingthe experimental curves of AZ91 in tensile tests. In thiscase climb of dislocations is not significant.

(4) Neither of the above mentioned models de-scribes the curve �(�) for AZ91 deformed in compres-sion tests. This is due to contributions of dynamicrecrystallization, which are not included in those mod-els.

Acknowledgements

The authors appreciate support from the GrantAgency of the Czech Republic under Grant 106/99/1717 and from the Grant Agency of the Charles Uni-versity under Grant 184/99.

References

[1] R. Kral, P. Lukac, Acta Univer. Carol. — Math. Phys. 39 (1998)49.

[2] P. Lukac, in: G.W. Lorimer (Ed.), Proceedings of the ThirdInternational Magnesium Conference, The Institute of Materials,London, UK, 1997, p. 100.

[3] G.A. Malygin, Phys. Stat. Sol. (a) 119 (1990) 423.[4] P. Lukac, J. Balık, Key Eng. Mater. 97–98 (1994) 307.[5] Z. Drozd, PhD Thesis, Charles University Prague, 2000.[6] P. Lukac, Z. Trojanova, Z. Drozd, in: E. Aghion, D. Eliezer

(Eds.), Proceedings of the Second Israeli International Conferenceon Magnesium Science and Technology, Magnesium ResearchInstitute, Beer Sheva, Israel, 2000, p. 308.

where �0max is a constant and K(�sf,�� ) is a function ofthe stacking fault energy and the strain rate. Fig. 5shows that Eq. (5) is valid from 100°C, i.e. from thetemperature from which the parameter C is positive.This means that at 100°C conservative slip becomes themain recovery process. The value of the parameter D ishigher than that for aluminium alloys [1], which meansthat climb of dislocations is a significant recovery pro-cess in magnesium alloys even if the temperature depen-dence of this parameter does not correspond to theprediction.

3.1.2. AE42 and AS21 – compression test:In this case the parameters A and B are also indepen-

dent of temperature. Parameter C is negative up to200°C, probably owing to complex processes during thecompression test. Parameter D is significant again andfor AS21 it depends on temperature. The Lukac–Balıkmodel [4] does not describe satisfactorily the experimen-tal curves at 300°C. Probably at this temperature amechanism connected with moving of dislocations innon-basal planes dominates.

3.1.3. AZ91 – tensile test:The Malygin model [3] describes the experimental

data better than the Lukac and Balık model in thewhole temperature range.

3.1.4. AZ91 – compression test:Neither model mentioned above describes the experi-

mental curves in a satisfactory. Drozd [5] has shownthat at 100°C and higher temperatures recrystallization