Thermally activated processes in microcrystalline Mg

Scripta mater. 42 (2000) 1095–1100 www.elsevier.com/locate/scriptamat

THERMALLY ACTIVATED PROCESSES IN MICROCRYSTALLINE Mg Zuzanka Trojanova´1, Zdene˘k Drozd1, Pavel Luka´c˘1, Kristia´n Ma´this1, Hans Ferkel2 and Werner Riehemann2 1

Department of Metal Physics, Charles University, Praha, Ke Karlovu 5, CZ-121 16 Praha 2, Czech Republic 2Department of Materials Engineering and Technology, Technical University of Clausthal, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany (Received November 15, 1999) (Accepted in revised form January 29, 2000)

Keywords: Powder processing, magnesium; Mechanical properties; Thermally activated process

1. Introduction Materials with small grains exhibit interesting mechanical properties for the technological use. However, the very high strength at room temperature may very often decrease rapidly with increasing temperature. The reason for a decrease of the mechanical properties at higher temperatures has not been explained up to now. Growth of the small grains with increasing temperature can cause the drop in the strength. In our previous paper we studied the thermal stability of the microstructure of microcrystalline Mg using internal damping method [1]. We estimated very stable grain structure; no grain growth was observed even at higher temperatures up to 550°C. The occurrence of diffusion processes could also lead to a rapid decrease of the yield stress and it may be apparent in the thermally activated analysis. The aim of the present work was to study deformation characteristics of microcrystalline Mg and to try to find an explanation for a rapid decrease of the flow stresses at elevated temperatures and to determine possible thermally activated processes.

2. Experimental Procedure The microscaled Mg powder having particle diameter of about 40 ␮m was prepared by gas atomisation of a Mg melt with Ar containing 1% oxygen for powder passivation. The powder was subsequently pre-compressed followed by hot extrusion at 150 MPa at temperature 400°C. The original more or less equiaxial grains changed into elliptical grains with the long axis parallel to the extrusion direction. The grain size was in the cross section about 3␮m and in the extrusion direction tens ␮m. Cylindrical specimens were deformed in tension in an INSTRON machine at an initial strain rate of 6.2⫻10⫺5 s⫺1 in the temperature region from room temperature to 300°C. Stress relaxation (SR) experiments (for 300 s) during the deformation were performed. In order to estimate parameters of the thermally activated processes from the SR the following theoretical relationship between stress drops rate ␴˙ and stress ␴ can be used [2] ln共⫺␴˙ 兲 ⫽ C ⫹ n ln ␴ 1359-6462/00/$–see front matter. © 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00342-0

(1)

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Figure 1. Temperature dependence of the yield stress.

where C is a constant and n is the stress sensitivity parameter defined as n⫽

冉 冊 d ln ⑀˙ d ln ␴

(2) T

where ⑀˙ is the strain rate. The stress sensitivity parameter n can be estimated as the slope of the plot ln(-␴˙ )vs ln(␴/␴0 where ␴o is a starting stress of the relaxation. The activation volume V is done by a simple relationship n k T ⫽ ␴ V,

(3)

where kT has its usual meaning. The activation volume V ⫽ b.d.ᐉ, where b is the Burgers vector, d is an effective obstacle width and ᐉ is the length of a dislocation segment pinned on the local obstacle. 3. Experimental Results and Discussion The temperature dependencies of the yield stress of pure Mg and two composites containing 1 and 3 vol.% of alumina nanoparticles (for details see [1]) are given in Fig. 1. The yield stress decreases rapidly with increasing temperature in the whole temperature range studied. Luka´c˘ [3] has reported that the critical resolved shear stress of pure Mg as well as Mg-Cd alloys decreases with increasing temperature between 77 and 230 K. The critical resolved shear stress of these materials is not depending on temperature between 230 and 300 K. Hauser et al. [4] studied the temperature dependence of the yield stress for Mg with various grain sizes and they estimated also a very rapid decrease of the flow stresses with increasing temperature depending on the grain size. Plots according to equation (1) are given in Fig. 2 for Mg deformed at 453 K for various starting stresses ␴0 of the SR. For the sake of a better survey not all curves are plotted. It can be seen that the stress relaxation curves are no straight lines which should be for a constant parameter n. The values of the stress sensitivity parameters for the onset (n1) and the end (n2) of the SR were estimated and are given in Table 1. The stresses correspond to the sequence of the SRs made along the stress-strain curve. The activation volume was estimated according to relation (3) and in Table 1 it is given also in b3 units. This experimentally estimated activation volume is the apparent one and should not be compared

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Figure 2. Stress relaxations for various starting stresses.

directly with the true (dislocation activation) volume Vd, corresponding to the dislocation motion in the slip plane. The basal slip system is the main slip system in Mg. The rapid decrease in deformation stresses indicates a presence of thermally activated processes very probably cohered with dislocation motion in non-basal slip systems. Dislocations moving in the basal plane form pile-ups in the vicinity of the grain boundary. The stress concentration on the tip of a pile-up can activate slip in a non-basal slip system; very probably in the pyramidal slip system. The dislocation motion in a non-basal system may be also thermally activated. The stress required to the polycrystal deformation is depending on grain size according to the well known Hall–Petch relation

␴ y ⫽ ␴ i ⫹ Kyd⫺1/ 2

(4)

where ␴i and Ky are material parameters and d is the linear grain size. The temperature dependence of both ␴i and Ky was observed in hexagonal metals with the primary basal slip and both quantities are also strain rate sensitive in contradiction to the fcc and bcc metals, where only temperature dependence of the ␴i parameter was estimated [5]. Armstrong [6] showed that ␴i is connected with the thermally activated stress for the easiest slip systems that are active in grains, while Ky is connected with the thermally activated stress for the most difficult slip systems. Then, ␴i and Ky are controlled by two different thermally activated processes, which can be related to the stress for single crystals by the relation

␴ y⫽⌿␶0⫹⌿KSd⫺1/ 2

(5)

TABLE 1. Values of the Parameter n and Activation Volume for Mg at T ⫽ 453 K ␴1 [MPa] 86.6 88.8 90.9 93.3 90,0 86.8 83.4

␴2[MPa]

n1

n2

V1 [m3]

V2 [m3]

V1 [b3]

Vd [b3]

68.4 70.8 71.1 69.8 — 62.2 58.9

16.3 16.4 15.2 12.3 10.0 11.1 11.0

10.6 10,0 10.1 9.7 — 8.3 11.0

1.2 ⫻ 10⫺27 1.2 ⫻ 10⫺27 1.0 ⫻ 10⫺27 8.2 ⫻ 10⫺28 7,0 ⫻ 10⫺28 7.8 ⫻ 10⫺28 8.3 ⫻ 10⫺28

9.7 ⫻ 10⫺28 8.8 ⫻ 10⫺28 8.9 ⫻ 10⫺28 8.7 ⫻ 10⫺28 — 8.3 ⫻ 10⫺28 1.2 ⫻ 10⫺27

36.0 36.0 30.5 25 21 23.8 25.3

3.6 3.5 3.1 2.5 2.1 2.4 2.5

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where ␺ is the Taylor orientation factor, related to the critical resolved shear stress of the single crystal, ␺␶0 ⫽ ␴i and KS is the stress intensity factor on the tip of the pile-up needed to the activation of a non-basal slip system. Altogether the thermally activated process in close packed hexagonal metal polycrystals with basal primary slip is a combination of two thermally activated processes occurring in the basal plane and in a non-basal plane. Then, the activation volume for polycrystals is a complex parameter. According to the thermal activation analysis dislocations can overcome obstacles in the basal slip plane at temperatures higher than the room temperature only solely the thermal excitation. The rate controlling thermally activated process seems to be motion of dislocations in non-basal slip systems (in the vicinity of grain boundaries). If ␶C is the stress on the tip of the dislocation pile-up in the grain boundary vicinity required to an activation of an accommodating or twinning system, the stress intensity Ky is given by [7] KS ⫽ C1

冉

冊

⌿ *Gb ␶ C 1⫺␯

1/ 2

(6)

where ␺* is the Sachs orientation factor for accommodating system, G is shear modulus, ␯ is Poisson constant and C1 is a numeric constant. It is important to note that KS is related to the non-basal system and then the temperature dependence of KS is determined by the temperature dependence of ␶c that may be proportional to the CRSS for this (non-basal) slip system [8,9]. The plastic strain rate is given by the Arrhenius equation

⑀˙ ⫽ ⑀˙ 0 exp关⫺共⌬H0 ⫺ ␶ c Vd兲/kT兴

(7)

where ⑀˙ 0 is a preexponential factor including the density of moving dislocation, Burgers vector, frequency factor and an average distance covered by a dislocation following a successful activation. ⌬H0 is the activation enthalpy and Vd is the dislocation (true) activation volume for non-basal slip. If the experimentally estimated stress sensitivity parameter n as n⫽

⭸ ln ⑀˙ ⭸ ln ⑀˙ ⭸ ␴ ⭸ ln ⑀˙ ⫽ ⫽ ⭸ ln ␴ ⭸ ␴ ⭸ ln ␴ ⭸␴

(8)

is insert to (3) ⭸ ln ⑀˙ ⭸ ␶ c ␴ nkT ⫽ kT ⭸␶c ⭸␴

(9)

then it follows for the dislocation activation volume Vd in a non-basal plane

冉 冊

Vd ⫽ kT

⭸ ln ⑀˙ ⭸␶c

(10) T

Hence, kTn ⫽ ␴ Vd

⭸␶c ⫽␴.Va , ⭸␴

(11)

where Va is an apparent (experimentally estimated) activation volume that is proportional to the dislocation activation volume by the relationship Va ⫽ Vd

冉 冊 ⭸␶c ⭸␴

. T

(12)

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The relations (5) and (6) determine the differential quotient (⭸␶c/⭸␴)T. Substituting into (12) we obtain Vd ⫽ Va

冉 冊

C1 ⌿ *Gb ⌿ ⫺1/ 2 d 2 1 ⫺ ␯ Ky

(13)

In order to obtain the true (dislocation) activation volume it is necessary to know Ky. It may be estimated from the SR experiment as follows: The Arrhenius equation can be rewritten in the form ln ⑀˙ ⫽ ln⑀˙ * ⫹

冉

and C2 ⫽ C1

冊

冊

1⫺␯ VdKy 2 * C2 ⌿ ⌿ Gb kT

(14)

⌬H0 kT is a constant. Substituting for Vd from relation (13) we obtain

where ⑀˙ * ⫽ ⑀˙ 0 exp ⫺ 2

冉

ln ⑀˙ ⫽ ⑀˙ *0 ⫹

Kyd⫺1/2 Va . 2⌿⌿* kT

(15)

The stress drop rate in a SR is proportional to the plastic strain rate i.e. -␴˙ ⫽ C⑀˙ . The slope of the ln(-␴˙ vs Va plot is given by d ln共 ⫺ ␴˙ 兲 Kyd⫺1/2 1 . ⫽ dVa 2⌿⌿ * kT

(16)

Knowing the grain size and the factors ␺ ⫽ 6 and ␺* ⫽ 2 [7,10], the Hall-Petch constant Ky can be estimated. Similarly the activation enthalpy is given by ⌬H ⫽ Vd

⭸␶c . ⭸T

(17)

In the experiment we measure ⭸␴/⭸T, substituting from (12) into (17) it follows for the activation enthalpy ⌬H ⫽ ⫺TVa

冉 冊冉 冊冉 冊 ⭸␴ ⭸␶c

⭸␴ ⭸T

冉 冊

⭸␶c ⭸␴ ⫽ ⫺TVa . ⭸␴ ⭸T

(18)

The slope of the dependence (15) gives a possibility to calculate Ky. In our case the dependence of the plastic strain rate at the start of the SR was plotted against the apparent activation volume. Substituting for ␺ ⫽ 6, ␺* ⫽ 2, C1 ⫽ 1 [7,10] we estimate Ky ⫽ 3⫻105 Nm⫺3/2. It is interesting to note that Frost and Ashby [11] have found for Mg Ky ⫽ 2.8⫻105 Nm⫺3/2 and Nussbaum at al. [12] and Mabuchi at al. [13] have reported Ky ⫽ 2⫻105 Nm⫺3/2 for AZ91 (Mg-9%Al-1%Zn) alloy. This is a very good agreement, especially if we consider that the results were obtained for materials prepared by different techniques. Alternatively Ky may be estimated from the one SR curve (Fig. 3). This method is, however, not suitable if two thermally activated processes take part in the SR. Substituting Ky to (13) (and using G ⫽ 15,6GPa and b ⫽ 3,2⫻10⫺10m, ␯ ⫽ 0.27 [14]) we obtain that the true (dislocation) activation volume is approximately ten times lower than the apparent one. From Table 1 it follows that the true activation volume amounts to magnitude of b3. Basal dislocations, density of which is certainly very high, are obstacles (the forest dislocations) for dislocations in the non-basal slip systems and therefore the activation volume for the non-basal dislocations should be so small. The activation energy was determined according to relation (18). The slope of the temperature dependence of the yield stress at 453 K is ⌬␴/⌬T ⫽ 5.105 MPa/K and the activation energy is ⌬H ⫽ 1.5 eV. The value is reasonable for the activation energy for dislocation motion in the pyramidal slip system. Obstacles in the basal plane with lower activation energy are already fully overcomed at lower temperatures. A form

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Figure 3. Dependence of stress drops rate on apparent activation volume.

accommodation of individual grains is realised by dislocations with higher elastic energy (they have longer Burgers vector). These dislocations have a lower mobility and they cannot easy cross slip. Then the activation energy for their motion is also higher. 4. Conclusions The strong temperature dependence of the yield stress indicates the occurrence of thermally activated processes during plastic deformation of microcrystalline Mg. The activity of non-basal slip systems is required for the grain accommodation in polycrystalline material. The glide of dislocations in pyramidal slip systems is very probably the main thermally activated process. The non-basal dislocations intersect the basal dislocations that are forest dislocations for the moving dislocation in non-basal systems. Acknowledgments The authors acknowledge support from the Grant Agency of the Czech Academy of Sciences under Grant A2112901. Z.T. is also most grateful to Deutsche Forschung Gemeinschaft for its financial support during her stay in Clausthal. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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