Materials Science and Engineering A268 (1999) 141–146

Change in stress, stress sensitivity and activation energy duringsuperplastic deformation of silicon nitride

N. Kondo a,*, Y. Suzuki a, T. Ohji a, E. Sato b, F. Wakai c

a National Industrial Research Institute of Nagoya, Hirate-cho, Kita-ku, Nagoya, Aichi 462, Japanb The Institute of Space and Astronautical Science, Yoshino-dai, Sagamihara, Kanagawa 229, Japan

c Materials and Structures Laboratory, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama 226, Japan

Received 14 October 1998; received in revised form 29 January 1999

Abstract

Stress sensitivity and activation energy for superplastic deformation were investigated for silicon nitride consisting ofrod-shaped grains. It was found that both the stress sensitivity and the activation energy increased during the deformation. Inaddition, an abnormal stress increment, observed in the superplastic deformation, was analyzed by a viscous flow model takinginto account grain rotation. It was demonstrated that the viscous flow model would be effective to explain the stress incrementduring superplastic deformation. The principle deformation mechanism is considered to be the non-Newtonian viscous flow ofgrain boundary glassy phase. At the last stage (more than 200% elongation), however, superplastic behavior is considered to bemainly controlled by the solution-precipitation with 2-dimensional nucleation. © 1999 Elsevier Science S.A. All rights reserved.

Keywords: Silicon nitride; Superplastic deformation; Deformation stress; Stress sensitivity; Activation energy; Viscous flow

1. Introduction

Superplasticity of silicon nitride based ceramics wasfirst reported by Wakai et al. [1], followed by otherreports [2–8]. These materials had initial microstruc-tures consisting of equiaxed grains, since such mi-crostructures had been believed to promote grainboundary sliding, which is the major mechanism ofsuperplasticity. However, the present authors foundthat silicon nitrides consisting of rod-shaped b-siliconnitride grains can also exhibit a superplastic elongationup to 280% (o=1.34) recently [7]. During the deforma-tion, the rod-shaped grains, which had been initiallyoriented in random directions, became oriented parallelto the tensile direction.

The authors recently analyzed the microstructuraldevelopment of the silicon nitride during superplasticdeformation using a stereological analysis method[9,10]. The axis-symmetrical three-dimensional (3-D)distribution of grain radius, aspect ratio and orienta-tion angle were calculated from two-dimensional (2-D)SEM observations on the sectioning planes for as-sin-

tered, 140% deformed (o=0.88) and 280% deformed(o=1.34) samples. The microstructural developmentobtained, i.e. changes of mean grain radius, aspect ratioand orientation angle during the deformation, are sum-marized in Table 1 [10]. Based on the measured mi-crostructural development, three modes of grainbehavior, i.e. grain rotation, grain elongation, andgrain translation, were considered to act during thedeformation. The contribution of each mode to gener-ating the strain was estimated, and it was found thatthe contribution varies during the deformation asshown in Table 2 [10].

Therefore, the stress sensitivity, n, and the activationenergy, Q, are also expected to change during the

Table 1Development of the 3-D average grain radius, r, aspect ratio, a, andorientation angle, u, during deformation

r (mm) ao u/p

0.00 3.550.130 0.2963.680.88 0.2010.1394.65 0.1241.34 0.164

* Corresponding author.

0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.

PII: S0921 -5093 (99 )00117 -3

N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146142

Table 2Strains generated by the three deformation modes at the early andlate stages of the deformation

Dorot (%)o Doelong (%)Dototala Dotrans (%)

0.45 (51)0.00–0.88 0.01 (1)0.88 0.42 (48)0.88–1.34 0.46 0.25 (54) 0.13 (28) 0.08 (18)

a Dototal, total strain at each deformation stage; Dorot, strain gener-ated by grain rotation; Doelong, strain generated by grain elongation;Dotrans, strain generated by grain translation.

min−1 during the deformation. The advantage of thistechnique is that the stress sensitivity can be measuredin almost the identical microstructure which changesalong with strain. The stress sensitivity, n, was calcu-lated by the following equation:

n=ln (Cs1//Cs2)

ln (P1/P2)(1)

where P is the nominal stress and Cs is the cross headspeed.

The activation energy for deformation was measuredby changing the temperature from 1600 to 1630°C atseveral strains, and under a constant cross-head speedof 0.015 mm min−1 (the initial strain rate was 2.5×10−5 s−1). This technique was also used to measure theactivation energy in almost the same microstructure.The activation energy, Q, was calculated by the follow-ing equation:

Q=nRln P2− ln P1

1/T2−1/T1

(2)

where R is the gas constant and T is temperature.Microstructures of the as-sintered and deformed

specimens were determined by scanning electron mi-croscopy (SEM). The SEM specimens were cut, groundand polished, and then plasma etched with CF4, fol-lowed by Au coating. The SEM observation for thetensile deformed specimen was conducted on the crosssection parallel to the tensile direction.

3. Results

A SEM micrograph of the as-sintered specimen isshown in Fig. 1. The material consisted of randomly

deformation. These parameters were studied previously,i.e. by Rouxel for silicon nitride–silicon carbide nano-composite [3] and by Wu for SiAlON [4]. However,they were only measured at the initial stage. The firstaim of the present study is to examine the change in thestress sensitivity and activation energy for deformationagainst the strain. And then, the deformation mecha-nism will be discussed based on the measured stresssensitivity and activation energy.

On the other hand, an abnormal stress increment wasoften observed in superplastic deformation of siliconnitrides or SiAlONs [1,3,4,7,10]. The microstructuraldevelopment, especially grain alignment by grain rota-tion towards the tensile direction, can be considered toclosely relate to the stress increment during deforma-tion, because the one-dimensionally aligned grains plau-sibly cause a ‘fiber reinforcement effect’ [4]. Wu et al.[4] examined the stress increment during the superplas-tic deformation of SiAlON and described it by a vis-cous flow model after taking account of the grainalignment and growth [4]. The second aim of this studyis to analyze the relationship between the microstruc-tural development and the stress increment.

2. Experimental

The silicon nitride used in this study was the same asused in previous studies [7,10], where the superplasticbehavior was reported. It was prepared by gas pressuresintering with Y2O3 and Al2O3 additives [11], obtaininga density of 3.2×10−3 kg m−3 consisting of rod-shaped b-silicon nitride grains without a-phase, asconfirmed by X-ray diffraction analysis. Chemical anal-ysis revealed that it contained 3.7 wt.% Y, 1.7 wt.% Al,and 3.5 wt.% O.

Dog-bone shaped tensile specimens with a gage of 10mm length and 3 mm diameter were prepared from thesintered body, through rotational grinding using dia-mond wheels and polishing using diamond pastes. Thedeformation test was conducted in 1 atm nitrogenatmosphere.

The stress sensitivities (stress exponents) at severalstrains were measured at 1630°C by changing the cross-head speed alternately between 0.013 and 0.018 mm

Fig. 1. Microstructure of as-sintered silicon nitride showing randomlyoriented rod-shaped b-silicon nitride grains.

N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146 143

Fig. 2. Microstructure of superplastically tensile deformed siliconnitride (about 300% elongation). Rod-shaped b-silicon nitride grainsaligned preferentially along the tensile direction.

Fig. 4. Measured stress sensitivity against the strain.

the cross-head speed. This period seemed negligiblyshort for the microstructural development; it requiredmore than 30 h to obtain 300% elongation. Thus, thestress sensitivities could be considered to be measuredin the identical microstructures for each measuringpoint.

The measured stress sensitivity against the strain isshown in Fig. 4. The stress sensitivity, which wasinitially about 1.5, first slightly and then largely in-creased as strain increased, and reached over 2.2 justbefore fracture. No hysteresis caused by the incrementor decrement of the cross-head speed was observed.

Fig. 5 shows an example of the stress–strain curveof the measurement of the activation energy for defor-mation. In this figure the deformation temperature waschanged from 1600 to 1630°C at 180% elongation. Thestresses were also determined a few minutes afterchanging the temperature; therefore, the activation en-ergies also could be considered to be measured in theidentical microstructures.

The measured activation energy against the strain isshown in Fig. 6. The activation energy, which wasabout 630 kJ mol−1 initially, was almost constant up

oriented rod-shaped b-silicon nitride grains. Fig. 2 is aSEM micrograph of the tensile specimen deformeduntil fracture. This test was conducted at a constantcross-head speed of 0.015 mm min−1 and a tempera-ture of 1630°C. The micrograph was taken from thecross section parallel to the tensile direction. Appar-ently, the grains which were randomly oriented beforethe deformation aligned preferentially along the tensiledirection according to the strain.

Fig. 3 shows the stress–strain curve for the measure-ment of the stress sensitivity. The cross-head speed wasalternately changed between 0.013 and 0.018 mmmin−1. Note an abnormal stress increment has oftenbeen observed in the superplastic deformation of sili-con nitrides and SiAlONs [1,3,4,7,10]. The stresses set-tled and became stable a few minutes after changing

Fig. 3. Stress–strain curve of the tensile test for measuring stresssensitivity. The cross-head speed was cyclically changed between0.013 and 0.018 mm min−1.

Fig. 5. Stress–strain curve of the tensile test for measuring activationenergy. In this case the deformation temperature was changed from1600 to 1630°C at 180% elongation.

N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146144

Fig. 6. Measured activation energy against the strain.

Following the above in essence, and applying themicrostructural parameters (Table 1) and the measuredstress sensitivity (Fig. 4), we consider the relationshipbetween the microstructural development, especiallygrain alignment by rotation, and the stress increment.

The simultaneous flow stress during the deformationcan be expressed as follows [4,13]:

s=A(1−6)q/n (3)

where n is the stress sensitivity, q is the stress concentra-tion factor and A is a coefficient. Note this equation isfor a constant strain rate deformation.

Since the stress concentration is considered to dependon the aspect ratio, a, and the orientation angle, u, ofthe grains, q is approximately given by a shear-laganalysis as follows [4,13]:

q=1+ (k−1)n (4.1)

k=cos2 u ·k//+sin2 u ·kÞ

=cos2 u ·�

1+�1

2+

1n�

a�

+sin2 u ·�3

2+

1n�

(4.2)

where k// is a stress concentration factor for a rod-shaped rigid phase with an aspect ratio, a, locatedparallel to the loading direction, and kÞ is that for arigid phase with a located perpendicular to the loadingdirection.

As seen from Table 1 and Fig. 4, n, a and u arefunctions of o. Therefore, s is a function of o.

The microstructural parameters (a and u in Table 1)which we obtained in the previous study [10], and themeasured stress sensitivity (n in Fig. 4) are applied tothe above expressions. Here, the amount of the grainboundary glassy phase is assumed to be 20 vol.%; thus,the volume fraction of the grains, 6, is assumed to be0.8. The calculated result is shown as a line in Fig. 7.The open circles show the true stress at each measuredpoint; they were transformed using Eq. (1) to be testedat a constant strain rate (3×10−5 s−1) condition.

to the 180% elongation, and then greatly increased upto 1000 kJ mol−1.

4. Discussion

4.1. Stress increment by grain alignment

The abnormal stress increment in the stress–straincurve must be closely related to the grain alignmentduring deformation. Wu and co-workers [4,12,13] ex-amined the stress increment during the superplasticdeformation of SiAlON and analyzed it by a viscousflow model taking account of the grain alignment andgrowth.

Here, the model is briefly summarized. Commonly,silicon nitrides produced by liquid phase sintering con-sist of rigid silicon nitride grains (volume fraction 6)and a soft grain boundary glassy phase. It is assumedthat the deformation proceeds only by viscous flow ofthe grain boundary glassy phase and rigid silicon ni-tride grains act as a dispersoid. The dispersoid is sur-rounded by a more viscous phase, because the viscousphase near the dispersoid is constrained by the disper-soid. When a far field stress is applied to cause defor-mation, a higher local stress is required to deform themore viscous phase near the dispersoid. This localhigher stress is expressed by a stress concentrationfactor, and this factor is affected by the shape andorientation of the dispersoid. If a rod-shaped grain islocated perpendicular and parallel to the tensile direc-tion the stress concentration factor should be minimumand maximum, respectively [13]. In the case of super-plastic tensile deformation of silicon nitride, rod shapedgrains, which orient randomly before deformation,align along the tensile direction. Therefore, the super-plastically deformed silicon nitride with one-dimension-ally aligned rod-shaped grains exhibits higherdeformation stress.

Fig. 7. Comparison of the measured and calculated result. A lineshows the calculated result based on the viscous flow model. Theopen circles show the true stress at each measured point.

N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146 145

It was found that the experimentally measured resultsagreed well with those estimated from the viscous flowmodel; therefore, the model is useful to estimate thestress correctly during superplastic deformation of sili-con nitrides. However, in the present study, the volumefraction of the grains was assumed to be 0.8. In contrast,the amount of grain boundary glassy phase has beenestimated at most to be 10 vol.% in the usual siliconnitrides. The above estimation was carried out for thecondition with a higher amount of grain boundary glassyphase.

This is very likely because of the following. Thisviscous flow model taking into account the effect ofgrain rotation during deformation [4,12,13] assumesdilute dispersions of rigid phase (silicon nitride grains)with no contact with each other. However, when theamount of rigid phase is high as is the case in this study,the contact of grains is very likely to occur. Then someprocess to accommodate the grain contact is required.The most plausible accommodation process seems to bethe solution–precipitation process [14–17]. The defor-mation temperature was 1630°C and was slightly higherthan the lowest possible temperature to sinter this siliconnitride by hot pressing, where the solution–precipitationprocess is a sintering mechanism [18]. This means thatthe solution–precipitation process can act as the accom-modation process, though it is not a principal deforma-tion mechanism in the former stage. However, as will bestated later, the solution–precipitation is so at the laststage. Thus, in order to apply the present model whichis based only on viscous flow, the higher amount ofglassy phase should be assumed.

4.2. Deformation mechanism

In the present work the stress sensitivity and activa-tion energy for deformation were measured. The stresssensitivity, n, which was about 1.5 initially, slowly andthen quickly increased as the strain increased, andreached over 2.2 just before fracture. The activationenergy for deformation, Q, which was about 630 kJmol−1 initially, was almost constant up to 180% elonga-tion, and then quickly increased up to 1000 kJ mol−1.The increments of the stress sensitivity and activationenergy were first observed in this work, and these will bea important clue in considering the deformation mecha-nism.

Newtonian viscous flow exhibits n=1 [19], and almostall glasses, including a glass with a similar compositionof the grain boundary glassy phase to this silicon nitride,are Newtonian liquids [20]. Actually, the measured stresssensitivity exhibits 1.5–2 until 200% elongation. Non-Newtonian viscous flow is considered to be consistentwith the result. In addition, as seen from Tables 1 and2, grain growth was not as activated because the grainradius and aspect ratio are almost constant during the

former stage of the deformation; the dominant deforma-tion mode was found to be grain rotation and transla-tion. This fact also supports non-Newtonian viscousflow, since the deformation did not require grain shapechange. Therefore, superplastic behavior up to 200%elongation is considered to be a non-Newtonian viscousflow of the grain boundary glassy phase.

As stated previously, silicon nitride grains tend toalign along the tensile direction during the deformationand the deformation stress becomes high. Then, thenon-Newtonian viscous flow is suppressed, and insteadsolution–precipitation becomes predominant.

At the last stage of the deformation (roughly morethan 200%), stress sensitivity exhibits ]2. Activationenergy also increased at this stage. Wakai [21] proposeda solution–precipitation creep model, where differentrate-controlling processes yield different stress sensitivi-ties. According to his model, an interface-reaction con-trolled creep with 2-D nucleation results in ]2. Wakai’smodel also mentioned that the stress sensitivity increaseswith the increment of an activation energy for thesolution–precipitation creep with 2-D nucleation. Thesimultaneous increment of the stress sensitivity andactivation energy correspond to his model. In addition,grain growth and elongation noticeably occurred at thelatter stage of the deformation as seen from Table 1.Therefore, superplastic behavior at the last stage isconsidered to be mainly controlled by the solution–pre-cipitation with 2-D nucleation. Then, the viscous flowmodel in Section 4.1 may not be applicable to thedeformation at the last stage.

5. Conclusions

The change in the stress sensitivity, n, and the activa-tion energy for deformation, Q, against the strain wasexamined. The stress sensitivity, which was about 1.5initially, decreased as the strain increased and reachedover 2.2 before fracture. The activation energy, whichwas about 630 kJ mol−1 initially, was almost constantup to 180% elongation, and then quickly increased up to1000 kJ mol−1.

An abnormal stress increment was analyzed by theviscous flow model taking account of grain rotation. Itwas found that the experimentally measured resultagreed well with the result calculated by the model. Theassumed viscous flow model explained well the stressincrement except the irregular volume fraction of theglassy phase.

The principle deformation mechanism up to 200%elongation is considered to be the non-Newtonian vis-cous flow of the grain boundary glassy phase. However,superplastic behavior is considered to be mainly con-trolled by the solution–precipitation with 2-D nucle-ation at the last stage.

N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146N. Kondo et al. / Materials Science and Engineering A268 (1999) 141–146146

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