Specimen geometry effects and deformation characteristics in ionic crystals

Specimen Geometry Effects and Deformation Characteristics in Ionic Crystals H. L. FOTEDAR, M. SRINIVASAN, D. A. WILSON AND T. G. STOEBE Division of Metallurgical Engineering, University of Washington, Seattle, Wash. 98105 (U.S.A.) (Received December 14, 1970)

S UMMA R Y The geometry of the process of plastic deformation is investigated in high purity single crystals of LiF and MoO. O f thefour slip planes in the NaCI structure which are equally stressed when the specimen is loaded along a (100) direction, it is shown that MgO shows a preference for slip along a plane with a long slip path in a rectangular specimen and LiF shows no particular preference under the same conditions. In contrast, NaCI prefers a short slip path. It is also observed that slip occurs to some extent on the ortho-

gonal slip plane in LiF and on all three other planes in MgO during the first stages of deformation. In LiF, it is shown that compression tests on samples of nearly square cross section give the most reproducible CRSS values, explaining experimentally observed CRSS variations in samples of rectangular cross section. Similar results are obtained in MgO. These observations are discussed in terms of the probability for nucleation of slip on different { 11O}planes in samples of varying cross sectional geometry.

RESUME La gOom~trie du processus de dkformation plastique est Otudide dans des monocristaux de LiF et de MgO de haute puretO. Bien que les quatre plans de glissement soient sollicitOs Ogalement dans les cristaux dOformks parallblement ,~ une direction (100), MoO se deforme prOfOrentiellement suivant le systbme qui, dans une Oprouvette rectangulaire, permet le 9lissement le plus long. Dans les m~mes conditions il n'y a aucun syst~me privil~gi~ dans LiF. NaC1 glisse au contraire prOfOrentiellement sur le plan qui donne le glissement le plus court. Dans LiF on observe Ogalement un peu de glissement suivant le plan perpendiculaire au plan principal, alors que dans MgO les autres

plans de glissement sont actifs tous les trois pendant les premiers stades de la dOformation. Dans LiF, les valeurs les plus reproductibles de la cission critique sont obtenues lorsque l' on comprime des kprouvettes de section sensiblement carrie, ce qui permet de comprendre que dans des kprouvettes de section rectangulaires on observe une dispersion des valeurs de la cission critique. Des rksultats semblables sont obtenus avec MgO. Dans l'interprOtation de ces observations on considkre la probabilitk de dOclencher le glissement sur diffOrents plans {110} dans des ~prouvettes dont on fait varier la forme de la section.

Z USA M M E N F A S S UNG In hochreinen LiF- und MgO-Einkr&tallen wurde die Geometric der plast&chen Verformung untersucht. Wird die Probe in (lO0)-Richtung verformt, dann herrscht in allen vier Gleitebenen der NaCl-Struktur die gleiche Schubspannung; es wird gezeigt, daft die Gleitung in einer MgO-Probe mit rechteckigem Querschnitt vorzugsweise auf einer Ebene mit langen Gleitwegen erfolgt, w?ihrend LiF unter denselben Bedingungen kein bevorzugtes Gleitsystem besitzt. Im Gegensatz dazu bevorzugt NaCl ein Gleitsystem mit kurzen Gleitwegen. Auflerdem wurde beobachtet, daft im Anfangsstadium der Verformung in LiF die

Gleitung teilweise auf der orthogonalen, in MgO dagegen auf den restlichen drei Gleitebenen erfolgt. In LiF miflt man bei Druckversuchen an Proben mit quadratischem Querschnitt die am besten reproduzierbaren CRSS- Werte ; das erkliirt die beobachteten Streuungen der CRSS-Werte yon Proben mit rechteckigem Querschnitt. f(hnliche Resultate liefert MgO. Diese Ergebnisse werden anhand der Wahrscheinlichkeit des Gleitbeginns auf verschiedenen {1lO}Ebenen in Proben mit verschiedenen Querschnitten diskutiert.

Materials Science and Engineering American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne-Printed in the Netherlands

273

DEFORMATION CHARACTERISTICS IN IONIC CRYSTALS INTRODUCTION

A considerable amount of work has been carried out over the past ten years on the deformation behavior of LiF single crystals 1-1°. This has included work on crystals of all shapes, sizes and impurity contents. One often notices discrepancies in reported values of deformation parameters in the data from different laboratories and even in work from the same laboratory, but this is usually explained as being due to variations in crystal purity. In numerous sets of experiments in this laboratory over the past few years, discrepancies have been noted in values of critical resolved shear stress (CRSS) obtained in nearly identical LiF single crystal samples. These samples were of the highest purity obtainable from the Harshaw Chemical Company, although they were not all from the same crystal batch. The discrepancies have usually been considered as being due to various causes, including slight variations in purity, irradiation (used to harden some of the crystals for cleaving), annealing conditions, specimen geometry, and the degree of lubrication of the ends of the crystals during compressive deformation. Studies in other materials have shown that the shape of single crystal samples can greatly influence the details of their mechanical.deformation characteristics 1~-18. In the case of aluminum for example, Wu and Smoluchowski 15 have shown that only those slip directions are favored which correspond to a short slip path across the crystal. In the NaC1 structure, deformation occurs on one or more of six slip systems 16 of the type {110} (150). In a typical compression testing geometry where the compression axis is along [001], four such slip systems are equally stressed. For compression along the long axis, the four slip planes are shown in Fig. 1, indicated by a, b, c, and d. In NaC1, slip generally shows a strong preference for one of the planes with the shortest slip distance T M . In other NaC1 structure materials, no detailed studies of the effects of specimen cross sectional geometry on the mode of deformation are available, although Alden 6 has shown that in LiF, strain hardening is independent of the length to thickness ratio of the specimen. The present research involves the determination of the geometrical details of deformation in two NaCl-structure materials, LiF and MgO. A wide range of studies have been performed in LiF because, as will be shown, specimen geometry

|[Y;. : T .......

\\ J

;/2-,.

/,,,"

,'k,/,/\,

Fig. 1. Crystal deformation geometry, showing shape nomenclature and the four possible slip planes for deformation along the long dimension, I. Slip directions are along the face diagonals as shown by the arrows, and the slip planes are denoted by a, b, c, and d.

causes the unexplained CRSS variations mentioned earlier. Experiments were performed in MgO in order to compare its behavior with that of LiF and NaC1.

EXPERIMENTAL AND GEOMETRICAL CONSIDERATIONS

One block of high purity LiF single crystal was cleaved along {100} planes into specimens of various shapes and sizes. These samples were annealed at 700°C for 48 hours and furnace cooled to remove surface dislocations caused by cleavage. Ionic conductivity studies 19 showed a divalent impurity concentration in these LiF crystals of about 3 mole p.p.m. One block of relatively high purity Norton MgO single crystal was similarly cleaved and the samples annealed in air at 1350°C for 50 h. By comparing yield stresses with previous work 2°, the MgO samples were shown to contain about 11 mole p.p.m, of Fe + 3 impurity. The samples were deformed in compression in a special jig 21 using an Instron universal testing machine at a deformation rate of 0.002 cm/min. The CRSS was determined from the proof stress at 0.1~ offset. The mode ofdeformatiori in typical samples was monitored after deformation by observing stress birefringence patterns using transmission polarized-light microscopy. The specimen geometry is reported in terms of the length l, width w and thickness t of the crystal, as indicated in Fig. 1. The sample thickness always refers to the shortest dimension of the specimen, Mater. Sci. Eng., 7 (1971) 272-277

274

H.L. FOTEDARet al.

while the length is the longest dimension. A sample of square cross section has a ratio w / t = 1 while samples of rectangular cross section have wit > 1.

planes, which seems random, is very important in determining the CRSS of the crystals, as discussed later.

DEFORMATION CHARACTERISTICS

The deformation characteristics of crystals having the NaC1 structure depend to a large extent upon how many of the four possible slip systems are activated. Significant amounts of slip rarely occur on all four systems. The most common case is one in which slip begins on two orthogonal slip systems (i.e., a and b, or c and d, Fig. 1) 18'22, one of which soon becomes the primary glide plane while the other becomes inactive 18. Dislocations on the inactive slip system act as barriers to slip on the main slip system, leading to the formation of deformation bands due to multiple cross glide 2, and Stage I work hardening 23- 25. The other important mode of deformation occurs when slip on an oblique plane is significant (planes such as a and c, Fig. 1, are at 120 ° to one another and thus "oblique"). The operation of oblique slip systems generally leads to Stage II work hardening in these crystals23-25. In LiF it is observed that during yielding, and throughout the first stage of work hardening, two orthogonal slip planes are of importance. While one of these planes becomes the primary glide plane, the orthogonal plane never becomes entirely inactive. Typical stress birefringence patterns illustrating the planes involved in deformation are shown for two different LiF crystals in Fig. 2. Such slip line patterns develop continuously after yielding. Figure 2(a) shows a crystal deforming predominantly by single slip on a plane with a short slip path, while Fig. 2(b) shows another crystal deforming predominantly on the two orthogonal slip planes with the short slip path. These photographs were taken after 1 ~ plastic strain. For both of these crystals, no discernible stress birefringence slip pattern was observed on viewing in the direction perpendicular to that shown, indicating no detectable deformation on the oblique pair of slip planes. Another important consideration regarding the mode of deformation of LiF is the choice of the operative pair of slip planes. By analogy with NaC1, one might expect slip on the planes with the shortest slip distance (a or b, Fig. 1), However, LiF seems to show little preference in this regard, with slip also being observed on the planes with the long slip distance (c or d, Fig. 1). The choice of

(a)

(b) Fig. 2. Transmission stress birefringence photographs of typical high purity LiF single crystals deformed 1~, showing slip line patterns. (a) shows a rectangular crystal where predominantly single slip has occurred on the short slip paths, with w/t= 1.65 and a CRSS of 85 g/mm 2. (b) shows a rectangular crystal where orthogonal slip has occurred on the short slip paths, with w/t = 1.18 and a CRSS of 169 g/ram 2. Magnification, 10 x.

In MgO, deformation is seen to occur to some extent on all four slip planes. A typical example of this is shown in Fig. 3, where (a) shows a photograph taken through the wide side of the crystal and (b) shows a photograph taken through the narrow side of the same crystal, both after 1 ~ plastic deformation. However, in MgO there is still one plane which becomes the Primary slip plane. It is observed that this primary slip plane is almost always one of those planes with the long slip path, in agreement with earlier observations in MgO 26. Mater. Sci. Eno., 7 (1971)272-277

275

DEFORMATION CHARACTERISTICS IN IONIC CRYSTALS TABLE 1:

I N F L U E N C E OF T H E W I D T H T O T H I C K N E S S R A T I O T H E O B S E R V E D CRSS IN H I G H P U R I T Y

CRSS range [g/mm 2]

Frequency O['observation Alldata

<80 80- 89 90- 99 100-109 110-119 120-129 130-139 140-149 150-159 160-169 170-179 >180

(a

W/t O N

tiF

w/t< 1.2 1.2< w/t< 1.4 w,/t< 1.4

1 6 4 7 8 17 8 2 3 5 3 4

0 3 0 3 4 13 6 0 0 3 i 1

0 0 2 3 1 4 2 1 0 1 1 0

l 3 2 1 3 0 0 I 3 1 1 3

If one analyzes the data for nearly square specimens only, wit < 1.2, the results become much more reproducible (see Table 1). The mean value is again at 122 g/mm 2, and 10 of the 34 observations are in the range 120-124 g / m m 2. Highly rectangular specimens (w/t ~>1.4) on the other hand, consistently show either very high or very low values of CRSS. Having noted that LiF samples of nearly square cross section give the most reproducible results,

(b) Fig. 3. Transmission stress birefringence photographs of a typical M g O crystal deformed 1%, showing slip line patterns. (a) shows the wide face and (b) shows the narrow face. For this sample, w/t=l.22 and the CRSS is 1.72 k g / m m 2. ( x 10).

220

200

EFFECTS OF SPECIMEN GEOMETRY

E E

•

•

wlt = LO to LI

A

w i t = LI to 1.2

180

Two types of geometrical effects can occur for compressive deformation. One effect is the influence of the specimen's cross sectional shape (w/t ratio), while the other is the influence of the specimen length compared with its width or cross sectional area (l/w or l/wt). Geometrically, too short a sample suffers from end effects due to constraint at the grips 6'27, yielding a high value of CRSS, although this problem can be reduced by using a suitable lubricant on both ends of the sample. Too long a sample, on the other hand, can give rise to bending and an inaccurate stress-strain curve. Using reasonably tall specimens (I/w ~ 3), a large number of LiF samples with different w/t ratios were deformed, giving a distribution of CRSS values as shown in Table 1. The most frequently observed CRSS range is 120-129 g/mm 2 and the median value of all observations is 122 g/mm z. However, the spread in the data is very large.

U) 03 ~

L~

L~

160

n" ILl "r q)

140

Q UJ ~'~ 0 U') W OC ,.J

o%

A

120

&

/x /x

/x

I00

U I--

/,,

U 80

GO

I 2.0

I

I

[

I

i 3.0

I

I

I

I

I 4.0

I

,~/w Fig. 4. Variation in observed CRSS with length to width (l/w) ratio for pure LiF single crystal samples with w/t< 1.1 and with 1.1 < w/t< 1.2. Band indicates CRSS values in the range 120-124 g/ram 2.

Mater. Sci. Eng., 7 (1971)272 277

H.L. FOTEDARet al.

276

the influence of the I/w ratio was investigated for samples of w/t ~< 1.2. The results are plotted in Fig. 4. Here it is seen that the most consistent results seem to be for samples with w/t<<,1.1 and I/w/>2.4; these samples give CRSS values consistently in the range 120-124 g/mm 2, noted by the cross-hatched area in the Figure. The influence of geometry on the work hardening characteristics of LiF has also been investigated. It is observed that the work hardening rate for Stage I is independent of the wit ratio as is illustrated for four samples in Fig. 5. The influence of variations in the cross sectional geometry is to shorten Stage I with decreasing w/t. Square cross section samples show a transition toward Stage II work hardening beyond 0.06 true strain 25 whereas only Stage I is usually observed in highly rectangular LiF specimens up to 0.08 true strain. ~" E

w

0.(

~ l

0.()2

I

w/t

= 105

w/t

z 1.13

wit

= 1.17

= 166

004

I

0.~]6

I

0.~

I

TRUE STRAIN

Fig. 5. Stress-strain curves for selected LiF samples with different wit ratios, as indicated, showing similarity of work hardening characteristics.

Several MgO crystals of different w/t ratios were also deformed to provide a comparison with LiF. It was generally seen that the CRSS values were consistently in the range 1.7 _0.1 kg/mm 2 for w/t < 1.3, beyond which the CRSS values increased rapidly. DISCUSSION

The importance of the cross sectional geometry on experimental reproducibility in LiF is apparently due to the lack of preference for slip in LiF along either a long or a short slip path, as discussed earlier. In rectangular specimens, it would be expected that slip along one of the planes with the shorter slip distance would have a low CRSS, since the probability per unit length that a dislocation would encounter an obstacle is lower in a short slip path.

Slip along a plane with a long slip path should have a correspondingly higher CRSS. It is typically observed that this correlation is, in fact, true, and this accounts for the wide variation observed in Table 1 for samples with w/t > 1.4. The same effect is observed in the MgO samples, where the major amount of deformation is almost always on a plane with a long slip path, and where rectangular specimens show a high CRSS compared with square samples. Experimentally, the most reproducible results are obtained in samples with a square cross section in both LiF and MgO. This is probably due to the nearly.equal probability that any of the four slip planes will become the primary glide plane. The observation that two orthogonal slip planes are operative in LiF during stage I work hardening is not surprising and has been postulated in the work hardening theory of Frank 28. The observation that all four slip planes are operative in MgO at 1 ~o strain is unexpected, but could be due to the much higher stress levels encountered in MgO as compared with LiF. The high CRSS is caused by impurities 2°, but during flow the high stresses can activate slip on oblique slip planes, which should lead to Stage II work hardening; hardening at a higher rate than Stage I in pure MgO single crystals 2° is indeed observed in these crystals. LiF samples With a square cross section show a transition to Stage II work hardening beyond 0.06 true strain while rectangular specimens generally do not show such a transition. This is probably caused by the early activation of oblique slip planes due to the more equal probabilities for slip on all four planes in this geometry. It has therefore been shown that specimen geometry is very important in the deformation characteristics of LiF and MgO single crystals. While it would be possible to use rectangular specimens for a series of tests, care should be taken to reproduce the w/t ratio exactly, and to reject all specimens which do not show slip in the shorter slip distance if consistent results are to be obtained. To avoid these problems, it is recommended that square cross section samples be used for reproducible results. ACKNOWLEDGEMENTS

The authors wish to acknowledge useful discussions with Prof. P. L. Pratt, and the assistance of Mr. A. Dhar who supplied some of the data used Mater. Sci. Eng., 7 (1971) 272 277

DEFORMATION CHARACTERISTICS IN IONIC CRYSTALS

in this paper. One author (D. A.W.) was supported by the 1968 Research Participation for High School Teachers and the 1969 In-Service Institute Programs in the Division of Metallurgical Engineering, sponsored by the National Science Foundation. This work was partially supported by the NASA Ceramic Materials Research Program at the University of Washington.

10 ll 12 13 14 15 16 17 18

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