In situ observations of the formation of plastic zone ahead of a crack tip in copper

Scripta METALLURGICA

Vol. IS, pp. 343-348, 1981 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved

IN SITU OBSERVATIONS OF THE FORMATIONOF PLASTIC ZONE AHEAD OF A CRACKTIP IN COPPER*

S. Kobayashi** and S. M. Ohr Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830

(Received January 13, 1981)

Introduction In situ electron microscopy has been shown to be a useful technique to study the structure of the plastic zone ahead of a crack (I-3). In thin f o i l s of stainless steel ( I ) , the plastic zone consisted of an inverse pile-up of screw dislocations, which have s p l i t into partials with stacking faults between them. Similar structures were also observed in bcc metals, but the dislocations were not s p l i t and frequently cross-slipped out of the original s l i p plane (2). These observations represented the f i r s t experimental confirmation of the Bilby-Cottrell-Swinden (BCS) model of fracture, where the plastic zone was considered to be coplanar with the crack and consisted of an inverse pile-up of dislocations (4). Since i t was expected that the detailed structure of the plastic zone ahead of a crack depended on the stacking fault energy of the materials, we have extended the studies to nickel and copper. Although nickel was believed to be a metal of high stacking fault energy, the plastic zone was in the form of a linear array of dislocations and the dislocations were often s p l i t into partial dislocations (5). From the contrast analysis, i t was found that a l l the partials did not l i e on a single plane but on parallel planes and hence the stacking faults were overlapping. I t was concluded that the overlapping stacking faults represented a twin l amella. The aim of the present work is to study the structure of the plastic zone in copper and to examine further the p o s s i b i l i t y of twin formation in the plastic zone. Experimental From polycrystalline copper sheets of commercial purity, specimens of 3 mmdiameter were punched and then annealed at 900°C for 3 hrs. The specimens were electropolished at 20°C to perforation from one side wlth an electrolyte of 24% ethyl alcohol, 5% iso-propyl alcohol, and 24% phosopheric acid and the balance water. The polished specimen was mounted in a bending holder (6), which can be t i l t e d ± lO ° inside a Hitachi HU 200E electron microscope. Since the specimens were polished from one side, tensile stress could be applied to the thinned area near a hole by placing the unpolished side of the specimen on the tension side of the bending holder. Structure of Plastic Zone When the tensile stress was applied gradually to the specimen, dislocations started to move and the number of dislocations in motion increased with the amount of deformation. A majority of the dislocations came from the thicker area of the specimen and slipped out at the edge of the electropolished hole. Following the s l i p a c t i v i t i e s , cracks were i n i t i a t e d at the edge of the hole and propagated rapidly into the specimen. During this propagation, many *Research sponsored by the Division of Materials Science, U. S. Department of Energy under contract W-1405-eng-26 with Union Carbide Corporation. **Present address: Toyota Central Research and Development Labs., Inc., Nagakute, Aichi, 480-11, Japan.

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dislocations were generated near the crack t i p and moved into the specimen to form the plastic zone ahead of the crack. The plastic zone was in the form of a thin ribbon of dark contrast as shown in Fig. la and Ib which are from two different copper specimens. The dislocations in the plastic zone are s p l i t into partial dislocations and the fringes due to stacking faults can be seen between the partials. These observations are very similar to those reported in stainless steel (1) and nickel (5). From the trace analysis, the s l i p plane in both cases was identified as ( I l l ) . As was found in bcc metals (2), a part of the plastic zone immediately ahead of the crack t i p is free of dislocations. Beyond this dislocation free zone, dislocations in the plastic zone form an inverse pile-up of dislocations; i . e . , the dislocation density is higher near the crack t i p and gradually decreases toward the end of the plastic zone. In order to study the structure of the plastic zone in more d e t a i l , contrast analyses were carried out as shown in Figs. 2 and 3. Thesemicrographs were taken near the end of the plastic zones shown in Figs. la and Ib, respectively, under different d i f f r a c t i o n conditions. In Fig. 2, there are two sets of parallel dislocations (A and B) and they frequently cross each other. Under the [IT1] reflection (Fig. 2a), both sets of dislocations are v i s i b l e , while only the dislocations of set A are v i s i b l e for g = [022] (Fig. 2b). There are three possible Burgers vectors of Shockley partials on the ( I l l ) s l i p plane. As shown in Table l , the Burgers vector of the dislocations of set B can be readily identified as I/6[~11]. However, i t is not simple to determine the Burgers vector of the dislocations of set A. This is due to the complication arising from the overlapping stacking faults (7,8). As w i l l be discussed l a t e r , the Burgers vector of the dislocations of set A can be identified as I/6[TT2]. It is concluded from the analyses that these partial dislocations are formed by s p l i t t i n g of perfect dislocations of I/2LlOl] which l i e on different parallel planes. The direction of the Burgers vector [~Ol] is perpendicular to the s l i p trace, indicating that the crack observed in Fig. la is nearly of mode I l l type. The dislocation arrangement within the plastic zone shown in Fig. 3 is much simpler than that in Fig. 2. Most of the dislocations (set A) are lying almost parallel to one another and the fringes due to stacking faults show a repeating sequence with every t h i r d f a u l t i n v i s i b l e . From this observation and the detailed analysis of the dislocation images to be discussed l a t e r , i t is concluded that a l l of the dislocations have the identical Burgers vector I/6[TT2]and l i e on different planes which produces overlapping stacking faults on parallel planes. The modulo three sequence of fringes is often observed at the interfaces of thin twins (8) and hexagonal -phases (g, lO). Since the formation of twin lamellae is energetically more favorable than the formation of i r r e g u l a r l y spaced stacking faults, the f a u l t is most l i k e l y a thin twin formed from the overlapping stacking faults on successive atomic planes. The electron d i f f r a c t i o n patterns taken from the faulted region showed well-defined extra d i f f r a c t i o n spots, which could be indexed as being due to a twin formed on ( I l l ) plane. The fact that the dislocations in the plastic zone are close to the screw orientation indicates that the crack in Fig. Ib is also a shear crack of mode I l l type. Determination of Burgers Vector According to the calculations of Howie and Whelan ( l l ) , the image of partials bounding an isolated stacking f a u l t i s , in addition to the g.b = 0 i n v i s i b i l i t y c r i t e r i o n , i n v i s i b l e for g.b = ±I/3 and is v i s i b l e as a dark l i n e for g.b = ±2/3. However, i t was reported that t h i s contrast behavior is modified when a partial dislocation separates e x t r i n s i c and i n t r i n s i c f a u l t s ; i . e . , the partial appears as a dark line for g.b = ±I/3 and a bright l i n e for g.b = ±2/3, respectively (7). Whenthe stacking faults are overlapping on parallel planes, the same situation arises for the partials which bound (3n+l) and (3n+2) faulted layers. In addition, for a partial which bounds a stacking f a u l t for which g.b = ±2/3 a strong contrast is observed only when the image l i e s on the faulted side. Theoretical intensity profiles for this type of defect have been calculated only at a certain depth in the f o i l by Tunstal] and Goodhew (7). Since the detailed contrast of dislocation image is expected to depend on the specific experimental conditions, theoretical micrographs of partial dislocations were computed for the conditions close to those found in Fig. 3. Since the dislocations in Fig. 3 are v i s i b l e under the [ ~ 0 ] r e f l e c t i o n , the Burgers vector of these dislocations should be either I/6[IT2] or I / 6 [ ~ l l ] according to the g.b = 0 c r i t e r i o n and the value of g.b for g = [200] is - I / 3 or -2/3, respectively (see Table I ) . The computed images for these two cases are shown in Fig. 4. We denote three kinds of dislocations as Al, A2 and A3 dislocations, as shown in Fig. 4. The Al dislocations separate unfaulted and faulted regions. The number of overlapping stacking faults increases by one at the partials moving from right to l e f t . The predicted contrast behavior of the Al and A3 dislocations is very similar to that expected of the partials bounding an

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TABLE l The Values of g.b for Three Possible Burgers Vectors of Shockley Partials on (111) Planes.

TT1

032

2O0

I161131]

I/3

1

I13

II6[TT2]

213

I

-I13

1/61311]

-I/3

0

-2/3

isolated stacking f a u l t ; i . e . , they are i n v i s i b l e for g.b = ±I/3 and v i s i b l e for g.b = ±2/3. On the other hand, the A2 dislocations which separate one and two faulted layers show anomalous contrast, observed by Mahajan (8). Reversing the sense of the reflection vector in Fig. 4 causes the contrast of an A2 dislocation to remain the same. On the other hand, the contrast of AI and A3 dislocations is interchanged. From the above discussions, the cases for g.b = ±I/3 and ±2/3 can be distinguished without d i f f i c u l t y . As seen in Figs. 3a and b, the images of A2 dislocations appear as dark lines (this is more prominent in Fig. 3b) and the images of Al and A3 dislocations are essentially i n v i s i b l e . Therefore, the value of g.b for these dislocations should be ±I/3 and the Burgers vector for Al, A2, and A3 is I/6[TT2]. However the dislocation marked by B in Fig. 3 shows different contrast from these dislocations; i t appears as a dark l i n e for both , g pairs (Figs. 3a and b) but i t exhibits stronger contrast for +g than -g. From this behavior and the change of fringe contrast due to stacking faults across t h i s dislocation, g.b is deduced to be *2/3 under the (200) reflections and the Burgers vector of a B dislocation is concluded to be 1/61311]. I t is now apparent that most of the dislocations within the plastic zone shown in Fig. Ib has the same Burgers vector I/6[TT2] and are of screw character. This means that these partial dislocations are not formed by a simple dissociation of perfect dislocations but some specific mechanism which is related to the twin formation. The structure of the plastic zone shown in Fig. 2 is rather complicated but i t is basically composed of two sets (A and B) of dislocations. I t can be seen in Fig. 2(b) that a l l of the dislocations of set B are i n v i s i b l e under g = [0~2] indicating that b.g = 0 for this reflection. Under g = [TTI], the B2 dislocations appear as dark lines while the Bl dislocations are s t i l l i n v i s i b l e . As discussed before, t h i s is the behavior expected of the contrast for g.b = ±I/3. Thus, i t is concluded that the Burgers vector of the dislocations of set B is 1/61311]. For the dislocations of set A, the A2 and A3 dislocations appear as bright and dark lines, respect i v e l y under g = [TTII as shown in Fig. 2(a). This is consistent with the contrast behavior expected for g.b = *2/3. The Burgers vector of the dislocations of set A are identified as 1/61TT2]. I t is not possible to determine from these micrographs how these two sets of dislocations are stacked with respect to each other. Twin Formation Although twinning is one of the deformation modes allowed' in fcc metals, i t is not common at room temperature in pure metals such as copper and nickel. However, twin lamellae are observed ahead of cracks during the present fracture experiments. The high rate of deformation and high stress concentration at the crack t i p clearly f a c i l i t a t e the twin formation. There are several experimental observations suggesting the reduction of stacking f a u l t energy due to hydrogen in copper (12) and nickel (13, 14). I t i s , therefore, very l i k e l y that the stacking f a u l t energy is reduced by hydrogen absorbed during electropolishing and the formation of twins in polished specimens is r e l a t i v e l y easier. Since the twin lamellae are essentially overlapping stacking faults on successive planes, extended dislocations lying in the plane adjacent to the twin boundary w i l l increase the thickness of the twin by one layer in the region between the two p a r t i a l s . Once a twin is formed, the twin lamellae can grow more easily because of a reduction of the stacking f a u l t energy in the v i c i n i t y of the twin boundary (15, 16). The simple structure observed in Figs. Ib and 3 probably corresponds to the stage where a thin twin is just formed. On the other hand, the more complex structure in Figs. la and 2 may represent a thin twin with extended dislocations on i t s boundary which is s t i l l in the early stage of formation.

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I. 2. 3. 4. 5. 6. 7. 8. g. 10. 11. 12. 13. 14. 15. 16.

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References S. M. Ohr and J. Narayan, Phil. Mag., 41, 81 (1980). S. Kobayashi and S. M. Ohr, Phil. Mag.-Tlg80), in press. F. Appel, U. Messerschmidt, and M. Kuna, phys. stat. sol., (a) 55, 529 (1979). B. A. Bilby, A. H. Cottrell, and K, H. Swinden, Proc. Roy. Soc., A27._22, 304 (]963). S. Kobayashi and S. M. Ohr, to be published. T. S. Noggle and J. Narayan, Proc. 34th Annual Meeting of Electron Microscopy Society of America, p. 438, Baton Rouge: Claitor's Publishing Division (1976). W. J. Tunstal] and P. J. Goodhew, Phil. Mag., 13, 125g (1966). S. Mahajan, J. Appl. Phys., 43, 5201 (1972}. M. J. Whelan and P. B. Hirsch, Phil. Mag., 2, 1303 (1957). H. Fujita and S. Ueda, Acta Met., 20, 759 (T972). A. Howie and M. J. Whelan, Proc. Roy. Soc., A267, 206 (1962). M. L. Rudee and R. A. Huggins, phys. stat. sol., 4, KlOl (1964). J. Leteurtre, J. Physique, 27, C3-IOg (1966). A. H. Windle and G. C. Smith-~, Metal Sci. J., 2, 187 (1968). N. Thompson, Fracture, ed. by B. L. Averbach, et al., John Wiley, N. Y. (1959), p. 369. H. Gleiter and H. P. Klein, Phil. Mag., 27, 1009 (1973).

(b) FIG. l Electron micrographs showing shear cracks of mode I l l type and their plastic zones in copper.

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FIG. 2 D i s l o c a t i o n s t r u c t u r e in the p l a s t i c zone of the crack shown in Fig. l a ;

I0~2].

(a) g :11"T1], (b) g :

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FIG. 3 Dislocation structure in the plastic zone of the crack shown in Fig. Ib; (a) g = 1200],

(b) g =1~001, (c) g =1~01.

FIG. 4 Theoretical micrographs of three overlapping stacking faults computed for the conditions close to those found in Fig. 3; g = |~00]. u = I l l , l , N =[013], w = 0.2, (a) b = I/6[TT2], (b) b = 1/6[~11].