High-strength materials: in-situ investigations of

PHILOSOPHICAL MAGAZINE A, 2002, VOL. 82, N O. 5, 925±942

High-strength materials: in-situ investigations of dislocation behaviour in Cu±Nb multi®lamentary nanostructured composites L. Thillyyzk, M. VeÂ ron§, O. Ludwig§, F. Lecouturierz, J. P. Peyradey and S. AskeÂ nazyz y Laboratoire de Physique de la MatieÁre CondenseÂe, Institut National des Sciences AppliqueÂes, Complexe Scienti®que de Rangueil, 31077 Toulouse, France z Laboratoire National des Champs MagneÂtiques PulseÂs, 143 avenue de Rangueil, BP 4245, 31432 Toulouse Cedex 4, France § Laboratoire de Thermodynamique et Physico-Chimie MeÂtallurgiques, 1130 rue de la Piscine, 38402 Saint Martin d’HeÁ res, France [Received 3 February 2000 and accepted in revised form 17 August 2001]

Abstract The fundamental mechanisms of the deformation of heavily deformed multiphase materials are not clearly understood despite the vast literature and the amount of data on this subject. This paper presents a new plastic ¯ow mechanism observed by in-situ transmission electron microscopy deformation on Cu±Nb continuous multi®lamentary nanostructured composites. The observed mechanism is interpreted in terms of dislocation loops nucleating in closely spaced parallel planes in the Cu channels. This behaviour explains many previous observations made on such composites such as the semicoherency of the interface and the 4° disorientation between the two phases. The modelling of the loop mechanism predicts the strength of the Cu±Nb nanocomposites. The very good agreement between the model and the experimental data suggests that the assumptions based on the in-situ observations are valid. The basic aspects of codeformation of fcc±bcc nanostructured systems are reviewed in this new context.

} 1. Introduction Heavily drawn metallic composites materials have been studied extensively both experimentally and theoretically. In the ®rst stages of co-deformation, the diŒerent phases are in the polycrystalline bulk state. Their deformation mechanisms are classical and the strength of the composite system follows the rule of mixtures (ROM). Once the size reduction reaches the nanometre scale, that is after a very high strain, the strength of the composite system is very much higher than that predicted by the classical ROM; see Gil Sevillano (1991) for a comprehensive review. It is unlikely that the usual behaviour of dislocations, such as Frank sources or pileups, operate any longer. Transmission electron microscopy (TEM) observations revealed a much lower dislocation density in the phases than would be expected for such heavily deformed k Present address: Laboratoire de MeÂ tallurgie Physique, Bd. M. et P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France. Email: [email protected]. Philosophica l Magazin e A ISSN 0141±8610 print/ISSN 1460-699 2 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080 /0141861011009474 3

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material (Spitzig et al. 1987; Dupouy 1995, Raabe et al. 1995). Some speculations have been made on the possible `whisker-like’ behaviour of the reinforcing phase (Spitzig et al. 1987, Gil Sevillano 1991, Dupouy 1995). Many models have been considered in order to understand and explain the strengthening mechanisms responsible for such a strong deviation from the ROM: discussions about the geometrically necessary dislocations storage (Funkenbush and Courtney 1985), the barrier role of the ®laments (Spitzig et al. 1987), the generation of dislocation pile-ups (Hangen and Raabe 1995) and more recently the substructure strengthening due to partial grain boundaries (Hong 1998) predicted the ultimate tensile strength (UTS) of Cu±Nb insitu composites, with more or less success. Experimentally, the drawing stress applied during the fabrication process is much smaller than the elastic limit of the harder phase. In this scheme, the embedded phase should not deform plastically as experimentally observed, unless there is a load transfer from the matrix high enough to force the ®bres to deform independently with their own mechanism, as discussed by Embury and Hirth (EH) (1994), and Sinclair et al. (1999). After such a large strain, the material has to store a large amount of energy. Since it cannot be stored only in the form of dislocations, there must be alternative storage mechanisms, such as an interphase surface increase or building of high internal stresses. From those studies, we sketched, in table 1, the deformation process of such composite materials, which are constituted of a ductile matrix phase in which is embedded a reinforcing phase. All these considerations lead to the following questions, as reported by EH: (a) In two-phase materials, what are the various roles of second-phase particles over a broad range of strains? (b) As materials approach the theoretical stress, what are the mechanisms of plastic ¯ow? (c) What factors limit the process of dislocation accumulation? (d) Where is energy stored during deformation? In this work, we shall focus on objective (b); since all the mechanisms of plastic deformation previously mentioned have been discussed from post-morte m TEM observations, we propose to discriminate the actual mechanisms using in-situ observations. Similar in-situ studies have been made for drawn pearlite (Janecek et al. 1999) and for metallic nanolaminates (Anderson et al. 1999) and succeeded in the observation of the deformation mechanism in such nanostructures. Therefore, this paper reports experimental observations on the in-situ deformation of Cu±Nb conductors and presents the interpretation of the phenomena observed during the in-situ tensile tests. Taking into account the observed dislocation behaviour, an analytical model is proposed to describe the mechanical properties of the continuous Cu±Nb nanocomposites. This model is numerically applied and compared with the experimental data. Based on this mechanism, we shall give some insight into the last two topics (c) and (d). } 2. Experimental procedure 2.1. Sample characteristics One of the main engineering interests in heavily deformed materials is the production of wires with high strength and high conductivity, such as copper-base d

a

Strong texture

Texture formation ROM

ROM

Embedded phase

Dislocations: Geometrically necessary? Pile-ups? Sources?

Plastic deformation in both phases

Composite

Very low No strain localization dislocation Similar behaviour in density both phases? Whisker-like behaviour?

Dislocations: Frank±Read sources Pile-ups

Mechanical Composite properties Matrix

Deformation mechanisms

Deformation process of composite materials.

True strain ² ˆ ln …Si =Sf †, where Si and Sf are the initial and ®nal sections respectively.

Elongated single crystals Nanometre scale

>6 (nanocomposites)

Embedded phase ( Nb)

Polycrystals Micrometre scale

Matrix ( Cu)

Microstructure

25), we expect a mechanism that allows the phases to undergo large deformation without fracture. This is only possible if unusually ®ne-scale plasticity occurs. The observed mechanism consisting of single dislocations nucleating and moving on closely spaced glide planes leads to such a homogeneou s deformation; this is more realistic than groups of dislocations, such as pile-ups, that would lead to localized deformation. The drawing stress applied to deform the conductors is large enough to trigger the loop mechanism in the Cu channels but is smaller than the elastic limit of the Nb ®bres and thus cannot activate dislocations in the Nb ®bres. However, the accumulation of the loops in the Cu channels covers the Cu±Nb interfaces with an array of dislocations which in turn shed load from Cu to Nb. Then, the Nb deforms plastically in a very homogeneous manner. EH used this to explain why the Nb ®laments can sustain large plastic deformation before fracture.

Figure 7. Post-mortem study of Nb ®bres, showing dislocation loops nucleated at the interfaces and with long elongated screw segments roughly parallel to the ®bre axis.

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} 5. Model of the deformation and application

5.1. Description of the model To explain the mechanical properties of lamellar aggregates, where a small size scale is attained, EH studied a two-phase ¬ system (where ¬ is the softer phase) and developed a dislocation model, considering the scaling law for dislocation spacing ¶ in the ¬ phase and the thickness d¬ of the ¬ layer. The essential point of the EH model is that, in very-®ne-scale structures, the concept of pile-ups and slip bands is meaningless; ®ne-scale plasticity cannot occur by groups of dislocations moving on slip planes separated by distances of the order of a micrometre but instead by single dislocations moving on closely spaced glide planes from one boundary to the next. Then single dislocation loops form in the ¬ phase and are deposited at the ¬ interface at a spacing ¶. Figure 8 illustrates this process. For clarity, the EH model supposes that the interface dislocations in ®gure 8 are of a pure edge nature so that the moving segments are screw dislocations. The following calculations have been made using the coordinates of ®gure 8. Note that the EH model uses diŒerent reference axes, as detailed in the original paper by EH. The resolved shear stress to move the dislocation segments in the ¬ phase, in the limit of large d¬ =¶, is the Orowan stress: ½ ˆ ½Orowan …¬†

ˆ

p…1

·b¬ ¶ ln ; 2pb¬ ¸†d¬

…1†

where b¬ is the Burgers vector of the ¬ phase.

Figure 8.

Sketch of dislocation distribution in Cu±0 channels between the Cu±Nb interfaces. Coordinates are used for calculations.

Dislocation behaviour in high-strengt h Cu±Nb

937

¬p ¬p ¬ The boundary conditions in ®gure 8 are "¬p xx ˆ " yy , "zz ˆ 0, "yy ˆ "yy ˆ 0, ¬ ¬ ¬p ˆ ¼zz ˆ 0, ¼xx ˆ ½=m and "xx ˆ "xx ‡ "xx . The superscripts ¬ and p denote the ¬ phase and plastic strain respectively; m is of the order of 0.4 for the active slip systems (estimated as the average of the Schmid factors for a fcc±bcc structure). It has to be noted that the last condition means that the phase only deforms elastically. The calculations of elastic stresses in are based on the Hooke law and the boundary conditions. They give

¼¬zz

2·

¼xx ˆ

1

ˆ

1

ˆ

1

¸ 2· ¸

"xx …"¬xx ‡ "¬p xx †

2·

1

ˆ ¼¬xx ‡

¸ 2·

¸

¼¬xx ‡ "¬p xx

2·

"¬p : ¸ xx For a layered structure, the plastic strain is related to ¶ by the relation 1

"¬p xx ˆ

mb¬ : X¬ ¶

…2†

…3†

Finally, the EH model allows one to calculate the yield stress in the Ox direction in the multilayer: ¼xx ˆ X¬ ¼¬xx ‡ X ¼xx

ˆ X¬

2· 0:4b¬ ½ ½ ‡ X ‡ X m¬ m¬ 1 ¸ X¬ ¶

ˆ …X¬ ‡ X †

X 0:8·b¬ ½ ‡ ; m¬ X¬ …1 ¸†¶

…4†

where ½ is given by equation (1). Note that X¬ ‡ X is the total volume fraction of the nanoscaled phases. We shall apply this model to the continuous nanocomposites, therefore we use equations (1)±(3). 5.2. Application to the simulation of the ultimate tensile strength of the Cu±17 vol.% Nb nanocomposite s The in-situ observations made on the Cu±17 vol.% Nb continuous nanocomposites revealed a deformation mechanism in the Cu channels similar to the assumption made in the EH model; in the ductile phase, single dislocations move on closely spaced glide planes from one boundary to the next. Furthermore, during tensile tests, the nanocomposite conductors exhibit very limited plastic strain before fracture (" < 3%). Their UTS can therefore be approximate d to their very high elastic limit. In this context the EH model can reasonably be applied to our structure. Since Cu and Nb have very similar elastic properties (shear moduli ·Nb ˆ 40 GPa and ·Cu ˆ 45 GPa), it can be considered, as in the EH model, that the two phases have the same shear modulus ·, and the same Poisson’s ratio ¸. To model the mechanical behaviour of the Cu±Nb nanocomposites, a modi®ed ROM must be applied, taking account of the contributions of all phases. As

L. Thilly et al.

938

described previously, there are six `phases’ in the Cu±Nb nanocomposite: the Nb ®laments and the copper channels Cu-0, Cu-1, Cu-2, Cu-3 and Cu-4. We have to consider the size of the phases (table 2); since dCu-2 , dCu -3 and dCu-4 are larger than 1 mm for all the nanocomposite diameters, it can be concluded that these three phases behave like bulk materials. Then their contribution is only the UTS of highly coldworked Cu: ¼Cu-ROM ˆ 450 MPa:

…5†

However, dCu-1 , dCu -0 and dNb are in the nanometre range. Since the Nb phase is embedded in the Cu-0 phase, they can be both compared to the ¬ system studied in the EH model. Thus we shall apply equation (4) to describe the mechanical behaviour of the Cu-0±Nb system. The total stress of the Cu-0 phase is then the classical equation (5) added to the Orowan stress because of the eŒect of Cu±Nb interfaces and dislocation spacing in the Cu-0±Nb system (equation (1)): ¼…Cu-0† ˆ ¼Cu-ROM ‡ MCu ½Orowan …Cu 0†;

…6†

with M Cu ˆ 3 (the Taylor factor calculated for fcc materials by Gil Sevillano (1991)). For the Cu-1 phase, the behaviour is assumed to be slightly diŒerent, since the Cu-0±Nb system is embedded in this phase. The eŒect of the dislocation spacing ¶ is assumed to be zero and the resolved shear stress ½b (Cu-1) to move dislocations in the Cu-1 phase is linked to the bowing of the dislocations in a very narrow channel bounded by impenetrable interfaces (Gil Sevillano 1991): ½b …Cu-1† ˆ

1:2·bCu d ln Cu-1 : 2pdCu -1 bCu

…7†

To this eŒect of the nanometre size, the classical ROM eŒect must be added (equation (5)): ¼…Cu-1† ˆ ¼Cu-ROM ‡ MCu ½b …Cu-1†:

…8†

Finally the stress of the Nb ®laments is the stress due to the elastic deformation of Nb in the Cu-0±Nb system, given by equations (2) and (3): ¼elas …Nb† ˆ MCu ½Orowan …Cu-0† ‡

1

0:8·b Cu : XCu-0 …1 ¸†¶

…9†

Summing, the total stress of the Cu±17 vol.% Nb nanocomposite is given by the following equation, which uses equations (5), (6), (8) and (9): 4

¼UTS Cu

Nb

ˆ

iˆ1

XCu-i ¼Cu-ROM ‡ XCu-0 MCu ½Orowan …Cu-0†

‡ XCu-1 MCu ½b …Cu-1† ‡ XNb ¼elas …Nb†:

…10†

It has to be noted that some theoretical studies suggested that internal stresses can be disregarded when computing the composite ¯ow stress if the ROM is applied with actual strengths of the individual phases in the composite, that is accounting for the constraints imposed by the presence of the interfaces (Gil Sevillano 1991). From this point of view, the EH model accounts for the internal stresses by relating the stress of the two phases through equations (2) and (3). Thus, equation (10) contains implicitly the internal stresses built during wire drawing.


Figure 9.

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Results of the predicted UTS of the Cu±17 vol.% Nb nanocomposite calculated with equation (10), compared with the experimental data at 300 K.

Table 2 gives the values of ¶ determined from the experimental observations during the in-situ deformation tests. The results of ¼UTS Cu Nb calculated with equation (10) for Cu±17 vol.% Nb are presented in ®gure 9 and compared with the experimental values of UTS. This ®gure shows the very good agreement between the UTS predicted by equation (10) and the experimental data. This result supports the assumptions based on the in-situ deformation tests. The very high UTS of the Cu±Nb nanocomposite s is explained by an increase in the elastic limit of each nanometre scaled phase of the material: (i) The dislocations’ behaviour in the inter®lamentary Cu channels Cu±0 is controlled by the width of the channel and the dislocation spacing. (ii) The dislocations in the sub®lamentary Cu channels Cu±1 obey a simpler Orowan type behaviour, inversely proportional to the size of the channel (iii) The Nb nano®laments deform essentially elastically, like whiskers. Considering feature (iii), the stress ¼elas (Nb) of the Nb ®bres at 300 K (equation (9)) was plotted versus the ®bres diameter in ®gure 10, for 68 nm < dNb < 394 nm (full circles) and ®tted with the following equation, which was extrapolated for dNb < 68 nm and dNb > 394 nm. ¼…Nb† ˆ 1330 ‡ 6100 exp

dNb ; 110

…11†

where ¼(Nb) is in megapascals and dNb in nanometres. The constant term of equation (11) is the limit when dNb is very large, that is the ROM term of highly coldworked bulk Nb and is to be compared with literature data for highly cold worked bulk Nb at 300 K: 1400 MPa. Moreover, the limit of the equation (11) when dNb

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Figure 10. The predicted stress of the Nb ®bres (equation (9)) plotted versus their diameter dNb (*): (ÐÐ), extrapolation for dNb < 68 nm and dNb > 394 nm using equation (11).

tends to zero is 7430 MPa. This corresponds to a resolved shear stress of ·=13, in the h110i textured Nb ®bres. This value is contained between the two theoretical bounds of the elastic limit for whiskers: ·/30 (model of MacKenzie (1949)) and ·=2º (model of Frenkel (1926)). It can then be concluded that equation (11) describes fairly well the stress of the Nb ®laments over a broad range of diameters; when dNb is greater than 500 nm, no size eŒect is visible, whereas, below this threshold, the stress of the ®laments tends to the stress of Nb whiskers. These considerations are in agreement with all the observations of the whisker-like properties of the Nb nano®laments described in § 2.1. } 6. Conclusion A study of the literature shows that many models for the deformation of fcc±bcc nanocomposite materials, derived from post mortem observations, have tried to explain the unusual properties of these structures: heavy deformation without fracture and high strength. Some purely theoretical considerations indicated new mechanisms of plasticity on a very ®ne scale that had not been veri®ed so far. Insitu tensile experiments have given the opportunity to investigate the dynamics of the deformation process in a very-well-de®ned structure, that is the continuous Cu±Nb nanocomposites fabricated at the Laboratoire National des Champs MagneÂtiques PulseÂ s, Toulouse, France. After a very high strain, the co-deformation of a very-®ne-scale fcc±bcc nanocomposite structure can be described as follow. The ductile fcc matrix is the ®rst

Dislocation behaviour in high-strengt h Cu±Nb Table 4.

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Deformation process of nanocomposite materials.

Microstructure

Deformation mechanism

Energy storage

Matrix

Nanometric single grains

Parallel single loops in close planes

Very high density of dislocation at interfaces

Embedded phase

Nanowhiskers

Single loops initiated by Elastic energy load transfer from the matrix

Composite

Strong texture

Coupled mechanisms through the interface, giving rise to very ®ne uniform deformation

Increase in fcc±bcc interface

phase to undergo plastic deformation by developing a series of parallel loops in closely parallel planes. The ®rst consequence of this mechanism is that the matrix deforms in a very homogeneous manner and can sustain a much higher strain than cold-worked bulk material. The second consequence is the covering of the fcc±bcc boundary by an edge dislocation array when the loops intercept the interface. These loops relax the mis®t stresses. The formation of this dense dislocation array sheds load to the bcc phase. The created tensile stress permits the bcc phase to deform plastically with its own mechanism. In turn, the bcc phase is able to reach high strains without fracture. The proposed mechanism accounts for the detailed microstructural characteristics such as the formation of the semicoherence and the 4° disorientation of the Cu± Nb interfaces. Moreover, its computation gives a good prediction of the experimental data. Considering the high dislocation density contained in the interfaces and the drastic increase in their surface after heavy cold drawing, it appears that the interfaces contain a large fraction of the total energy, showing that traditional storage through dislocations is not su cient to absorb the large amount of energy required to achieve large deformation. This work brings new elements to the fundamental questions addressed in the introduction which can be summed in table 4, for large strains. ACKNOWLEDGEMENT The authors would like to thank Professor J. D. Embury greatly for encouragement in this work and for helpful discussions. References A N DE RSO N, P. M., F OECKE, T., and H AZZLEDINE, P. M., 1999, Mater. Res. Soc. Bull., February, 27. D UPO UY, F., 1995, Doctoral Thesis, Institut National des Sciences AppliqueÂ es, Toulouse, France. D UPO UY, F., S NOECK, E., C A SANOVE, M. J., R OUCAU, C., PE YRA DE, J. P., and A SKEÂNAZY, S., 1996, Scripta mater., 34, 1067. E MBU RY, J. D., and HI RTH, J. P., 1994, Acta mater., 42, 2051. F RENK EL, J., 1926, Z. Phys., 37, 572. F UNK EN BUSH, P. D., and C OU RTN EY, T. H., 1985, Acta mater., 33, 913. G IL S EVIL LAN O, J., 1991, J. Phys.,III, Paris, 1, 667.

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H ANG EN, U., and R AABE, D., 1995, Acta mater., 43, 4075. H ONG, S. I., 1998, Scripta. metall., 39, 1685. J AN ECEK, M., LOUCH ET, F., D OISNEAU-CO TTIGNIES, B., B REÂ CHE T, Y., and G UE LTON, N., 2000, Phil. Mag. A, 80, 1605. MacKenzie, J. K., 1949, Doctoral Thesis, Bristol. P ELIS SIE R, J., and D EBRENNE, P., 1992, French Japanese Seminar on In-situ Electron Microscopy, Nagoya, Japan. R AA BE, D., H ERIN GH AUS, F., H A NG EN, U., and G O TTSTEI N, G., 1995, Z. Metallk., 86, 405. S INCLAIR, C. W., EM BUR Y, J. D., and W EATHER LY, G. C., 1999, Mater. Sci. Engng A, 272, 90. S NO ECK, E., LECOUTUR IER, F., T HILLY, L., C ASA NO VE, M. J., R AKOT O, H., C OFFE, G., A SK EÂN AZY, S., P EYRA DE, J. P., R OUCAU, C., PANT SYRNY, V., SHIKOV, A., and N IK ULIN, A., 1998, Scripta. metall., 38, 1643. S PITZIG, W. A., PELTON, A. R., and L AABS, F. C., 1987, Acta metall., 35, 2427. W O OD, J. T., G RIFFIN, A. J., E MBU RY, J. D., Z HO U, R., N A STASI, M., and V ERON, M., 1996, J. Mech. Phys. Solids, 44, 737.