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The analysis of dislocation networks formed in Zircaloy-4 during high temperature creep
263
Journal of Nuclear Materials 115 (1983) 263-270 North-Holland Publishing Company
THE ANALYSIS TEMPERATURE
OF DISLOCATION CREEP
NETWORKS
FORMED IN ZIRCALOY4
DURING HIGH
I. ARMAS and M. BOCEK Kernfor~chungsrentrum Karlsruhe, Institut fiir Material - und Festkijrperforschung II, Postfach 3640, D -7500 Karlsruhe, Federal Republic of Germany
Received 21 October 1982; accepted 18 November 1982
A TEM analysis of the Burgers vectors of hexagonal network dislocations in Zircaloy-4 crept at 800°C has shown that these networks are formed by parallel sets of predominantely screw dislocations with an (a) type Burgers vector. These dislocations lie in intersecting (1010) prism planes, however the networks themselves form by interaction in the basal plane. The main glide system in Zircaloy4 at 800°C is the prism system (lOi0); l/3(1 120) which is also the operative system at low temperatures. Hence the networks formed in the (0001) plane are obviously non-glissile in this plane. Especially at higher temperatures however the networks can easily leave the basal plane. Mechanisms are proposed to explain the lack of edge dislocations in the crept specimens.
1. Introduction
In the past decade, stimulated by safety considerations about pressurized light water reactors, remarkable interest concentrated on the problem of high temperature plasticity of Zry-4 cladding material. The plastic properties were extensively examined in a broad ’ temperature range from normal operating temperatures up to 1200°C. The results mainly served for cladding deformation code development in licensing procedures. Though being more general, physical based deformation models have the disadvantage of high complexity. Evidently the application of property related constitutive equations for code calculations requires a more detailed knowledge of the n+cropliysical mechanism.
Valuable information about these mechanisms can be obtained from the investigation of deformation substructures. Unfortunately less information is available about the dislocation substructure on zirconium or zirconium alloys for deformation temperature above 400°C. Most of the electron microscopic examinations have been conducted on cold worked zirconium. Perhaps Bailey [l] was the first to examine the dislocation distribution in zirconium deformed at room temperature by means of transmission electron microscopy (TEM). According to this observations, in less pure zirconium (containing oxygen and nitrogen) after cold work the dislocations were comparatively straight and
0022-3 115/83/0000-0000/$03.00
0 1983 North-Holland
appeared more restricted to the prism planes (1OiO). It was assumed that the dislocations had Burgers vectors (BV) of the (a)-type i.e. *a(1 120). Thus the dislocations turned out to have predominately screw character. In annealed samples hexagonal shaped dislocation networks were observed lying almost in the basal plane. Studies of the dislocation movement and traces observed during electron beam heating and heating stage experiments at temperatures above 400°C have shown that this movement was governed by dislocation climb on planes of the type (1 lzO> or (1121). From these observations the importance of the climb mechanism for the formation of the dislocation networks was recognized. Bedford and Miller [2] performed BV-analyses of dislocation networks observed in a-zirconium which, after deformation up to 10% strain at temperatures between 0” and 4OO”C, has been annealed at 600°C. In contrast to the observations of Bailey (1) the hexagonal networks which appeared also after low straining at temperatures between 500°C and 600°,C did not lie on a single plane or family of parallel planes. The dislocation lines forming these networks had (a)-type BVs and were of mixed character. Furthermore, it was shown that dislocation glide was almost always compatible with slip on the (lOi0); j (1120) system. Therefrom it was concluded that slip on the basal glide system cannot be considered as the leading mechanism for the formation of planar hexagonal networks observed. The authors proposed that the mechanism compatible with
264
I. Armas,
M. B&k
/ Dislocation networks in Zircaloy-4
their observations is based mainly on interactions between arrays of dislocations which line up parallel along a single direction and are mobile in the prism planes. Recently BoEek and Armas [3] performed TEM examinations on Zry-4 tensile specimens crept at 800°C at stresses of approximately 15 MPa. Dense two-dimensional hexagonal dislocation networks were the typical substructure observed. These were similar to networks observed at lower temperatures on ol-zirconium as reported above [1,2], and were obviously of the type observed in different metals and alloys after high temperature flow [4]. Rather than forming cells these networks expanded through the grains. The observations indicated that the networks were generated by the interaction of systems of almost parallel dislocations. The development of networks was obviously accomplished during the early creep period. It was the aim of the present investigation to analyse these networks formed at high temperature (i.e. T 2 0.4 TM, where TM is the absolute melting temperature) in detail.
Fig. 1. Early stage of network formation. TO= 29 MPa).
A and B screw dislocations
2. Experimental procedure Sheet-type tensile specimens were prepared from a Zry-4 plate which was fabricated according to ASTM B 352-67 T. As-received material was cold rolled to 0.82 mm and thereafter annealed 54O”C/l h in vacua. The specimens had an average grain size of 15 pm and an (0002)-preferred orientation. These flat Zry-4 specimens were crept in an Instron machine at a nominal stress up to strains between 2 and 20%. The deformation was carried out in vacua at 800°C. By electropolishing in a solution of methanol, n-butanol and perchloric acid in the ratio 55 : 35 : 10 at a potential of 30 V, thin foils for TEM examination were prepared from sections perpendicular to the longitudinal axis of the specimen. Following the high temperature deformation usually the Zry-4 tensile specimens were rapidly cooled down in a helium steam. TEM foils prepared from these quenched specimens desintegrated during the polishing treatment. However foils could be easily prepared from
lines in intersecting
prism planes ( T= 8OO’C. s#train c = 0.15.
I. Armas, M. BoEek / Dislocation networks in Zircaloy-4
Fig. 2. Interacting A and B screw dislocations (T = SOOT, c = 0.15, To = 29 MPa). (a) arrows the same area as in fig. 2a but out of contrast; (c) network formation.
265
indicate
where reactions
t ake place; (
266
I. Armas,
M. BoEek / Dislocation networks rn Zircaloy-4
Fig. 2 (continued)
specimens which after quenching were annealed for 1 h at T = 550°C.Obviously during quenching large thermoelastic stresses are generated in this anisotropic material, which, in the polishing solution, lead to an enhanced selective corrosion. Most of the stresses could be revealed by the annealing treatment. However to avoid uncontrolled changes in the deformation substructure during the additional thermal treatment, the crept tensile specimens were slowly cooled down to 2OO’C in the tensile machine. The foil preparation from these specimens did not present any difficulties. The foils were examined in a JEOL electron microscope operated at 200 kV and equipped with a double tilt type holder.
3. Results Under present loading conditions more or less regular dislocation networks developed during high temperature creep. These networks obviously extended through the grains. Three-dimensional cell substructures, as often observed in similar investigations, could not be revealed in the present case.
An early stage of network development is shown in fig. 1. Sytems of parallel dislocation lines (A, B) are typical for less deformed specimens. The Burgers vectors of these lines (determined by means of the invisibility criterion) turned out to be of the (a)-type. The analysis has shown that the dislocation lines in fig. la are screw dislocations lying along the (lOi0) and (OilO) plane traces respectively. Their BVs form an angle of 120°. A couple of interacting screw dislocations can be seen in fig. 2a. By the interaction new dislocation segments with (a)-type BV are generated. These, in fig. 2b indicated by arrows, can be distinguished from the reacting dislocations by lack of contrast. Fig. 2c shows several meshes of a network knitted by the A and B dislocation lines. Hexagonal dislocation networks, as that shown in fig. 3, turned out to be prototypical for steady state deformation. The density of these networks generated under present conditions was between IO6 and 10’ cmW2. The basic hexagonal cell of this network is formed by the dislocation lines A, B and the resulting dislocation C. In the analyses all the lines became invisible in the (0002)-reflection and hence their corresponding
I.’ Amtas,hf. BoEek / Dislocation networks in Zircaloy - 4
267
Fig. 3. Network (T = 8OO”C,c = 0.15, T, = 29 MPa).
BVs are of the (a)-type. Therefrom it was concluded that the reaction by which the network is formed is of the type A $a[lZlO]
B ++a[21103
= fa
;; 1120].
O&ally the A and B lines were screw dislocations lying on intersecting prism planes and hence were parallel to the basal plane. As already considered by Bedford and Miller [2] in this case a hexagonal network can form which lies predominantely in the basal plane. If in the present case only one of the lines A and B resp. preserve their screw character the other one as well the resulting C line will be of mixed character. The habit plane of the networks estimated from stereo micrographs (see fig. 4) by means of an approximate trace analyses [S] turned out to be close to the basal plane.
In fig. 5 straight slip traces resulting from different slip systems are shown. The plane of fig. 5 is close to the (0001) plane, the traces follow the (1 l?O) directions. Hence from fig. 5 together with the results shown in fig. 1 one can conclude that the slip lines in fig. 5 are generated by dislocations moved in the prismatic planes {lOiO}. This evidently confirms the results of slip line studies on a-zirconium [6], that the (lOi0). l/3( 1120) system is the active slip system at high temperatures.
4. Discussion The above analysis has shown that the networks formed at high temperatures are composed from dislocations with screw - and or mixed character. Their habit plane turned out to be close to the basal plane. Because the (1010); f(ll?O) system is the operative
Fig. 4. Stereoxnicrographs. Tilt axes parallel to g (2110). (T = SOO”C,c - 0.15, G = 29 MPa). PS: in fig. 4b, [2110] should be [2iiOj.
I. Armas, M. BoEek / Dislocation networks in Zircaloy - 4
Fig. 5. Slip bands (T = SOO”C, c = 0.15, direction close to (0001) direction.
T, = 29 MPa)
beam
NETWORK IN THE BASAL PLANE
LOOP 2’
LOOP I’-
LOOP 1
LOOP2
CATIONS FORMING THE NETWORK
‘NETWORK IN THE BASAL PLANE INT’ERACTING EffiE OISL~CATI~NS
Fig. 6. On substructure creep in a-Zircaloy.
formation
during
high
temperature
269
glide system in Zry-4, the resistance to move this network in the basal plane should be high. Principally the (0001); f (llz0) system could serve as a geometrical possible cross slip system for screw dislocation segments of the network. However taking into account that in reality the screw dislocations will contain jogs and/or will be split up into partials, the mobility of the networks in the basal plane will in general be much less than their mobility in the (lOTO> planes. At high temperatures when climb of edge dislocations will facilitate the mobility of the mixed dislocation segments of the network, large parts of the networks can easily leave the basal plane in which they originally have formed. This perhaps explains the apparent contradiction between the observations regarding the habitus plane of the networks reported in [l] and [2] respectively. According to the above idea networks at low temperatures, due to their reduced mobility, are expected to be more tightly confined to the basal plane as in the case of high temperatures. An other important problem connected with the network formation concerns the role of the edge dislocations. As already mentioned from the analysis there is reliable evidence, that the networks are predominantly formed by screw dislocations. The same was found by Bailey in a-zirconium 111. According to the observations these networks, as schematically shown in fig. 6, obviously form in the basal plane by screw dislocation segments generated from loops (1, 2) operating in intersecting (1010) planes. The edge components of the loops will interact along the line A’A which is common to (lOi0) and (1120) planes respectively. The edge dislocation segments of the interacting loops will either form a new dislocation line along A’A (attractive interaction) or the opposite signed edge segments of the individual loops will probably annihilate in the (lOiO> plane after the screw segments have been incorporated into the network. In the first case the edge dislocation line with the BV ba = b, + b, can, according to the observation of Bailey [ 11, climb in the (1120) plane and possibly annihilate with edge dislocations resulting from the interaction between the corresponding loops 1’ and 2’ respectively. As already considered by the authors [3] both the loop system 1, 2 and l’, 2’ will generate a network by a “knitting” mechanism [4] in the basal plane. If the screw dislocations of the loops 1, 2 and l’, 2’ are of opposite sign, then the screw dislocations from parallel (lOi0) slip planes can mutually annihilate in the network. Lindros and Miekk-Oja [7] suggested that these networks will act as collectors of glide dislocations from
270
I. Armas, M. BoEek / Dislocation
parallel glide planes. Supposing that during steady state deformation a constant mesh size will be preserved then for each dislocation incorporated into the network another dislocation is annihilated. The annihilation mechanism is promoted by the applied stress and will depend sensitively on temperature [3]. Thus the formation of networks can be suggested as a self regulating mechanism which maintains a given strain rate, which is determined by the macroscopic variables T,u and by the microstructure of the material. According to the above, the latter is characterized by the network density which during flow adapts the value pN so that an equation of state F(i, a, T, pN) = 0 will be obeyed. 5. Conclusions Two-dimensional hexagonal dislocation networks are typical for the deformation substructure in Zircaloy-4 crept at 8OO’C. In accordance with other investigations performed on mainly cold worked a-zirconium [ 1,2] the networks observed are formed predominantly by sets of parallel screw dislocations with (a)-type BV lying in intersecting prismatic (1010) planes. In accordance with observations on a-zirconium the prism system {IOiO}; f (11~0)was identified as the main glide system in Zry-4 at 800% From this and from the dislocation analysis, the networks which form
networks in Zircaloy
-4
in the basal plane are supposed to be non-glissile in this plane. However, especially at higher temperatures, the networks will easily leave the basal plane. Hence no common habitus plane will exist for networks formed during high temperature flow. It is suggested that the edge dislocation segments from interacting loops either annihilate in the (IOiO) plane after the screw segments are incorporated into the network (repulsive interaction) or the edge segments react to form a new edge dislocation which can climb in the (1120) plane and possibly will annihilate with opposite signed dislocations formed on a parallel (lOi0) plane.
References [l] J.E. Bailey, J. Nucl. Mater. 3 (1962) 300. [2] A.J. Bedford and D.R. Miller, J. Australian. Inst. Metals 16 (1971) 147. [3] M. B&k and I. Armas, J. Nucl. Mater. 105 (1982) 293. [4] H.M. Miekk-Oja and V.K. Lindros, in: Constitutive Equations in Plasticity, Ed. AS. Argon (The MIT-Press, Cambridge, Mass., 1975) p. 327. [5] J.W. Fxlington, Practical Electron Microscopy in Material Science (Mac Millan Technical Library). [6] A. Akhtar, Met. Trans. 6A (1975) 1217. 171 V.K. Lindros and H.M. Miekk-Oja, Phil. Mag. 17 (1968) 119.
Journal of Nuclear Materials 115 (1983) 263-270 North-Holland Publishing Company
THE ANALYSIS TEMPERATURE
OF DISLOCATION CREEP
NETWORKS
FORMED IN ZIRCALOY4
DURING HIGH
I. ARMAS and M. BOCEK Kernfor~chungsrentrum Karlsruhe, Institut fiir Material - und Festkijrperforschung II, Postfach 3640, D -7500 Karlsruhe, Federal Republic of Germany
Received 21 October 1982; accepted 18 November 1982
A TEM analysis of the Burgers vectors of hexagonal network dislocations in Zircaloy-4 crept at 800°C has shown that these networks are formed by parallel sets of predominantely screw dislocations with an (a) type Burgers vector. These dislocations lie in intersecting (1010) prism planes, however the networks themselves form by interaction in the basal plane. The main glide system in Zircaloy4 at 800°C is the prism system (lOi0); l/3(1 120) which is also the operative system at low temperatures. Hence the networks formed in the (0001) plane are obviously non-glissile in this plane. Especially at higher temperatures however the networks can easily leave the basal plane. Mechanisms are proposed to explain the lack of edge dislocations in the crept specimens.
1. Introduction
In the past decade, stimulated by safety considerations about pressurized light water reactors, remarkable interest concentrated on the problem of high temperature plasticity of Zry-4 cladding material. The plastic properties were extensively examined in a broad ’ temperature range from normal operating temperatures up to 1200°C. The results mainly served for cladding deformation code development in licensing procedures. Though being more general, physical based deformation models have the disadvantage of high complexity. Evidently the application of property related constitutive equations for code calculations requires a more detailed knowledge of the n+cropliysical mechanism.
Valuable information about these mechanisms can be obtained from the investigation of deformation substructures. Unfortunately less information is available about the dislocation substructure on zirconium or zirconium alloys for deformation temperature above 400°C. Most of the electron microscopic examinations have been conducted on cold worked zirconium. Perhaps Bailey [l] was the first to examine the dislocation distribution in zirconium deformed at room temperature by means of transmission electron microscopy (TEM). According to this observations, in less pure zirconium (containing oxygen and nitrogen) after cold work the dislocations were comparatively straight and
0022-3 115/83/0000-0000/$03.00
0 1983 North-Holland
appeared more restricted to the prism planes (1OiO). It was assumed that the dislocations had Burgers vectors (BV) of the (a)-type i.e. *a(1 120). Thus the dislocations turned out to have predominately screw character. In annealed samples hexagonal shaped dislocation networks were observed lying almost in the basal plane. Studies of the dislocation movement and traces observed during electron beam heating and heating stage experiments at temperatures above 400°C have shown that this movement was governed by dislocation climb on planes of the type (1 lzO> or (1121). From these observations the importance of the climb mechanism for the formation of the dislocation networks was recognized. Bedford and Miller [2] performed BV-analyses of dislocation networks observed in a-zirconium which, after deformation up to 10% strain at temperatures between 0” and 4OO”C, has been annealed at 600°C. In contrast to the observations of Bailey (1) the hexagonal networks which appeared also after low straining at temperatures between 500°C and 600°,C did not lie on a single plane or family of parallel planes. The dislocation lines forming these networks had (a)-type BVs and were of mixed character. Furthermore, it was shown that dislocation glide was almost always compatible with slip on the (lOi0); j (1120) system. Therefrom it was concluded that slip on the basal glide system cannot be considered as the leading mechanism for the formation of planar hexagonal networks observed. The authors proposed that the mechanism compatible with
264
I. Armas,
M. B&k
/ Dislocation networks in Zircaloy-4
their observations is based mainly on interactions between arrays of dislocations which line up parallel along a single direction and are mobile in the prism planes. Recently BoEek and Armas [3] performed TEM examinations on Zry-4 tensile specimens crept at 800°C at stresses of approximately 15 MPa. Dense two-dimensional hexagonal dislocation networks were the typical substructure observed. These were similar to networks observed at lower temperatures on ol-zirconium as reported above [1,2], and were obviously of the type observed in different metals and alloys after high temperature flow [4]. Rather than forming cells these networks expanded through the grains. The observations indicated that the networks were generated by the interaction of systems of almost parallel dislocations. The development of networks was obviously accomplished during the early creep period. It was the aim of the present investigation to analyse these networks formed at high temperature (i.e. T 2 0.4 TM, where TM is the absolute melting temperature) in detail.
Fig. 1. Early stage of network formation. TO= 29 MPa).
A and B screw dislocations
2. Experimental procedure Sheet-type tensile specimens were prepared from a Zry-4 plate which was fabricated according to ASTM B 352-67 T. As-received material was cold rolled to 0.82 mm and thereafter annealed 54O”C/l h in vacua. The specimens had an average grain size of 15 pm and an (0002)-preferred orientation. These flat Zry-4 specimens were crept in an Instron machine at a nominal stress up to strains between 2 and 20%. The deformation was carried out in vacua at 800°C. By electropolishing in a solution of methanol, n-butanol and perchloric acid in the ratio 55 : 35 : 10 at a potential of 30 V, thin foils for TEM examination were prepared from sections perpendicular to the longitudinal axis of the specimen. Following the high temperature deformation usually the Zry-4 tensile specimens were rapidly cooled down in a helium steam. TEM foils prepared from these quenched specimens desintegrated during the polishing treatment. However foils could be easily prepared from
lines in intersecting
prism planes ( T= 8OO’C. s#train c = 0.15.
I. Armas, M. BoEek / Dislocation networks in Zircaloy-4
Fig. 2. Interacting A and B screw dislocations (T = SOOT, c = 0.15, To = 29 MPa). (a) arrows the same area as in fig. 2a but out of contrast; (c) network formation.
265
indicate
where reactions
t ake place; (
266
I. Armas,
M. BoEek / Dislocation networks rn Zircaloy-4
Fig. 2 (continued)
specimens which after quenching were annealed for 1 h at T = 550°C.Obviously during quenching large thermoelastic stresses are generated in this anisotropic material, which, in the polishing solution, lead to an enhanced selective corrosion. Most of the stresses could be revealed by the annealing treatment. However to avoid uncontrolled changes in the deformation substructure during the additional thermal treatment, the crept tensile specimens were slowly cooled down to 2OO’C in the tensile machine. The foil preparation from these specimens did not present any difficulties. The foils were examined in a JEOL electron microscope operated at 200 kV and equipped with a double tilt type holder.
3. Results Under present loading conditions more or less regular dislocation networks developed during high temperature creep. These networks obviously extended through the grains. Three-dimensional cell substructures, as often observed in similar investigations, could not be revealed in the present case.
An early stage of network development is shown in fig. 1. Sytems of parallel dislocation lines (A, B) are typical for less deformed specimens. The Burgers vectors of these lines (determined by means of the invisibility criterion) turned out to be of the (a)-type. The analysis has shown that the dislocation lines in fig. la are screw dislocations lying along the (lOi0) and (OilO) plane traces respectively. Their BVs form an angle of 120°. A couple of interacting screw dislocations can be seen in fig. 2a. By the interaction new dislocation segments with (a)-type BV are generated. These, in fig. 2b indicated by arrows, can be distinguished from the reacting dislocations by lack of contrast. Fig. 2c shows several meshes of a network knitted by the A and B dislocation lines. Hexagonal dislocation networks, as that shown in fig. 3, turned out to be prototypical for steady state deformation. The density of these networks generated under present conditions was between IO6 and 10’ cmW2. The basic hexagonal cell of this network is formed by the dislocation lines A, B and the resulting dislocation C. In the analyses all the lines became invisible in the (0002)-reflection and hence their corresponding
I.’ Amtas,hf. BoEek / Dislocation networks in Zircaloy - 4
267
Fig. 3. Network (T = 8OO”C,c = 0.15, T, = 29 MPa).
BVs are of the (a)-type. Therefrom it was concluded that the reaction by which the network is formed is of the type A $a[lZlO]
B ++a[21103
= fa
;; 1120].
O&ally the A and B lines were screw dislocations lying on intersecting prism planes and hence were parallel to the basal plane. As already considered by Bedford and Miller [2] in this case a hexagonal network can form which lies predominantely in the basal plane. If in the present case only one of the lines A and B resp. preserve their screw character the other one as well the resulting C line will be of mixed character. The habit plane of the networks estimated from stereo micrographs (see fig. 4) by means of an approximate trace analyses [S] turned out to be close to the basal plane.
In fig. 5 straight slip traces resulting from different slip systems are shown. The plane of fig. 5 is close to the (0001) plane, the traces follow the (1 l?O) directions. Hence from fig. 5 together with the results shown in fig. 1 one can conclude that the slip lines in fig. 5 are generated by dislocations moved in the prismatic planes {lOiO}. This evidently confirms the results of slip line studies on a-zirconium [6], that the (lOi0). l/3( 1120) system is the active slip system at high temperatures.
4. Discussion The above analysis has shown that the networks formed at high temperatures are composed from dislocations with screw - and or mixed character. Their habit plane turned out to be close to the basal plane. Because the (1010); f(ll?O) system is the operative
Fig. 4. Stereoxnicrographs. Tilt axes parallel to g (2110). (T = SOO”C,c - 0.15, G = 29 MPa). PS: in fig. 4b, [2110] should be [2iiOj.
I. Armas, M. BoEek / Dislocation networks in Zircaloy - 4
Fig. 5. Slip bands (T = SOO”C, c = 0.15, direction close to (0001) direction.
T, = 29 MPa)
beam
NETWORK IN THE BASAL PLANE
LOOP 2’
LOOP I’-
LOOP 1
LOOP2
CATIONS FORMING THE NETWORK
‘NETWORK IN THE BASAL PLANE INT’ERACTING EffiE OISL~CATI~NS
Fig. 6. On substructure creep in a-Zircaloy.
formation
during
high
temperature
269
glide system in Zry-4, the resistance to move this network in the basal plane should be high. Principally the (0001); f (llz0) system could serve as a geometrical possible cross slip system for screw dislocation segments of the network. However taking into account that in reality the screw dislocations will contain jogs and/or will be split up into partials, the mobility of the networks in the basal plane will in general be much less than their mobility in the (lOTO> planes. At high temperatures when climb of edge dislocations will facilitate the mobility of the mixed dislocation segments of the network, large parts of the networks can easily leave the basal plane in which they originally have formed. This perhaps explains the apparent contradiction between the observations regarding the habitus plane of the networks reported in [l] and [2] respectively. According to the above idea networks at low temperatures, due to their reduced mobility, are expected to be more tightly confined to the basal plane as in the case of high temperatures. An other important problem connected with the network formation concerns the role of the edge dislocations. As already mentioned from the analysis there is reliable evidence, that the networks are predominantly formed by screw dislocations. The same was found by Bailey in a-zirconium 111. According to the observations these networks, as schematically shown in fig. 6, obviously form in the basal plane by screw dislocation segments generated from loops (1, 2) operating in intersecting (1010) planes. The edge components of the loops will interact along the line A’A which is common to (lOi0) and (1120) planes respectively. The edge dislocation segments of the interacting loops will either form a new dislocation line along A’A (attractive interaction) or the opposite signed edge segments of the individual loops will probably annihilate in the (lOiO> plane after the screw segments have been incorporated into the network. In the first case the edge dislocation line with the BV ba = b, + b, can, according to the observation of Bailey [ 11, climb in the (1120) plane and possibly annihilate with edge dislocations resulting from the interaction between the corresponding loops 1’ and 2’ respectively. As already considered by the authors [3] both the loop system 1, 2 and l’, 2’ will generate a network by a “knitting” mechanism [4] in the basal plane. If the screw dislocations of the loops 1, 2 and l’, 2’ are of opposite sign, then the screw dislocations from parallel (lOi0) slip planes can mutually annihilate in the network. Lindros and Miekk-Oja [7] suggested that these networks will act as collectors of glide dislocations from
270
I. Armas, M. BoEek / Dislocation
parallel glide planes. Supposing that during steady state deformation a constant mesh size will be preserved then for each dislocation incorporated into the network another dislocation is annihilated. The annihilation mechanism is promoted by the applied stress and will depend sensitively on temperature [3]. Thus the formation of networks can be suggested as a self regulating mechanism which maintains a given strain rate, which is determined by the macroscopic variables T,u and by the microstructure of the material. According to the above, the latter is characterized by the network density which during flow adapts the value pN so that an equation of state F(i, a, T, pN) = 0 will be obeyed. 5. Conclusions Two-dimensional hexagonal dislocation networks are typical for the deformation substructure in Zircaloy-4 crept at 8OO’C. In accordance with other investigations performed on mainly cold worked a-zirconium [ 1,2] the networks observed are formed predominantly by sets of parallel screw dislocations with (a)-type BV lying in intersecting prismatic (1010) planes. In accordance with observations on a-zirconium the prism system {IOiO}; f (11~0)was identified as the main glide system in Zry-4 at 800% From this and from the dislocation analysis, the networks which form
networks in Zircaloy
-4
in the basal plane are supposed to be non-glissile in this plane. However, especially at higher temperatures, the networks will easily leave the basal plane. Hence no common habitus plane will exist for networks formed during high temperature flow. It is suggested that the edge dislocation segments from interacting loops either annihilate in the (IOiO) plane after the screw segments are incorporated into the network (repulsive interaction) or the edge segments react to form a new edge dislocation which can climb in the (1120) plane and possibly will annihilate with opposite signed dislocations formed on a parallel (lOi0) plane.
References [l] J.E. Bailey, J. Nucl. Mater. 3 (1962) 300. [2] A.J. Bedford and D.R. Miller, J. Australian. Inst. Metals 16 (1971) 147. [3] M. B&k and I. Armas, J. Nucl. Mater. 105 (1982) 293. [4] H.M. Miekk-Oja and V.K. Lindros, in: Constitutive Equations in Plasticity, Ed. AS. Argon (The MIT-Press, Cambridge, Mass., 1975) p. 327. [5] J.W. Fxlington, Practical Electron Microscopy in Material Science (Mac Millan Technical Library). [6] A. Akhtar, Met. Trans. 6A (1975) 1217. 171 V.K. Lindros and H.M. Miekk-Oja, Phil. Mag. 17 (1968) 119.