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Parameters of Dislocation Structures and Factors Determining Flow Stress at Stages III and IV
Parameters of Dislocation Structures and Factors Determining Flow Stress at Stages HI and IV N. A. Koneva, D . V. Lychagin, L. A. Teplyakova and E. V. Kozlov Civil Engineering Institute, Tomsk, USSR
ABSTRACT The quantitative study of substructure evolution was made by the transmission diffraction electron microscopy and the clas sification of substructure types was done at plastic deforma tion stages of f.c.c. alloy. It was established that transi tion to stage III and IV of the plastic flow is connected with "phase" transition in a substructure and with the appearance of the substructure new parameter that is the excess disloca tion density. Long range stress field values were measured at dislocation-disclination stages of substructures. It was found that long range stress fields play a significant role in the flow stress. KEYWORDS Dislocation-disclination substructures; long range stress fields; excess dislocation density. INTRODUCTION At plastic deformation one can observe the appearance and de velopment of local smooth and discrete disorientation of crys tal lattice both in single crystals and in polycristals. The substructures, observed at these deformations, that is at the first, transition stage and at the second stage of stressstrain curves have purely dislocation nature. The substructu res, observed at the beginning of stage III of stress-strain curves, differ qualitatively from the first one. There toge ther with separate dislocations and their tangles with conti nuous disorientations of a crystal lattice, the discrete disorientations introduced by continuous and ragged boundaries of different perfection degree are present. These substructures we shall call dislocation-disclination substructures (Koneva and colleagues, 1986). At stage III of stress-strain curves 385
386 they cover gradually the whole material volume. The aim of the present work is the quantitative investigation of the substructure evolution at great deformations at stage III and IV and revealing of the relation between substructure parameters and flow stress. The work was done on f.c.c. single crystals and polycrystals based on Ni and Fe deformed at long (LRO) and short (SRO) range order state of solid solution. The materials and experimental procedure are given in the work (Koneva and colleagues, 1982, 1985a, 1986). EXPERIMENTAL RESULTS Figure 1 shows the dislocation-disclination substructures and their elements received experimentally.
Fig. 1. Dislocation-disclination substructures and their elements: 1 - one-sized and 2 - two-sized disoriented "stripped", 3 - "spotted" substructure, 4 - ragged subboundary, 5 - dipole and 6 - loop of partial disclination.
387 At stage IIIthe disoriented "stripped" substructure (microbands) is formed, which may be one-sized (Fig. 1.1) as well as two-sized (Fig. 1.2). The typical elements of such a substruc ture are separate ragged subboundaries (Fig. 1.4), dipoles of partial disclinations (Fig. 1.5) and loops of partial disclinations (Fig. 1.6). The continuous disorientations with big wave length and with rather small but gradually increasing disorientation gradient are additionally put on these substructu res. This fact is confirmed by bending the contours observed in microphotographs. The substructure with complicated charac ter of discrete and continuous disorientations, with numerous components of dislocation density tensor, with specific "spot ted" contrast is distinguished at stage IV (Fig. 1.3). These substructure is also called as fragmentary or subgrain subst ructure. There are several quantitative parameters of substructure. The most general one is the average scalar dislocation density p . The main parameter of dislocation-disclination substructure is an excess dislocation density n (Koneva and colleagues, 1986): = (1)
/ Γ Λ 7 . ///·^/ί/
where 3J00/- disorientation gradient, / - Burger's vector. The correlation between the accumulation velocity of scalar dislo cation densitydp foL S , the accumulation velocity of excess dislocation density αρ±/οίε and stages of stress-strain cur ves (Koneva and colleagues, 1985) is revealed (Fig. 2). Roman numerals indicate stages of stress-strain curves. The accumu lation velocity of the scalar dislocation density is at its maximum at stage II, decreases at stage III and is practical ly constant at stage IV. The «* ΰ accumulation velocity of exc cess dislocation density attains ^ ^ its maximum at stage III and 'çs 1 then decreases. At stage IV 1 dp/cLe and dp+/d£ are equal 1 / 2V < and are of low"values. This is connected with intensive pro ^ cesses of dislocations annihi lation.
Ψ
n
à
a
■!2
\ 8
¥
μ
γ/ds
4fa
li I
ÜJ
d»ffl/m
1
Ofi
i
Û,8
t\
e1
Fig. 2. Dependence of scalar and excess density (a) and its accumulation ve locity (b) in strain.
388 Figure 3 shows the excess dislocation density as the function of the scalar dislocation density where critical values of the scalar dislocation density is poited out too, when /r?+ begins to increase rapidly. ~
Pig. 3. Dependence of excess dislo cation densi ty on scalar dislocation density.
0
fo'2M
*
6
ß-W
For all investigated specimens jDcr variation lies in small in ternal 1,5 ... 3-1010 cm"2. It testifies to the fact that the formation of new substructure type is a result of the selforganisation process in dislocation structure. If we take the material with the same range order, the data for single crys tal and polycrystals with different grain size will be put on the same curve with the same J)Cz value. This reflects the phe nomenon of the so called "phase" transition in dislocation structure. Volume material occupied by one substructure type may be determined as phase of dislocation structure. On the whole the picture of flow-stress formation is rather complicated and it is not described only by interdislocation interection. As it was pointed out in the paper (Koneva,and Kozlov, 1982), flow stress consists of the following contribu tions: 1)oontact resistanance dislocations which are propor1/2 y tional to 0 ( 6cont ); 2)barrier resistance which is propor tional to boundary density M ( 6ga^ ); 3)long range stress fields which are proportional to Ω+ i^£^ ); 4)fluctuation cor rection connected with the dislocation structure dispersion ( 6f ). There is one more type of contribution for polycrystals that is contribution of the Hall-Petch type ( éHp )·
é =
(2)
where o^s is a contribution made by the hard solution streng thening,'which is not usually very large. For stages of dislo cation structure such contributions as é^s , 6Cont , éx , éHP are typical and when fluctuation correction is constant the linear dependence of é on βΛ'^ is observed (Koneva and col leagues, 1985b). At stage III and IV of dislocation-disclination substructures the contributions to flow stress depending on the resistance of dislocations on subboundaries £* and
389 on long range stress 4/ are important. At stage IV, when dislocation-disclination substructures cover the whole material volume the flow stress turns to be proportional to the excess dislocation density the subboundary density and to disorien tation between fragment (Pig· 4).
Pig. 4· Dependence of flow stress on excess dislocation density, subboundary den sity and on disorientation between microbands. ο/Λφ was determined according to disorientation gradient and bending contour picture (Koneva and colleagues, 1986):
4*= Wnu-V)
· èy>/d/
O)
where G - shear modulus, t - foil width, )) - Puasson coeffici ent. The value of this contribution are shown on Pig. 5.
Pig. 5. Dependences of flow stress and long range stress on β"ζ (a) andarf on/^(b).
390 The total contribution £V and é* was determined by extrapolation of the straight-line sector of o ( p l/ ) dependence as the difference àé between the flow stress and extrapolation value (Fig· 5 - dotted line). On Fig. 5 the dependence of hé on J)± is shown. Δ é is a considerable part of the flow stress. CONCLUSION Thus, from the experiment described in this paper, it can be concluded that strengthening mechanisms are controled by sub structure type. At average deformation values flow stress is determined by interdislocation interaction. At stage III and IV that is with large deformation values, the contribution to flow stress depending on the dislocation resistance on subboundaries and on the long range stresses formed by disloca tion charges increase. The former contribution depends on subboundary disorientation. REFERENCES Koneva, N. A., and E. V. Kozlov (1982). Nature of work harde ning. Izv. Vyssh. Ucheb. Zab. Phys., 8t 3-14. Koneva, N. A., and colleagues (1985a). Types of dislocation substructures and stages of stress-strain curves of f.c.c. alloys. In H. J. Mc Queen et.al. (Ed.). Proc. 7th Int. Conf. on the Strength of Metals and Alloys, Vol. I, Pergamon Press, Oxford et.al., pp. 21-26. Koneva, N. A., and colleagues (1985b). Experimental investiga tion of stress dependence on the dislocation density of f.c.c. alloys. In H. J. Mc Queen et.al. (Ed.), Proc. 7th Int. Conf. on the Strength of Metals and Alloys, Vol. I, Pergamon Press. Oxford et.al., pp. 27-32. Koneva, N. A., and colleagues (1986). Dislocation-disclination substructures and strengthening. In V. I. Vladimirov (Ed.), Theoretical and Experimental Investigation of Disclinations. Phys. Tekh. Inst. Press, Leningrad, pp. 116-126.
ABSTRACT The quantitative study of substructure evolution was made by the transmission diffraction electron microscopy and the clas sification of substructure types was done at plastic deforma tion stages of f.c.c. alloy. It was established that transi tion to stage III and IV of the plastic flow is connected with "phase" transition in a substructure and with the appearance of the substructure new parameter that is the excess disloca tion density. Long range stress field values were measured at dislocation-disclination stages of substructures. It was found that long range stress fields play a significant role in the flow stress. KEYWORDS Dislocation-disclination substructures; long range stress fields; excess dislocation density. INTRODUCTION At plastic deformation one can observe the appearance and de velopment of local smooth and discrete disorientation of crys tal lattice both in single crystals and in polycristals. The substructures, observed at these deformations, that is at the first, transition stage and at the second stage of stressstrain curves have purely dislocation nature. The substructu res, observed at the beginning of stage III of stress-strain curves, differ qualitatively from the first one. There toge ther with separate dislocations and their tangles with conti nuous disorientations of a crystal lattice, the discrete disorientations introduced by continuous and ragged boundaries of different perfection degree are present. These substructures we shall call dislocation-disclination substructures (Koneva and colleagues, 1986). At stage III of stress-strain curves 385
386 they cover gradually the whole material volume. The aim of the present work is the quantitative investigation of the substructure evolution at great deformations at stage III and IV and revealing of the relation between substructure parameters and flow stress. The work was done on f.c.c. single crystals and polycrystals based on Ni and Fe deformed at long (LRO) and short (SRO) range order state of solid solution. The materials and experimental procedure are given in the work (Koneva and colleagues, 1982, 1985a, 1986). EXPERIMENTAL RESULTS Figure 1 shows the dislocation-disclination substructures and their elements received experimentally.
Fig. 1. Dislocation-disclination substructures and their elements: 1 - one-sized and 2 - two-sized disoriented "stripped", 3 - "spotted" substructure, 4 - ragged subboundary, 5 - dipole and 6 - loop of partial disclination.
387 At stage IIIthe disoriented "stripped" substructure (microbands) is formed, which may be one-sized (Fig. 1.1) as well as two-sized (Fig. 1.2). The typical elements of such a substruc ture are separate ragged subboundaries (Fig. 1.4), dipoles of partial disclinations (Fig. 1.5) and loops of partial disclinations (Fig. 1.6). The continuous disorientations with big wave length and with rather small but gradually increasing disorientation gradient are additionally put on these substructu res. This fact is confirmed by bending the contours observed in microphotographs. The substructure with complicated charac ter of discrete and continuous disorientations, with numerous components of dislocation density tensor, with specific "spot ted" contrast is distinguished at stage IV (Fig. 1.3). These substructure is also called as fragmentary or subgrain subst ructure. There are several quantitative parameters of substructure. The most general one is the average scalar dislocation density p . The main parameter of dislocation-disclination substructure is an excess dislocation density n (Koneva and colleagues, 1986): = (1)
/ Γ Λ 7 . ///·^/ί/
where 3J00/- disorientation gradient, / - Burger's vector. The correlation between the accumulation velocity of scalar dislo cation densitydp foL S , the accumulation velocity of excess dislocation density αρ±/οίε and stages of stress-strain cur ves (Koneva and colleagues, 1985) is revealed (Fig. 2). Roman numerals indicate stages of stress-strain curves. The accumu lation velocity of the scalar dislocation density is at its maximum at stage II, decreases at stage III and is practical ly constant at stage IV. The «* ΰ accumulation velocity of exc cess dislocation density attains ^ ^ its maximum at stage III and 'çs 1 then decreases. At stage IV 1 dp/cLe and dp+/d£ are equal 1 / 2V < and are of low"values. This is connected with intensive pro ^ cesses of dislocations annihi lation.
Ψ
n
à
a
■!2
\ 8
¥
μ
γ/ds
4fa
li I
ÜJ
d»ffl/m
1
Ofi
i
Û,8
t\
e1
Fig. 2. Dependence of scalar and excess density (a) and its accumulation ve locity (b) in strain.
388 Figure 3 shows the excess dislocation density as the function of the scalar dislocation density where critical values of the scalar dislocation density is poited out too, when /r?+ begins to increase rapidly. ~
Pig. 3. Dependence of excess dislo cation densi ty on scalar dislocation density.
0
fo'2M
*
6
ß-W
For all investigated specimens jDcr variation lies in small in ternal 1,5 ... 3-1010 cm"2. It testifies to the fact that the formation of new substructure type is a result of the selforganisation process in dislocation structure. If we take the material with the same range order, the data for single crys tal and polycrystals with different grain size will be put on the same curve with the same J)Cz value. This reflects the phe nomenon of the so called "phase" transition in dislocation structure. Volume material occupied by one substructure type may be determined as phase of dislocation structure. On the whole the picture of flow-stress formation is rather complicated and it is not described only by interdislocation interection. As it was pointed out in the paper (Koneva,and Kozlov, 1982), flow stress consists of the following contribu tions: 1)oontact resistanance dislocations which are propor1/2 y tional to 0 ( 6cont ); 2)barrier resistance which is propor tional to boundary density M ( 6ga^ ); 3)long range stress fields which are proportional to Ω+ i^£^ ); 4)fluctuation cor rection connected with the dislocation structure dispersion ( 6f ). There is one more type of contribution for polycrystals that is contribution of the Hall-Petch type ( éHp )·
é =
(2)
where o^s is a contribution made by the hard solution streng thening,'which is not usually very large. For stages of dislo cation structure such contributions as é^s , 6Cont , éx , éHP are typical and when fluctuation correction is constant the linear dependence of é on βΛ'^ is observed (Koneva and col leagues, 1985b). At stage III and IV of dislocation-disclination substructures the contributions to flow stress depending on the resistance of dislocations on subboundaries £* and
389 on long range stress 4/ are important. At stage IV, when dislocation-disclination substructures cover the whole material volume the flow stress turns to be proportional to the excess dislocation density the subboundary density and to disorien tation between fragment (Pig· 4).
Pig. 4· Dependence of flow stress on excess dislocation density, subboundary den sity and on disorientation between microbands. ο/Λφ was determined according to disorientation gradient and bending contour picture (Koneva and colleagues, 1986):
4*= Wnu-V)
· èy>/d/
O)
where G - shear modulus, t - foil width, )) - Puasson coeffici ent. The value of this contribution are shown on Pig. 5.
Pig. 5. Dependences of flow stress and long range stress on β"ζ (a) andarf on/^(b).
390 The total contribution £V and é* was determined by extrapolation of the straight-line sector of o ( p l/ ) dependence as the difference àé between the flow stress and extrapolation value (Fig· 5 - dotted line). On Fig. 5 the dependence of hé on J)± is shown. Δ é is a considerable part of the flow stress. CONCLUSION Thus, from the experiment described in this paper, it can be concluded that strengthening mechanisms are controled by sub structure type. At average deformation values flow stress is determined by interdislocation interaction. At stage III and IV that is with large deformation values, the contribution to flow stress depending on the dislocation resistance on subboundaries and on the long range stresses formed by disloca tion charges increase. The former contribution depends on subboundary disorientation. REFERENCES Koneva, N. A., and E. V. Kozlov (1982). Nature of work harde ning. Izv. Vyssh. Ucheb. Zab. Phys., 8t 3-14. Koneva, N. A., and colleagues (1985a). Types of dislocation substructures and stages of stress-strain curves of f.c.c. alloys. In H. J. Mc Queen et.al. (Ed.). Proc. 7th Int. Conf. on the Strength of Metals and Alloys, Vol. I, Pergamon Press, Oxford et.al., pp. 21-26. Koneva, N. A., and colleagues (1985b). Experimental investiga tion of stress dependence on the dislocation density of f.c.c. alloys. In H. J. Mc Queen et.al. (Ed.), Proc. 7th Int. Conf. on the Strength of Metals and Alloys, Vol. I, Pergamon Press. Oxford et.al., pp. 27-32. Koneva, N. A., and colleagues (1986). Dislocation-disclination substructures and strengthening. In V. I. Vladimirov (Ed.), Theoretical and Experimental Investigation of Disclinations. Phys. Tekh. Inst. Press, Leningrad, pp. 116-126.