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A MECHANISM FOR AUTOWISTING AND THE LOW-FREQUENCY HYDRIDE PRECIPITATION
PEAK IN THE BCC METALS
I. Ritchie
To cite this version:
I. Ritchie. A MECHANISM FOR AUTOWISTING AND THE LOW-FREQUENCY HYDRIDE
PRECIPITATION PEAK IN THE BCC METALS. Journal de Physique Colloques, 1987, 48 (C8),
pp.C8-179-C8-184. �10.1051/jphyscol:1987824�. �jpa-00227128�
A MECHANISM FOR AUTOTWISTING AND THE LOW-FREQUENCY HYDRIDE PRECIPITATION PEAK IN THE BCC METALS
I.G. RITCHIE
Materials Science Branch, Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, ROE 1L0, Canada
~isum;
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A l'aide d'un modsle de l'autotorsion et du pic y instable associe'dans le fer a, mod&le rgalisc par P. ~sti; (11, on montre qu'on peut attribuer l'autotorsion et la composante transitoire du pic basse fre'quence de pricipitation de l'hydrure dans le V, le Nb et le Ta, 'a l'instabilit; du processus d& pic y en prcsence des inter- stitiels de l'hydrog$ne mobile. Dans ce modgle, la composante transitoire du pic basse frgquence de prgcipitation de l'hydrure et l'autotorsion associ6e sont dues \a la transformation graduelle des dislocations longues, droites, vis en dislocation courbes, non-vis.Donc, le pic basse frcquence de prgcipitation de l'hydrure est la relaxation de Snoek-KFster des dislocations vis, et ce pic est tronqug,
2
une tempgrature voisine de la solubilitS finale h l'6tat solide de l1hydrog2ne.Abstract
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Using a model of the autotwisting and associated, unstable, y-peak in a-iron, developed hy P. Astie (11, it is shown that the autotwisting and the transient component of the low-frequency, hydride precipitation peak in V, Nb and Ta may he attributed to the instahil- ity of the y-peak process in the presence of mobile hydrogen intersti- tials. In this model, the transient component of the low-frequency, hydride precipitation peak and the associated autotwisting are due tothe gradual conversion of long, straight, screw hydride dislocations to bowed-out, non-screw dislocations. As a consequence, the low- frequency, hydride precipitation peak is the Snoek-K'cister relaxation of screw dislocations, truncated at a temperature close to the terminal solid solubility of hydrogen.
I
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INTRODUCTIONInternal friction (IF) techniques at low frequencies (0.5 to 10 Hz) 12-77 and resonant-bar frequencies (1 kHz to 40 kHz) 18-12] have been used to study hydride precipitation and to map the terminal solid solubility (TSS) boundaries in metals.
At both low and high frequencies, the hydride precipitation process is marked by a
"precipitation" peak of IF that is sharply truncated at the TSS /2-121. In torsion pendulum experiments, the precipitation peak is accompanied by significant zero-point drifting of the pendulum, variously referred to as self-twisting or autotwisting.
Some workers have attributed autotwisting to the Poynting effect (31, hut more recent work has demonstrated that the autotwisting is associated with the movement of hydride dislocations [4,13,14), i.e., misfit dislocations punched into the lattice around hydride precipitate particles during precipitation.
Systematic studies of the precipitation peak and autotwisting (at low frequencies) have been reported on V [3,4,9,10,121, Nb [4,8], Ta [3,4,111, Ti [2,71 and Zr 15,141.
From these, it is clear that at least two distinct mechanisms, giving rise to two different IF peaks, have been labelled as hydride-precipitation peaks. The first, at ].ow frequencies, is characterized by the fact that its height decreases with thermal cycling through the TSS. This is the low-frequency precipitation peak. The second, observed at kHz frequencies, is characterized by the fact that its height increases
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987824
C8-180 JOURNAL DE PHYSIQUE
with thermal cycling through the TSS and is labelled the high-frequency precipitation peak.
The high-frequency precipitation peak is adequately explained by the overlapping of the hydrogen Snoek-K6ster relaxation (s-K(~,H)) of non-screw (1) components of the hydride dislocations with the TSS 18-11,151. Truncation of the IF peak close to the TSS on heating is due to a decrease in the density of hydride dislocations and a radical change in the internal stress. The reverse process occurs on cooling, accompanied by the substantial thermal hysteresis normally associated with TSS phenomena. An increase in the height of the high-frequency precipitation peak with thermal cycling is simply related to the generation of an increasing density of hydride dislocations during repeated cooling through the TSS.
The low-frequency precipitation peak behaves very differently. It contains at least two components at the same temperature: a transient component and an equilibrium component, both strain-amplitude independent. The transient component is dominant in those systems where the specific volume change on hydride precipitation is greatest 141. The equilibrium component is greatest in V, which has the smallest specific volume change of the common hydride formers (4). From the behaviour of the transient component of the low-frequency precipitation peak and associated autotwisting, it is clear that the two phenomena are intimately related and caused by the presence of hydride dislocations. During the last decade, there has been a rapid increase in our understanding of the intrinsic relaxation properties of dislocations in the bcc metals in terms of geometrical kink migration and the thermal generation of kink- pairs [15]. This has been accompanied by an equivalent increase in our understanding of the S-K relaxations 115-191. The hydrogen S-K relaxations involve the same intrinsic kink processes mentioned above in the presence of hydrogen interstitial atoms with dislocation-core mobility 116-181. Ilnfortunately, there has not been an equivalent increase in our understanding of the intrinsic dislocation relaxations in the high-temperature hcp metals, Ti, Hf and Zr 1191. Consequently, in the following, we will consider only the bcc hydride formers V , Nb and Ta, and a-Fe, in which hydrogen is only very weakly soluble and there is no known hydride. Nevertheless, we want to emphasize that the low-frequency precipitation peaks in Ti and Zr are very similar to those in V, Nb and Ta. For this reason, we expect that a similar model to that outlined below will emerge for Ti and Zr when more is known about the intrinsic dislocation relaxations in these metals.
This paper presents a model for the transient component of the low-frequency
precipitation peak and associated autotwisting in V , Nb and Ta. Towards this end, we will summarize the experimental properties of the peak that have to be explained by a satisfactory model.
I1
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PROPERTIES OF THE LOW-FREOUENCY PRECIPITATION PEAKThis summary of the properties of the transient component of the low-frequency hydride precipitation peak in V , Nb and Ta is drawn mainly from the work of Yoshinari and Koiwa 141.
i) The peak is truncated at approximately the TSS temperature, i.e., the trunca- tion temperature increases systematically with increasing hydrogen concentra- tion in the samples, and follows the TSS.
ii) There is a marked hysteresis in the truncation temperature on heatin$ and cooling through the TSS.
iii) The height of the peak decreases on repeated thermal cycling, while the height of S-K(~,H) increases.
iv) At temperatures higher than the TSS, there is little or no autotwisting. The autotwisting rate increases rapidly as the sample is cooled through the TSS.
The disappearance of the autotwisting rate around the truncation temperature is more gradual on heating.
v) The height of the peak on the first thermal cycle increases with increasing hydrogen content in the metal.
vi) The height of fhe peak is directly proportional to the heating or cooling rate, i.e., Q&
\TI.
All of these properties can be rationalized, at least qualitatively, in terms of the fundamental instability of long, straight, screw dislocations (O) in the bcc metals in the range of the y-peak [1,20-231. This interpretation becomes more transparent if we review, vary briefly, the intrinsic dislocation relaxations in the bcc metals and the modification of these properties in the presence of dislocation-core mobile hydrogen interstitials.
111
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INTRINSIC DISLOCATION RELAXATIONS AND THE HYDROGEN SNOEK-KBSTER RELAXATIONS The low-frequency relaxation spectra of deformed, pure, bcc transition metals, constructed mainly from the work of Schultz and coworkers r20,21], are summarized in Figure 1. These spectra are characterized by two main features: (a) a group of overlapping peaks labelled a'/a at low temperatures, and (b) a peak labelled y at high temperatures. The maior component of a'/a is due to kink-pair generation on non-screw(1)
dislocations, while y is due to the same process on screw (O)dislocations. More details of these peaks and their interpretation can be found elsewhere f15,19-231. The important points to note here are that y is enhanced by low-temperature deformation and is unstable (accompanied by autotwisting) in its own temperature range on the first heating after deformation [1,20-231. Furthermore, on thermal cycling to a temperature just above the range of y, the height of the major component of a1/a increases, while the height of y decreases, i.e., there is a conversion of screw components to non-screw components in the dislocation population.
The autotwisting in the range of peak y on the first heating after low-temperature deformation is irreversible (11. Further autotwisting can be induced, but only after another low-temperature deformation.
When the bcc metals are charged with hydrogen, the expected modifications to the low frequency relaxation spectra are shown schematically in Figure 2. The a'/a complex and y peak are suppressed in each spectruxu and replaced by
S-K(I,H)
and S-K(3,H), respectively, at higher temperatures. S-K(;,H) is well-known in V, Nb, Ta and a-Fe[15], but there appears to be little direct evidence for S-K(B,H) except for the case of a-Fe, as shown in Figure 3 1231. Nevertheless, the S-K(O,X) for other inter- stitial~ (X = C, N or 0) is well estahlished [161. In fact, we believe that in V, Nb and Ta, the transient component of the low-frequency precipitation peak is none other than the S-K(Q,H) relaxation of unstable, screw dislocation segments. This is the hasis of the model outlined below.
IV
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MODEL OF THE TRANSIENT LOW-FREQUENCY HYDRIDE PRECIPITATION PEAK IN V, Nb AND Ta a) Oualitative considerations. Since the basic mechanisms for peak y and S-K(B,H) are similar, except for the presence of core-mobile hydrogen interstitials in the latter case, it is expected that the behaviour of the S-K(@,H) peak will mimic the behaviour of peak y, except for those attributes directly due to the presence of hydrogen. This is the case, and the properties i) to v) listed in section I1 can be accounted for as follows.i) S-K(B,H) is truncated at the TSS for two reasons: a) the density of hydride dislocations is decreased on heating through the TSS and increased on cooling through the TSS, and h) there is a radical change in the internal stress experienced by the hydride dislocations in the vicinity of the TSS. The role of internal stress in increasing the heights of kink-pair relaxation peaks is well established 115,191.
ii) The hysteresis of the truncation temperature is the hysteresis of the TSS itself (241, although the magnitudes of the contributions of elastic and plastic accommodations of the hydrides to the observed hysteresis are difficult to calculate.
iii) The peak height of S-K(@,H) decreases, while that of S-K(~,H) increases during thermal cycling because long, unstable, screw segments are converted to non- screws.
iv) The autotwisting is due to the conversion of unstable screw segments to non-
C8-182 JOURNAL DE PHYSIQUE
screw segments. Unlike the case of peak y, where autotwisting occurs only on the first heating after low-temperature deformation, hydride precipitation itself generates new screw dislocation segments on each thermal cycle. This ensures some reversibility of the autotwisting associated with S-K(Q,H) on each thermal cycle.
v) The height of S-K(Q,H) on the first thermal cycle increases with hydrogen content because the density of hydride dislocations increases.
b) 0-' ~?l/f. Because the behaviour of the S-K(Q,H) peak mimics the behaviour of peak p w e can use a model already developed by Astie [I1 to explain the instability of peak y and the associated autotwisting in a-Fe. With reference to Figure 4, it is assumed that all the dislocations involved in S-K(@,H) are the same length, AB = Lo, at T = 0 K, all segments are assumed to experience an internal stress of magnitude
1.1 I.
Half of them experience +ri and half --r.
Geometrical kinks are not taken in40 account. Non-screw segments are assumed to behave like segments of strings, so that their radii of curvature can be expressed as R = pb/r, where p is the line tension and b the Burgers vector. It is further assumed that there is always an additional stress, AT (accidental or deliberate), that polarizes the two groups of dislocations. Finally, it is assumed that both T and AT are weaker than the stress necessary to activate sources. Of course, this will not be the case during cooling through the TSS. Nevertheless, using the above assumptions and following thecalculations of ~ s t i g [I], the changing length L(T) on whick kink-pair generation can occur ca? he czlculated as a function of the heating rate, T. Calculation of the area (AS
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AS ) swept-out by kink-pair generation on the screw segments (see Figure 4) yields the autotwisting and transient IF peak.The resulting equation for L(T) is
where vD is the Debye frequency, k T501tzmann1s constant, the critical separation of kinks in the kink-pair generation model 1191, AH(ri) th% relaxation enthalpy and E, the exponential integral. The equations for the reduced autotwisting strain, y(T)/y,, and reduced internal .friction,
Qi'
areNumerical solutions of these equations are presented as two families of curves in Figures 5 and 6. These show that 0-' T during heating, and Q-I l/f. Thus the model accounts for all of the p r o p e w e s i) to vii) listed in s e w o n 11. An equivalent model for cooling would be much more difficult to formulate. However, it is not unreasonable to expect a similar process to proceed in reverse, as fresh screw dislocation segments are created by the precipitation of hydrides.
V
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CONCLUSIONSA model is presented that attributes the transient component of the low-frequency, hydride-precipitation peak and associated autotwisting in V, Nb and Ta to S-K(O,H).
The model accounts, at least qualitatively, for all of the primary characteristics of the low-frequency, hydride-precipitation peak and astotwisting reported jn the literature.
VI
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32
(1984) 1259.0
0 200 400
600 800
Temperature ( K )
Fig. 1 Schematic diagram of the positions and shapes of the intrinsic dislocation relaxations at about 1 Hz in pure, deformed bcc metals.
0
0 200 400 600
Temperature
(K)
Fig. 2 The suppression of the intrin- sic dislocation relaxations (broken curves) and their replacement by the Snoek-Koster relaxations in hydrogen- charged, deformed bcc metals.
S-K(O,H) is shown truncated at the TSS
.
JOURNAL DE PHYSIQUE
Q-'x 10'
--Deformed at 7 7 K
--Deformed and hydrogen charged at 7 7 K
T f O K t finite
Temperature ( K )
Fig. 3 Pure iron deformed 3% in tension Fig. 4 Schematic evolution of two screw at 77 K (curve 1) compared with an iden- dislocation segments under the influence tical sample after charging with hydrogen of opposite internal stresses -hi and -r
(curve 2). and a polarizing stress AT. i
.- .
0
--
(D 0
0 e
. .
0 0
m 0
0 m
.- .
0 0 Autotwisting
Fig. 5 Calculated curves of transient Fig. 6 Calculated curves of transient damping and autotwisting as a function damping and autotwisting as a function of of-temperature for various heating rates temperature for various frequencies (f (T from 1 K/min to 5 K/min) and constant from 0.25 Hz to 3.0 Hz) and a constant frequency of 0.5 Hz. heating rate of 2 K/min.
