thermally activated deformation. ii. deformation of sintered iron
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Thermally activated deformation. II. Deformation of sintered ironT. O'D. Hanley, A. S. Krausz, and N. Krishna Citation: Journal of Applied Physics 45, 2016 (1974); doi: 10.1063/1.1663539 View online: http://dx.doi.org/10.1063/1.1663539 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/45/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The influence of premolding load on the electrical behavior in the initial stage of electric current activatedsintering of carbonyl iron powders J. Appl. Phys. 113, 214902 (2013); 10.1063/1.4808339 Sound absorption with fibrefree sintered aluminium in combination with thermally activated concrete slabs J. Acoust. Soc. Am. 123, 3443 (2008); 10.1121/1.2934248 Identification of Sintered Irons with Ultrasonic Nonlinearity AIP Conf. Proc. 657, 1257 (2003); 10.1063/1.1570276 Thermally activated deformation. I. Method of analysis J. Appl. Phys. 45, 2013 (1974); 10.1063/1.1663538 Effects of Irradiation on Thermally Activated Flow in Iron J. Appl. Phys. 36, 2317 (1965); 10.1063/1.1714471
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Thermally activated deformation. II. Deformation of sintered iron T. 0'0. Hanley, A. S. Kratusz, and N. Krishna
Department of Mechanical Engint !ering. University of Ottawa. Ottawa. Canada (Received 27 August 1973)
The atomic processes associated with the plastic deformation of commercial-quality sintered iron were investigated. Stress relaxation tests were carried out over the l7-19-kg mm- 2 range of initial stress levels at room temperature. The ex, perimental results were analyzed with the deformation kinetics theory discussed in Paper I. The aL talysis showed that the rate-controlling mechanism is associated with a system of two consecutive eJllergy barriers. At high stress levels only the first barrier is effective. The corresponding activatio n volume of - 200 b3 , measured in these tests, suggested that the Peierls-Nabarro mechanism was r 'ate controlling at this level. It is proposed that the second barrier is either the second half of th e "camel-hump" Peierls-Nabarro barrier or the resultant of a series of dragging-point barriers contn )lling the spreading of the double kink.
INTRODUCTION
There is an increasing interest in the plastic behavior of sintered iron. Precision-fit sintered components deform plastically during service life. Whi.le the total amount of plastic strain which occurs in these components is small, the effect is crucial on thelir performance. Coining or other operations, whicl'l follow sintering in the production of high-accuracy components, are further examples of the need for underntanding the plastic-deformation processes in sintered r.netals. Numerous engineering studies have been carri ed out in which the plastic properties of sintered metals were investigated, but little information is availabl€~ on the associated phYSical processes. It is the purpos.e of this paper to report the results of a study in which the atomic process which controls the deformation rab~ in sintered iron was investigated.
A previous publication! discussed the proces:s of breaking and establishing atomic bonds which rl~sults in a macroscopic permanent change of shape and s.howed that the rate of this process can be described by the kinetics equation (discussed in Paper I) as
Rate=f(li,k). (1 )
The contribution of an activation event Ii and the rate constant k depend on the structure which changes s'ubstantially during large-scale plastic flow. To obtai.n information on the stress dependence of the deformaUon rate and through this on the atomic processes, it is necessary to keep the strain change during measuremer.\ts small enough so that structural changes are negligible. To achieve this condition the stress dependence of de-formation rate was measured in stress relaxation experiments. To obtain physically meaningful information on the atomic processes, internal stresses were also determined. A deformation kinetics analysis, described
TABLE I. Chemical composition of the powder.
Element
C 8 P Mn 8i Acid insolubles Fe
Content \%)
0.02 0.02 0.02 0.15 0.13 0.23 balance
2016 Journal of Applied Physics. Vol. 45. No.5. May 1974
in Paper I, was carried out and information was obtained on the structure of the energy barrier system.
EXPERIMENTAL PROCEDURE
Specimens were machined to 5.08 + O. 025 mm in diameter and - 50 mm in length from Domtar MP 32 sintered iron of extensive commercial use. The chemical composition of the powder is shown in Table 1. The sintered iron was produced by the standard commercial process. 2 A typical tenSile-load-elongation curve measured at a strain rate of 0.1 min-! is shown in Fig. 1.
Stress relaxation tests were carried out on a model TTC-M Instron tensile testing machine. This is a hard machine and care was taken to use rigid grips and loading fixtures to keep plastic deformation as small as possible during stress relaxation. Stress relaxation tests were carried out over four orders of magnitude of stress rate.
400
300
200
100
o 0.2 0.4 0.6· 0.8 1.0 1.2
ELONGATION mm
FIG. 1. Tensile-load-elongation curve of Domtar MP 32 sintered iron measured at a strain rate of 0.1 min-t.
Copyright © 1974 American Institute of Physics 2016
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2017 Hanley, Krausz, and Krishna: Thermally activated deformation. II 2017
~E 17
E
(f)
~ >--(f) 16
0.1 10 100
TIME sec
FIG. 2. A typical stress-relaxation result obtained in sintered iron. In the figure CT. is the measured (applied) normal stress.
Internal stresses were measured with the combined positive and negative stress relaxation method proposed by Gibbs. 3,4 All tests were carried out at -30±O. 5°C. A typical stress relaxation behavior is shown in Fig. 2.
DEFORMATION KINETICS ANALYSIS
To obtain information on the atomic processes which control the plastic deformation of sintered iron a kinetics analysis has been carried out using the methods described in Paper I. It was shown there that the kinetics equation [Eq. (1)] can be expressed formally for a system of m parallel barriers as
m
R=6 6/PfikfJ -PbJkbJ) (2) J =1
and for a system of n consecutive barriers, using tJ = 1iki , as
(3)
The measured curves were replotted in the - da,/ dtvs-a;, coordinate system. A typical example is shown in Fig. 3. Kinetics theory considerations lead to the conclusion that in the high stress range the deformation rate is controlled by activation over a single energy barrier in the forward direction. A least-squares fit was carried out over this range and the preexponential factor 61Pf~f1 and the activation volume V,I were evaluated (Table IT).
Because in the low stress range all of the measured curves deviated from the Simple one-term behavior, backward activation was analyzed next. A single-barrier kinetics analysis was carried out in the In(R - 6tPftkfl)vs-a;, coordinate system. In none of the test was a long enough straight-line segment noticed to indicate the presence of backward activation over a single barrier. The steepness of the curve further supported the sug-
TABLE II. Activation parameters obtained from the analysis.
I
'0 CI>
101 en
N
'E E co .¥
·be
-2 I 10
0:: I
o
o
I 17.5
I
o
o o
o
°
o o
o
T
o
o 0°0
o _
I
18.0 18.5
0'0 kg mni2
FIG. 3. Typical behavior of the rate of stress change vs applied stress; Stress relaxation was carried out at the ~ = 18. 9 kg mm~ level.
gestion that the backward activation volume is not small enough to allow activation to occur against the stress and that, consequently, backward flow is negligible (Fig. 4). It was concluded from first-level kinetics analysis that plastiC flow in sintered iron occurs over two or more different types of energy barriers.
A thorough investigation of the experimental results proved that the measured curves could not be matched with the parallel system kinetics described by Eq. (2). It was concluded that the two barriers are combined in series and an analysis was carried out with Eq. (3). This equation was written in the following form for the first step of the second-barrier analysis:
I (Qe.6 _ 1\ = I ~) _ l}1 + lig n R ~ n Ag 2kT a;, , (4)
realizing from the previous step that P3t;l ~O. In Eq. (4) 6Plkl is known from the single-barrier analysis and log [(6Plk /R) -'1] was plotted as a function of the measured
Applied stress level at the beginning of stress relaxation
Internal stress CT,
Preexponential factor
Activation volume
CTg (kgmm-2)
17.03±0.27 19.05±0.15
(kgmm-2)
14.67±0.63 17.06 ±O. 24
J. Appl. Phys., Vol. 45, No.5, May 1974
In(- aplAfl)
-45±18 -100±6
154±64 297 ± 14
436±63 440±55
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2018 Hanley, Krausz, and Krishna: Thermally activated deformation. II 2018
'0
'" '" o N 'E 0 E 0
~ 103t- 0 -
o ... "' 0 ~
",,-
, Ie 0::
17.5 18.0 18.5
CTa kg mrii2
FIG. 4. An example of the analysis of the backward activation over the first energy barrier, The circles indicate values obtained from the measured behavior.
stress uB
(Fig. 5). The range over which a straight-line relation was obtained indicates the validity limit of the two-barrier system. Good matching was obtained for all of the tests over the whole stress range (Fig. 6). Table II presents the activation parameters obtained from the analysis.
At the lower stress level a significant variation of the activation parameters was observed among individual specimens as indicated in Table II. With increasing deformation the specimens acquired an increasingly similar flow history and, in consequence, the scatter in the activation parameters was less at the higher stress level.
DISCUSSION
Conrad,5 Christian and Masters, 6 Altshuler and Christian,7 and others8 have found evidence that at low temperature the rate of the thermally activated plastic deformation of iron is controlled by the Peierls-Nabarro mechanism. The activation volume l'tt = 154 - 297 b3
measured in sintered iron is in good agreement with this
o
o
102
o
o 10
"'=11 0..0::
""
o
o
17.5 18.0 18.5 0;, kg mrTi2
FIG. 5. A typical result of the analysis for consecutive energy barriers. The circles indicate calculated values, and the slope of the line is related to Vf2 according to Eq. (4).
sure barrier heights, the present kinetics analysis provides approximate activation energy values within - 30%. This analysis indicated that the height of the second barrier may be about 20% above the first barrier.
mechanism at the initial high stress level of the relaxa- '~
tion process. The kinetics analysis indicated that in ~
sintered iron the backward flow over the energy barrier ~
system is negligible. This result is also in agreement with the behavior of the Peierls-Nabarro mechanism. Further indirect evidence follows from the conclusion that the measured preexponential factor 0prAft (Table II) was well within the phySically reasonable values when an activation energy of AE}t ",0.9 eV was conSidered. An applied stress of 19 kg mm-2 decreases this activation energy to the apparent activation energy value cited by Conrad4 for iron and ascribed to the Peierls-Nabarro barrier.
As the stress decreased during relaxation, the effect of a second barrier became evident. It was found that this barrier is combined in series with the first barrier. While activation energy measurements obtained in tests at various temperatures should be carried out to mea-
J. Appl. Phys., Vol. 45, No.5, May 1974
a: ,
150 160
FIG. 6. Typical stress relaxation vs applied stress results. The triangular symbols represent the measured values, the curves were calculated according to the kinetics theory [Eq. (4) 1. Curve (a) corresponds to an initial stress level of a ~ =16.75 kgmm-2 and curve (b) to ag=18.9 kgmm-2• The open circles indicate calculated initial relaxation rates.
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FIG. 7. The "camel-hump"-type Peierls-Nabarro energy barrier.
Guyot and Dorns have discussed a" camel-hump"shape energy barrier in association with the PeierlsNabarro mechanism (Fig. 7). These two consecutive energy barriers have equal heights with respect to the initial energy level. While the results of the present analysis indicated that the second barrier may be slightly higher, it is not pronounced enough to rule out this energy profile. A temperature-change test should be carried out to measure the barrier heights directly in order to clarify further the possible operation of this mechanism.
Condensation of point defects along dislocation lines can have a particularly strong effect in commercialquality sintered iron. After activation over the PeierlsNabarro barrier the kinks spread sideways. Along a clean dislocation line only the periodic potential field of the crystal matrix acts. Because these barriers are low the kinks can spread at a high velocity and only the thermal activation over the first, or Peierls-Nabarro, bar-
APPENDIX
rier is noticeable. Point defects, however, are strong obstacles and can slow down kink spreading very effectively. These dragging points present a series of consecutive barriers. Because point defects constitute identical barriers, their effect in mathematical formulation of deformation kinetics appears as a single second barrier. The rate equation in this case is (see Appendix)
x (v;,PN +nVp<! \1-1 exp - 2k T (TOft} J (5)
where n is the number of point defects. The analysis of the experimental results carried out for this mechanism showed that the second barrier is composed of about 102
point defects-a reasonable number. The study indicated that a series combination of a Peierls-Nabarro hill and several dragging points may also be considered to be the rate-controlling mechanism of the thermally activated plastic flow in sintered iron.
ACKNOWLEDGMENT The financial assistance provided by the National Re
search Council of Canada and by the University of Ottawa is gratefully acknowledged. The authors are indebted for the sintered specimens donated by the Metals Powder Division of Domtar Chemicals Ltd.
For a Peierls barrier followed by a succession of n point-defect barriers, Eq. (3) can be written
( 1 kpN k pN k PN)-1 R=OPlk pN +-+ ... +--+ ... +-- , kpdl kpdl kpdn
(AI)
where the subscript PN denotes the Peierls-Nabarro barrier and the subscript pdi denotes the ith point-defect barrier. The general term in the ratios of rate constants is
k pN = (_ .6.CirN -ljpNT)[ (_ (C!dl)1 - (ljpN + '\ibPN + ljPdl + '\ibMl + ... + ljpdl)T)]-l k exp kT exp kT '
pal
with (Clu )1 denoting the energy at the top of the ith point-defect barrier with respect to the energy in the valley in front of the Peierls-Nabarro barrier so that
(Clu)l = .6.CjpN - .6.ClpN + .6.C1Pdl - .6.C:pdl + ... + .6.C1PdI'
If VlPdI = v;,PdI == VPd and .6.C1PdI == .6.Ctpdl == .6.C!a for all of the point-defect barriers, then
k pN _ (_ .6.CtPN - .6.CL _ v;,PN + (2i -lHpa ). k -exp kT kT T
pdl
This ratio substituted in Eq. (Al) yields
With u== exp(- 2VpdT/kT) the summation becomes
un/ 2 U-n/2 _ un/ 2
= U 1/ 2 U-1/ 2 _ U 1/ 2
J. Appl. Phys., Vol. 45, No.5, May 1974
(A2)
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= ex (_ (n -1) Vpd T ) sinh(n Yed T/ kT) • p k T sinh(lj,d T/k T)
(A3)
For point defects lj,d is of the order of 1 b3, so that VT/kT is small and the expression in Eq. (A3) reduces to
n exp[ - (n -l)lj,d T/kT]. Then with tensile stress ueff = 2T replacing the shear stress, Eq. (A2) becomes
IA.S. Krausz and H. Eyring, J. Appl. Phys. 42, 2382 (1971). 2N. Krishna, M. A. Sc. thesis (University of Ottawa, 1971)
(unpublished) . 3G. B. Gibbs, Philos. Mag. 13, 317 (1966). 4H. Conrad, Mater. Sci. Eng. 6, 265 (1970). 5H. Conrad, in Dislocation Dynamics, Proceedings of the 2nd Battelle Inst. Materials Science Colloquium, Seattle,
J. Appl. Phys., Vol. 45, No.5, May 1974
1967, edited by A.R. Rosenfield, G. T. Hahn, A. L. Bement, Jr., and R. 1. Jaffee (McGraw-Hill, New York, 1968).
6J.W. Christian and B.C. Masters, Proc. R. Soc. Lond. 281, 223 (1964).
7T.L. AltshulerandJ.W. Christian, Philos. Trans. R. Soc. Lond. 261, 253 (1967).
8p. Guyot and J. E. Dorn, Can. J. Phys. 45, 98~ (1967).
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