42.

43. 44.

45. 46. 47. 48. 49.

50. 51. 52. 53. 54.

P. Fleischmann, F. Lakestani, and J. C. Baboux, "Analise spectrale et energetique d'une source ultrasonore en mouvement. Application a l'emission acoustique de l'aluminium soumis a deformation plastique," Mater. Sci. Eng., 29, No. i, 205-212 (1977). D. Delipkumar, V. S. R. Gudimetla, and W. E. Wood, "Amplitude distribution analysis of acoustic emission," Exp. Mech.. 19, No. 12, 438-443 (1979). J. Holt and D. J. Goddard, "Acoustic emission during the elastic--plastic deformation of low-alloy reactor pressure vessel steels. I. Unlaxial tension," Mater. Sci. Eng., 44, No. 2, 251-265 (1980). G. G. Martin, "The effect of strain rate on acoustic emission from aluminum alloys," in: Ninth World Conference on Nondestructive Testing, Melbourne, 1979, 4J-4. M. A. Hamstad, R. G. Patterson, and A. K. Mukherjee, "Acoustic emission generated in unflawed 7075-T651 aluminum under uniform biaxial loading," ibid., 4J-10. M. A. Hamstad, E. M. Leon, and A. K. Mukherjee, "Acoustic emission under biaxlal stress in unflawed 21-6-9 and 304 stainless steel," Met. Sci., 15, No. 11/12, 541-548 (1981). G. Airoldi, "A533B and A508 steels: development of deformation processes with temperature as studied using acoustic emission," ibid., 16, No. 3, 153-158 (1982). K. H. Adams, B. R. Bass, J. E. Borhaug, et al., "An experimental investigation of delayed acoustic emission in beryllium," Lawrence Raidation Lab., Livermore (1969) (Report UCRL: N 13402). T. F. Brouillard (F. J. Laner (ed.)), Acoustic Emission: A Bibliography with Abstracts, IFl/Plenum Data Co., New York et al. (1979). E. J. Siegel, "Kilocycle acoustic emission during creep in lead, aluminum, and cadmium. I. Experimental," Phys. Status Solidi (A), 5, 601-606 (1971). E. J. Siegel, "Kilocycle acoustic emission during creep in lead, aluminum, and cadmium. II. Theoretical," ibid., 607-615. J. Gilman, "The mlcrodynamic theory of plasticity," in: Microplasticity [in Russian], Metallurgiya, Moscow (1972), pp. 18-37. R. T. Sedgwick, "Acoustic emission from single crystals of LiF and KCI," J. Appl. Phys., 39, No. 3, 1728-1740 (1968).

ACOUSTIC EMISSION IN PLASTIC DEFORMATION OF METALS (REVIEW). REPORT 2 UDC 534.16:539.214

A. A. Yudln and V. I. Ivanov

Distribution of Signal Amplitudes. Oscillographic observations have shown that the acoustic emission signal from a single act of deformation may with satisfactory approximation be represented in the form of a damping rf pulse:

[([)

=

[Aexp(---!-~-)sin2~vo (t-- T), t > T;

(1)

1

[0, t < T , where A is amplitude, T is the time of appearance of the signal, ~ is the constant of time determined by the Q-factor of the equivalent circuit describing the response of the specimen, the piezotransducer, and the rf apparatus, and 9@ is the normal resonant frequency of the piezotransducer (A and T are random values). According to experimental data, the range of change in A reaches three orders of magnitude of the value. An analysis of the distribution of A may provide useful information on the deformation process. In addition, crack formation and development normally causes acoustic emission signals of higher amplitude than does deformation ([55], for example)*; therefore, the appearance of hlgh-amplltude signals may serve as a criterion of approaching failure. *For [1-54] see Report i. Scientific-Production Association of the Central Scientific-Research Institute for Machine Building Technology, Moscow. Translated from Problemy Prochnosti, No. 6, pp. 99107, June, 1985. Original article submitted June 6, 1984.

0039-2316/85/1706-0851509.50

9 1986 Plenum Publishing Corporation

851

E~N !

o

2

3

~

f

--

Number of the amplitude analyzerchannel Fig. I. The amplitude distribution of acoustic emission signals for Ducol W-30 steel obtained in tension of a specimen in the f o r of a double cantilever b e ~ . Channels 1-5 correspond to the following i n t e ~ a l s of the values of amplitude in mV: 0.05-0.5; 0.5-5; 5-50; 50-500; 50050,000, respectively [36].

I0 3

102

r

E Z

tO t

IL.A___~j I01

10 ~

Amplimde, rel. um~

Fig. 2. Amplitude distribution of the acoustic emission signals for Cu--10 Ge alloy [14]. The amplitude distribution is obtained experimentally in the form of a histogram of the distribution of the maxima of the acoustic emission signals, i.e., of the maxima of the envelope. In the case of discrete acoustic emission, when the signals of type (I) do not overlap, it actually gives the distribution of the amplitudes A of the individual pulses. Continuous acoustic emission is a dense superposition of individual pulses, and here the amplitude distribution acquires a different sense. These two cases must be considered individually. The description of the amplitude distribution of discrete acoustic emission is based on the works of Pollock [56, 57], the essence of which we will present with insignificant changes. Let us assume that during the time of observation t n(t) acoustic emission events occurred. Let n~(a, t) be the probability (standardized to n) of an event [A > a], i.e., nx(a, t) is the number of those events at the moment of time t for which the amplitude A exceeds the specified valuea (0 ~ a < =). Then n(a, t) = n(t)-nt(a, t) is a function of the distribution of amplitudes A. Pollock, following the description used in seismology [58], assumes nt (a, t)

852

-

k (t) .0

,

(2)

where k(t) is some function of t, and b is a constant. amplitudes is

O.(a,t) Oa

m(a,t)=

Ont(a,t)

The density of the distribution of

hk (t) ob+l

(3) "

Let C be the threshold of discrimination. The number of intersections of it by the signal (i) with the amplitude A > C is equal to v(A) = ~oTln (A/C). The linear relationship between v and in A has been confirmed experimentally [56, 59, 43], which may be considered as an additional Justification for selection of description (I). The total number of intersections during the time t (total count) is equal to

N (t, C i = ~ v (a) m (a, t) da ---- ~2oTk

(4)

(t)

bCb

C

If Co is the level of interferences, during the time t will be

then the maximum possible number of recorded events

P (t, Co) = T m (a, l) da -- k(t) co Cob " Having eliminated k(t) from Eqs. Pollock theory:

(4)

and

N (t, C)

(5),

=

we o b t a i n

the

(5) basic

relationship

of the

~~ (-~)b P(t, Co), .

(6)

-U

linking N and P and expressing the relationship of the total count N to the threshold C. In place of P(t, Co) it would be more desirable to introduce the total count of events above the threshold:

N~ (t, C) = ~ m (a, t).da = n~ (C, t) -- k(t)co .

(7)

c Then instead of Eq. (6) we have the following relationships:

Therefore, tO one another.

for distribution

N (t, C) = ---U N,, (t, C);

(8)

(t, C) = "~ i" (t, C).

(8a)

(3) the counting rate N and the activity N a are proportional

Experience in general confirms these concepts. For an Mg single crystal Fisher and Lally [18] es%abllshed that as a rough approximation Na has a tendency to remain constant. According to Eqs. (7) and (8), this means fulfillment of Eq. (2) with b = i. It must be kept in mind that a change in amplitude is equivalent to a change in threshold. In [56, 57] Pollock also noted that more than once he was encountered "normal" distribution, for which b = i. For Ducol W-30 steel (0.16 C, 1.35 Mn) an exponential rule (2), (3) with b = 0.41 has been confirmed (Fig. i) [56]. For Cu--10 Ge alloys, in which deformation occurs by twinning, we have [14] b = 2.2 (Fig. 2). The departure from this distribution at low amplitudes is caused by the fact that here the emission approaches continuous acoustic emission. The cases presented are the limiting in the sense of values of b: normally the value of b ~ 0.4-2, and it is small in cases when deformation occurs as a small number of large Jumps, which is characteristic of brittle high-strength steels. For comparatively soft metals b acquires higher values. The physical sense of the value of b is not clear. seismologists are discussed in [60].

Attempts

to analyze it made by

To determine b it is not necessary to obtain the histogram of the amplitude distribution. Delipkumar et al. [43] found the value of b in the following manner. With the help of a calibration pulsator and a receiving transducer they first established the v - In(A/C) straight line relationship, the slope of which determlmes 9oY. Then from the results of tension tests of compact specimens with a notch and a preliminarily created fatigue crack

853

2

t

o

1

2

3

N. ~o-5

F i g . 3. Typical relationships of the count o f t h e number o f e v e n t s Na t o t h e t o t a l count f o r A I S I 4340 s t e e l from fracture toughness tests. For specimen AI b/v@T = 0.0089; v@T = 83; b = 0.74 and for specimen A2 b/~@T = 0.0119; vet = 83; b = 0.98 [43].

n1 (a)

1o'

tO 1 i 0,0250.t

\

Io;

2x ~ i 1

I I fo

!

i[

I

1

o,f

L y

b

1

/O o, V

Fig. 4. Approximation of the experimentally found amplitude distribution (dashed lines i) for specimen A1 of AISI 4340 steel by the Pollock function n,(a) = ka -b with b = 0.91 (a) and by the function n,(a) = Ba-be -ma with b = 0.51 and m = 0.27 (b) [43]. they constructed the N -- N a relationship, the slope of which according to Eq. b, since ~@T is already known from the preceding experiment.

(8a) determines

Figure 3 presents an example of N(N a) lines for two identical specimens AI and A2 of AISI 4340 steel. The values obtained of b = 0.74 and b = 0.98 satisfactorily agree with the values of 0.91 and 1.09, respectively, found by approximation of the distribution histograms by Eq. (2). In the opinion of Dellpkumar et al. of [43] thls method of determination of b has important practical value since it sharply simplifies the procedure for finding the amplitude distribution. The description of Pollock, despite some successes, cannot be considered satisfactory since the standardized integral of Eq. (3) diverges with a + 0. This does not make it possible to express the distribution parameters through the moments (average and dispersion). In a number of cases the function (2) poorly describes the amplitude distribution in the whole range of amplitudes (Fig. 4). Delipkumar et al. [43] showed that a good approximation is given by the function

nl ~, 0 = B (t) a - * - " ~ ,

(9)

where b and m are constants. It is possible to be convinced that for Eq. (9) Eqs. (8) and (Sa) remain in force with a different coefficient of proportionality. Obviously this may explain the fact that distribution (2) describes well the data presented in Fig. 3, although it does not agree with the data for the same specimen presented in Fig. 4. Distribution (9) also leads to a divergent standardized integral and therefore does not solve the problem of description of the amplitude distribution.

854

t#,I/F sec

f066 2 105 6

6 g 6 10 8

J

2

2 ,16

i

o

~

2

3

~

s c.m~ v

Fig. 5. The counting rate ~ as a function of the threshold of discrimination C for polycrystalline copper with different values of deformations. The deformation increases in the series of lines i-i0 [14, 31]. Now let us consider continuous acoustic emission. In [14, 31] attention was devoted to the fact that the form of the N(~) counting rates depends strongly upon the selected threshold of discrimination C. From this data it is possible to construct the N(C) relationships for different values of the parameter c (Fig. 5). The line i corresponds to the maximum in N(e) (e ~ 0.04%) and the remainder to higher deformations. They may be described by the equation =

Noexp (-- rzC),

(i0)

where No does not depend upon ~ (which means convergence of all of the lines in Fig. 5 at a pole on the in N axis) and a increases with an increase in e. For copper single crystals the same authors found a different relationship: = v o exp (-- ~2C2),

(Ii)

where vo is the resonant frequency of the transducer and 8 is a constant dependent upon e. We should note that in Eqs. (i0) and (ii) N is a function of e and C, but since for active tension the value of E is proportional to the time t, this is equivalent to the relationship N(t, C). Equations (i0) and (ii) indicate the presence of an amplitude distribution of continuous acoustic emission. In contrast to the case of discrete acoustic emission, here as the amplitude distribution is understood the single distribution for the envelope A(t) of the acoustic emission process ~(t). Let m,(a, t) be the density of this distribution, i.e., m,(a, t)da is the probability of the fact that A(t) satisfies the condition a~_ A(t)<~_ a + da. There exists the general relationship (it is given in [14] without derivation) m, (C, 0 " " a~T (t, c ) / a c .

(12)

Therefore, knowledge of N as a function of C makes it possible to find the above-determined amplitude distribution m, (C, t). Applying Eq. (12) to Eqs. (I0) and (ii), we obtain the following expressions for polycrystalline materials and single crystals, respectively [14 ] m(P)(C, t) = c~exp (-- c~C); (i 3)

m~S)(C, t) = 219C exp (-- [32C2).

(13a)

(Both distributions are standardized to unity.) Distribution (13) was also obtained in [i, 61] for straight-carbon steels although, according to the statements of the authors, in them burst-type acoustic emission was observed.

855

The experimental relationships (13) and (13a) allow independent verification. the expression for the rms signal

u (0 =

Uslmg

(c, Oac) o

for Eqs. (13) and (13a) we find:

o(P)(t) = 6~0; I " U(S)(t) - ~(t)

(14) (14a)

The values of U measured directly and calculated using Eqs. (14) and (14a) agree very well [14, 31]. According to the data of [14], for steels and alloys deformed with the formation of Luders bands the experimental data is described best of all by a combination of distributions (13) and (13a). With not-too-high values of N (increased C) Eq. (13) is fulfilled better, while in the opposite case Eq. (13a) is a better approximation. We should note that Eq. (13a) coincides (with 8 not dependent upon t) with the Rayleigh distribution for the envelope of the normal steady signal known from statistical radio engineering [62, 63]Z. Ono [64], considering from the very start the acoustic emission signal as a steady Gausslan process and using the known equation [65] for number of overshoots of the random signal beyond the threshold, determined that for a narrow-band signal the m,(a, t) distribution is a Rayleigh distribution, and for a broad-band signal a Gaussian. It has been shown experimentally that the Rayleigh distribution approximates well the experimental data for narrow- and broad-band conditions of recording of signals. In addition, Ono [64] observed that for continuous acoustic emission an exponential expression is unsuitable. An interesting example of the amplitude distribution is presented for polycrystalline zince in [66]. The authors observed a two-modal distribution in which the first maximum, at low amplitudes, corresponds to slip and the second, at triple the amplitudes, to twinning. A quantitative analysis of the distribution was not given. It is apparently possible to state that at least for discrete acoustic emission a correct description of the amplitude distribution has still not been found. Also lacking are attempts to establish the amplitude distribution of acoustic emission signals in the general case, from which the distributions for discrete and continuous acoustic emission would follow as particular cases. Spectral Content of the Signals. A study of the spectrum of acoustic emission signals may have both theoretical value (determination of the length of action of the acoustic emission sources, an analysis of their fine time structure) and applied (distribution of the contributions to acoustic emission from deformation and fracture, separation of the useful signals from the extraneous interferences) [67, 68]. In analysis of the spectral data the main role is played by the relationship relating the effective amplitude of the spectral density of the mechanical stress pulse caused by a Jump in deformation, i.e., its limiting frequency Vlim, and the length (time of existence) To of this pulse: Vlim~T~'"

(15)

In the case of acoustic emission this fact was first noted by Stephens and Pollock [69], who assumed a Gaussian form of the pulse. The value To also determines the effective width of the correlation function of the pulse. The most interesting and useful data on acoustic emission was obtained by Hatano [70, 41] and especially by Fleischman and others [42, 71]. The first author investigated narrowband recording by five resonant piezotransducers with frequencies of v ~ 0.i, 0.4, I, 2, and 4 MHz. A disadvantage of this method is that the study of the energy spectral density of the acoustic emission signal SE(v, e) as a function of E is possible only on different specimens. However, the authors state that a spread in results from specimen to specimen was not

856

.~. t',~,~), lim. units

1:1"-, ,I

\\

~

//

d MPa

\

o*(~)

'

~"

!

U FI /\

"\2 N 12o

5 F i g . 6.

10

~.%

The experimental s p e c t r a l

acoustic emission density S~(v, ~) and the stress o as a function of deformation e for A1 with a grain size of 3.6 mm at different frequencies 9: I) 0.94 MHz; 2) 1.56 MHz; 3) 2.17 MHz [42].

s~f ~,~). Io~/1~'-Iz

2f

\,~_f •9 - -23

-

0-4

O,2 \

6,04

,t,l

i

,

i

i

I

0,1 0,2 0,4

lli,ll

I

f

I

2

i

i

i

iJ

~, MHz

F i g . 7. The a c o u s t i c e m i s s i o n e n e r g y spectral d e n s i t y S ~ ( v , e) as a f u n c t i o n o f v f o r 2024 a l u m i n u m a l l o y w i t h d i f f e r e n t deformations e: i) 2%; 2) 4%; 3) 6%; 4) 8% [41]. observed. The investigation was made on commercial-purity polycrystalline aluminum [70] and 2024 (4.6 Cu, 1.3 Mg) and 5046 (4.9 Mg) aluminum alloys [41]. Fleischman and others used an improved method with broad-band recording. They studied 99.99 polycrystalline aluminum with different grain sizes of d = 0.2-3.6 mm [42] and single-crystal 99.99 AI [71]. The results of both groups of works agree well with each other and basically lead to the following. i. With v = const, S$(v, e) as a function of e has the form of a curve with a maximum (Fig. 6). Actually, this means that the relationship of the power of the individual spectral constituents to deformation is represented by the same bell-shaped curve as the relationship to deformation of the full acoustic emission power (Fig. 9). 2. The deformation e = Cma x at which S~ has a maximum (as a function of E) increases linearly with an increase in frequency v and also in grain size d [42], i.e., Emax ~ yd.

(16)

3. The level of the S ~ - ~ c u r v e s d r o p s w i t h a n i n c r e a s e i n frequency v (Fig. 6), i.e., with any e = const the value of S~ as a function of v steadily drops with an increase in v (Fig. 7). 857

05

J

1.0~ ~sec

g5

F i g . 8. Standardized autocorrelation function of the acoustic emission signal K~ (~) for AI with different values of deformation c [70]: I) 0.5%; 2) 0.875%; 3 ) 20%.

~, #sec

V~ #W 5

# 0,6

3

0,4 "co v I

5

I

1o

i

r

i

o 20 E,%

0,2 0

Fig. 9. The relationship of the acoustic emission power W (solid line) and the length of the deformation Jump To (dashed line) to deformation e for 99.99 AI [70]. 4. With an increase in deformation, enrichment of the spectrum by the high-frequency components occurs. As may be seen from Fig. 7, wlth c = 2% the S~ (~ = 4 MHz)/S~ (~ = 0.I MHz) ratio is 0.025 and with c = 4% 0.24, i.e,, it increases by almost i0 times. Wlth E > 4% the form of SE as a function of ~ does not change since the spectral composition stabilizes. In [42] it was also shown that with an increase in e the finer the grain size, the more rapidly enrichment of the spectrum occurs. 5. The standardized correlation function of the acoustic emission signal (it was found by the Fourier transform of the spectral density S~ wlth respect to the variable u according to the Wiener-Khinchin theorem) is a steadily decreasing function of the correlation interval (Fig. 8), and the greater the deformation, the more sharply the drop occurs [70]. The latter means that for A1 the length To of acts of plastic deformation decreases with an+in crease in ~ (Fig. 9): from 0.6 ~sec with c = 1% to 0.2 ~sec wlth e = 8%. Then to remains constant. Figure 9 also shows the curve of the full acoustic emission power. The decrease in the value of To with an increase in ~ may be followed in Fig. 7 If Eq. (15) is taken into consideration. In dislocation language the reduction in to means a decrease in the average length of mobile sections of dislocations or in the length of their free passage as the result of the increase in dislocation density with an increase in deformation, and in semiphenomenologlcal language, shortening of the deformation Jumps. On the other hand, these numerical values of To indicate the fact that the limiting frequency of the spectrum, as a rule, exceeds i MHz (in accordance with the data of Fig. 7) and the spectrum itself is close to the spectrum of white noise. This was shown very visibly even earlier in [72], where the conclusion was drawn of the validity of models according to which the acoustic emission source is strongly localized in space and has a short tlme of existence ~ i ~sec). 6. From the fact of the steady decrease in the correlation function of the acoustic emission (Fig. 8) yet another important conclusion may be drawn. Acoustic emission energy

858

is emitted not in the form of vibrations but in the form of pulses. In turn, this indicates the inadequateness of the vibration model of an acoustic emission source proposed, for example, in [4]. 7. Fleischmann et al. [42] noted that the energy spectral density is proportional to the deformation rate and the volume of the working portion of the specimen. This fact must be considered as a generalization of Eq. (I, 4a)* relative to the full power to the case of the powers of the individual spectral constituents of the acoustic emission signal. 8. For a single crystal of AI [71] the above-presented rules are preserved. The area of the sharpest drop in T@ corresponds to the stage of linear strain hardening (stage II), and the area of the slow drop, to the stage of parabolic hardening (stage III). In the tests of Rouby and Fleischman [71] stage I was practically absent as the result of the selected direction of tension. From other data we note another important practical conclusion [72] obtained for A-533B low-alloy steel. The low-frequency area of ~he spectrum is related to crack development, and the hlgh-frequency area, to plastic deformation. Condition of the Theory of Acoustic Emission in Plastic Deformation. According to modern concepts, plastic deformation is caused by the movement of dislocations, and therefore acoustic emission is related basically, according to the works of Scofield [5], to one or another dislocation process in the metal. A large number of dislocation models have been developed. For example, Sedgwlck [54] came to the conclusion that the emission pulses are caused by avalanche multiplication of dislocations according to a transverse sllp mechanism as the result of the action of Frank-Reid sources with double securing and that the counting rate is proportional to the mobile dislocation density (I, i). Kiesewetter and Schiller [27], considering the generation of dislocations by Frank--Reid sources and the formation of accumulations in front of obstacles as an original vibratory process, obtained a relationship similar to (I, i):

U2"pmVo,

(17)

where U ~ is the average power of the acoustic emission signals, 0m is the mobile dislocation density, and V@ is the volume of the working portion of the specimen. James and Carpenter [21] derived a relationship differing significantly from (I, i): ,~ ~

(18)

where N is the counting rate. According to the determinations of these authors, 10s-106 dislocations participate in each acoustic emission pulse; i.e., rupture of the dislocations from the obstacles causing acoustic emission pulses has an avalanche character. Gusev et al. [73] improved this model and obtained the relationship

~,,,pm.

(19)

n

Here A = ~ A ~ N ~ is the "united acoustic emission parameter," where N i is the number of jumps i=!

with an amplitude of A i and n is the adopted number of levels of dlscretization of amplitude. A fuller dislocation discussion is presented in [14]. Let fl be the area covered by a dislocation in a single Jump of deformation, f be the average value of fi, and n@ be the number of Jumps in a unit of time. The plastic deformation of a single Jump is proportional to fl and for the deformation rate we have

s,-~nof

(20)

The energy liberated in a single Jump is E i ~ fl ~. The elastic displacement of the surface of the specimen and the corresponding plezotransducer signal are proportional to E i. Consequently, the mean square of the signal will be

*The formulas with the number I are in Report I.

859

Here the assumption has been made of the statistical independence of the individual jumps in movement of the dislocations, in view of which ~ 2 ~ ~ and the energies of the Jumps are additive. The average area covered f is related to the average length of free passage of the dislocations L: fNL

(22)

for the case of simultaneous movement of straight sections of dislocations and 7NL 2

(22a)

for the case of obstacle-free expansion of dislocation loops. Relationship (22a) is valid for single crystals with a fcc lattice; L : const for stage I, and L~

-l

(23)

for stage If. From Eqs. (21), (22a), and (23) we obtain the basis (I, 6) where n = 0 for stage I and n : 1 for stage II. For polycrystalline materials it is more correct to use Eq. (22), which in combination with (23) leads to (I, 6) with n : i/2. Dislocation models have been used for explaining the influence on the acoustic emission parameters of structural changes in alloys [23, 9], grain size in polycrystalline materials [5, 33, 35], the stacking defect energy [26], spectral data [42], etc. The models considered, as for others existing in the literature, possess serious disadvantages such as sketchiness, fragmentariness, and insufficiency of the original assumptions. Normally, each of them explains only a single fact and does not cover the multitude of other related facts. It is almost impossible to establish a relationship between the different models. These disadvantages have objective reasons, including the complexity of the observed appearances of acoustic emission and a shortage of information on the movement of individual dislocations and especially of collections of them. We should not that relationship (18) (and probably (19))contradicts the well-verified relationship N ~ ~ (this disadvantage is not characteristic of formulas (I, i) and (17)). In calculations of the acoustic emission characteristics using dislocation models the assumption is made explicitly or implicitly of the lack of correlation of the movement of individual dislocation segments, which contradicts the avalanche character of the Jumps, confirmed, in particular, by determinations of the elastic energy liberated in them [8]. A somewhat special position is occupied by the works of V. D. Natsik, V. S. Boiko, and others (the review of [7]), which consider more strictly the acoustic emission of dislocations. However, as the result of the above complications they are considered as only extremely simple models. To describe acoustic emission, models of a different type, which may be called semiphenomenological, have been used, such as in the work of Gillis [74]. The author assumes that in single crystals the act of emission is created by the formation of a packet of slip intersecting the whole cross section of the specimen, and in a polycrystalline material of a packet of slip within the limits of a grain. Simple discussions lead to the following relationships for the activity Na of a single crystal and of a polycrystalllne material, respectively: N~)= N~PL

l ~L; !

eVo,

(24) (24a)

where ~@ is the axial deformation in the packet of sllp, AX is the average axial elongation in the formation of a single packet, L is the length of the specimen working section, Vo is its volume, and ~ is the deformation rate. Relationships (24) and (24a) coincide with (I, 3) and (I, 2), respectively, if N a is assumed proportional to the counting rate ~. The author himself does not emphasize this assumption. Calculation of Eqs. (24) and (24a) is noteworthy in certain respects. Despite the sketchiness (also characteristic of dislocation models), it is more obvious than dislocation calculations and provides a very clear interpretation of the coefficients of proportionality in relationships (I, 2) and (I, 3). It is also not difficult to see that all of the calculations of (20)-(23) may be obtained by considering in place of the area covered by a disloca-

860

tion in a Jump the deformation in the packet of slip, etc. In addition, for averaging of the equation of type (21) it is necessary to assume not the statistical independence of the Jumps of displacement of the sections of dislocations but the independence of formation of the individual packets of slip, which is more acceptable. In just this way is solved one of the significant contradictions of the dislocation approach. The development of the theory of acoustic emission in plastic deformation requires the creation of a stochastic model of deformation which would take into consideration the time and spatial discontinuity of this process. Such a model may be constructed both on the atomic level (and the dislocation level) and on the semiphenomenological level (level of packets of slip). Taking into consideration determinations of the size of the Jumps in deformation producing the observed acoustic emission events (Report I), as a first approximation the second approach is preferable. In connection with this it is useful to compare the position in the theory of acoustic emission accompanying the plastic flow of metal with the position in a similar area, the theory of hydrodynamic noises [75]. The latter is based on a strict phenomenological formulation of the problem of emission of sound by an arbitrarily moving liquid (or gas) and models of a semiphenomenological character (models of cavitation, turbulence, etc.). A similar approach to acoustic emission in plastic deformation is very promising in this stage. The elements of a stochastic approach to the analysis of acoustic emission exist in a number of works (such as [76, 77]), but they are directed in a different direction than described above. Further work in this direction is necessary. LITERATURE CITED 55. 56. 57.

58. 59. 60.

61. 62. 63. 64. 65. 66.

67. 68. 69. 70.

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A SYSTEM APPROACH TO THE DESIGN OF COMPUTER-AIDED

TESTING COMPLEXES. COMMUNICATION i.

DEFINING THE SYSTEM STRUCTURE

V. G. Grishko

UDC 62-50.001.5

In this article we consider some elements of system design of computer-aided testing complexes (CATC)* which allow us to develop effective design solutions consistent with the CATC objectives. Technological success in the development of CATC elements and components, such as measuring devices, automatic control systems for testing conditions, automatic dataprocessing systems, testing machines and their subassemblies, does not necessarily ensure significant progress toward the creation of effective testing complexes. In order to attain this goal, we need to ensure uniformity of methodologlcal, functional, and design approaches, which is feasible only when the main CATC characteristics are carefully coordinated among themselves. The necessity of a system approach in the design of computer-alded testing complexes is not a new conclusion: system approach has been always used in varying degrees. However, it is only in recent years, when we have managed to eliminate most of the technological constraints on the design of CATC functional elements, while at the same time substantially increasing the level of our expectations from testing equlpment~ especially for determination of the mechanical characteristics of materials under extreme loads, that the system approach in design is acquiring a new quality. The modern level of the technology makes it possible to develop different implementations for a testing complex with given functional characteristics, and each of these implementations is realizable and effective. The choice of a particular implementation can hardly be left to the personal preference of the designer, and it is therefore desirable to develop a formal design procedure that will determine the required complexity, reliability, and cost levels of hardware and software for particular classes of experimental studies and at the same time select the CATC structure ensuring optimal fulfillment of the research tasks in llne with given effectiveness criteria. *CATC comprises one or several testing machines functioning jointly with a system for automatic control of the test conditions and a system for automatic data processing of the experimental results. Kiev. Translated from Problemy Prochnosti, No. 6, pp. 107-111, June, 1985. article submitted August 14, 1984.

862

0039-2316/85/1706-0862509.50

9 1986 Plenum Publishing Corporation

Original