Fracture energy analysis via acoustic emission

IntJ Fatigue8 No 2 (1986) pp 67-71

Fracture e n e r g y a n a l y s i s via acoustic emission L. I. M a s l o v a n d O. M. G r a d o v

The results of previous studies on acoustic emission during fatigue loading are used to relate the characteristics of the acoustic signals to the fracture processes occurring at the crack tip. At stresses below the yield point of the material, discrete acoustic emissions are produced, their amplitude distribution being described by a monotonically decreasing function. At stresses near the yield point, the signals are continuous with a peak observed in the amplitude distribution function, while above the yield point the acoustic emission resumes the character it had below the yield point. It is shown that these emissions correspond to the formation of individual microfractures, to the process of macroplastic deformation and to stepwise crack propagation of the structurally disordered material, respectively. Key words: fatigue; acoustic emission; amplitude analysis; plastic deformation; fracture mechanism

Acoustic emission (AE) signals are classified according to their duration into continuous and discrete types. Continuous emission is characterized by low amplitude and high frequency, while for discrete emission the signals are of high amplitude and low frequency. The m i n i m u m pulse duration for the acoustic emission to be referred to as continuous has been agreed3 ,2 To analyse the plastic strain and fracture of a precracked specimen or a real component, it is assumed that, for the internal energy to be released in the form of either elastic waves or acoustic emission, an excess of internal energy must accumulate at the crack tip on the macro- and microlevels simultaneously. To determine the correlation between the various crack tip processes and the types of AE, it would seem necessary that the AE data be interpreted statisticalh'. This would make it possible to relate the character and power of A E signals to the stress/strain pattern at the crack tip as well as to the origin of these signals, when analysing the discrete character of metal fatigue) F r o m the data obtained in the authors' experiments on specimens and pressure vessels, 4 it has been shown that, depending on the loading conditions, the amplitude distribution of AE signals may be approximated by either the Rayleigh or Gaussian law for random values, while a power function describes the decrease in the n u m b e r of pulses with increasing amplitude. Therefore it has been inferred that a monotonically decreasing function N i = J(ni) must describe the discrete AE whereas continuous or quasi-stationary AF, signals must be characterized by a function with a maximum Ni = ,f(n~). Discrete A E signals are observed at ffi < e r . These signals can be described or approximated by differential and integral power functions: Ni = An7 b

(1)

ZNi = B n i "

(2)

where N, is the n u m b e r of pulses with amplitude hi, or Ni is the total n u m b e r of pulses with an amplitude greater than n, respectively. E c c e n m c tension tests on notched and fatigue cracked specimens have shown 4.s that not only does the A E count change with loading (depending on the stress level), but more importantly the character of the A E signals changes accordingly. For C r - M o steel grades of average strength, it has been established that: 4's •

•

•

below the yield point (o;, < o',~), ,\', = J[ni) is a monotonically decreasing function described by Equations (i) and (z) where a = o. 7 3-5 and b = ~.47 t.5. At'~ signals are discrete or random where the stress is near to that of the yield point ( ~ ~ o-,,), the function Ni = j(ni) exhibits a peak. The signals are thosc of continuous or quasicontinuous acoustic emission at stresses considerabh, greater than that at the yield point (o;, ~> o',, m o-v), the amplitude distribution function resumes the discrete eharaetcr it had below the yield point (see Fig. 1).

The fact that the distribution of At'; counts below and above the yield point can be described by power functions indicates the occurrence in both cases of random events (AE signals) with zero mcan value and standard dcviation equal to one. Evidently, the amplitude or power of ,'\1;, signals is quite different at ~ < o',~ and if, > o-. Itowevcr, the narrow amplitude distrihution of counts in both cases implies that they are produced by ,,\1~ nucleation sites of n e a r h the same energy release density. In the continuous Al L that fits the Gaussian model at ~ m o',,, there is a great a m o u n t of superposition of random events, b, AI'; signals differing in power and amplitude. This p h c n o m c n o n is accounted for by the high density of AI;, counts near the yield point, conventionally perceived as continuous. Thus, in the strained crack tip

0142-1123/86/020067-5 $3.00 © 1986 Butterworth & Co (Publishers) Ltd Int J Fatigue April 1986

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Stressdistributionat the cracktip Loadingdiagram Characteristicsof AE signals a AE zone

oF Oy °AE

YVi

,J~

L

il,

0"i

< Oys

~/

J

P;astic deformation zone, 2rys.~

Compactspecimen

/

°ii

°ys

°i

Oys

n:,A:

Fig. 1 The variation of AE signals (amplitudedistribution) with loading (stress)condition region circumscribed bv the condition ~ ~ s,~, one should expect signals of both high and low amplitude not only because they have different sources, but because they are asynchronous. From the data obtained it may be concluded that when < ~,~ individual fracture sites exist that generate low amplitude AE signals of roughly the same power. With increasing stress these fracture sites grow in n u m b e r and density until a maximum is reached near the yield point, when macroplastic deformation occurs at the crack tip. D u r i n g the stage of discrete crack propagation or crack jumping when if, > c% A E signals are generated either in small series or as individual pulses with high amplitude. This type of emission is due to the discrete character of the fracture of small volumes of metal at the crack tip which are in a state of structural disorder." Therefore, the type of At:~ signal must bc related to the level of stress as well as to the w)lumc of crack tip material inw)lved in the micro- and macroplastic deformation of fracture. In other words, the diversity of acoustic emission indicates that crack tip plastic deformation is a discontinuous, stage-by-stage process leading to discrete failure. l.et us now consider the AI-{ activity in a fatigue precracked compact specimen under tension loading. Acoustic emission analysis combined with fractographic investigations have shown that at o- < o',~ a 'go-off' zone of individual microfracture sites can be identified in the crack tip macroplastic strain region. This zone is defined by the relationship:"

microplastic defi, rmation and v is Poisson's ratio. Depending on the stress level, the homogeneity of structural components and the internal energy, fracture sites occur in areas of unfavourably located or oriented grains, subgrains or particles of the second phase at stress concentrators. Thus acoustic emission sources are randomly distributed in the crack tip area, while the generation of AE signals is of a quasi-stationary character described by the if, value. The authors' results show that the local microfracture zone size a\t:, as determined via AE analysis, is proportional to the applied stress, or: O'~E aAE = c o n s t a n t

(4)

where if\K, the stress corresponding to the start of AE, is a constant for an alloy with a given base. D u r i n g h)ading, the area of AE generation constantly changes in size, while the integral of ff{~ over the line a(t) (limiting this line) remains constant. This integral relates the density of the released energy to the contour of limited signal generation:

~a(t) a~F (t, 0) d a = c o n s t a n t Since o'{~. (t, proportional and also the The contour over the area

(5)

O) increases with increasing stress ~,(t) (being to ~,(t)), it is necessary to reduce a(t) in time size of the A E activity area at the crack tip. integral can be rearranged to give the integral of increased AE activity:

~a(t)~,E(t, O) da = 5a(t)cr;."E l~ d a 2 y~E =

(3)

= 5fS(t) rot (CY2E~ ) d a = constant

where a xL. is the size of the elastic strain range of the local microfracture zone, 7~ is the energy of formation of microplastic sites, 7,s cr u is the AE related strain at the stage of

68

(6)

where ~ is a unit vector over the a(t) contour m o v i n g in the counter-clockwise direction and 3'(t) is the square of

Int J Fatigue April 1986

Fig. 2 The fracture surface of a compact specimen

the A E zone limited by the aft) contour. The equation:

~ S ( t ) rot (o~E Ta) d a = c o n s t a n t

(7)

exp~sses the law of conservation of vector flux, rot (~2 E x l~), through S(t) square in time. On the other hand, rot (~{E 1,) is also part of the vector l~{E characterizing the acoustic emission capability of the material, this capability depending on the structural sensitivity of the vector to mechanical loading. With increasing load up to o'o(t) = o'~, A E activity is determined by the size of the plastic deformation zone, ary~. Therefore:

jjS(t)

rot (craE/,y) d2rys = constant

(8)

where 0",~ is the yield point of the material under conditions equal to ~xE activity. Numerous fractographic investigations have revealed a macrostriation pattern on the fracture surface of compact specimens loaded to failure under various loading conditions, provided that the material exhibits elastic-plastic behaviour (see Fig. z). Each striation is formed when the crack front stops during discrete or stepwise crack propagation, the distance jumped being equal to the size of the irreversible deformation zone, 2ryJ ,8 The presence of a dimpled microrelief on a plane through the striation macrosurface (2r,) has been established by microfractography. Note that this dimple pattern changes over one discrete crack increment (see Figs 3a-f). The dimples on the macrostriation ridges are in a state of equilibrium (Figs 3a and 30 while shear dimples are observed between the ridges, particularly in the centre of the 'valley' (Figs 3b-e). Between the two ridges which mark the length of one crack increment is a depression on the comparatively

Int J Fatigue April 1986

flat fracture surface corresponding to the region of maximum strain (see Fig. sb). MicrostructuraI analysis has confirmed the existence of a maximum strain or failure zone (zrl<) between macrostriation ridges (see Figs $c, 3d and 4). Data obtained via this type of analysis indicate that the formation of the irreversible plastic deformation zone (zr~) is accompanied by continuous acoustic emission fitting the Gaussian m d e l . In addition, statistical analysis of experimental data on dimple relief in the zr v zone shows that this particular kind of fracture is characterized by dimples with inclusions on the bottom. From this observation it follows that the particles are located in hollows. The density of the specific energy released during cracking near inclusions and the formation of a fracture 'quantum' may be expressed as: me i

~c

d

(9)

where S<, is the density of released specific energy, y~ is the specific energy released during formation of the fracture quantum and dis the critical size of the quantum. Calculations show that the value of S<. is close to or more than that of the absolute latent heat of melting, which is released on the transition of the metal into a premelted or pseudomelted state. Each quantum is considered to be an elemental heat source. Since in the zr~ zone all heat sources (N) of the same activity generate heat svnchronoush': N

~(&,

i) 4, i = (&) 2,-F

(10)

i-I

Assume that the maximum strain of failure zone, zri, identified in the space between the macrostriation ridges is the

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Fig. 3 (a--f) Microfractographs of the fracture surface of a compact specimen

Fig. 4 Microstructural analysis of the fracture zone at the crack tip

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Int J Fatigue April 1986

the energy released per unit time is proportional to the melting temperature the fill-in frequency of the pulse is characteristic of the photon area of the solid body spectrum due to heat conduction, the envelope of the pulse describes the temperature fall at the crack tip and is a monotonically decreasing function of time (see Fig. 5)-

• A peak amplitude D signalduration N number of counts per event R rise time U energy (proportional to the square of amplitude) Umax ~ T m (proportional to melting temperature) U(t) ~ T(t) (proportional to temperature) ~0s (= 2~rN/D) frequency

• •

Conclusions

AI

N I-

D

Threshold

-I

Fig. 5 Schematic of a powerful AE signal

result of overstress described by the relation ~ > ff,~.5 The density o f the internal energy released on fracture in the volume is close to the latent heat of melting, s This implies that in this zone the material must be in structural disorder or in the premelted state, causing the release of a powerful pulse of excess internal energy in the form of heat and elastic stress waves or acoustic emission. It is known s that substantial crack tip plastic deformation is the major cause of defects, the accumulation of which brings about a specific state of structural disorder. It is estimated that the disordered layer may be as thick as 0.5 p.m, from which it is inferred that the disordered zone failure (zrr) takes place within a thin layer. Moreover, when substantial plastic deformation occurs, say during mechanical grinding, so-called 'red points' or areas about i - i o gm in diameter overheated to a near melting temperature are observed. 9,10 Further experimental evidence - - the observation of the absence of superstructural reflections at considerable localized elastic strain in M6ssbauer spectroscopy and the appearance of non-equivalent iron positions in X-ray structural analysis9,1° - - indicates that plastic deformation induces an o r d e r disorder structural transition which alters the structural and magnetic state of an iron-based alloy. Thus discrete high amplitude acoustic signals are emitted during crack jumping when the material at the crack tip is in a state of structural disorder, provided ~ > 0",~. Analysis of A E phenomena of a thermoflucuation character has shown that the generation of heat in a narrow area of the crack tip significantly- affects the AE pattern, causing a proportional increase in the AE intensity from the zq: zone and to its decrease as heat dissipation. This change in the character of AE intensity with time suggests that the duration of the fracture quantum is determined by the rate of heat transfer in the material, ie by heat conduction, melting heat and heat capacity. The observation of a powerful AE pulse per unit time testifies to the formation a of fracture quantum possessing the following specific features:

Int J Fatigue April 1 9 8 6

Acoustic emission data obtained during fatigue testing have been analysed and shown to reveal the inhomogeneity of the plastic strain region at the crack tip. Emissions corresponding to the formation of individual microfractures, to the process of macroplastic deformation and to fracture of the structurally disordered material are established. It has also been shown that A E signals provide a means to distinguish the different densities of accumulated and released internal energy. The kinetics and energy of A E released during the accumulation of microdistortions up to a state of maximum disorder in the limited crack tip zone have been discussed.

References 1.

Bianchetti, R., Hamstad, M. A. and Mukherjee, A. K. J Testing and Evaluation 4 No 5 (1976) pp 313-318

2.

Radon, J. C. and Pollock, A. A. "Acoustic emissions and energy transfer during crack propagation' Engng Fract Mech 4 (1972) pp 295-310

3.

Rogers, L. M. and Monk, R. G. in Service Monitoring of Structural Integrity by Acoustic Emission Analysis, 2nd Nat Conf on Cond Monit Process Int, London, UK, 10-11 May 1983, pp 1-24

4.

Paraev, S. A., Roznov, V. N., Maslov, L. I., Zaharov, Yu. V., Gorbachev, V. I. and Vasiliev, V. N. 'Primenenie Statisticheskogo Analiza Signalov AE dlya Kontrolya Napryazennogo Sostoyaniya i Razrysheniya Metallicheskih Materialov' Welding Production Nikimt 5 No 2 (1978) pp 142-149 (in Russian)

5.

Paraev, S. A., Maslov, L. I., Roznov, V. N. and Zaharov, Yu. V. 'Svyaz mezdu AE, Formirovanie Zoni Plasticheskoi Deformatzii v Usloviyah Kvasiploskoi Deformatzii' Voprosi Atomnoi Nauki i Tekhniki, M, Nikimtl No 7 (1980) pp 186 194 (in Russian)

6.

Maslov, L. I. Papers of Ship Research Institute, No 60 (Tokyo, Japan, 1980)

7.

Uaslov, L. I. 'The constancy of density of deformation energy at macro- and microlevels in case of automodelle elasticplastic behaviour of materials' Proc 6th Int Conf on Strength of Metals and Alloys, Melbourne, Australia, 1982 pp 16-24

8.

Maslov, L. I. 'Energeticheski Analis Protzessov Razrusheniya' Voprosi Atomnoi Nauki i TekhnikL M, Nikimt 1 (1983) pp 4-10 (in Russian)

9.

Ermakov, A. E., Yurchikov, E. E. and Barinov, V. A. Phyzika Metallov i Metallovedenie 52 No 6 (1981) pp 11841193 (in Russian)

10.

Elsukov, E. P., Sarinov, V. A., Galakhov, V. R., Yurehikov, E. E. and Ermakov, A. E. Phyzika Metallov i Metallovedenie 55 No 2 (1983) pp 337-340 (in Russian)

Authors The authors are with the A. A. Baikov Institute of Metallurgy, USSR ,\cademv of Sciences, I.eninskv pr. 49, \'-?~4 Moscow, USSR. Inquiries should be addressed to Dr Mash)v in the first instance.

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