v-‘U .- .‘O .‘ A-. o ~ ‘I _ r. . . ‘n. -o ‘4‘.-‘.- - '. AN INVESTIGATION OF ACOUSTIC EMISSION FROM COATED AND UNCOATED IONIC CRYSTALS 'E-‘hesés for the Dagma‘ of Ph. D. MICHIGAN STATE UNIVERSITY Robert T. Sedgwi-ck I965 a“ MIICHGAN , III IIIII II IIIIIIII II IIII II m I.- I 31~-eut H: "(ICE-F”; MICIIIES'JRSIHKQ III-III” University This is to certify that the thesis entitled AN INVESTIGATION OF ACOUSTIC EMISSION FROM COATED AND UI‘ICOATFD IONIC CRYSTALS presented by ROBERT T . SEDGWI CK has been accepted towards fulfillment of the requirements for Eh.D. degree in Doctor of PhilosoPhy in Mechanics Vr70 INK/1+— Major u'ubofessor Dr. T. Triffet 0-169 -‘-—- MICHIGAN TATE UNIVERSITY LIBRARY '3" ~ KI ABSTRACT AN INVESTIGATION OF ACOUSTIC EMISSION FROM COATED AND UNCOATED IONIC CRYSTALS by Robert T. Sedgwick Single crystals of LiF and KCl, some of which were coated with either NaCl or CaFZ, were subjected to incre- mental compressive stress along a [lOO] direction. A continu- ous record of stress and strain was kept together with data from ultrasonic damping and acoustic emission measurements. The experimental techniques and the electronic equipment used are discussed in detail. It was found that the presence of a thin surface film (500 A) raised the entire stress-strain curve for KCl and increased the slope of the linear portion of the elastic range of the curve for LiF. This phenomenon, called the Roscoe effect, is attributed to dislocation pile—ups created when leading dislocations emanating from active sources are prevented by the film from leaving the crystal through the surface. The release of these pile-ups was evidenced by the large number of acoustic emission bursts following the removal of a film from its strained substrate crystal. Both coated and uncoated specimens of LiF exhibited acoustic emission peaks in the macroscopic elastic range having their maximums at a strain of approximately 6° = 10'“3 and skewed toward larger values of120 ~2.li l 0100 .72.0 I 200-- i .30 .1.6 tress l 2 Wm : .60 ..1.2 | 100“ l 'oh0 00.8 . u I x at- .3 I w it I _. ’ ”+1 : .20 .L0.n . . I | o_ . . l J I ll 0 20 no 60 80 100 120 1&0 1 O Str_in_1_x lo‘h) Figure 20. Acoustic Emission Histo ram.and Dam in Data for Specimen I0 Plotted Against a Contracted Strain ScaIe. The acoustic emission histogram superimposed upon the stress- strain curve and the logarithmic decrement curve (x ) for specimen 10 (K01, one NaCl film). The vertical dashed line indicates the value of strain at which the film was etched off. 35 experiments involved ultrasonic damping data. The ampli- tudes of successive echos were recorded after each load increment. The logarithm of the ratio of an amplitude to its successive amplitude was used as a measure of the ultrasonic damping. Figures 21 and 22 are examples of damping curves for both coated and uncoated specimens of LiF and K01 respectively. The actual experimental points for these curves are plotted in Appendix III. Ultrasonic damping data are also plotted in Figures 1n to 20. The vertical dashed lines in Figures 16,.18 and 20 indicate that the thin film has been etched away at that value of strain. It is particularly significant that many acoustic bursts occur immediately after the film is removed. It is also apparent from these Figures that the number of bursts occuring at this time is far greater than at any other time during the specimen's loading history. The foregoing curves indicate several things of interest which will be discussed in the next section. However, some important points should be emphasized. First of all, Fig- ures 11 and 12 show that the presence of a thin film on both LiF and K01 does increase the value of stress correspond- ing to a given value of strain above that for uncoated speci- mens. This fact is especially significant for the case of LiF shown in Figure 11 since the data plotted there are entirely within the elastic range. The greater slope of the coated specimens indicates that the presence of a thin surface film raises the value of E for the substrate material. Note, however, that the slope of the curve for specimen 3, 36 0.9ir 0.8 ‘L 0.7" 006 0 0051' / O.ni- 0.2 i0 L ' W 50 30 n0 50 Strain ( xIO'h) Figure 21. Logarithmic Decrement Curves for LiF. The number On each curve identifies the specimen. The actual experimental points are plotted in Appendix III. 37 Ln 0.8‘ 0.6i O.S« 0.7+ O.n< 0.3. Al/A2 T 0.2 11 ——-‘— E j‘ V #— lo éo 30 no 50 Strain ( x lo-h) Figure 22. number on each curve identiiies the specimen. Logarithmic Decrement Curves for K01. experimental points are plotted in Appendix III. The :The actual 38 which is coated with CaF2, is less than that for uncoated specimen 1. This is probably due to the fact that the test on specimen 3 was terminated at an early value of strain. Had the test been carried to larger values of strain, it is believed that the best straight line through the experimental points would have been one of greater slope. This can be seen by looking in detail at the experimental points in Appendix III corresponding to the stress-strain curves for specimens 1 and 3. For any given strain, the points associ- ated with specimen 3 are at a higher value of stress than those associated with specimen 1. No direct correlation can be seen between E for the substrate and the ratio of elastic constants, ell, of the film and substrate material. Note, in Figure 11 that the slope of the stress-strain curve for specimen 9 which had one NaCl film is greater than that for specimen 3 with one side coated with CaFa, and Specimens n and 5, each with two sides coated with NaCl. This fact indicates that the interface energy due to atomic lattice misfit between the film and substrate plays a pre- dominant role in creating the Roscoe effect. The expression aF - aS aS can.be used as a measure of the amount of lattice misfit at the filmrsubstrate interface where a represents the atomic lattice Spacing and the subscripts F and 8 stand for film.and substrate respectively. The lattice constants for LiF, Can, NaCl and KCl 39 are n.02, 5.n5, 5.63 and 6.28 A respectively (n8). The lattice misfit parameter calculated from these values are shown in the chart of Figure 23 for the four cases used here. Substrate Film 3F - as 3S LiF NaCl 0.nOO LiF CaFZ 0.356 K01 NaCl -0.10h K01 CaF2 -O.132 Figure 23. Lattice Misfit Parameters. The chart shows the lattice miSfit parametersfhrvarious combinations of ionic crystals. The larger the absolute value of the lattice misfit parameter, the greater is the misfit between the film and substrate material; hence the greater is the interface energy. The negative signs simply indicate that as is greater than a? for that particular combination. Note that the lattice misfit parameter is greater for LiF substrates coated with NaCl than for those coated with CaFZ. Hence, if interface energy is an important factor in creating the Roscoe effect, LiF Specimens coated with NaCl should exhibit a somewhat larger stress for a given value of strain than would a similar Specimen coated with CaFZ. This is found to be true and can be seen in Figure 11. The slopes of the linear portion of the stress-strain curves for specimens n, 5 and 9, coated with NaCl, are all greater n0 than that for specimen 5, coated with CaFZ. The misfit parameters for the K01 Specimens indicate that the interface energy should be greater for those coated with CaF2 than for those coated with NaCl. This is evidenced in the stress-strain curves of Figure 12 where, in general, for a given strain, the stress is greater for Specimen 8, coated with CaF2, than for specimens 7, 10 and 11, coated with NaCl. There is one exception, however, in the range of strain between 20 and 55 x 10'“; namely, the curve for specimen ll crosses over the curve for specimen 8. This may be due to the fact that specimen 11 had two sides coated while specimen 8 was coated only on one side. Only a portion of the stress-strain curve for Specimen 2 is shown in Figure 11. For values of strain greater than 15 x 10'h this curve varied drastically from the other curves Shown. However, internal cracks were clearly visible in that spechmen at a very low value of strain, 20 x lO'h. This anomalous behavior must have been due to severe stress concentrations produced by internal imperfections within the undeformed crystal. The stress-strain curves for coated and uncoated speci- mens of KCl are shown in Figure 12. Although there is no well-defined linear elastic region apparent in these curves, the effects of the thin films are seen at very low values of strain. The curves for specimens 8 and 10 which are coated with CaFZ and NaCl reapectively indicate that for a given value of strain, the corresponding stress is sig- nificantly increased above that for uncoated specimen 6. hl Figure In shows a histogram of acoustic emission counts taken from specimen 1 (uncoated LiF) superimposed upon a portion of the elastic region of the stress-strain curve. Note that the counts attain a maximum at a strain of ap- proximately 10'3. Also it is interesting to note that the distribution of counts is not symmetrical but is skewed toward larger values of strain. This distribution is typical for_LiF in the elastic range but is not observed in K01 as can be seen in Figure 15. The maximum number of acoustic emissions in LiF occurred at strains of the order of 10"3 in Specimens l and 2 which had no film and in specimens 5 and 9 which.were coated with NaCl. The maximum was shifted to higher values of strain for specimens 3 and n.which were coated with one CaF2 film and two NaCl fihms respectively. Since the value of e11 for NaCl is less than the value of °11 for LiF, it must be concluded that interface energy between the film and sub- strate partly determines the value of 6, at which maximum acoustic emission occurs. As was mentioned previously, the interface energy is a function of the lattice misfit parameter. Hence, if the film-substrate interface energy does move the initial acoustic emission distribution peak to the right, it should be expected that Specimen n, which had two sides coated with NaCl, should exhibit the largest value of 6, , the strain at which.maximum acoustic emission occurred. This is indeed the case, as a value of 6,2 3.8 x 10.3 was observed for Specimen n. It should be remembered that the lattice misfit n2 parameter is not the only quantity affecting the film-sub- strate interface energy. If epitaxial growth is attained during film deposition, the lattice misfit is probably the major contribution to the distortion at the surface and therefore the most important factor controlling the inter- face energy. However, if the film grows in a more random way, the effect of the lattice misfit parameter is minimized. Thus, the interface energy can be thought of more realisti- cally as being the residual strain energy of distortion across the film-substrate interface. However, since it is difficult to obtain an exact indication of the interface energy, it must be assumed that at least the first few atomic layers of the film are deposited epitaxically and that the lattice misfit parameter indicates the relative magnitudes of the interface energy. Figure 16 gives a good example of acoustic emission occurring after the removal of NaCl surface films from a LiF crystal. The vertical dashed line indicates the value of strain at which the film was etched. The large number of acoustic emissions occurring after etching as compared to the number before film removal is typical. Note also the drop in the stress strain curve immediately after etch- ing. A plot of Similar data for K01 is shown in Figure 20. The logarithmic decrement taken from ultrasonic damp- ing data for uncoated LiF (Specimen l) is also shown in Figure 1h. A general increase of damping with strain is evident. A comparison of this curve with that for specimen 5 in Figure 16 indicates that the presence of a surface 1&3 film also causes in increase in damping. A similar increase in ultrasonic damping can be seen for K01 if the curves of Figures 15 and 17 are compared. Figure 15 gives the damp- ing curve for uncoated KCl (Specimen 6) while Figure 17 gives that for K01 having one Side coated with NaCl (speci- men 10). The effect of a surface film on the logarithmic decrement is particularly apparent in Figures 21 and 22. Appendix IV contains the raw data for all of the speci- mens, some of which were not mentioned above. IV. DISCUSSION Typical stress-strain curves for ionic single crystals can be compared and a general distinction made between "hard" and "soft" crystals (n9); if this criterion is used, crystals such as MgO and LiF must be considered hard while NaCl and K01 must be classified as soft. The evidence pre- sented in the preceding section further indicates that LiF and K01 are governed by different deformation mechanisms. Although the nature of these differences can not be pre- dieted from the macroscopic stress-strain curves, acoustic emission data does provide a means for comparing the micro- scopic deformation characteristics of the two types of crystalline materials. A. Model for LiF It will be assumed that a random, three-dimensional network of grown-in dislocations is present in an undeformed single crystal of LiF, and that many dislocation segments within this array lie on {110} planes, favorably oriented for slip. It is also reasonable to assume that these seg- ments will be distributed randomly throughout the crystal, with their lengths symmetrically distributed about some mean length. The points of their emergence from the slip plane will act as effective pinning points. When stress is applied, the favorably oriented segments will then operate as dislocation sources according to the doubly-pinned, nu LLS Frank-Read mechanism (29). For this reason the distance between two points of emergence is referred to as the loop- length for that particular dislocation source; and earlier investigators have concluded that these loop-lengths,,2 , will be normally distributed about a mean length,.& , according to the formula Nut) = (L/£,2)1exp(-I/,€.) (1) where N(1) is the distribution of 1o0p-lengths and L is the total length of dislocation within the crystal. Two points are of special significance concerning the operation of such sources and the multiplication process involved in accommodating the macrosc0pic strain. First of all, it is evident that the longer loop-lengths will operate at lower values of stress than the shorter ones. This is indicated by Cottrell's equation (52) I = 2r = 2Hb/1‘ ’ (2)-- where r is the critical radius of a bowed-out dislocation loop, H the shear modulus, b the Burgers vector and T‘, the critical resolved shear stress. The critical values are reached when a straight doubly-pinned dislocation segment of length i is bowed out by the applied stress and attains a semi-circular configuration. Any slight increase in shear stress will cause the pinned segment to act as a Frank-Read source, emitting many dislocation loops without requiring additional stress. Hence, as the applied stress is in- creased, some of the shorter 1o0ps may bow out, but the h6 longer ones will be subjected to the critical value of shear stress for multiplication first. The Probability, P(l/1). of finding a loop-length whose inverse lies between 1/1 and 1/2 + d(1/1) is defined by the equation aware/mum» = (2771)}? exm-L/NdU/X) (3) where 27K1/1)d(1/1) represents an element of area in inverse loop-length Space. This is represented schematically in Figure 2n. 27T(1/£)P(1/1) ‘ 1/1 Figure 2n. Sketch of Symmetrical Inverse Loop-length Distribution. ‘The distribution shown is that which is present in the undeformed crystal. The second point concerns the rate of dislocation multiplication once a source becomes operative. In LiF single source multiplication occurs very rapidly, creating an avalanche effect; in fact an entire slip band can be formed in as little as one tenth of a second (#9). It is postulated here that an avalanche of dislocations emanating from a Frank-Read source can create an elasto-plastic wave it? of sufficient energy to be picked up by the acoustic emission apparatus. Hence, in a previously undeformed crystal, the distribution of acoustic emission counts should give a relative estimate of the initial loop-length distribution, if the interaction between dislocations produced by different sources is small. However, such interaction can pin dis- location sources which have not reached the critical value of stress necessary for multiplication and, thus, effectively create more but shorter loop-lengths. That is, dislocation interaction may skew the loop~length distribution curve toward the side of shorter loops, or larger 1/1., as shown in Figure 25. 27T(1/J2)P(1/1) l 1/1. l/A Figure 25. Sketch of Skewed Inverse Loop:length Distributipn. The distribution shown is that which is present after dislocation interaction takes place. It is evident that the release of dislocation pile- ups also gives rise to acoustic emission bursts, as will n8 be discussed later. There are reasons to believe, however, that the skewed distribution of acoustic bursts which occurs in the elastic range of LiF is due to the Operation of dislocation sources. First, if the distribution is attributed to the release of pile-ups, it is difficult to explain elastic recovery. Elastic strain energy can be stored in a crystal in the form of dislocation pile-ups in such a manner that the back stresses cause elastic recovery when the applied load is removed. If, however, these pile-ups are released before removal of the applied load, there will be little or no elastic re- covery, from which it follows that such a process must not be dominant for linearly elastic materials such as LiF. (Also, pile-ups released when the film is etched off, even in the elastic range of LiF, produce many more acoustic emissions than are observed to take place in the initial distribution. This is also true for K01 which does not even exhibit the initial distribution of counts. W'Hence, the distribution of acoustic emission counts in the elastic range must be primarily a result of the operation of dislocation sources rather than the release of pile-ups. For this reason, an analysis of the distribu- tion provides a means for interpreting the dislocation deformation mechanism, at least for LiF. B. Skewed Acoustic Emission Distribution It is apparent that the curve of Figure 25, which represents the probability of finding an inverse loop-length 1+9 between 1/1 and 1/1 + d(l/£), and which is skewed to the right by dislocation interaction, resembles the acoustic emission curve for the elastic range of LiF shown in Figure 1h of the-last section. However, before any direct correlation can be made between acoustic counts and inverse loop-length distribution, two important factors must be considered. First, an expression relating dislocation source 100p- length,l , to the macroscopic strain, 6 , must be developed in order to show that when 65 = E, , the strain at which maximum acoustic emission occurs, the value of.l obtained is a reasonable value for the most probable loop-length. If one dislocation loop is considered, the offset 8 , which is measured along a slip plane, is given by the . equation (5n) 5 = (A"/A')b = k"(o.7o7)b] /A (h) where A" is the slipped area on a slip plane of total area A', A is the cross sectional area of the specimen, b is the Burgers vector and the factor of 0.707 enters here because in LiF the {110} planes are favored for slip. The resolved shear strain, 7/ , is then found to be y = Ema/0.707) = A"b/[2(A3)%] <5) The axial strain for a given offset, .8 , is found by geometry in this case to be e = As/s = 0.7078/8 = A"b/(2AS) (6) 50 where S is the undeformed length of the specimen and C58 is the deformation. Hence, for A = l/n in2, 8 = 3/2 in, and b = a/0.707, where a is the lattice spacing for LiF and is equal to n.02 A (53), the above formula gives A" = 0.3376 x 108 in2 . (7) It is known from simple elastic theory that the resolved shear stress, 7', for this case can be written as ’7‘ = 072 = EAS/(ZS) = EA"b/(hAS) . (8) Hence, when the shear stress reaches the critical value for the operation of a dislocation source of length ,1, the expression for‘T in Equation (8) can be set equal to Cottrell's expression, Equation (2), for critical resolved shear stress as a function if loop-length. This yields EMb/ (MAS) = ZPb/i (9) and it is found that .1 = 8}AAS/(EA") = 23.71AV x 10'8/(E6) , where V is the volume of the Specimen, p.is the shear modulus, and use has been made of the expression (7) for A". Let 23.7iiv x 10'8/3 = 01 ’. -(10) a constant with the dimensions of inches; then .1 = 01/5 , (11) which is the desired relation. It is assumed here that 51 the strain is a result of dislocation motion only; i.e., any strain due to a change in the lattice parameter has been neglected in the calculation. Since 60 , the value of strain in the elastic region of LiF for which maximum acoustic emission occurs, was ob- served to be of the order of 10'3, this should give a reason- able value for the most probable loop-length when substituted into the above equation. To evaluate Cl in Equation (10), a ratio of IJ/E tion (5h) 6.28/15 can be calculated from the equa- H/E (012 + chu)/(2¢uh + 3612) (12) where the accepted values of c12 and can for LiF are n.2 x 1011 and 6.28 x 1011 dynes/cme, rSSpectively. If this ratio and the Specimen dimensions are used, the most probable dislocation 100p-length is found to be I, = 0.9n5 x 10LL 3. . (13) This is within one order of magnitude of the critical loop- length of about lOub suggested by Cottrell (55) for a "typical" applied stress. Granato and Lucke (50) assumed a symmetrical distribu- tion of loop-lengths about a mean length ,8,. Therefore, the second factor which must be considered before a direct correlation can be made between acoustic counts and inverse loop-length distribution is the cause and character of the skewed acoustical curve; and, of course, this must be ac- companied by a satisfactory physical explanation of the 52 correSponding inverse loop-length distribution curve. The skewness of the acoustic emission curve can be defined by subtracting the Symmetrical part of the curve, as illustrated in Figure 26. This symmetrical portion will N(€) E Figure 26. Skewness of Acoustic Emission Curgg; The curve shown is the remaining portion after the symmetric curve has been subtracted. bereferred to as the 'primary' distribution, since it is assumed that the initial distribution of loop-lengths is random and therefore symmetrically distributed about some mean length. The curve obtained by subtracting the primary distribution curve from the total curve will be called the 'eeeondary' distribution. It is assumed due to the Operation Of shorter dislocation sources created during deformation. Plots constructed from actual experimental data follow. It can be seen from Figure 27 that the secondary dis- tribution is also skewed towards shorter lOOp-lengths. It is reasonable to imagine that the secondary curve too is 53 80~ 70‘» 60~ 50v h0~ Counts 30V 20» 104. o E 16 1% 26 2% 36 35 ab u? 56 Strain ( x 10'“) Figure 27. Plots of Nontsymmetrical Portion of Acoustic Emission Distribution. The plots shown are for the elastic range of LiF. Sh composed of a symmetrical part and a portion which is skewed toward shorter loop-lengths. Here, however, only second order effects will be considered. The entire acoustic emission distribution curve will be assumed to consist of a symmetric portion centered about 6, and a symmetric secon- dary portion, as shown in Figure 28. N(€) Figure 28. Breakdown of Total Acoustic Emission Distribution Curve. It is assumed that the total curve is the sum 0 Ewe—symmetric curves. The ratio of amplitudes of the secondary and primary acoustic emission distribution curves can be used as a measure of the amount of skewness due to dislocation interaction, i.e. Nl/NO in Figure 28. It is found from the eXperimental data that Specimens l and 2, which are uncoated LiF, have values for Nl/NO of O.hOO and 0.38h respectively. Specimen 9, which has one side coated with NaCl, has a value of 0.357 while Specimens k and 5, both of which have two sides coated . ‘ 55 with NaCl, have values of 0.1h2 and 0.211 respectively. These results indicate that the presence of a surface film reduces the value of Nl/NO' i.e. reduces the amount of skew- ness in the acoustic emission distribution. The reduction can only be due to one of the following: (1) The number of acoustic emission counts may be increased in the region 6 < 6,. (2) The number of acoustic emission counts may be reduced in the region 6 > 6.. (3) The maximum in the acoustic emission distribution, N0, may occur at a . g H larger value of strain. It is not likely that the presence of a film could create any dislocation sources with loop-lengths longer than..£o. In fact, if anything, it would have a tendency to shorten the effective loop-lengths near the surface. Hewever, it was mentioned before that surface sources are not important for the deformation of LiF. Nor is it probable that a thin film could cause less dislocation interaction and thus lower the amplitude of the secondary portion of the curve. For these reasons, (1) and (2) above are probably not important; and it can be concluded that the presence of a surface film has a tendency to shift N0 toward larger values of strain. It will be shown later (page 77) that this is due to the combination of a real and an apparent shift in the loopolength distribution toward shorter loop- lengths. It is quite reasonable that the plot of 27T(l/1)P(l/1)d(l/1) versus 1/1 of Figure 25 should be similar to the plot of 56 N versus (5 shown in Figure 28. As emphasized earlier, the dislocation sources with the longest loop-lengths will be activated at the lowest stress increments; and these sources will continue to operate until the stress is somehow reduced below the critical value for dislocation multiplication. For example, if a leading dislocation becomes pinned by internal imperfections, other dislocations or a surface film, and if the barrier is Of sufficient strength, the following dislocations will become piled up. The back stress from the pile-up will then reduce the stress at the source below the critical value for Operation. As additional stress increments are applied, further straining must be accommodated by one of the following mechanisms: (a) Release Of the pile-ups, thus allowing an inoperative source to become Operative again. (b) Operation of a shorter source created during deformation and, therefore, one lying on a slip plane very near a plane on which a source has previously operated. (c) Operation Of a source which has not previously Operated, hence, m one with a shorter lOOp-length. It should be noted that (a) and (b) are closely related to previously operative sources while (c) is concerned with previously inoperative sources. Hence, it is logical that mechanism (c) should be more prevalent at lower strains. Since the longer sources attain their critical operating stress at smaller values of strain, it follows that mechanism (c) is more likely to occur whenwfl >.&, that is, in the first 57 part Of the curve shown in Figure 25. When 1 > ,0, , i.e. 1/1 < l/Qo , the number of previously inOperative sources which are available to Operate at a given critical value Of stress increases as the critical stress value increases. This can be seen by letting 71 be the critical stress required to operate a source Of loop- length.21:>90, and letting N1 be the number of these lOOps. Then as 71 increases, Ni increases. Note, however, that for,21<110, N1 decreases as ‘T1 increases. Since the number of previously inoperative loops is now decreasing, the strain can not be accommodated simply by the Operation of these loops. Hence, when.fiw<.fi,all Of the available, previOusly inoperative loops of the proper length will Operate and the remaining strain must be accommodated by the reactivation Of a blocked source or by the Operation of a new source created during the deformation process. As the stress continues to increase, fewer of the primary sources and more Of the secondary sources will Operate. This is shown schematically in Figure 29 (a) and again in Figure 29 (b), where the probability of finding the inverse Of a loop-length between 1/1 and 1/1 + d(l/£) is plotted against l/fl . Figure 29 reflects the fact that a finite number of primary dislocation sources whose loop-lengths are symmetri- cally distributed about a mean length I. are initially present within the crystal. The secondary sources, i.e. the reactivated or newly-created sources, begin to operate at 1 =.flo , when the number Of primary sources attaining their critical stress for multiplication is at a maximum; 58 2 7T(:L/,Q)P(1/1) 27T(FL/1)P(1/l) i X. -..___ __-__-_ O H 2? < he 1/1 (a) (b) Figure 29. Relationship Between the Primary and Secondary Distribution. The portion subtracted from the total dis- EFISEEIBE'EEE be represented by a displaced symmetric curve as in Figure 28. and at the point where the primary sources are exhausted, the number of secondary sources reaches a maximum. The foregoing discussion indicates that it is feasible to make a direct correlation between the acoustic emission distribution Of Figure 28 and the probability distribution of inverse loop-lengths shown in Figure 29. However, a correlation of this type is more meaningful if both dis- tributions are expressed in terms Of probability. The Ob- served acoustic emission distribution function, N(€), divided by the total number of acoustic emissions in the distribution, Nt’ gives the probability density; which, when multiplied by d6 , becomes the desired total proba- bility function. It should be noted that the factor, d6 , 59 -does not alter the form Of the distribution. Hence the probability Of finding N acoustic emissions between (E and e 4- d6 can be expressed as P(€)d€ = N(€)d€ /[fN(€)d€] (M) or simply as me) = n/N. . (15) where it is understood that N is a function Of e and Nt represents the total number of emissions. Figure 30 indicates the similarity between the two probability functions. PK) 27T<1/1)P(1/1) |\ I ‘\ l \ I \\ I \ | I\ ' '\ ( P \ P IP \ P : \> E \\ P" ’ P"\/ "’ L/‘xi ; ‘J 60 E, 6 1/1/ 1/1, 1/1 Figure 30. Similarity Between Acoustic Emission and Inverse Loop-leng_h Probability Functions. The primed numbers refer to the primary curves and the double-primed numbers to the secondary curves. The probability Of Observing N acoustic emissions while the specimen is being strained from E to 63 + d6 is the sum of two probabilities; 60 name = [1mm + p"(e)]de (16) where P'(€)d€ = (A/NO) e exp(-€/e.,)de (17) and P"(€)d€ = (B/N1)(€ - 6°)exp Ream/eke (18') Equation (17) is taken from elementary statistical theory and expresses the contribution Of the symmetrical part Of the acoustic emission count distribution to the probability Of Observing a given number Of acoustic emissions between 6 and E + d6 . This is a normal distribution, symmetrical about 60 , the strain at which the maximum number Of acoustic emissions, NO, occurs. Ehuation (18) is similar except for the fact that the distribution it represents is transfered along the 6 axis an amount 60 , and it expresses the contri- butiOn Of the skewed part Of the acoustic emission count distribution to the total probability curve. In the same way, the probability of finding an inverse loop-length between 1Z2 and 1X1 + d(1[2) can be expressed as 27T(1/1)[P'(1/2) + P'<1/x)]d(1/1) (19) where 27T(1/1)P'(1/1)d(1/,2) = w (20) 27mm 13 expt-fo/flmu/I) 61 and 27T(1/.2)P"(1/,e)d<1/,e) = awn/1 - 1/1.) exp Elli/1 - mica/r) Equation (20) is the same as EQuation (3) and represents the symmetrical portion Of the total probability curve while Enuation (21) represents the skewed part. A direct correla-' tion between the two probabilities gives (A /No) exp(-€/e.)d + [3(6 -€.)/N]] exp [-(E-EJ/eJ d6 = 2W(1/1)1§exp<-9a/Jz)au/Jz) <22) 4' 27T(1/£ - 1/1.) exp [31,(1/1 - 1/1.)] 4(1/1) . But gince it was assumed that the primary distribution is due to the original distribution Of loopalengths and that the secondary distribution is caused by dislocation inter- action, the primary and secondary probabilities can be con- sidered independent and therefore equated separately to obtain (ti/Now exp(-€/e.)d6 = 27T<1/Jz)1‘3exp(~!./J2>du/1> (23) and [B(€ -€.)/Nl] exp [-(6 «Q/eJde = (21;) awn/x .. wafexp [aim/1 - l/j.)]d(1/Jl) It should be noted that the independence of the primary and secondary distributions is of a special type. Clearly it is possible that the change in the distribution of inverse 62 loop-lengths due to dislocation interaction may depend upon the distribution initially present in the undeformed crystal. However, for any given crystal, the primary distribution is fixed and can not be changed by deformation. This implies that, although the primary distribution can influence the secondary distribution, the inverse is not true. Hence for any given primary curve, the primary and secondary.curves should be independent. P(€)d€ can new be expressed as a function Of (l/I): P(€)d€ = emfu/i) «phi/Maud) + aim/1 - 1mm? exp [4271/12 - 1w] 4(1/1) 25) ‘And equating the arguments and the coefficients Of the exponents in Enuation (23) gives 6 = (dime (26) which agrees with Equation (ll), and A = 27TNo/e? (27) while from.Equation (2h) it follows that B = 2W1?N1/6021§ (28) It is worth emphasizing that,.since N(€) can be measured in the manner described above (e.g. Figure 1h), the proba- bility distribution of inverse loopolengths can in effect be determined experimentally. The first term on the right in Ehuation (25) is, of course, the original distribution of inverse loop-lengths in the undeformed crystal. The 63 second term causes the skewness in the distribution and is itself caused by the deformation. The expression for P(€)d€ as a function Of 1/1 should be useful in calculating average values of variables which depend primarily on dislocation source loop—length. For any variable, A(1[£), the average value, I, can be expressed as (56) I = fl(1/1)P(e)de/[fp(e)de]. (29) As an example, the average elastic strain due to dislocation motion can be calculated by substituting the expression 6 = 01(1/1) , obtained from Equation (11), into this equation: '6' = clfll/i )P(€)de/[f1>(e)d€] (30) where the limits Of integration should extend from zero to the value Of l[£ at the yield point. For simplicity, Equation (30) can be written as 'e' = 0111/12 (31) and a substitution of y>= l/fi made. The value Of 11 can then be calculated by making use of Equation (25): 6 6? I1 = 27Tlozj‘y2 exp(-£y)dy o S? + 271.2fy2 up [-flJy 1&9] 45’ (32) O Q. " (ZW‘QIZ/Xoif'y exp E'Ixy ' l/aoc)] dy O 6L) where the upper limit Of integration, éy/Cl, is the value of 1/1 at the yield point and is obtained from Equation (11). Integrating from zero to €y/Cl gives _ '2 2 2 2 e 11 — («arr/10%“)o €v/Cl + Moe/c1 + 2) exp(-)(° /cl) - 2] -(27T/1.)exp(Z/1.) [(I? 5.2/0? + 21,6/01 + 2) ”pugs/cl) - 2] (33) +(37TflJexp(fl/fl.) [(l’fiv/Cl 4- 1) exp(-£.€y/Cl) - 1] Similarly, 12 = ZWIEfy emu-Lynx O E: . 2 o "' 271.1) fy exP [‘fin(y " l/jc)] d, - (3,4) O a ' - {2 ”’Tfll;}£)’;xp [- Q,(y ~ 1AM] 4: or 12 = -27T[(,P°€,/Cl + l) exp(oj°€Y/cl) - 1]. «277' expWy.) [we/c1 + 1) exp(-I.€y/cl) - i] (35) + (27Tju/1.) exp(!./1.)[exp(-£,€y/Cl) - 1] The substitutions cl =e°fl°, 6.: me. and 1,=!./2 can . now be carried out in Enuations (33) and (35). It is found that 1101 = 27T€,[2 - (m2 + 2m + 2) exp(-m) . + 3 exp(l/2) - (1/2) eXp(l/2 - m/2) (m2 + 3m + 6)] and for m = 3, 65 11c1 = 27T€°(l.69) . (.36) The value m = 3 effectively assumes that the secondary acoustic emission curve is symmetric, with yield occuring after all secondary sources cease to Operate. For the non-symmetrical case a larger value Of m should be used. Also, 12 = 21r[1 - (m + l) exp(-m) + (l/2)exp(l/2) - (In/2 + 1/2) exp(l/2 - m/2)] or 12 = 27T(o.895) (37) when the substitution, m = 3, is made. Equation (31) now gives 'e'= 1.81; e. (38) The expression for C1 above comes from Equation (11) evaluated at €“=.€o and.€,, the strain at the yield point, is taken to be equal to some numerical factor, m (here set equal to 3), times 6,. The relationship between,fl.and.fl,can be Obtained from Figure 30. The value of'E denotes the macroscopic strain at which the dislocation sources Of average length, I , become op- erative, provided the strain due to changes in the lattice parameter is neglected. Hence,‘g is and should be greater than.€°, the critical strain for the most probable loop- length, since the distribution is skewed. 66 In order to estimate the error involved in neglecting the portion of the elastic strain due to changes in lattice parameter, it is possible to compare the energy needed to strain the specimen an amount corresponding to a strain 6 as calculated by continuum mechanics with that obtained from dislocation theory. It is assumed here that if no dislocation motion occurs, the entire strain is due to changes in the lattice parameter. This gives rise to homogeneous deformation, and for small strains, the strain energy can be approximated by continuum theory. The energy necessary to cause an axial deformation equivalent to a strain. 6 can be expressed as w = (l/2)E€2 and w = (l/ZTTQAM for pure axial compressive stress and pure shear, respectively (57). It is assumed that the strain energy associated with a change in lattice parameter, "c' can be calculated from the axial stress formula, we = (l/2)E 62 (39) while that associated with dislocation motion, from the pure shear formula, wd = (l/2)72/p. (H0) Ehuation (hO) can be re-written as wd = aha/£2 (1(1) by using equation (2) and the ratio Of the strain energy due to change in lattice parameter to that due to disloca- tion strain becomes 6? Wc/Wd (1A.) (E/H) (eEIE/bz) (1(2) (l/u) (E/y) (631?.2/b2) Equation (12) gives Eflu = 15/6.28 and it is known that b = 5.6 A (see page 50); also, since 6. is Of the order Of 10’3 and.90=3 10’+ A (Equation 13), Equation (h2) can be rewritten as wc/wd =3 2 “#3) This states that the energy needed to strain a crystal an amount 6 by reducing the lattice parameter, is twice that needed to Obtain the same strain by dislocation motion. It is therefore concluded that as long as there are mobile dislocations Of sufficient number to accommodate the strain, very little or no change in lattice parameter should be Observed. This implies that the contribution to the total strain by lattice parameter changes probably is not important for €‘< 6, , but becomes increasingly important as the active dislocation sources become exhausted. It was found that the average dislocation strain, 6— , is equal to 1.8u6; for the case when the crystal is strained from zero to BE; . If the entire strain were a result of lattice parameter changes, it would be expected that the average strain for this case would be 1.56; . This seems to indicate that at least on the average, the mobile dis- ‘locations are more than able to accommodate the total strain in the region up to 36; . Consequently, neglecting lattice 68 parameter changes in the above calculations seems justified. Of course, in the elastic range of LiF, the average stress needed to operate a dislocation source of length.l can now be written as? = E 6 = 1.814136 for the case when m = 3. Furthermore, since (1Z2) is linearly related to 6 ,'an average dislocation loopmlength Of ,Z'= (l/l.8h)1, ‘can be Obtained. It is interesting to compare the average values 6', E and I Obtained here to the corresponding average values for the case Of no dislocation interaction, that is when the average values are 6. , E60 and 01/6, respectively. This indicates that dislocation interaction raises the average values Of stress and strain at which a dislocation source of length,£ becomes Operative by‘a factor of 1.8u while simultaneously reducing the average loopalength by the same factor. Thus, the factor 1.8a constitutes a measure Of the dislocation interaction effect in the elastic range Of LiF. It is also possible to compare the number 1.8h with the calculated ratio, R, of the amplitudes Of the primary and secondary distribution curves. Equations (17) and (18) evaluated at 6, and 6. respectively give P*(e.) = Aee/NOE ., (um and rue.) B(€.°€3V[N1 expu =€./e.)] . (15) Hence R = ANleoexp(°€O/€I )/ [NOB(€I '60)] 69 and, since 6. = 26° , R = ANl/ [BN0 exp(l/2)] (11.6) If the expressions for A and B from Equations (27) and (28) are used, R = (M1. )2 exp(-1/2) A (h?) or by applying Equation (11) R = (€a/6.)2 GXP(-1/2) = h 61p(~l/2) = 2.h2 . (he) The ratio Of amplitudes, R, is also a dimensionless measure Of the dislocation interaction and compares favorably with the factor 1.8a. ' The amplitudes Of the primary and secondary acoustic emission distributions for Specimen l are given in Figures 1h and 27 respectively. The ratio Of these amplitudes is 2eh5 which is in excellent agreement with R and comparable in magnitude to the factor 1.8h. C. Reversibility 'Since the distribution N(6) is observed entirely within the elastic range Of LiF, the model must also explain reversi- bility in this material. But it is reasonable to believe that the sources can also act as sinks when the applied stress is removed and the internal stress distribution is mainly due to the back stress created by dislocation pile- ups. Probably many dislocations will never return to their source because Of interactions, while some dislocations will 70 have completely left the crystal. However, such irreversi- bility must be tOO sensitive to be measured by the instruments used here. NO stress concentrations could be detected in the relaxed specimens by ordinary polarized light techniques. D. Yield Point The yield point Of LiF should also be explained by the model presented here. In the elastic range, the model is governed by an exhaustion phenomenon in which all of the original dislocation sources and those created during elastic deformation are eventually used up. It was postulated, however, that these sources ceased to Operate when the back stress from dislocation pile~ups attained a critical value. Thus, the macroscopic yield stress should be due to one or a combination of the following mechanisms; (1) The stress reaches a critical value which is great enough to cause the dislocation pile-ups to overcome their barriers and hence create a dynamic avalanche effect. (2) The stress reaches a critical value which is sufficient to cause crossoslip from the existing slip planes. This mechanism pro- duces 'bandabroadening'. (3) Many new sources, which are not associated with the original dislocation sources or those created in the early stages Of elastic . deformation, are created at the yield stress. Since cross-slip is difficult in LiF at room temperature (58-60), and since the applied stress would be insufficient to create many new sources, it is believed that (2) and (3) are not probable under the present conditions. Hence, the yield point in LiF is most likely due to a dynamic 71 avalanche effect created when many dislocation pile-ups overcome their barriers. It can be seen in Figure lb, and this will be discussed later, that removal Of the film does cause a sudden drop in the stress-strain curve. This must be due to the release Of dislocation pile-ups directly beneath the surface film, or those which were created because Of the stress concen- trations associated with the surface pileuups. In the natu- ral yield of a clean LiF crystal, however, it is probable that many interior pile-ups also break away. E. Easy_Glide and Work Hardening The present model for LiF is not concerned specifically with the easy glide and work hardening regions Of the stress strain curve. However, a brief summary Of the present under- standing Of these regions will be sufficient to complete the model and show that no direct conflict arises. A recent review article by Nabarro 23.31 (61) gives a good account of the current state of knowledge for hard ionic crystals. In a typical stress-strain curve for LiF, the rounded yield point is followed by a reduction in stress and a flat portion called the easy glide region, or Stage I. In this region the glide bands which have already been formed are spreading through the virgin crystal. In the light Of the model presented here, this would be due to a dynamic multi- plication effect occurring when the blocked sources become unblocked at the macroscopic yield point; and it might be expected to continue until dislocation interaction once 72 again causes the process to slow down or stop. The stress- strain curve then enters a linear workahardening region called Stage II hardening. In this region the entire crystal becomes filled with glide bands; these bands widen and eventually, cracks form and failure occurs. F. Model for KCl “There is no definite distribution Of acoustic emissions in the early stages of deformation of KCl crystals comparable to that Observed in the elastic range Of LiF. However, if the tape is scanned Just above noise level, acoustic emissions are Observed. Figures 31 and 32 show acoustic data plotted from counts taken at two different levels, but the level used in Figure 31 is the one comparable to that used for the LiF specimen shown in Figure 1h. The meaning may be that in KCl, dislocations are not created in the avalanche- type bursts characteristic Of LiF. Figure 32 indicates that the bursts created in KCl are Of relatively low mag— nitude; thus, they may be caused either by many slowly moving dislocations or very few rapidly moving dislocations. In view of these Observations, an exhaustionutype theory can not explain the early stages of deformation in KCl. It is believed that the lack of high-magnitude acoustic data is due to the fact that dislocations move at a much slower rate in KCl than in LiF (h9). Sources in KCl will, therefore, be blocked much easier than those in LiF, due to the smaller dynamic forces associated with the moving dilecations. However, there is no indication that either 300.. 2009 Stress gin/m2 1000- 73 ~50 no 30 Counts r10 Figure 31. 30 Strain ( x lo'h) ho f 50 Histogram Of Acoustic Emissions Counted at Normal Tri er Level. The data are lotted fro S N's—61 fi"_T_"lms,. p m Pecimen '7 (K01, two 300’ 200" Stress sin/mm2 100w O '. Inlml J g ; l4 5 0 0 10 20 30 MO 50 Strain ( x lo’u) Figure 32. .Histogram of Acoustic Emissions Counted Just Above Noise Level. ‘The data are plottedfifrom Specimen 7 (KCI, two NaCl films). 75 dislocation multiplication or the release Of pile-ups gives rise to appreciable acoustic emission, except in the case when surface films are removed, as shown in Figure 20. Even then the number Of acoustic emissions, when compared to that for LiF, is relatively low. The difference in dislocation velocity in LiF and KCl is undoubtedly due to the differences in the chemical composi- tion and structure Of the two materials. In general it might be speculated that materials in which dislocation velocity is high are more likely to exhibit a macroscopic yield point than are those in which dislocation velocity is low. The case when energy barriers capable of supporting large dislocation pile-ups exist within or on the surface of such a material may constitute an exception; but even then the barriers must be overcome in order for an abrupt drop in the stress-strain curve to occur, as happened when the surface films were etched from the deformed K01 spechmens tested here. G. Effect Of Thin Film on Dislocation multiplication It was brought out previously that four mechanisms Of substrate hardening due to the presence Of a solid surface film have been mentioned in the literature; these are: (1) Dislocation pile-ups beneath the surface film due to a difference in elastic moduli Of the film and substrate material. (2) A change in the image force acting on dislocations very near the surface. (3) Inhibiting Of cross-glide at the crystal- line surface. 76 (h) Inhibiting Of surface sources. Although all of these mechanisms are possible, it is believed that the effects Of greatest magnitude are due to dislocation pile-ups beneath the surface film. This is substantiated by the fact that a large number Of acoustic emissions are always Observed when the surface films are etched away. Furthermore, general cross-glide is unlikely in LiF at room temperature (58-60) and surface cross-glide arising from the removal of the thin film could not account for the large number Of acoustic emissions Observed. It has already been Observed that surface sources are not imp portant for the deformation Of LiF (28). In the'work-hardening region or both LiF and KCl, the presence Of a thin film is known to cause an increase in the rate Of work-hardening. This effect is, without doubt, due to the fact that the film prevents dislocations from leaving the crystal through the surface. or much greater interest is the effect Of the thin film during the early stages Of straining, i.e., in the elastic range. The fol- lowing discussion pertains only to LiF, since it has a well- defined, linear elastic region, while KCl does not. The stress-strain curves Of Figure 11 prove that the slope in the elastic region is affected by the presence of a thin film. Furthermore, a greater increase in slope is Observed for film materials with larger values Of °ll' A change in the lepe Of the elastic portion Of the stress- strain curve means that the thin films have an effect on Young's modulus, E, of the substrate. The relationship 77 JL€,= 23.7 x 10’8 VM/E (h9) can be Obtained from Equations (10) and (11) evaluated at 6 = 6.; and for the specimens used in this work, the ex- pression becomes I,€,= 8.89.1 10~8WE . (50) It was Observed experimentally that the presence Of a surface film caused an increase in both E and 6,. Hence if Ecuation (50) is to be true, the presence Of the film must cause a corresponding increase in the ratio P/j, ; and it is reasonable to seems that I, decreases while at the same time ,u. increases. - The shift in the loop-length distribution is probably due to two separate factors. First, the back stresses from dislocation pile-ups would tend to strengthen the crystal in the same manner as would a shortening Of the mean dis- location lOOp-length of the original dislocation sources. This would cause only an apparent reduction in I.. Secondly, the surface film would reduce the effective loop-lengths Of dislocation sources near the surface Of the crystal, causing a real reduction in I. . Finally, ,u must increase ifE increases since they are related by the equation (62) E = mew 3).)/(p+>() '. (51) H. Mobile Dislocation Density In the model presented for LiF, the mobile dislocation ‘ density should be highest when the greatest number of initial 78 sources are at their critical stress for multiplication. This occurs at a strain of 6. when the most probable lOOp- length,,L,, has attained its critical stress. Gilman (63) and Johnston (6h) have developed an expression for mobile dislocation density as a function of strain. This expression is PM = (,00 +36) exp(-¢6). ‘ . (52) where PM is the mobile dislocation density, R is the initial dislocation density,B is a constant and Cl) is called the attrition coefficient. By the above reasoning.the mobile dislocation density will attain a maximum at a value Of strain which satisfies the equation (d PM/de )6“ = o (53) which gives . . «150,9, +36.) exm-Cfié.) +B-xp(-¢€J = 0 - or ¢sB/(B€.+ P.) -V i (51*) For LiF, B :65 109 dislocations/one (on) and e, 2: 10‘3 from page 51. If these values are used in the expression for CI) , it follows that B 6, >> p , hence. ’4) z l/eole'B. Thus the expression for mobile dislocation density becOmes )_ PM = (,0. 4» BE ).exp(-€/€.) (55) which is an equation Of the same form as Equation (17) for 79 P' (6)d6 provided 9 is small. This fact agrees with the model presented here, since it is to be expected that the greatest number of acoustic emissions due to dislocation multiplica- tion in LiF should occur at the strain for which the mobile dislocation density is a maximum. If the relationship ,2 = 01/6 of Equation (11) and the substitution of y = 1/1 are applied to Equation (55) it becomes PM r: (B +Bcly). exp(- joy) (56) ~-‘. and the average value can be written as fin pr(1/,€)P(€)d€/[fp(e)d€] ' (57) or simply where 12 is given by equation (35) and was found equal to 27T(O.895) for m = 3, and I3 = I”; + BCly) exp(-£°y) P(6)d€ . (59) When the proper substitutions are made and the integration carried Out, it is found that FM is of the order of 106 mobile dislocations/cmz. This is certainly a reasonable average value for mobile dislocation density in the elastic» range of LiF. The value of 101° to 1012 dislocations/cm2 estimated by'Van Beuren (65) for "moderately deformed" polar crystals is several orders of magnitude higher than the value Obtained here. The difference lies in the fact that 8O etch-pit techniques give estimates of total dislocation 6 density whereas the value Of 10 dislocations/cm2 calculated above is for mobile dislocation density only. I. Ultrasonic Damping The ultrasonic damping data can perhaps best be used to Obtain a qualitative estimate of the relative density Of stationary dislocations. The piezoelectric crystal was of the same dimension as the cross section Of the specimen;' hence the damping effect is an integrated one in that it averages the total damping across the entire specimen cross section. It is to be expected, however, that most Of the dislocation pile-ups due to the thin films would be near the crystal surface. Additionally, the large size Of the piezoelec- tric crystal probably introduced reflections from the sides of the specimen; but this should not affect the relative magnitudes appreciably, since the effect should be approxi- mately the same for all specimens. It will be remembered that the ultrasonic generator had to be disconnected during the application of each load increment and for a short thme thereafter, until the acoustic emission ceased, because Of interference between the acoustic emission and ultrasonic damping signals . Two important observations can be made on the basis Of damping data plotted in Figures lh-22. Damping in general increases with strain, and is greater in the coated specimens. Both facts support the models developed here for LiF and KCl. The increase in damping with strain indicates that dislocation 81 density increases in this case, which.must be true. Further- more, the fact that damping is greater in the coated crystals, as seen in FigUres 21 and 22, indicates that dislocation density is greater due to pile-ups beneath the film. Since the effect is averaged over the specimen cross section, however, it is surprising that the difference in damping in the coated and uncoated specimens is so distinct. Either the density of dislocations beneath the film is much greater than the internal dislocation density, or the stress field created by the surface pile-ups helps to create other pile-ups further away from the surface. Although the second possibility seems preferable, both are compatible with the models presented. It was seen in Figure 21 that the logarithmic decrement is a linear function Of strain. This can be represented by the equation ln (Al/A2) =0L€ + b, (60) where Stress sm/mm2 200” IV ./’ . y/ 100 ” /// //’ /’l . ' /”:"' . ./ .{/ 0 if c 3 9 t 7 ¥ 0 10 20 30 no 50 60 Strain ( x 10‘9) Figure 39. Stress-strain Curve for Specimen 6. (K01, No Film.) 101 1100) 300» Stress 0 10 20 30 E0 50 6o Strain ( x 10'8) Figure no. Spress-strain Curve for Specimen 7. (K01, Two NaCl FiLms.) 102 hOG- 300r Stress (arm/1mm2 ZOOF 100- 0 A . c : : t 0 10 20 30 no 50 6O Strain ( x 10'“) Figure hl. Strgss-strain Curye for Specimen 8. (K01, One C‘FZ Films) 103 u00.. 300 - Stress gnu/mm2 200‘- 100‘» ; 0 10 20 30 ad 50 60 Strain ( x 10'“) Figure AZ. Spress-strain Curve for Specimen 10. (K01, One NaCl Film.) 10h 1100 .. 300 a Stress sun/mm2 200 ' 100.. 0 10 20 30 16 50 60 Strain ( x 10'9) Figure h3. Spress-strain Curve for Specimen ll; (K01, Two NaCl Films.) 10 / 0.9" S - ' 0.6‘ 0.5" T OOH‘ A1/52 0.3~ 0.2- 001‘) O A j 0 10 ‘20 30 50 1.0 Strain ( x lO’h) Figure uh. Logarithmic Decrement-strain Curve for Specimens l. 3 and . 106 0.7" 0.60 0.2:. 0.10 o 10 20 30 no 50 Strain ( x 10’") Figure us. Logarithmic Decrement-strain Curve for Specimens 6, 7 and 11. 107 Appendix IX: Raw Data Notes: a. Units of stress are gm/mmz. b. The value in the fitrain column must be multiplied by 10' . c. The oscilloscope gain used in recording acoustic emission was 1000 MV/cm. 0 d. The background noise on the oscilloscope was 1/h.cm, i.e. 250 MV. e. The sweep speed was 50 micro-sec/cm. f. The number or numbers directly under the column heading COUNTS/INCREMENT denote the trigger level setting used in counting the acoustic emissions. Specimen l STRESS STRAIN LN(A1/A2) COUNTS/INCREMENT 1/2 cm 8.u3 0 0. 0 8.03 0 0.88% 0 8.03 1.23 0.082 0 8.u3 1.23 0.k82 0 8.u3 1.23 0.u66 u 1.20 1.85 , 0.u66 0 1k.05 2.u6 0.u66 1 19.67 3.08 0.u66 0 25.29 3.08 0.u89 13 30.91 8.32 0.089 9 36.53 5.55 0.502 hl 12.15 7. 0 0.502 22 50.06 9. 6 0.502 9 56.20 11.10 0.509 130 6u.63 11.71 0.509 95 75.87 12.33 0.5%9 89 87.11 13.57 0.5 5 25 109.59 15.02 0.585 16 120.83 16.03 0.585 u8 132.07 16.03 0.626 #3 1 8.93 17.27 0.626 6 1 5.79 18.50 0.626 3 179.8 19.10 0.733 52 191.0 20.35 0.805 39 219.18 21.60 0.805 27 108 Specimen 1 - continued STRESS STRAIN LN(Al/A2) COUNTS/INCREMENT 1/2 cm 236. 0 21.60 0. 781 6 217. 2 22.20 0. 781 9 258. 52 22.20 0. 763 9 275. 38 22.20 0.829 18 286.62 22 81 0.805 22 300.67 23.13 0.805 7 323.15 21.6 0.805 2 310.01 25.90 0.779 17 356-87 27 75 0.779 10 368.11 29.60 0.779 7 381.97 30.81 0. 895 1 393.10 32.70 0. 895 5 110.26 33.90 0.895 2 115.88 35.80 0. 895 0 3.98 37.60 0. 895 1 155.22 10.10 0. 895 2 169.27 11.90 0. 895 0 Specimen 2 0.70 0.62 0.105 0 1.11 1.23 0.105 0 2.11 1.23 0.105 0 2.81 1.23 0.105 0 1.22 1.23 0.105 0 5.62 1.23 0.105 0 7.33 1.23 0.105 0 9. 1 1.23 0.105 0 12.65 1.23 0.105 0 16.15 1.23 0.105 1 20.10 1.23 0.105 1 23.90 1.85 0.105 10 26.70 2.17 0.105 23 29.50 3.70 0.105 22 3%. 0 8. .91 0.105 17 3 . 0 17 0.105 27 13.50 7.10 0.105 38 17.10 8 .63 0.105 22 50.60 9. 86 0.105 21 51.80 11.10 0.105 11 61.10 12. 33 0.105 1 65.10 13. 57 0.105 1 72 0 15 13 0.105 15 76.17.90 0.105 3 80.10 20.36 0.105 a 81.50 25.30 0.125 0 109 Ill Specimen‘3 STRESS STRAIN LN(A1/A2) COUNTS/INCREMENT 1/2 cm 0.35 0 0.652 0 1.76 0 0.652 0 3.16 0 0.652 0 5.62 0 0.732 0 8.13 0.93 0.732 0 10.53 0.93 0.732 0 13°82 0.93 0.820 1 1 . 1.51 0.820 3 21.80 1.85 0.779 0 26.00 1.85 0.779 5 31.60 3.08 0.875 2 36.50 3.08 0.875 10 11.90 3.08 0.875 13 52.30 5.55 0.875 6 60.00 5.55 0.875 17 69.30 9.25 0.875 20 76.10 11.10 0.875 8 87.10 13.56 0.875 30 90.60 11.80 0.875 12 Film Removed (H2308) 88.50 15.30 0.875 27 87.50 16.00 0.875 81 85.00 17.10 0.875 30 85.00 18.00 0.875 5 81.50 19.00 0.875 7 81.50 20.00 0.875 15 81.50 21.00 0.875 2 Specimen 1 STRESS STRAIN LN(Al/A2) COUNTS/INCREMENT 1/2 3/h 1 2 5.51 0 0.712 0 0 0 0 8.26 0 0.712 0 0 0 0 8.26 0.65 0.712 0 0 0 0 13.77 0.65 0.712 0 0 0 0 19.30 1.36 0.712 0 0 0 0 21.80 1.36 0.712 0 0 0 0 30.10 1.36 0.712 16 8 8 5 38.50 2.77 0.712 0 0 0 0 17.00 2.77 0.712 1 l 1 0 52.30 3.18 0.712 2 l 0 0 57.90 1.19 0.712 0 0 0 0 110 Specimen 1 - continued STRESS STRAIN LN(A1/A2) COUNTS/INCREMENT 1/2 3/1 1 2 68.80 5.60 0.712 1 0 0 0 79.80 7.00 0.712 1 3 0 0 93.80 9.10 0.712 1 0 0 0 101.50 9.85 0.798 0 0 0 0 121.00 11.25 0.798 2 1 1 0 137.50 12.00 0.798 3 2 2 2 151.00 12.70 0.798 2 2 2 0 176.00 13.10 0.798 0 0 0 0 201.00 11. 0 0.798 6 3 3 2 223.00 17.60 0.798 76 17 15 21 5.00 19.00 0.798 12 22 22 10 2 7.00 23.30 0.798 121 58 56 28 28 .00 2 .60 0.798 3% 17 17 8 30 .00 2 .10 0.693 2 12 9 3 328.00 27.50 0.798 62 39 39 23 312.00 28.90 0.798 23 16 15 9 357.00 29.60 0.798 6 3 3 2 379.00 31.00 0.798 29 18 18 9 396.00 31.80 0.798 28 18 18 9 393.00 31.80 0.798 158 92 91 55 116.00 31.80 0.798 6 11 10 21 7.00 32. 0 0.798 6 39 36 15 1 5.00 33. 0 0.798 7 1 3 0 182.00 3 .60 0.798 25 11 11 10 198.00 3 .00 0.798 20 13 13 5 520.00 36.00 0.798 6 0 0 0 536.00 36.70 0.798 23 11 13 9 556.00 37.10 0.798 11 7 6 3 585.00 39.50 0.798 31 17 17 5 590.00 12.%0 0.798 12 5 5 3 618.00 13. 0 0.798 5 1 1 1 630.00 15.90 0.798 21 13 13 8 638.00 18.70 0.798 13 8 7 2 616.00 51.50 0.798 1 3 3 1 616.00 51.10 0.798 3 2 2 1 616.00 57.90 0.798 2 1 1 0 616.00 60.70 0.867 0 0 0 0 616.00 65.00 0.867 2 2 2 0 616.00 68.50 0.867 0 0 0 0 616.00 71.30 0.867 0 0 0 0 616.00 7%.10 0.867 0 0 0 0 616.00 7 .10 0.867 2 1 1 1 616.00 81.00 0.867 0 0 0 0 616.00 87.50 0.867 1 0 0 0 619.00 91.80 0.867 0 0 0 0 652.00 97.30 0.811 1 0 0 0 655.00 101.00 0.867 0 0 0 0 666.00 105.10 0.867 0 o 0 0 Specimen 1 - continued STRESS 675.00 689.00 697.00 708.00 717.00 Specimen_5 2.75 5.50 8.26 13.80 21.80 33.00 11.00 55.10 66.00 79.80 85.10 99.00 121.00 113.00 176.00 215.00 218.00 215.00 212.00 212.00 212.00 Specimen 6 STRESS OOOU'I U‘lU'lU'l N e U'lU'lU'lN STRAIN 110.00 113.80 119.30 121.30 129.20 0 O O C O O O O 0 -eunotr~r6101nnr+q moommmomwNH raw mwmmqurwmoo 11.13 15.55 16.97 18.10 19.10 Film Removed 19e80 23.30 28.30 31.80 111 LN(A1/A2) 0.867 0.867 0.867 0.911 0.911 1.051 H OOOOOOOOO H HHHHHHHHH \HUIWBUIWWW H (H20) [—1 O 0 U1 |—' 1.051 1.051 1.051 LN(A1/A2) 0.329 0.329 0.329 0.329 COUNTS/INCREMENT 1/2 3/1 1 2 2 0 0 0 2 0 0 0 3 1 1 1 1 0 0 0 1 2 2 l 1 0 0 0 2 0 0 0 8 5 5 0 5 2 2 1 10 1 g 2 6 6 1 8 8 8 0 6 2 2 0 8 3 2 0 36 20 19 6 11 6 6 0 1: 22.2 2 15 1 1 1 11 % 2 0 13 1 0 9 2 0 0 105 S9 16 15 161 153 153 27 111 69 51 19 6 0 0 COUNTS/INCREMENT 1/2 1 0 0 1 Specimen 6 - continued STRESS 5.50 8.26 10.95 13.78 19.30 21.80 30.23 35.80 11.30 16.80 52.25 57.90 63.20 71.20 85.10 96.10 107.20 118.30 132.00 1 6.00 1 2.20 176.00 193.00 201.00 215.00 231.00 212.00 253.00 270.00 281.00 300.70 .316.00 .333-00 .350.00 .361.00 379.00 385.00 1110.00 1127.00 1138.00 152.00 162.00 1171.00 195.00 506.00 518.00 525.00 571418.00 STRAIN 112 LN(A1/A2) 0.329 O SEES 000000000 0 e e e e e wwwww 0000 0000 e K» O O 0.300 COUNTS/INCREMENT 1/2 HHNNOI—‘OHHI—‘OOOOWHOHWOWOHNOHHHOOOONOWOHHHOOI—‘OOOUJOO 113 Specimen 6 - continued STRESS STRAIN LN(A1/A2) COUNTS/INCREMENT 1 2 560.00 253.00 0.310 0 570.00 259.00 0.310 1 581.00 262.00 0.310 0 587.00 267.00 0.310 0 598.00 271.00 0.310 0 601.00 278.00 0.310 0 612.00 281.00 0.310 0 618.00 290.00 0.310 0 621.00 296.00 0.310 0 621.00 301.00 0.310 2 629.00 310.00 0.310 0 629.00 319.00 0.3%0 2 629.00 326.00 0.3 5 0 635.00 335.00 0.385 0 610.00 310.00 0.385 1 610.00 350.00 0.385 1 616.00 357.00 ‘0.385 1 651.00 368.00 0.385 0 651.00 376.00 0.385 0 655.00 383.00 0.385 0 660.00 388.00 0.385 1 666.00 392.00 0.385 0 666.00 39 .00 0.151 0 666.00 39 .00 0.151 0 677.00 101.00 0.151 1 680.00 105.00 0.151 0 685.00 106.00 0.151 2 675.00 109.00 0.151 2 691.00 110.00 0.151 0 691.00 112.00 0.151 3 691.00 111.00 0.151 1 680.00 117.00 0.151 0 685.00 118.00 0.151 0 680.00 121.00 0.151 5 685.00 122.00 0.151 5 682.00 125.00 0.151 0 677.00 126.00 0.151 7 671.00 128.00 0.151 7 671.00 131.00 0.151 1 671.00 133.00 0.151 0 666.00 135.00 0.151 6 666.00 136.00 0.151 5 666.00 137.00 0.151 0 655.00 139.00 0.151 5 655.00 110.00 0.151 1 619.00 110.00 0.151 1 111 Specimen 7 STRESS STRAIN LN(Al/A2) coUNTS/INCREMENT 1/2 Just Above Noise Level 2.75 0.71 0.351 0 0 2.75 2.12 0.351 0 0 5.50 2.83 0.351 0 0 8.26 2.83 0.351 0 0 11.00 3.51 0.351 0 0 16.50 1.95 0.351 0 0 19.25 5.65 0.315 0 0 21.17 6.36 0.368 1 1 33.00 7.07 0.368 0 l 11.00 8.18 0.329 0 1 55.10 12.00 0.357 0 2 66.00 15.55 0.367 2 1 $1.10 19.10 0.385 1 2 5.50 23.30 0.385 2 6 93.60 28.30 0.385 0 0 101.50 33.20 0.385 0 0 115.50 38.90 0.385 0 2 126.50 19.50 0.368 0 3 137.80 55.90 0.368 0 0 118.50 61.50 0.368 0 0 159.50 68.60 0.105 0 0 168.00 77.00 0.105 1 1 18 .10 86.20 0.105 0 0 19 .00 93.20 0.105 0 0 209.00 99.00 0.105 0 1 226.00 106.70 0.105 1 1 212.00 111.50 0.105 0 2 259.00 120.00 0.105 1 3 270.00 121.50 0.105 0 0 287.00 132.00 0.105 1 8 302.00 139.00 0.105 0 1 319.00 111.00 0.105 0 0 336.00 150.00 0.105 1 2 352.00 157.00 0.138 1 7 369.00 163.00 0.138 0 5 388.00 168.00 0.138 0 0 110.00 175.10 0.138 0 1 130.00 181.00 0.393 0 0 115.00 185.00 0.393 0 1 165.00 191.00 0.393 0 2 187.00 197.00 0.393 0 0 503.00 203.00 0.393 0 0 517.00 206.00 0.393 0 1 525.00 21 .00 0.393 0 0 5 8.00 21 .00 0.393 0 0 5 5.00 223.00 0.393 0 0 Specimen 7 - continued STRESS 581.00 598.00 613.00 621.00 610.00 652.00 677.00 695.00 710.00 725.00 712.00 751-00 767.00 781.00 792.00 801.00 817.00 829.00 810.00 855.00 860.00 877.00 888.00 Specimen 8 STRAIN 231.00 235.00 212.00 215.00 250.00 253.00 259 000 263.00 270.00 275.00 280.00 286.00 290.00 296.00 300.00 301.00 309.00 313.00 318.00 321.00 326.50 331.00 337.00 310.00 STRAIN is e .e e e e e e EgOonmUImCDCDCDl-J NO-P'WUJWNNNN l-' oomwwwwww N H NH O‘WO e 115 LN(A1/A2) 0.393 #rpwrtnpwrinfi- WWNNOOOO oooooooo axm~r4\nuvwwr LN(A1/A2) pr 0‘ -Q~JCH3~LQ Hcr \nvd5ir0fimir° 01 000000000 00UNTS/IN0REMENT 1/2 Just Above Noise Level OOOOOOOOOOOOOOOOOOOOOOOO OOHHOOOOOOOOOOOOOOOI—JOOOO COUNTS/INCREMENT 1/2 0 00000000000 Specimen 8 - continued STRESS 101.72 112.68 129.26 1 6.12 l 2.12 178.72 195.30 217.78 236.60 258.52 281.00 297.86 313.32 338.61 365.30 393. 0 115. 8 138.36 153.82 181.63 505.80 533.90 561.81 592.91 619.61 616.30 671.59 699.69 716.55 733.11 753.08 769.91 786.80 798.0 809.2 826.11 818.62 8 5.18 876.72 887.96 90 .82 91 .06 932.92 911.16 STRAIN 31.79 39.65 286.13 288.96 116 LN(A1/A2) :ppppppppppp-ppp— U‘LU'IUIWNN O‘O‘O‘O‘O‘w Eppppmmppppp N #rawra- vun hue-dxrq-e <3c>owrcnan3cnaerURMlowrvuntbowr080wwvunvrwunvur¢r f;§3nanpwrcw:¢:¢wr¢f§$; 1::- «we fifi‘dfififiggfi: O O O O O O O O O O O C O O O O O O O O O 0 O O 0 O O O O O O O O O O O O O O O O O O O OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO UlU'lP'F' FH4~PQ COUNTS/INCREMENT 1/2 ONUJOOOOOOHOOI—‘Ol—‘OOOOOWHOOOOHHOI—‘HOl—JHOOOOONHOOO Specimen 9 Specimen 10 5.51 5.51 8.26 11.02 16.52 22.03 30.29 11.31 57.30 71.35 85.37 99.11 117 STRAIN 0.71 0.658 1.11 0.658 2.12 0.658 2.12 0.693 2.12 0.693 2.83 0.693 3.53 0.732 1.95 0.732 6.36 0.732 6.36 0.732 7.07 0.693 8.18 0.693 8.%8 0.693 9. 9 0.693 12.01 0.693 13.12 0.693 19.78 0.693 26.85 0.693 32.50 0.693 35.33 0.693 11.68 0.693 Removed Film (H20) 55.81 0.693 55.81 0.693 50.87 0.693 18.75 0.693 17.31 0.693 16.63 0.693 17.31 0.693 0 0.693 0 0.658 0 0.658 0.71 0.658 1.11 0.658 2.12 0.658 2083 00655 1.21 0.693 9.19 0.651 16.96 0.651 21.02 0.655 33.21 0.655 COUNTS/INCREMENT 1/2 O‘OOOOOOO OOOOOOOOOOOO Specimen 10 - continued STRESS 112.91 123.92 137.69 151.16 167.98 187.26 206.51 228.57 7.81 2 7.12 289.15 311.18 335.96 357.99 371.52 369.01 357.99 352.37 192 AA 335.30 330.%6 327. 5 327.65 327.65 327.65 Specimen 11 STRAIN 10.98 19.16 56.53 63.59 73.18 81.95 91.11 99.62 107.39 117.28 127.17 135.65 111.13 152.60 156.81 Remove 160.38 165.32 163.91 162.50 162.50 161.08 161.08 161.79 161.08 161.08 161.08 161.08 1.11 .2.12 3.53 8.18 11.30 17.66 18.37 19.08 19.78 118 LN(A1/A2) 0.693 0.693 0.693 0.652 0.655 0.693 0.637 0.652 0.693 0.673 0.673 0.637 0.651 0.693 0.651 Fihm (H20) 0 O O 0 00000000000 .purpnpqrpzpqrrnpq: \nUUnxannxnUUflMnu> -Q-e~r<—e~rQ~e~chn COUNTs/INCREMENT 1/2 OOOOI—‘ONHONI—‘OOOO H HOOO‘OOWNN‘OU“) OOF'NUJOOOOOO §pecimen 11 - continued STRESS 87.88 101.35 111.07 126.38 131.61 112.91 151.17 162.18 173.19 200.71 217.26 239.29 258.57 275.09 269.58 269.58 269.58 266.83 261.07 261.07 261.07 261.32 STRAIN , 20.19 23.32 27.55 33.91 120.11 OOOOOOOOOOO 119 LN(A1/A2) O‘O‘ON 2::- 00 0000000000000 mmmmmmmmmtrrp oooooowwwqfiflm HHHHHH P 0.501 Removed Film (H20) 128.58 131.11 IBM-24 136.35 137.06 137.06 131-23 131.11 129.29 0.501 0.501 0.501 0.501 0.501 0.501 0.501 0.501 0.501 COUNTS/INCREMENT 1/2 I-‘O OOOI—‘OOOONOOOO I-‘N UIUICDO‘ COO-E10 HICHIGQN STQTE UNIV. LIBRQRIES 31293003838863