Ultrasonic Characterization of Surface Modified Layers BRET J. ELKIND, MOSHE ROSEN, and HAYDN N.G. WADLEY Nondestructive techniques are required for the in-process characterization of rapidly solidified and surface modified layers to fulfill the role of sensors in emerging intelligent materials processing technologies. In steels, where surface modification via directed high energy sources is being investigated for surface hardening, it has been found that a difference exists in the Rayleigh wave velocity of martensite and pearlite. The difference in velocity can be used to characterize the hardness of a surface modified layer on a pearlite substrate. By varying the Rayleigh wave frequency (and thus the depth of wave penetration) and measuring velocity dispersion, it has also been possible to determine nondestructively the depth of modified surface layers on both AISI 1053 and 1044 steels produced by electron beam melting. I. INTRODUCTION RAPID solidification processing (RSP) refers to solidification processing where the cooling rate exceeds 102 K 9 s -~. The emergence of this innovative approach to materials processing has resulted in the ability to produce novel microstructures which bestow improved properties upon materials processed by these techniques (Figure 1). These high technology materials possess microstructures with enhanced chemical homogeneity, extended solid solubility, microcrystallinity, refined precipitate distributions, and metastable phases, some of which are amorphous. This has resulted in significant improvements in corrosion, erosion, wear resistance, and improved strength. One of the methods for the production of rapidly solidified microstructures is that of surface modification by directed high energy beams (lasers and electron beams). These sources of high intensity heat are capable of rapidly melting (e.g., in less than a few milliseconds) a thin surface layer before heat has appreciably diffused to the substrate. This results in a very steep temperature gradient normal to the surface, and thus a mechanism for rapid quenching of the melt (by the substrate) upon removal of the heat source. By rapidly scanning the heat source over the sample surface, cooling rates in the 103 to 108 K 9 s -L range are achieved and solidification velocities of up to 1 to 10 m 9 s -L induced. The application of this process to near net shape components eliminates the need for appreciable further processing and thus can optimize process productivity. Two broad classes of RSP surface microstructures are currently being investigated. One is concerned with the formation of amorphous surface layers on crystalline metal substrates. The second is the formation of modified crystalline surface layers with or without chemical modification. Chemical modification with this technique can be achieved by incorporating alloying powders into the melt prior to its solidification. The formation of amorphous surface layers or the layer glazing process, as it is sometimes referred to, has been demonstrated to be technically feasible, but its widespread application is limited by two problems: the difficulty of producing deep (>20 p~m) amorphous layers and the elimiBRET J. ELKIND and MOSHE ROSEN are with the Materials Science Department, The Johns Hopkins University, Baltimore, MD 21218. HAYDN N. G. WADLEY is with National Bureau of Standards, Gaithersburg, MD 20899. Manuscript submitted August 15, 1985. METALLURGICALTRANSACTIONS A nation of cracking. The former problem arises either from the reduction of temperature gradient for deeply melted layers, which causes a reduction of solidification velocity to a value below the threshold for glass formation,2 or from the occurrence of amorphous to crystalline transitions in the heat affected zones of previously vitrified material during sequential melting passes in adjacent material. The cracking problem, on the other hand, arises because of the large tensile residual stresses that are produced by solidification shrinkage strains. Microcrystalline modified surface layers may possess enhanced resistance to erosion, wear, and corrosion. These beneficial attributes are important in a diversity of high technology applications where rrfaterial performance has been the primary limitation. If this material's processing approach is to be utilized in practice, it is important to control spatial nonuniformities (of microstructure and chemistry), porosity, cracking, depth of modification, and surface topology. Microstructural and chemical heterogeneity are believed to be caused by uncontrolled variations in process variables--principally temperature gradient, solidification rate, cooling rate, and by convective mixing in the melt. Microstructural inhomogeneities may also be caused by the annealing of already processed material by subsequent melt passes in adjacent material. Clearly, if the potential of surface modification with directed high energy sources is to be fully realized, techniques (or sensors) need to be developed to measure, in process, key process variables (those controlling microstructure) and to detect cracking and other deleterious conditions. With such a capability it may then be possible to use automated process control 3 as a means for reliably producing uniformly high quality material. Previous research4 has shown the potential of acoustic emission for detecting cracking during surface modification. The work to be reported here is concerned with development of an ultrasonic technique to characterize the depth of surface modified microcrystalline layers and their hardness. The basis of the technique stems from the difference in ultrasonic velocity between the layer and substrate. In this study, the technique has been applied to the characterization of a surface modified layer on a steel substrate. The phenomenon responsible for the technique (the difference in ultrasonic velocity of substrate and layer), it should be noted, is actually more pronounced if the surface layer is amorphous, because the elastic constants, and thus ultrasonic velocity, of the substrate (crystalline) and the layer U.S. GOVERNMENTWORK NOT PROTECTED BY U.S. COPYRIGHT VOLUME 18A, MARCH 1987--473 Conventional Microstructures [ J r I "~ ! Composition Refined I and Process ~l Microstructures] Coarse Dendrites, Eutectics and Other Microconstituents De:ent"l lOCi Fine Dendrites, EutecUca and Other Microconstituents [ Extended Solid Solutions I Microcrystalline Structures Metastable Crystalline Phases ~ v 7 Amorphous So ds Increasing Homogeneity Microstructures Increasing Cooling Rate (K/s) Fig. 1 - - Microstructural consequences of rapid solidification. Note: These classifications are very approximate and depend on compositional and process variables as well as on the cooling rate.' (amorphous) are more different. Consequently, the microcrystalline layer study is in some respects a worst case test of the approach. When applied to steels, electron beam surface modification has been observed to cause substantial improvements in hardness due to the formation of martensite/bainite and carbide precipitate refinement. 5 Systematic investigations have shown that the hardness and depth of modification are controlled by scanning rate. 6'7's Thus, variation of the scan velocity could provide a convenient potential method for the control of hardness and melt depth, provided they can be measured in-process. The use of ultrasonic surface acoustic waves (Rayleigh waves) has been investigated here for the characterization of the depth and hardness of electron beam modified surface layers. Rayleigh waves are ultrasonic waves that propagate at the surface of materials. The particle displacements in the wavefront prescribe elliptical motion involving both shear and longitudinal components, the amplitudes of these motions decreasing exponentially with depth below the surface. The rate of decrease in amplitude is, however, dependent upon wavelength; at a depth of approximately one wavelength, the particle amplitude is only about 20 pct (and the particle energy is only 4 pct) of that at the surface. The velocity of Rayleigh waves in a homogeneous, isotropic, half-space is dependent only upon the density and elastic constants and is independent of wavelength (or frequency). In inhomogeneous materials with weakly depth dependent elastic properties, however, the Rayleigh wave velocity varies with wavelength (or frequency) (i.e., with depth of penetration) because waves of different frequency sample a different net modulus. Thus, the measurement of velocity dispersion could potentially provide a rapid, nondestructive method for selectively probing sub-surface properties. 9,~~ II. Several plate samples, 7.6 cm x 2.5 cm x 0.6 cm in size, were austenitized at 1025 ~ for 45 minutes. One sample was subsequently quenched in ice-brine to produce a sample of bulk martensite. The remaining samples were slowly (furnace) cooled to 650 ~ isothermally transformed for 15 minutes, and then air-cooled to room temperature. This resulted in samples with a bulk pearlitic microstructure. After completion of preliminary ultrasonic and microstructure characterizations, each of the pearlitic samples was subjected to an identical electron beam surface modification process. A 25 KV accelerating voltage was used to accelerate a 0.25 cm diameter, 9 mA electron beam onto the specimen surface. The beam power, calculated by multiplying the beam current by the accelerating voltage, was 225 watts. This beam was scanned over the sample length at the relatively slow rate of 0.3 cm 9 s -~. After each scan, the beam was translated 0.0254 cm across the width of the specimen, and the scan repeated so as to modify the entire surface. The time for a single scan was 7.5 cm - 0.3 cm 9 s -~ = 25 seconds and for the entire surface modification approximately 40 minutes. Thus, substantial tempering of prior modified material is anticipated to have occurred during subsequent passes. B. Specimen Characterization Following heat treatment, the samples were characterized to provide baseline hardness, density, longitudinal and shear ultrasonic velocity, and metallographic data of bulk (pearlitic) and surface layer microstructures. C. Rayleigh Wave Measurements In the present investigation, Rayleigh wave speed measurements were conveniently made by means of the mode conversion device shown in Figure 2. Longitudinal waves were generated by a piezoelectric transducer attached to a 2024 aluminum wedge. The wedge made contact with the sample over an area of 2.54 cm x 0.07 cm with a contact angle of about 60 deg. This resulted in the conversion of longitudinal elastic displacements to Rayleigh waves that EXPERIMENTAL A. Specimen Preparation Tests were, in the main, performed on AISI 1053 steel, the composition of which is given in Table I. An additional AISI 1044 alloy was used to confirm the approach. Table I. Element Wt pct C 0.528 474--VOLUME 18A, MARCH 1987 Mn 0.71 Composition of AISI 1053 Steel Samples P S 0.012 0.022 Si 0.17 Cr 0.039 Ni 0.034 Mo 0.011 Co 0.009 Cu 0.051 METALLURGICALTRANSACTIONS A Rayleigh Wave Mode Conversion Device Sliding Mount t- II II II ~_._.l~_~J Transmitting / Transducer ~ ) II II Receiving /I ~ T r a n s d u c e r [ . ~ ) Longitudinal~ ~ / . . , . . A l u m i n u m ~ . ~ ~" Waves ~ W.dges ~ ~ff/lllllllllllllllll~'_ Surface Mod fed Layer I ~ _.~_____ _ Non-treatedSubstrato lr T Fig, 2 - - Schematic diagram of the mode conversion technique for generation and detection of Rayleigh surface waves on surface modified samples. propagated across the surface to the second wedge. Mode conversion at the second wedge then occurred, and the resuiting longitudinal waves propagated through the wedge and were detected, again, piezoelectrically. The insertion loss* at 2.25 MHz was 43 dB and compares favorably with *The insertion loss was calculated from 20 • log~o (V/Vo) where Vo is the voltage applied to the transmitting transducer and the V, that measured across the receiving transducer. other methods of generation (see page 22 of Reference 11). By varying the resonance frequency of the piezoelectric transducer pair, it was possible to vary the frequency of the Rayleigh waves between 2.2 and 15.5 MHz. The lower frequency limit was imposed by the need for the wedge contact width (700/zm) to be greater than or equal to onehalf of the Rayleigh wavelength (1400/xm at 2.1 MHz in steel with a Rayleigh wave speed of - 3 m m 9 -I) if unacceptable insertion losses were to be avoided. The high frequency limit was determined by the ultrasonic attenuation characteristics of the material. The Rayleigh velocity was obtained by dividing the wedge separation by the time-of-flight (TOF) of a Rayleigh wave pulse between the wedge pairs. The TOF's for both the entire path (wedges and sample) and through the wedges alone were measured separately using a pulse-echo technique. The TOF of the Rayleigh pulse was then found by subtraction. The accuracy of a TOF measurement was four parts in 104 while that of measuring the wedge separation was 1 part in 103. Thus, the accuracy of the Rayleigh wave velocity was approximately +--5 m - s -~ (for a velocity of 3000 m 9 s- ~). III. RESULTS A. Homogeneous Samples The results of preliminary characterization of homogeneous pearlitic and martensitic microstructure specimens are shown in Table II. Noteworthy, in Table II, is the obserTable II. Measured Physical Properties of Homogeneous AISI 1053 Samples Physical Quantity Density Shear wave velocity Longitudinal wave velocity Rockwell macrohardness Pearlite 7796 Kg 9 m -3 3239 m 9 s-~ 6011 m 9 s -~ Martensite 7779 Kg 9 m 3 3167 m 9 s5945 m 9 s -~ Rs = 91.5 Rc = 57.0 METALLURGICALTRANSACTIONS A vation that both the longitudinal and shear wave velocities in pearlite are greater than those of martensite, an observation that has been reported by others.~2 For isotropic linear elastic materials, the density and wavespeeds can be used to determine Young's modulus, the bulk and shear moduli, and Poisson's ratio.9 Furthermore, it is possible to predict the Rayleigh wave velocity, VR, using the relation: VR= ( 0 . 8 7 + 1~222u) • Vs 1+ where v is Poisson's ratio and Vs, the shear wave velocity. These deduced quantities for homogeneous material are given in Table III. B. Microstructure of Surface Modified Material The surface modified samples were sectioned (perpendicular to the electron beam pass direction), polished and etched in 2 pct nital to reveal the microstructures produced and to facilitate microhardness measurements. Figure 3 shows, at low magnification, a view of a region about midway across the width of AISI 1053 modified material. In Figure 4 a similar region is shown together with a microhardness depth profile. Starting at the bottom, it can be seen that the substrate had a pearlite microstructure with a grain size of - 2 5 / x m (see Figure 5 for a more detailed view). As one progresses vertically toward the surface (upward in Figures 3 and 4), the peak temperature experienced during modification increases. This at first results in dissolution of cementite, then a transformation to austenite, and finally melting during the heating part of the thermal cycle. Rapid cooling from these states then produces a wide spectrum of microstructures that are vertically separated. Subsequent melt passes further complicate the microstructures due to tempering in the heat affected zone. The first modified microstructure encountered above the substrate is a transition zone approximately 300/zm thick (Figure 4), composed of a mixture of partially dissolved lamellar cementite, ferrite, and spheroidal carbides. This transition zone corresponds to a layer that did not exceed the eutectoid temperature during heating. Thus, only carbide dissolution and no transformation to austenite occurred on heating. Therefore, upon subsequent cooling, the carbon supersaturated ferrite underwent a fine scale precipitation resulting in a distribution of spheroidal carbides. The presence of these carbides and a higher dissolved carbon content in the ferrite evidently increased the hardness (Figure 4), since no martensite or bainite was evident. Above the transition zone a layer of acicular microstructure was observed (Figure 4). This corresponds to a region where the eutectoid temperature was exceeded and Table III, Deduced Physical Properties of Homogeneous AISI 1053 Samples Physical Quantity Young's modulus (E) Bulk modulus (K) Shear modulus (G) Poisson's ratio (v) Rayleigh wave velocity (VR) Pearlite 211.9 GPa 172.7 GPa 81.78 GPa 0.295 0.3002 m 9 s -j Martensite 203.1 GPa 170.9 GPa 78.00 GPa 0.301 2939 m 9 s -~ VOLUME 18A, MARCH 1987--475 Fig. 3--A section of surface modified AISI 1053 steel. The plane of the micrograph is perpendicular to the direction of electron beam motion (2 pet nital etch). austenite had nucleated. The dimensions of the acicular features increased with vertical distance from the transition zone consistent with an increase in prior austenite grain size due to more extensive (but still solid state) heating. This increase in grain size probably accounts for the diminishing hardness as one approaches the top of the layer. Detailed examination of this region (Figure 6(b)) indicates that the dominant microstructure is either a lower bainite, or (possibly) a tempered martensite. A distinctive microstructure transition occurs at the upper end of the acicular zone as one encounters the region that underwent melting. This zone of melting was - 3 3 0 / z m in depth. It is shown at higher magnification in Figure 6(a). The microstructure is acicular consisting in the main of upper bainite, but it also contained significant volumes of ferrite and, in places, small dark etching regions reminiscent of very fine (unresolvable) pearlite. At lower magnification (Figure 3) alternate light (low hardness) and dark etching bands are observed. The dark areas correspond to dense distributions of very fine spheroidal carbides and are the heat affected zones of subsequent melt passes. Microhardness measurements were made on the surface modified AISI 1053 alloy and are summarized in Table IV. The low hardness (Re = 22 to 29) for the melt layer is consistent with the microstructure observed. Harder layers would presumably have been obtained by using lower heat flux, faster scan speed, and reducing the overlap of successive melt passes. However, even for the last pass (not subsequently tempered), the hardness of the melt layer was still at most only Rc = 39. Table IV. To test the method developed on the AISI 1053 alloy, additional Rayleigh wave measurements were made on a similarly treated AISI 1044 alloy whose microstructure is shown in Figure 7. The depth melted was - 4 5 0 / x m , the acicular (but unmelted) layer was 125/zm thick, and transition zone thickness approximately 200/zm. C. Rayleigh Wave Measurements Figure 8 shows a plot of the measured Rayleigh wave velocity as a function of wavelength (penetration depth) for the surface modified layer and the unmodified pearlitic substrate as obtained from the unmodified reverse side of the sample. It can be seen that the substrate exhibits a constant velocity independent of wavelength with an average value of 3001 - 1 m 9s -1 in excellent agreement with the predicted value (in Table III) from bulk wave measurements. The absence of dispersion from a homogeneous sample indicates that the experimental approach does not introduce any significant velocity measurement errors. The velocity measured on the surface modified layer exhibits significant dispersion. At high frequencies (shallow penetration depths) a limiting velocity of 2960 --- 2 m 9 sis achieved. This represents the velocity of the layer and is - 2 0 m " s -l greater than the value predicted from bulk wave measurements on a homogeneous martensite sample. This difference is most probably due to the bainite microstructure of the layers since bainites are well known to have elastic properties intermediate between those of pearlite and martensite. ~2 We see in Figure 8 that as the wavelength Properties of Surface Modified AISI 1053 Alloy Region Thickness Microstructure Melt layer Acicular layer Transition zone Substrate 0.330 mm 0.435 mm 0.300 mm 5.2 mm tempered upper bainite bainite pearlite/spheroidal carbides pearlite 476--VOLUME 18A,MARCH1987 Hardness R,. = 22 to 29 R,. = 27 to 30 R,. = 22 to 29 RB = 94.0 METALLURGICALTRANSACTIONSA Surface 1 I ! 1 0.1 0.2 ? I 0.3 0.4 Melt Layer ( 0.5 E E "" 0.6 r r Acicular Layer 9 0.7 .jl _o 0 m 0.8 r O c C~ 0.9 l 1.0 Transition Zone 1.1 F 1.2 1.3 I 1.4 I 150 Substrate r ] Low Values for Light Etching Regions I I 200 250 300 Vickers Hardness I 350 Fig. 4 - - A narrow region of the sample shown in Fig. 3 at a higher magnification revealing the vertical separation of microstructure (2 pct nital etch) together with the microhardness variation with depth. increased the velocity began to approach the value of pearlite consistent with an enhanced contribution of the substrate to the elastic constants sampled by the wave. The Rayleigh wave velocity for the AISI 1044 steel is shown in Figure 9. The velocity for the substrate is different from that of the AISI 1053 steel, but a similar dispersion is observed on the surface modified layer. Interestingly, the penetration depth at which dispersion becomes detectable is less than that in the AISI 1053 steel. IV. DISCUSSION Rayleigh waves propagating over the surface of electronbeam modified surfaces sample only the modified (mar- METALLURGICAL TRANSACTIONS A tensitic) layer at high frequencies (since the wave does not penetrate the layer) and some combination of the layer and substrate (pearlitic) at lower frequencies. In the high frequency region, the velocity is found to be approximately frequency independent, consistent with wave propagation in an approximately uniform, nondispersive medium. Then the limiting velocity can be viewed as a characteristic of the layer microstructure and not its depth. The velocity for AISI 1053 surface layers is intermediate between that anticipated for martensite and pearlite, and is consistent with the observed bainite state. There thus appears considerable merit to the use of this asymptotic value to characterize layer hardness. Rayleigh waves with greater penetration depths yielded velocities that were intermediate between those of the sub- VOLUME 18A, MARCH 1987--477 Fig. 5 - - A typical region of the substrate microstructure revealing its coarse pearlitic nature (2 pct nital etch). strate and the layer. Provided the substrate is much thicker than the layer, then when the wavelength (penetration) is very much greater than the layer thickness, the velocity approaches the Rayleigh velocity for pearlite because contributions from the layer become increasingly small. This limit was not reached in these samples due to their finite thickness, but sufficient data for a depth determination were nevertheless obtained. If we had continued to longer wavelengths, the limiting velocity achieved would have been that of a plate (Lamb) wave which has a different velocity to that of the surface wave. This consideration, however, would be of import only if one were attempting to characterize the substrate hardness beneath an overlayer. To determine the layer thickness, the region of interest is the intermediate velocity region, where the velocity results from the simultaneous sampling of several different microstructures. For example, in AISI 1053 at a frequency of 4.2 MHz (penetration depth = 705/~m), the Rayleigh velocity was 2960 m 9s-~; however, at 2.2 MHz (penetration depth = 1357 /xm), the apparent Rayleigh velocity was 2984 m" s -j. The velocity thus depends upon both the characteristic velocities of the layer and substrate and the layer depth. (a) (b) Fig. 6--Typical microstructure present in (a) the melted and (b) the acicular layers of AISI 1053 steel (2 pct nital etch). Fig. 7 - - A section of surface modified AISI 1044 steel. The plane of the micrograph is perpendicular to the direction of electron beam motion (2 pct nital etch). 478-- VOLUME 18A, MARCH 1987 METALLURGICAL TRANSACTIONS A ..-_-- ,, XL= [V--Vs] 3000 Substrate 2990 E 2980 o > 2970 r Surface Modified 2960 [ AIS1-1053 Steel ] 2950 I 0 I I 200 I I I I I I I 400 600 800 1000 Penetration Depth IX] (/~m) I I 1200 I I 1400 Fig. 8--Variation of the Rayleigh wave velocity with wavelength (penetration depth) for AISI 1053 steel. 2965 2960 lr.t--~ i Substrate 2950 m 2940 u > Jr O~ -$ 2930 Substituting data from Figure 8 into this expression yields a value for a modified layer depth of 600 to 800/zm, the variability depending upon the precise value of wavelength taken. Metallography for AISI 1053 indicated that the combined acicular and melt depth was --850/xm, in reasonable agreement to that deduced bearing in mind the simplicity of a law of mixtures model. A more complete analysis incorporating exponential weighting of the Rayleigh wave particle displacement might give a more exact inversion, and thus deeper insight, into the functional behavior of the modulus with depth. However, for the present purpose, this simple approach appears sufficient, at least for the AISI 1053 alloy. Indeed, an even simpler depth determination criterion such as the penetration depth at which the velocity curve increases 2 m 9 s-1 above the short wavelength velocity limit predicts the metallographically deduced depths of hardening for both AISI 1053 and 1044 alloys to within ---25/xm. The Rayleigh wave technique has proved, therefore, to be an accurate and reproducible technique for determining the depth of hardening of surface modified steels. Since it is nondestructive, and methodologies which would not interfere with processing are emerging, it can potentially be used for on-line quality control purposes. If account is taken of the effect of sample temperature fluctuations on the velocity, it could serve the role of a process control sensor for feedback control of depth of modification and hardness, particularly if emerging noncontact measurement methodologies are utilized. Surface M o d i f i e d / ~ ~ m 2920 XA LVL -- Vs_l |-! V. [ AISI-1044 Steel ] 2910 I I l 1 I I I I 200 300 400 500 600 700 800 900 Penetration Depth IX] (/~m) Fig. 9--Variation of the Rayleigh wavespeed with wavelength (penetration depth) for AISI 1044 steel. The inverse problem of deducing the layer properties from velocity dispersion data is complex and is the object of ongoing study. Here, we use a very simple analysis that gives results of reasonable accuracy. For the case where the wave penetrates the surface modified layer, we may, to a first approximation, assume the apparent velocity to be determined by the layer thickness: wavelength ratio according to a law of mixtures: v =x • VL + (1 --X) • Vs where Vz = the velocity of the layer vs = the velocity of the substrate x = XL/A, the ratio of layer thickness to wavelength (n.b. we define (x = 1 for A --< XL) In the long wavelength limit, x tends to zero and the apparent velocity is vs, while for A < xL, the velocity becomes that of the layer, VL. TO determine the layer depth, we rearrange the equation above: METALLURGICALTRANSACTIONSA SUMMARY 1. Samples of pearlitic plain carbon steels were subjected to an electron-beam glazing process resulting in a (casehardened) microstructurally modified surface layer, 2. Hardness and ultrasonic velocity data indicated that the modified surface layers possessed a higher hardness but a lower velocity than the substrate materials. This decrease in velocity may be a good indication of the level of hardness attained in the modified layer. 3. Dispersion of the Rayleigh wave velocity can be utilized to make a nondestructive estimate of the depth of the microstructurally modified surface layer. ACKNOWLEDGMENTS We are grateful to Dr. R. Schaefer for his assistance and advice with electron beam surface modification, to C. Brady for help with metallography, and to the Defense Advanced Research Projects Agency for funding of this work under DARPA Order Number 4275 (Major S. Wax, Program Monitor). REFERENCES 1. M. Cohen, B. H. Kear, and R. Mehrabian: Rapid Solidification Processing: Principles and Technologies H, M. Cohen, B.H. Kear, and R. Mehrabian, eds., Claitor's Publishing Division, Baton Rouge, LA, 1980, p. 1. VOLUME 18A, MARCH 1987--479 2. W.J. Boettinger, E S. Biancaniello, G.M. Kalonji, and J. W. Cahn: Rapid Solidification Processing: Principles and Technologies H, M. Cohen, B. H. Kear, and R. 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B. llic, E Stanke, C. H. Chou, and T. C. Shyne: Proc. 1979 Ultrasonic Symposium, IEEE, 1979, p. 273. 6. 7. 8. 9. METALLURGICAL TRANSACTIONS A
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