Friction, Lubrication, and Wear Technology (1997) Part 7 docx

where d = F/4 r 2 , and I 0 is the ultrasonic intensity irradiated on the defect, f( ) is the backscattered amplitude, is the attenuation coefficient in the material, F is the area of the transducer, r is the depth of the defect, and d is the solid angle subtended by the probe as seen from the defect. Because f( ) a 2 f 2 in the Rayleigh regime, I sc /I 0 a 6 f 4 (f is the ultrasonic frequency)! This means that very efficient transducers with a center frequency as high as possible must be employed in order to obtain a sufficiently high SNR for a given excitation voltage of the transducer. For other defect shapes, expressions similar to Eq 2 also hold true (Ref 20). Therefore, the electronic systems and probes in a HAIM system must be designed such that the highest SNR is obtained and losses are absolutely minimized. In the setup currently used by the authors, the detection limit for defects is 30 m for inclusions of a few millimeters depth, provided the ultrasonic attenuation in the material examined is less than 1 dB/cm at 50 MHz. Figure 8 shows a block diagram of a typical HAIM system. This system also comprises a scanning system to obtain B-scan and C-scan images with a step-resolution of 10 m (Ref 21). A-scans generate ultrasonic data in which the amplitude is recorded as a function of time. In a B-scan, the amplitude is recorded in varying shades of gray or a color scale as a function of time and one coordinate. C-scans generate amplitude data as a function of two coordinates. In general, the maximum amplitude in C-scans is recorded for the image built up within a preset gate having a time delay that defines the time-of-flight of the signal and, hence, the depth of its origin within the sample. After rectification, the portion of interest of an A-scan is cut out by a gate and the signal strength within this gate is used to build up the image. The authors' system has been used to detect and evaluate defects, lack of adhesion between two different materials, homogeneity, and surface damage of components. Details about the design of the focusing probes can be found elsewhere (Ref 22). Various electronic systems are used for HAIM. Fig. 8 Block diagram of a typical HAIM system. A transmitter excites the transducer, in this case a polyvinylidene-difluoride (PVD F) transducer. In order to obtain sufficient spatial resolution, pulses of less than 100 ns are needed. A large bandwidth for both the electronics and the transducer are then necessary. The transducer employed may be excited by either an exponentially decaying step- pulse (broadband excitation), typical in NDE electronics, or by an rf carrier pulse (narrowband excitation). The component is scanned by either an xyz scanning system or by a robotic system. Source: Ref 21 Applications of HAIM High-frequency acoustic imaging is used to test bonding interfaces (Fig. 9). The typical sample used for adhesion tests for biomedical applications consists of a metal slab (15 × 10 × 2 mm, or 0.59 × 0.4 × 0.08 in.) bonded by a glue to a plastic slab of the same size. Using a 50 MHz focusing probe with broadband excitation by a spike pulse, ultrasound was sent through the surface of the plastic slab and the backscattered echo from the bonding interface was detected by a peak detector. The C-scan (16 × 16 mm, or × in.) shows typical distribution patterns of adhesive in the interface. Areas of large change of the acoustic impedance appear as bright colors (light in gray scale), low reflecting areas appear as dark colors (dark in gray scale). An enhanced sensitivity to surface damage can be obtained by radiating the acoustic energy under an oblique angle to generate surface waves. Surface wave scattering by defects is, therefore, the dominant source of contrast in a HAIM image, just as it is in SAM images. Fig. 9 C-scan image of a bonded structure obtained by high- frequency acoustic imaging. Center frequency of the probe was 50 MHz. The color scale (gray scale) is c alibrated in relative intensity (dB). The width of the image is 16 mm. Original image is in color. Further details are explained in text. Scanning Laser Acoustic Microscopy Principles of SLAM The operating principle of a SLAM is outlined in Fig. 10. A sample is insonified under a certain angle with respect to the surface of the sample. In a homogeneous sample, the ultrasound causes a ripple of the surface, off which a laser beam is reflected. The spatial and temporal periodic displacements of the surface cause the laser beam to be partially diffracted and frequency to be shifted by the Doppler effect. By a knife edge, one diffraction order is blocked. This then leads to an alternating current (ac) in the photodiode, because its output contains a mixing product between the undiffracted zero order and the still-present diffracted part. The frequency of the ac component is equal to the sound frequency, and its magnitude is proportional to the sound amplitude. Fig. 10 Schematic showing key components and parameters of SLAM. The sound waves traveling through the sample under an angle, , generate a surface ripple with a wavelength of /sin . The soundwaves are detected by an optical knife-edge device in which the angle of reflection, , is modulated by an amount, , depending on the local amplitude of the surface ripple, according to the amount of scattering by defects present in the sample. The images obtained are acoustic holograms equivalent to Gabor holography in its original form. A quadrature receiver is used to detect the phase of the image required for holographic reconstruction. Here, the reference phase necessary for quadratic detection is obtained from the rf source driving the transducer. The images are obtained in real-time (that is, with 25 frames/second). This technique makes possible the detection of coherent surface waves of extremely small amplitude ( 10 -6 nm/ bandwidth). When pores, inclusions, and cracks are present in the sample, the sound wave is scattered by these defects, which in turn become visible as a modulation of the otherwise homogeneous surface ripple. By rastering the laser beam over the surface of the sample, this modulation can be measured and displayed on a television screen (the rate of image buildup is the TV rate). The resolution in such images is given by the wavelength of the ultrasound and is typically 50 m in most solid materials at 100 MHz. It is obvious that the images obtained by SLAM are acoustic shadowgraphs, provided the size of the imaged structure is large compared with the wavelength. If the size becomes comparable to , diffraction patterns are obtained. If the surface of the sample is not optically reflective, the dynamic ripple caused by the sound field is then transmitted to a light- reflecting layer that is coupled acoustically to the sample surface by water. Reconstruction of Images by Holography In addition to the simple detection of defects in a given sample, SLAM techniques can be used to study their characterization and sizing. In general, this is a complex problem, because the SLAM provides two-dimensional images of a three-dimensional defect geometry deblurred by diffraction effects. Therefore, a defect appear much larger than it really is. It is possible, however, to detect both the amplitude and phases of the acoustic field in a SLAM image, allowing reconstruction of the defect by acoustic holography techniques (Ref 23). Acoustic holography is a two-step process. First, the amplitude and phase of the acoustic field emanating from an insonified object are detected in a plane adjacent to its surface. Second, from these field data, the scattered field in the defect plane, , can then be reconstructed with a resolution of 1 wavelength. The relation between the fields (x,y,0) and (x,y, z) in two parallel planes in the sample under investigation, separated by a distance z, is given by a linear filtering process (Ref 24): (k x ,k y ,k ) = 0 (k x ,k y ,0) · exp (ik z · z) (Eq 4) where k z = and is the corresponding fields in k-space. k x and k y can be interpreted as the x- and y- component of the wave vector of a plane wave with amplitude 0 . Thus, the field distributions between the detection plane and the object can be obtained by calculating the two-dimensional Fourier transform of the field , multiplying it with the filter function exp(- k z · z), and Fourier back-transforming it into spatial coordinates. This process is called back-propagation. Because outside + = k 2 the filter function is steeply increasing, the filtering is restricted to the innerface of the circle with radius k so that noise is reduced. The SNR in the back-propagated image can be further enhanced by deconvoluting the field data with the transfer function of the laser detection scheme employed in the SLAM, resulting in a total improvement of the SNR of approximately 10 dB compared with the original image. Figure 11 shows the image of an iron inclusion in an Si/SiC bending bar obtained at an ultrasonic frequency of 100 MHz (Ref 24). The diffraction of the sound-field waves at the inclusion causes concentric ring patterns. Such images are typical for SLAM. However, by subsequently calculating the field distributions in planes of increasing depth, an image with an apparently optimal defect contrast is obtained that corresponds to the depth of the defect. Fig. 11 SLAM image of an iron inclusion in an Si/SiC bending bar as obtained at the output detector. (a) z = 0 mm (the plane of detection at the surface of the sample). (b) to (f) Reconstructed images at various z (in increasing steps of 200 m). As can be seen in (c) and (d), the defect appears focused, yielding a depth of approximately 500 m. SLAM parameters: ultrasonic frequency, 100 MHz; field of view, 2.8 × 2.8 mm 2 . Source: Ref 24 Summary Acoustical imaging has gained tremendously from the comprehensive theoretical description of the contrast mechanisms involved and from the availability of high-speed computers. Such computers allow modeling and interpretation of the complex contrast underlying acoustic images and efficient handling of the large amount of data involved. Applications are primarily in NDE and materials characterization; some of these applications are related to problems in tribology. In the future, high priority must be given to the integration of software that permits the reconstruction of defects by synthetic aperture techniques (Ref 2, 25, 26) and the use of robotic scanning systems in order to scan components of complex shape. References 1. C.F. Quate, A. Atalar, and H.K. Wickramasinghe, Acoustical Microscopy With Mechanical Scanning A Review, Proc. IEEE, Vol 67, 1979, p 1092-1113 2. A. Briggs, An Introduction to Acoustic Microscopy, Microscopy Handbooks, Vol 12, Oxford University Press, 1985 3. P. Höller and W. Arnold, Micro-Non-Destructive Testing of the Structure of New Materials, Conference Proceedings of Ultrasonics International 1989, Butterworth Scientific, 1989, p 880-888 4. L.W. Kessler and D.E. Yuhas, Acoustic Microscopy 1979, Proc. IEEE, Vol 67, 1979, p 526-536 5. R. Weglein, Acoustic Micro-Metrology, IEEE Trans. Sonics Ultrasonics, Vol SU-32, 1985, p 225-234 6. A. Atalar, Improvement of the Anisotropy Sensitivity in the Scanning Acoustic Microscope, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, Vol 36, 1989, p 164-273 7. J.I. Kushibiki and N. Chubachi, Material Characterization by Line-Focus Beam Acoustic Microscope, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, Vol SU-32, 1985, p 189-212 8. R. Weglein, SAW Dispersion in Diamond Films on Silicon by Acoustic Microscopy, Rev. Quant. NDE, 1992 (to be published) 9. A. Atalar, L. Degertekin, and H. Köymen, Acoustic Parameter Mapping of Layered Materials Using a Lamb's Wave Lens, Proceedings of 19th International Symposium on Acoustical Imaging, H. Ermert and H.P. Harjes, Ed., Plenum Press, 1992 (to be published) 10. J. Attal, L. Robert, G. Despaux, R. Capalin, and J.M. Saurel, New De velopments in Scanning Acoustic Microscopy, Proceedings of 19th International Symposium on Acoustical Imaging, H. Ermert and H.P. Harjes, Ed., Plenum Press, 1992 (to be published) 11. A. Kulik, G. Gremaud, and S. Sathish, Direct Measurements of the SAW Ve locity and Attenuation Using Continuous Wave Reflection Scanning Acoustic Microscope (SAMCRUW), Acoust. Imaging, Vol 18, 1991, p 227-236 12. K.K. Liang, S.D. Benett, B.T. Khuri- Yakub, and G.S. Kino, Precise Phase Measurements With the Acoustic Microscope, IEEE Trans. Sonics Ultrasonics, Vol SU-32, 1985, p 266-273 13. S.W. Meeks, D. Peter, D. Horne, K. Young, and V. Novotny, Microscopic Imaging of Residual Stress Using a Scanning Phase-Measuring Acoustic Microscope, Appl. Phys. Lett., Vol 55, 1989, p 1835-1837 14. H. Vetters, E. Matthaei, A. Schulz, and P. Mayr, Scanning Acoustic Microscope Analysis for Testing Solid State Materials, Mater. Sci. Eng., Vol A122, 1989, p 9-14 15. C.H. Chou and B.T. Khuri-Yakub, Acoustic Microscopy of Ceramic Bearing Balls, Acoust. Imaging, Vol 18, 1991, p 197-203 16. K. Yamanaka, Y. Enomoto, and Y. Tsuya, Acoustic Microscopy of Ceramic Surfaces, IEEE Trans. Sonics Ultrasonics, Vol SU-32, 1985, p 313-319 17. K. Yamanaka, Study of Fracture and Wear by Using Acoustic Microscopy, Ultrasonic Spectroscopy and Its Applications to Materials Science, Y. Wada, Ed., Special Reports of Japanese Ministry of Science, Education and Culture, 1988, p 44-49 18. S. Pangraz, E. Verlemann, and T. Holstein, unpublished results 19. I. Ishikawa, T. Semba, H. Kanda, K. Katakura, Y. Tani, and H. Sato, Experimental Observation of Plastic Deformation Areas, Using an Acoustic Microscope, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, Vol 36, 1989, p 274-279 20. I.N. Ermolov, The Reflection of Ultrasound From Targets of Simple Geometry, Nondestr. Test., Vol 5, 1972, p 87-91 21. S. Pangraz, H. Simon, R. Herzer, and W. Arnold, Non- Destructive Evaluation of Engineering Ceramics by High-Frequency Acoustic Techniques, Proceedings of the 18th I nternational Symposium on Acoustical Imaging, G. Wade and H. Lee, Plenum Press, 1991, p 189-195 22. R.S. Gilmore, K.C. Tam, J.D. Young, and D.R. Howard, Acoustic Microscopy from 10 to 100 MHz for Industrial Applications, Philos. Trans. R. Soc. (London), Vol A320, 1986, p 215-235 23. Z. Lin, H. Lee, G. Wade, M.G. Oravecz, and L.W. Kessler, Holographic Image Reconstruction in Scanning Laser Acoustic Microscopy, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, Vol 34, 1987, p 293-300 24. A. Morsc h and W. Arnold, Holographic Reconstruction by Back Propagation of Defect Images Obtained by Scanning Laser Acoustic Microscopy, Proceedings of 12th World Conference on NDT, J. Boogard and G.M. van Dijk, Ed., Elsevier Science, 1989, p 1617-1620 25. V. Schmitz, W. Müller, and G. Schäfer, Synthetic Aperture Focusing Technique State of the Art, Proceedings of 19th International Symposium on Acoustical Imaging, H. Ermert and H.P. Harjes, Ed., Plenum Press, 1992 (to be published) 26. K.J. Langenberg, Applied Inverse Problems for Acoustic, Electromagnetic and Elastic Scattering, Basic Methods of Tomography and Inverse Problems, P.C. Sabatier, Ed., Adam Hilger, Bristol, 1987, p 125-467 Microindentation Hardness Testing Peter J. Blau, Oak Ridge National Laboratory Introduction MICROINDENTATION (MICROHARDNESS) HARDNESS TESTING is an important tool for characterizing the near- surface characteristics of materials, surface treatments, and coatings. It is extensively used in both applied and research aspects of tribology. It is a subgroup of the general field of penetration hardness testing, but the relatively low applied forces (typically, 0.01 to 10 N, or 1 to 1000 gf) make it particularly sensitive to the near-surface mechanical properties of materials. Some common uses of microhardness testing include: • Investigating the variations in penetration hardness between various phases in a microstructure • Initial characterization of the surfaces of materials for wear applications • Quality control of surface treatments or coatings • Profiling the depth of hardened surface layers and coatings • Assessing the nature of subsurface damage on or below machined surfaces • Assessing the nature of subsurface damage on or below wear surfaces In addition to hardness number determination, there are other specialized uses of microindentation techniques in friction and wear technology. These include: • Use of microindentations as wear markers (see the section "Wear Measurement Using Microindentations" in this article) • Use of microindentations to generate cracks to determine fracture toughness of brittle materials (Ref 1) The development of instrumented microindentation testing equipment in recent years permits direct monitoring and recording of the instantaneous force versus the displacement depth for hardness tests. Such equipment offers the advantage of not requiring optical measurement of the indentation. However, it demands very accurate penetration depth calibrations. This type of testing is described in the article "Nanoindentation" in this Section. In this article, the focus will be on more traditional tests involving optical microscopy measurement of the impressions. Principles of Microindentation Testing The purpose of microindentation hardness testing is to obtain a numerical value that distinguishes between the relative ability of materials to resist controlled penetration by a specified type of indenter which is generally much harder than the material being tested. (A notable exception is in the microindentation testing of very hard materials, like diamond, where the indenter and test specimen can be equal or nearly equal in hardness.) After preparing the specimen via the application of good metallographic practice in order to avoid residual damage to the test surface, the testing procedure involves the following sequence of steps: 1. Mounting the prepared specimen so that its test surface is perpendicular to the direction of indentation 2. Causing the indenter to move downward and impinge on the surface of the specimen at a specified rate 3. Allowing the indenter to remain for a specified residence time after it stops moving 4. Retracting the indenter 5. Measuring a characteristic dimension of the residual indentation 6. Using the geometry of the indenter to calculate a hardness number Nearly all commercially available microindentation hardness testers perform steps 2 through 4 automatically. The accuracy and reliability of the numbers obtained in performing microindentation hardness tests are strongly dependent on three factors: the machine, the operator, and the material characteristics. The machine must be correctly calibrated for both the applied force and the optical measuring accuracy. It must also be isolated from vibrations during the test. The operator must be familiar with the correct mounting and specimen preparation methods (such as rigidly mounting the specimen, keeping the test surface level, and using sound metallographic polishing practice to avoid the introduction of factors detrimental to specimen preparation), capable of measuring indentations consistently and correctly, able to recognize invalid indentations, and aware of the need to avoid touching the machine during its operation. The material may not be homogeneous or the method of fabrication applied in its production may give it hardness numbers significantly different from those published in tables of "typical values." One of the greatest sources of error in determining microindentation hardness numbers is in the reading of the indentation lengths. This problem becomes particularly important when hard materials are being tested or low forces are being used. Hardness numbers should not be operator dependent. Therefore, all the individuals using the given hardness tester should be tested to see how closely the measurements of indentation length agree on the same set of reference impressions. Personal correction factors may need to be given to each person so that measurements on reference specimens agree. Well-polished austenitic stainless steel or nickel specimens are good for laboratory optical reading reference specimens because they tend to provide nicely shaped impressions and remain untarnished. Periodic rechecking, approximately once a year, is desirable because an individual's vision is subject to change. If a critical series of measurements are to be made more frequently, then recalibration must be performed before each series is started. If the hardness testing apparatus does not read directly in micrometers, each reader should be familiar with the proper eyepiece ("filar") unit-to-micrometer conversion method. A "filar" unit is a unit of measure that relates to a scale that is visible in the measuring eyepiece of the testing machine. If the filar eyepiece is used with different objective lenses, the conversion between the filar units and micrometers must be obtained for each objective lens. This conversion factor is derived by measuring the number of filar units that correspond to the observed spacings on a precision, etched microscope slide that is graduated directly in micrometers ("stage micrometer"). As noted above, each individual using the system should have his or her own personal filar factors to maintain consistency within the laboratory. The numerical values obtained by microindentation hardness testing techniques are dependent on a combination of material properties (for example, elastic modulus, compressive yield strength, mechanical properties, anisotropy, and so on) that interact under the stress state imposed by the indenter. Therefore, hardness numbers should not be considered basic properties of a material or a coating, but rather numbers that indicate the response of a given material to the imposed conditions of the penetration test. The two most commonly used microindentation techniques are the Vickers and the Knoop microindentation tests. Other indenter geometries have been developed for special purposes. These will not be discussed here; the reader is instead referred to books, published standards, and review articles included in Ref 2, 3, 4, 5, 6, 7, 8, 9, and 10. Most commercial microindentation hardness testers still in use today use gages calibrated in gram-force (gf). However, the correct International Organization for Standardization (ISO) unit for force (that is, "load") is the Newton (N). Aside from the hardness scales that report a relative index or number of dimensionless units (such as Rockwell hardness numbers), indentation hardness numbers are commonly expressed in units of pressure. Units of force and pressure are related to the traditional microindentation hardness units as follows: To convert from To Multiply by gf N 0.00981 kgf N 9.81 kg/mm 2 GPa 0.00981 GPa kg/mm 2 102.0 Historically, Knoop microindentation hardness is calculated as force per unit of projected area of the indentation, whereas the Vickers hardness (sometimes known as diamond pyramid hardness, or DPH) is expressed as a force per unit facet area. This difference in the area is one factor that can lead to slightly different hardness numbers under the same applied indenter force, especially at relatively low indenter loads (that is, 0.01 to 1 N, or 1 to 100 gf); Knoop numbers are usually higher than Vickers numbers obtained at the same load. Standard Reference Materials for Microindentation Hardness The U.S. National Institute of Standards and Technology, or NIST (formerly the National Bureau of Standards, or NBS), in Gaithersburg, MD, has developed materials whose microhardnesses can be used for calibration purposes. Known as Standard Reference Materials (SRM), they can be purchased for either Knoop testing or Vickers testing over the range of 0.25 to 0.98 N (25 to 100 gf). Each specimen comes with a certificate and a set of microhardness numbers for that specimen. Both materials are electroformed deposits and have the designations listed in Table 1. Table 1 Standard reference materials used to calibrate Knoop and Vickers microindentation hardness equipment Catalog No. Scale Material Microhardness, kg/mm 2 SRM 1893 Knoop Copper 125 SRM 1894 Vickers Copper 125 SRM 1895 Knoop Nickel 550 SRM 1896 Vickers Nickel 550 Vickers Microindentation Hardness Test The Vickers indenter is more widely used throughout the world than the Knoop indenter. The face-to-face angle of the Vickers indenter was selected so that Vickers hardness numbers would be comparable to those obtained from the established Brinell hardness test that preceded it. It was recognized that the diameter of Brinell hardness indentations (d B ) varied between 0.25 and 0.5 times the ball diameter (D B ). Using the mean of d B = 0.375 D B gave a ratio of surface contact area to the projected area (circular area of the indentation viewed from above) for the Brinell case of 1.08:1. This ratio is approximately the same for a Vickers pyramid when the face-to-face apex angle is 136°; hence, this angle was chosen for the Vickers pyramid. Figure 1 shows the shape of the tip of a Vickers hardness (diamond pyramid hardness) indenter and defines the symbols used in subsequent equations. Fig. 1 Key dimensions and geometry for the tip of a Vickers indenter. (a) Diagonals d and d . (b) Face-to- face apex angle There is some confusion in the literature as to the symbols used for microindentation hardness numbers using the Vickers indenter. Three commonly used symbols are DPH, VHN, and HV P , where P represents the applied force. The later symbol is preferred by ASTM. The general equation for Vickers hardness uses the average value of the two diagonals, d*, where (Eq 1) to calculate the hardness value (Eq 2) where P is the applied force, usually expressed in units of grams-force or kilograms-force, and C V is a proportionality constant. Vickers Indenter Versus Knoop Indenter. The Knoop indenter has both advantages and disadvantages over the Vickers indenter in microindentation testing. Because it is more blunt, the Knoop indenter tends to promote less cracking during the indentation of brittle materials (the penetration depth is 0.635 that of the Vickers indenter, assuming equal test [...]... 13 15 15 13 Material Pure metals Aluminum 0.21 0.19 0.19 98.65 2.46 2 .71 2.59 0. 57 0.46 0.42 0.66 2.44 2.49 2.44 0.049 0. 47 2.90 2 .73 2 .73 1.00 1.03 1.01 14.22 0.2 27 0.21 0.22 0.23 2.88 3.34 2 .73 0.48 0.41 0. 37 0 .77 2.92 2.92 2 .76 3.32 2 .76 2 .76 1.06 1.04 1.14 8.83 13 .7 Silver Titanium Zinc Bearing steel AISI 52100 Carbides and nitrides Boron carbide Chromium carbide Hafnium carbide Silicon... Coatings, Thin Solid Films, Vol 152, 19 87, p L131-L133 27 W.A Glaeser, Wear, Vol 40, 1 976 , p 135-1 37 28 A Begellinger and A.W.J de Gee, Wear, Vol 43, 1 977 , p 259-261 29 M.M Khruschov, Proceedings of Conference on Lubrication and Wear, Institute of Mechanical Engineers, 19 57, p 655 Nanoindentation H M Pollock, School of Physics and Materials, Lancaster University (England) Introduction ONE REASON for the... ASTM, 1985, p 272 -285 17 P.J Burnett and D.S Rickerby, Thin Solid Films, Vol 154, 19 87, p 403-416 18 B Jönsson and S Högmark, Thin Solid Films, Vol 114, 1984, p 2 57- 269 19 M Antler and M.H Drozdowicz, Wear of Gold Electrodeposits: Effect of Substrate and of Nickel Underplate, Bell Syst Tech J., Vol 58 (No 2), 1 979 , p 323-349 20 E.H Enberg, Testing Plating Hardness and Thickness Using a Microhardness... Ives of the National Institute of Standards and Technology Correlation of Microindentation Hardness Numbers with Wear There are many kinds of wear, as indicated in the Section titled "Wear" in this Volume The types of localized stresses and directions of relative motion vary considerably between the various kinds of wear Sometimes the stress conditions experienced by a wear surface are more similar to... hardness and wear rates may not necessarily correlate Classic Russian studies of abrasive wear have established relationships of relative hardness to relative wear rates (Ref 29) However, this relationship does not always hold There may not necessarily be a correlation between microindentation hardness numbers of the unworn surface and wear due to the following reasons: Workhardening In wear of metals and. .. 19 57 H Bückle, Progress in Micro-Indentation Hardness Testing, Met Rev., Vol 4, 1959, p 49-100 D.R Tate, A Comparison of Microhardness Indentation tests, ASM Trans., Vol 35, 1945, p 374 -389 J.H Westbrook and H Conrad, Ed., The Science of Hardness Testing and Its Research Applications, American Society for Metals, 1 973 7 P.J Blau and B.R Lawn, Ed., Microindentation Techniques in Materials Science and. .. 384, Annual Book of ASTM Standards, ASTM 10 "Test for Microhardness of Electroplated Coatings," B 578 , Annual Book of ASTM Standards, ASTM 11 A.A Ivan'ko, Handbook of Hardness Data, U.S Department of Commerce, National Technical Information Service, 1 971 , transl from Russian 12 B.C Wonsiewicz and G.Y Chin, A Theory of Knoop Hardness Anisotropy, The Science of Hardness Testing and Its Research Applications,... using the relationships between depth and diagonal length for Vickers and Knoop indenters, one can estimate a change in depth due to a change in the diagonal length due to wear: (Eq 7) where z is the incremental wear depth, d0 is the length of the diagonal of the hardness indentation before wear occurs, df is the length of the indentation diagonal after wear occurs, and C is a constant whose value is... Burnett and D.S Rickerby (Ref 17) , Hcomp is determined to be: Hcomp = fc Hc + fs Hs X3 (Eq 5) where fc and fs are the respective volume fractions of coating and substrate materials being deformed; Hc and Hs are the respective coating and substrate hardnesses; and X is the interfacial parameter The constraint parameters were found to be strongly dependent on the relative radii of the substrate and coating... J Appl Phys., Vol 11, 1 972 , p 75 8 24 J.B Pethica, R Hutchings, and W.C Oliver, Composition and Hardness Profiles in Ion Implanted Metals, Nucl Instrum Methods, Vol 209/210, 1983, p 995-1000 25 M El-Shabasy, B Szikora, G Peto, J Szabo, and K.L Mettal, Investigation of Multilayer Systems by the Scratch Method, Thin Solid Films, Vol 109, 1983, p 1 27- 136 26 V.C George, A.K Dua, and R.P Agarwala, Microhardness . Coatings, Thin Solid Films, Vol 152, 19 87, p L131-L133 27. W.A. Glaeser, Wear, Vol 40, 1 976 , p 135-1 37 28. A. Begellinger and A.W.J. de Gee, Wear, Vol 43, 1 977 , p 259-261 29. M.M. Khruschov,. National Institute of Standards and Technology. Correlation of Microindentation Hardness Numbers with Wear There are many kinds of wear, as indicated in the Section titled " ;Wear& quot; in this. Vol 35, 1945, p 374 -389 6. J.H. Westbrook and H. Conrad, Ed., The Science of Hardness Testing and Its Research Applications, American Society for Metals, 1 973 7. P.J. Blau and B.R. Lawn, Ed.,