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DK2159_half 10/6/05 1:26 PM Page Adhesion Measurement Methods Theory and Practice DK2159_title 10/6/05 1:59 PM Page Adhesion Measurement Methods Theory and Practice Robert Lacombe Boca Raton London New York A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc Preface This volume has arisen out of a short course on adhesion measurement methods given in conjunction with a series of symposia on surface related aspects of materials science technology The conference Web site* caught the attention of John Corrigan, who at that time was an acquisition editor for Marcel Dekker As I had long been contemplating writing a volume on adhesion measurement to use as supporting material for a short course on adhesion measurement, John did not have to work very hard to convince me that it would be a good idea to write a volume on this topic In addition, John and I felt that such a volume would fill an important gap in the engineering science literature because there was no single text devoted to adhesion measurement technology notwithstanding the fact that an enormous body of literature existed on the subject in scientific journals and edited volumes Having thus decided to engage in the project, I concluded that the main purpose of the volume would be to provide a useful reference work and handbook for the practicing engineer/scientist who has a need to confront problems of adhesion either in support of manufacturing operations or in the development of new products Thus, this book is meant to be used and kept handy for any and all of the following purposes: As a monograph/reference work to be used either for self-study or to become aware of what has been done in the realm of developing methods and useful tools for measuring the adhesion of coatings and thin films As supplementary reading material for courses on materials science, mechanics of materials, or engineering design of laminate structures at the advanced undergraduate or graduate level As a handbook for looking up useful information and formulae on adhesionrelated matters, such as driving force formulae for various modes of delamination, methods for estimating stress buildup, and material property data in support of “back-of-the-envelope” calculations As an introductory reference work for accessing the vast scientific and engineering literature on adhesion measurement A substantial bibliography of some 40 key reference works plus over 500 articles and books is organized topicwise to provide a convenient introduction to the veritable ocean of information available in the literature The contents of the book are organized into seven chapters and five appendices in the following order: Chapter gives a brief introduction to the subject, including * Those interested in surface-related phenomena such as adhesion, cleaning, corrosion, and the like can go the conference Web site at www.mstconf.com; there you will find the programs and abstract listings of some 24 previous symposia on these topics, as well as up-to-date information on current and future symposia an attempt to define the term adhesion for the purpose of providing a definition that is both accurate and useful in practice Chapter provides an overview of the most common adhesion measurement methods plus a few exotic methods to round out the mix From the point of view of this work, adhesion measurement techniques fall into one of the three following categories: qualitative, semiquantitative, and fully quantitative techniques Each of the methods discussed has its uses and drawbacks, and the intent is to make this as clear as possible Something akin to a Consumer Reports format is adopted to help the reader interested in selecting a method with which to address current adhesion problems Anyone just getting involved with adhesion-related issues should find this chapter helpful Chapter lays the foundation required to step up to the problem of implementing fully quantitative adhesion measurement methods To this, however, one has to confront headlong the thermal-mechanical behavior of the materials with which one is dealing This comes about from the simple fact that all adhesion measurement methods in some way or another apply an external load to the structure tested and then draw conclusions based on the observed deformations or mechanical reaction forces observed The most general formalism available for dealing with this type of behavior is the continuum theory of solids, which is treated in some detail in this chapter Inescapably, the level of mathematical treatment rises considerably over that given in Chapter Every attempt is made to avoid excessive rigor and abstract formalism, which does more to flaunt the level of erudition as opposed to shedding light on the technical matters at hand Thus, those who subscribe to the International Journal of Solid Structures will most likely find the mathematical level quite pedestrian, whereas members of the laity could find the discussion fairly heavy sledding This should in no way, however, prevent anyone from using the results presented in succeeding chapters to practical advantage Chapter deals with the discipline of fracture mechanics, which draws directly on all the supporting material presented in Chapter Fracture mechanics is the ultimate organizing tool for performing fully quantitative adhesion measurements It provides the concepts of stress intensity factor and strain energy release rate, which are two of the most useful quantitative measures of adhesion strength Thus, from the point of view of fracture mechanics, a delamination is nothing more than a particular kind of crack occurring at an interface in a bimaterial structure Chapter attempts to draw all of the above material together and make it seem more coherent and relevant by providing several specific and detailed examples of adhesion measurement in action Thus, extensive examples of the peel test, the scratch test, and the pull test are presented It is hoped that the reader will gain significant insight and intuition into how adhesion testing is carried out in practice and perhaps find some answers to specific problems of interest Chapter deals with the problem of measuring the residual or intrinsic stress in a coating or other laminate structure Whoever reads through the previous three chapters will quickly realize that residual stress is one of the key factors governing the delamination behavior of coatings and laminates and is a critical parameter in most fracture mechanics formulae for stress intensity factors and strain energy release rates Thus, a fairly comprehensive overview of most of the useful stress measurement methods is provided Use of one or more of these methods can be considered as providing an indispensable foundation for developing effective adhesion measurement procedures Chapter concludes with more examples taken from the author’s direct experience in wrestling with adhesion problems in the microelectronics industry Silicon chips and ceramic multichip modules used to package these chips into useful devices give rise to a welter of adhesion-related problems because the number of interfaces involved is so varied and extensive that most structures can be looked at as one extensive interface The presentation here is informal and intended to provide insight and intuition as to how adhesion problems and adhesion measurement happen in the “real world.” Several appendices are provided to make the volume more useful as a day-today handbook and handy reference for looking up simple formulae and material property data for performing back-of-the-envelope type calculations Rudimentary calculations for estimating the stress expected in a coating or the driving force for delamination can be very helpful for making decisions regarding which processes or materials one should employ for fabricating a specific device Appendix A provides an overview of vector and tensor calculus for those with a need to brush up on the topic both regarding performing elementary calculations and in understanding more fully the mathematical developments in Chapters and Appendix B gives a quick overview of the most useful aspects of strength of materials theory, which essentially amounts to computing all the ways a beam can bend This is important material because bending beams figure heavily in many adhesion measurement schemes and stress measurement experiments Appendix C gives an extended table of material property data required for nearly all the formulae in Appendices B and D This type of data tends to be scattered far and wide in a variety of texts and reference works, which by Murphy’s second law are never at hand when most needed Thus, having these data located next to the formulae that require them should prove convenient Appendix D provides a list of the most useful formulae from fracture mechanics that can be applied to the most common failure modes observed in coatings and laminates Finally, a two-part bibliography is given that should prove handy in obtaining useful references from the vast technical literature In closing, I would like to state that this is very much a work in progress It makes no attempt at being fully comprehensive or definitive in any sense Rather, the goal is to provide a volume extensive enough to be useful but not so vast as to be more of a burden than a help In this regard, it is clear that much of relevance had to be left out It is hoped that future editions will correct this problem to some extent I invite any and all constructive criticisms and suggestions to correct errors or improve the presentation I am most readily reached at the e-mail address given below and will give due attention to any and all who respond Finally, this work would not be complete without giving recognition to my longtime friend, colleague, and co-worker Dr Kashmiri Lal Mittal (Kash to his friends) Kash has certainly been a key inspiration in completing this work A cursory look at the references will make it clear that his contributions to the adhesion literature have been monumental In addition to editing the Journal of Adhesion Science and Technology, he has published 81 (and counting) edited volumes dealing either directly or indirectly with problems of surface science and adhesion His many comments and corrections to this work have been indispensable My thanks go also to John Corrigan, who gave the initial impetus that got this project going Many thanks, John, wherever you are Robert H Lacombe MST Conferences, LLC Hammer Drive Hopewell Junction, NY 12533-6124 E-mail: rhlacombe@compuserve.com The Author Robert Lacombe, Ph.D., received his doctoral degree in macromolecular science from Case Western Reserve University and was a postdoctoral fellow at the University of Massachusetts, working on problems of polymer solution thermodynamics Following his stint in academia, he was an IBM physicist for 20 years and worked on problems relating to thin film wiring technology for both semiconductor chips and multichip modules After IBM, he worked for an independent consulting firm on hybrid nonintrusive inspection and evaluation techniques, as well as problems of materials compatibility of both semiconductor and microelectronic packaging devices He is an expert in the area of stress buildup in laminate structures and using the techniques of fracture mechanics in solving problems of delamination and cracking in composite devices He has been a leader in the areas of materials characterization and published some of the first mechanical response data on monolayer nanostructures in the early 1980s In addition, he pioneered innovative uses of largescale computation using finite element methods and applied this expertise directly to problems affecting product development and manufacturing Dr Lacombe is Chairman of MST Conferences and has organized over 20 international symposia covering the topics of adhesion and other surface-related phenomena since 1998 He is credited with over 40 publications and patents Dr Lacombe is a leading innovator in the field of subsurface inspection methods dealing with flaws in structural parts of air, auto, marine, and aerospace vehicles As part of his activities with MST Conferences, he teaches a semiannual course on adhesion measurement methods in conjunction with the symposia 426 Adhesion Measurement Methods: Theory and Practice 475 “Stability of Conductor Metallization in Corrosive Environments,” A.T English and P.A Turner, J Electronic Mat., 1, (1972) 476 “The Stylus of Scratch Method for Thin Film Adhesion Measurement: Some Observations and Comments,” D.W Butler, C.T.H Stoddart, and P.R Stuart, J Phys (D): Appl Phys., 3, 877 (1970) 477 “Diffusion in Gold-Aluminum,” C Weaver and D.J Parkinson, Phil Mag., 22, 377 (1970) 478 “Adhesion of High Energy Surfaces,” C Weaver, in Adhesion Fundamentals and Practice (Maclaren and Sons, London, 1969), p 46 479 Thin Film Phenomena, K.L Chopra (McGraw-Hill, New York, 1969), p 313 480 “Scratch Test for Measuring Adherence of Thin Films to Oxide Substrates,” M.M Karnowsky and W.B Estill, Rev Sci Instrum., 35, 1324 (1964) 481 “The Adhesion of Metals to Crystal Faces,” P Benjamin and C Weaver, Proc Roy Soc., 274A, 267 (1963) 482 “The Adhesion of Evaporated Metal Film on Glass,” P Benjamin and C Weaver, Proc Roy, Soc., 261A, 516 (1961) 483 “Adhesion of Metal Films to Glass,” P Benjamin and C Weaver, Proc Roy, Soc., 254A, 177 (1960) 484 “Measurement of Adhesion of Thin Film,” P Benjamin and C Weaver, Proc Roy, Soc., 254A, 163 (1960) 485 “Adhesion of Evaporated Aluminum Films,” C Weaver and R.M Hill, Phil Mag., 3, 1402 (1958) 486 “L’Epitaxie dans les Lames Polycrystallines,” O.S Heavens and L.E Collins, J Phys Radium, 13, 658 (1952) 487 “Some Factors Influencing the Adhesion of Films Produced by Vacuum Evaporation,” O.S Heavens, J Phys Radium, 11, 355 (1950) F.22 TAPE TEST 488 “Adhesion Measurement of Thin Films to a Porous Low Dielectric Constant Film Using a Modified Tape Test,” L.L N Goh, S.L Toh, S.Y.M Chooi, and T.E Tay, J Adhesion Sci Technol., 16(6), 729 (2002) 489 “Surface Analysis and Printability Studies on Electron Beam Irradiated Thermoplastic Elastomeric Films From LDPE and EVA Blends,” S Chattopadhyay, R.N Ghosh, T.K Chaki, and A.K Bhowmick, J Adhesion Sci Technol., 15(3), 303 (2001) 490 “Determination of the Acid-Base Properties of Metal Oxide Films and of Polymers by Contact Angle Measurements,” E McCafferty and J.P Wightman, J Adhesion Sci Technol., 13(12), 1415 (1999) (tape test correlated with acid-base and contact angle) 491 “Effects of Nitrogen Plasma Treatment of Pressure Sensitive Adhesive Layer Surfaces on Their Peel Adhesion Behavior,” M Kawabe, S Tasaka, and N Inagaki, J Adhesion Sci Technol., 13(5), 573 (1999) (180˚ tape test) 492 “Effect of the Functional Groups of Polystyrene on Its Adhesion Improvement and Corrosion Resistance,” R Kurbanova, A Okudan, R Mirzaolu, S Kurbanov, I Karata, M Ersưz, E Ưzcan, G Ahmedova, and V Pamuk, J Adhesion Sci Technol., 12(9), 947 (1998) (tape pull on lattice of squares) 493 “Structure Effect on the Peel Strength of Polyurethane,” S.L Huang, S.J Yu, and J.Y Lai, J Adhesion Sci Technol., 12(4), 445 (1998) (180° tape peel) General Adhesion Measurement References 427 494 “Complex Dynamic Behavior in Adhesive Tape Peeling,” M.C Gandur, M.U Kleinke, and F Galembeck, J Adhesion Sci Technol., 11(1), 11 (1997) (novel peeling dynamics study) 495 “Silicone Pressure Sensitive Adhesives With Selective Adhesion Characteristics,” S.B Lin, J Adhesion Sci Technol., 10(6), 559 (1996) (180˚ tape peel test) 496 “Use of High Temperature and High Humidity to Test the Adhesion of Sputtered Copper to a Polyimide Surface Modified by an AC Nitrogen Glow Discharge,” J.B Ma, J Dragon, W Van Derveer, A Entenberg, V Lindberg, M Anschel, D.-Y Shih, and P Lauro, J Adhesion Sci Technol., 9(4), 487 (1995) (160–170˚ peel test) 497 “Quantifying the Tape Adhesion Test,” G.V Calder, F.C Hansen, and A Parra, in Adhesion Aspects of Polymeric Coatings, K.L Mittal, Ed (Plenum Press, New York, 1983), p 569 498 “Estimation of Paint Adhesion and Comaprison Test of Adhesion Tapes,” H Nuriya, Jitsumu Hyomen Gijutsu, 26(2), 86 (1979) 499 “Adhesion of Paints and Similar Coatings Parameters Determining the Tear-off Method for the Judgement of Adhesion,” J Sickfeld and E Hosp, Farbe Lack, 85(7), 537 (1979) 500 “Semi-quantitative Measurement of Pressure Tape Adhesion,” John Ott, Metal Finishing, 61 (January 1978) 501 “Strong Adhesion of Vacuum Evaporated Gold to Oxide or Glass Substrates,” G.J Zydzik, L.G Van Uitert, S Singh, and T.R Kyle, Appl Phys Lett, 31, 697 (1977) 502 “A Technique for Detecting Critical Loads in the Scratch Test for Thin Film Adhesion,” J.E Greene, J Woodhouse, and M Pestes, Rev Sci Instrum., 45, 747 (1974) 503 “Relationship Between Substrate Surface Chemistry and Adhesion of Thin Films,” R.C Sundahl, J Vac Sci Technol., 9, 181 (1972) 504 “Adhesion Mechanism of Gold Underlayer Film Combinations to Oxide Substrates,” K.E Haq, K.H Behrndt, and I Kobin, J Vac Sci Technol., 6, 148 (1969) 505 “Interface Formation During Thin Film Deposition,” D.M Mattox and J.E McDonald, J Appl Phys., 34, 2393 (1963) 506 “On the Cleaning of Surfaces,” J Strong, Rev Sci Instrum., 6, 97 (1935) 507 “Evaporated Aluminum Films for Astronomical Mirrors,” J Strong, Publ A S P., 46, 18 (1934) F.23 THEORETICAL STUDIES 508 “On the Non-linear Elastic Stresses in an Adhesively Bonded T-Joint With Double Support,” M Kemal Apalak, J Adhesion Sci Technol., 16(4), 459 (2002) 509 “An Internal Variable Theory of Adhesion,” E Bitterlin and J.F Ganghoffer, J Adhesion Sci Technol., 12(8), 857 (1998) 510 “A Two-Dimensional Stress Analysis of Adhesive Butt Joints of Dissimilar Adherends Subjected to Tensile Loads,” T Sawa, K Temma, T Nishigaya, and H Ishikawa, J Adhesion Sci Technol., 9(2), 215 (1995) 511 “Butt Joint Tensile Strength: Interface Corner Stress Intensity Factor Prediction,” E.D Reedy, Jr., and T.R Guess, J Adhesion Sci Technol., 9(2), 237 (1995) 512 “Power-Logarithmic Stress Singularities at Bi-material Corners and Interface Cracks,” J.P Dempsey, J Adhesion Sci Technol., 9(2), 253 (1995) 513 “Analysis and Design of Adhesively Bonded Double Containment Corner Joints,” M Kemal Apalak, R Davies, and Z Gul Apalak, J Adhesion Sci Technol., 9(2), 267 (1995) 428 Adhesion Measurement Methods: Theory and Practice 514 “Relationship Between Adhesion and Friction Forces,” J.N Israelachvili, Y.-L Chen, and H Yoshizawa, J Adhesion Sci Technol., 8(11), 1231 (1994) (largely theoretical with some surface force measurements) 515 “Cracks at Adhesive Interfaces,” K Kendall, J Adhesion Sci Technol., 8(11), 1271 (1994) (covers variety of tests: peel, wedge, lap shear) F.24 THERMAL METHODS 516 “Thermal Gradient Adhesion Meter,” E.N Sokolov, Lakokrus Mater Ikh Primen., 45 (1986) 517 “Indicator for Metal Film-substrate Adhesion,” D Guidotti and S.H Wen, IBM Technical Disclosure Bull., 28(5), 2078 (1985) 518 “Thermographic Detection of Polymer-Metal Adhesion Failures,” B.E Dom, H.E Evans, and D.M Torres, in Adhesion Aspects of Polymeric Coatings, K.L Mittal, Ed (Plenum Press, New York, 1983), p 597 F.25 TOPPLE BEAM METHOD 519 “On the Non-linear Elastic Stresses in an Adhesively Bonded T-Joint With Double Support,” M Kemal Apalak, J Adhesion Sci Technol., 16(4), 459 (2002) (detailed finite element analysis of T joint) 520 “Measurement of the Adhesion of Silver Films to Glass Substrates,” A Kikuchi, S Baba, and A Kinbara, Thin Solid Films, 124, 343 (1985) 521 “Some Factors Affecting the Adhesion of Thin Metal Films,” D.W Butler, C.T.H Stoddard, and P.R Stuart, in Aspects of Adhesion, Vol 6, D.J Almer, Ed (CRC Press, Cleveland, OH, 1971), p 53 522 “Thin Film Adhesion: Effect of Glow Discharge on Substrate,” C.T.H Stoddart, D.R Clarke, and C.J Robbie, J Adhesion, 2, 270 (1970) 523 “A Simple Film Adhesion Comparator,” D.W Butler, J Phys (E): Sci Instrum., 3, 979 (1970) F.26 WEDGE TEST 524 “The Role of Interfacial Interactions and Loss Function of Model Adhesives on Their Adhesion to Glass,” A Sharif, N Mohammadi, M Nekoomanesh, and Y Jahani, J Adhesion Sci Technol., 16(1), 33 (2002) 525 “Plasma Sprayed Coatings as Surface Treatments of Aluminum and Titanium Adherends,” G.D Davis, P.L Whisnant, D.K Shaffer, G.B Groff, and J.D Venables, J Adhesion Sci Technol., 9(4), 527 (1995) 526 “Effectiveness of Water Borne Primers for Structural Adhesive Bonding of Aluminum and Aluminum-Lithium Surfaces,” K.L Meyler and J.A Brescia, J Adhesion Sci Technol., 9(1), 81 (1995) (wedge test, single lap shear, floating roller peel) 527 “Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions,” D.B Bogy, J Appl Mech., 93, 377 (1971) Index A acoustic emission methods, references, 401–402 acoustic spectroscopy coupling scratch test with, 23 scratch test negating use of, 27 acoustic waves, for stress measurement, 277; see also SAWs (surface acoustic waves) test acoustoelastic constants, 276 addition, operations for vector, 340 adhesion definitions of, 2–5 stability maps, 333 adhesion, applying fracture mechanics to back-of-the-envelope calculations, 180–181 decohesion number approach, 174–180 elementary computational methods, 163 problem of nickel on glass, 183–185 problem of polyimide on glass-ceramic, 181–183 references, 185–186 thin coating on rigid disk, 163–174 adhesion measurement contaminants and, definitions of adhesion, 2–5 electromagnetic test, 56–60 indentation debonding test, 17–20 nomenclature and usage, 5–6 notes, 68–73 overview of, 7–8 peel test, 8–11, 14–17 references, 400–401 science of, SOM theory, 369 tape peel test, 11–14 theoretical foundations of, see continuum theory advanced peel test, 193–194 alligator clamp, peel test equipment, 189 aluminum fully quantitative peel test, 198 peel energy for polymides and, 196 wedge test for aluminum sheets, 41–42 American Society for Testing and Materials (ASTM), 42 ANSYS programming systems, 329 arrays manipulating matrix, 351–352 manipulating tensor, 344–347 transpose of array, 344 arrest energy, 38 automatic mesh generation, 329 axisymmetric delamination, 387 B back-of-the-envelope calculations fracture mechanics applied to adhesion, 180–181 nickel on glass, 183–185 polyimide on glass-ceramic, 181–183 Barkhausen noise, 297–299 beam-bending balancing shear force with downward load, 124–125 deformation, 113–114 elastic-plastic analysis and, 210–213 equations for, 372–375 final solution to, 129–130 fully quantitative peel test, 200–204 Hooke’s law, 370 obtaining beam deformations, 126–129 overcoming limitations of SOM theory, 118–121 SOM theory and, 112–118, 369 stress function, 121–123 tensile force as result of, 114–115 treating peel strip as, 200–201 beam-bending tests advantages/disadvantages of, 43 applying to coating and film stresses, 251–252 Brazil nut test, 40–41 double-cleavage drilled compression test, 39–40 four-point bend test, 34–36 overview of, 32 recommendations, 44 standard double cantilevered beam test, 35–37 tapered double cantilevered beam test, 37–40 three-point bend test, 32–34 topple beam test, 42–43 wedge test, 41–42 429 430 Adhesion Measurement Methods: Theory and Practice beam equation, 205 beam stiffness, 116 Beltrami-Michell equation of compatibility, 133 biaxial tension overview of, 108–110 thin coating on rigid disk and, 163–165 biharmonic equation, 122 blister test, 27–32 body force defined, 77 uniaxial tension and, 107 boundary element method, numerical, 135 Bragg diffraction of x-rays, 269 Brazil nut test comparing to other beam-bending tests, 33 overview of, 40–41 brazing process, contaminants and, brittle coatings adhesion testing, 242 blister test disadvantage, 32 indentation debonding test on, 19 pull test for, 14–17 scratch test most effective for, 26–27 brittle lacquer method, for measuring coating and film stresses, 302 brittle substrates, 183–185 C cantilevered beams, see simple beams, bending of displacement formulation in, 132 measuring coating and film stresses, 251–256 mixed formulation in, 134 stress formulation in, 133 capacitive measurement, of coating and film deflection, 259–260 Cartesian coordinates, 166, 371 case studies, adhesion measurement, 309–336 contamination sensitivity, 310–317 improperly cured film, 317–325 stressed pin in pin-to-board interconnect technology, 325–332 case studies, elastic peeling elastic-plastic loading and unloading case, 227–231 elastic-plastic peeling/unloading case, 226–227 Cauchy’s strain tensor, 93 centrifugal loading test, 405–406 ceramics GC (glass-ceramic), 179, 181–183 in pin-to-board interconnect technology, 327 polyimide coating on ceramic substrates, 317 channeling behavior, Z factor for, 386 circle cut test, 44–46 cleanliness, surface adhesion and, climbing drum test, coating and film stress, measuring brittle lacquer method, 302 cantilevered beam method, 251–256 capacitive measurement of deflection, 259–260 improperly cured film case study, 322–325 introduction, 249–251 laser holographic, 265–269 magnetic methods, 297–299 methods generally, 251 optical measurement of deflection, 257–259 photoelastic method, 280–295, 302 Raman spectroscopy, 299–300 Rayleigh wave method, 280 skimming longitudinal waves for surface stress measurement, 279–280 strain relief methods, 294–297 stress pattern analysis by thermal emission (SPATE), 301–302, 304–302 surface-skimming SH waves, 280 through-thickness measurement, 279 ultrasonic measurement, 272–279 vibrational resonance method, 260–265 x-ray measurement of, 269–272 coatings delamination, 3–4 failure processes, 10–11, 383–389 fracture mechanics, 397 stress behavior of flexible coating on rigid disk, 135–138 coatings, flexible adhesion testing, 242 blister test advantages, 32 indentation debonding test for, 19–20 peel test for tough, 8–11 pull test for, 14–17 stress behavior of, on rigid disk, 135–138 cohesive failure, comma convention, for gradient of a function, 356 compatibility compatibility relation, 120 overcoming limitations of SOM theory, 119–120 compounds, material properties of common, 379 conservation of energy theorem strain energy principles and, 141 usefulness of, 146–147 constitutive behavior, of materials general, 93–96 homogeneous isotropic materials, 96–99 constrained blister test, 28–30 contaminants affecting surface adhesion, Index contamination sensitivity case applying peel test to, 312–314 equipment and test condition, 311 fluorine contamination, 314–317 continuum theory beams and, 112–130 deformation and strain, 89–93 examples, 99–106 homogeneous isotropic materials, 96–99 J integral, 146–151 motion in solids, 86–89 numerical methods, 134–135 overview of, 75–77 solving field equations, 106–112 special stress states, 83–86 strain energy principles, 138–146 stress in solids and, 77–83 stress of flexible coatings on rigid disks, 135–138 stress/strain relationship, 93–96 thermoelasticity field equations, 130–134 coordinates Cartesian, 166, 371 cylindrical, 166–168, 171, 364–365 principal stress, 83–84 spherical, 366–367 copper substrates Brazil nut test for, 41 testing adhesion of epoxy coatings to, 17–18 cracks, 385–387 calculating decohesion number, 179–180 DCDC test for, 40 decohesion cracks creating fracture problem, 318–319 decohesion model of Suo and Hutchinson, 174–179 driving force formulae, 331–332 fracture mechanics and, 155–159 polyimide on glass-ceramic, 181–183 strain energy approach to, 159–161 stress intensity factor approach to, 161–163 virtual crack generation modeling, 330 wedge test for, 42 Z factor for surface cracks, 385–387 crystal lattice, x-ray measurement of distortion of, 269, 271 curl operator, 357–359 curvature moment curvature diagram for elastic-plastic material, 223 radius of, in peel testing, 210–211 cut test circle cut test, 44–46 overview of, 233–237 simplified model for, 237–241 431 cylindrical coordinates thin coating on rigid disk, 166–168, 171 vector operators in, 364–365 D DCB (double cantilevered beam) tests comparing beam-bending tests, 33 standard, 35–37 tapered, 37–39 DCDC (double-cleavage drilled compression) test comparing beam-bending tests, 33 comparing DCB test to, 39 decohesion defined, fracture problem at polymide/ceramic interface, 318–319 decohesion number calculating, 179–180 nickel on glass problem, 184–185 polyimide on glass-ceramic problem, 182 Suo and Hutchinson, 174–179 deflection in beam theory, 117 capacitive measurement of, 259–260 optical measurement of, 257–259 deformation and strain concept of, 89–93 examples equations for, 99, 102–106 fields for homogeneous isotropic thermoelastic material, 100–101 deformation calorimeter, 194–197 deformation gradient, 91 deformations beam, 126–127 elastic vs plastic, 223 peel strip, 217 SOM theory and, 113–114, 118–119 delamination axisymmetric, 387 coatings, 3–4 decohesion model of Suo and Hutchinson, 174–179 defined, fracture mechanics and, 155–159 improperly cured film case, 317–318 modeling, 320–321 peel test controlling rate of, 10 strain energy approach to, 159–161 thin coating on rigid disk calculations, 163–174 thin film stresses causing, 3–4 wedge spallation, 26 Z factor for, 385–387 432 Adhesion Measurement Methods: Theory and Practice destructive methods, of adhesion measurement, determinants, of arrays, 345–346 dialetric medium, electromagnetism, 286–288 diamond coatings, 299–300 diamondlike carbon coatings, 23–24 displacement field deformation and strain process, 92 displacement formulation, 131 displacement formulation elasticity field equations, 131–132 in mixed formulation, 133–134 displacement gradient, 91 divergence operator, 356–357 divergence theorem motion in solids and, 88 strain energy and, 141 DLC (diamondlike carbon) coatings, 23–24 Doppler interferometer disadvantages of, 55–56 laser spallation test with, 52 double cantilevered beam test, see DCB (double cantilevered beam) tests double-cleavage drilled compression test, see DCDC (double-cleavage drilled compression) test driving force circle cut test, 45 crack propagation, 331–332 laminate structures, 383–389 stability maps and, 334 thin coating on rigid disk calculations, 173–174 Dundurs’ parameters, 236 dyadic vector notation finding gradient of vector, 359 redundancy of, 351 dynamic modulus test advantages/disadvantages of, 63–65 overview of, 61–63 recommendations, 65 E eigenvalue problem, spectral theorem, 352–354 elastica equations, 218–225 elasticity field equations, 130–134 elasticity tensor, 81, 94–95 elastic loading/unloading, 224–225 elastic-plastic analysis, 210–231 analysis strategy and assumptions, 218 basic goal, 217 elastic peeling case, 225–226 elastic-plastic loading and unloading case, 227–231 elastic-plastic peeling/unloading case, 226–227 equations for, 217 equations of the elastica, 218–225 fully quantitative peel test, 210–213 for soft metals, 213–217 elastic strain energy, 170 electrochemical cleaning methods, 295 electro-deposited copper, 377 electromagnetic test, 56–60 electromagnetism birefringent medium, 289 boundary element method for, 135 dieletric medium and, 286–288 electromagnetic radiation, 284–285 Maxwell’s equations, 281–285 photoelasticity and, 285–287 summary, 288 elements, material properties of common, 378–379 energy fields, 138–146 epoxy coatings on aluminum substrate, 197 Brazil nut test for, 41 indentation debonding test for, 17–18 scratch test effective for, 26 equilibrium, SOM theory of static, 370 equilibrium crack depth, 178–179 etchants, blister test, 31–32 Euclidean space, 150–151 Eulerian description, 90 Euler’s strain, 93 F failure coatings, 10–11, 383–389 cohesive, four-point bend test, 34–35 threshold adhesion failure and, 22–23 ferromagnetic materials, 297–298 Feynman Lectures, 367–368 field, mathematical, 338 field axioms, 338 field equations, 106–112 biaxial tension, 108–110 elasticity, 130–134 examples of simple deformations, 99, 102–106 for homogeneous istotropic thermoelastic material, 100–101 overcoming limitations of SOM theory, 118–121 overview of, 106–107 triaxial tension, 110–112 uniaxial tension, 107–108 Index film case study, improper curing, 317–325 ceramic substrate coated with polyimide layer, 317 decohesion cracks creating fracture problem, 318–319 delamination, 317–318 modeling delamination, 320–321 stress measurements, 322–325 film stress delamination and, 3–4 equation for, 253–254 fracture mechanics and, 397 general, 391–392 in laminate structures and coatings, 396–397 in solids, 397–398 finite element applying to pin-to-board interconnect, 328–329 numerical method, 134–135 finite stress levels, 156–158 flexible coatings adhesion testing, 242 blister test, 32 indentation debonding test, 19–20 peel test, 8–11 pull test, 14–17 stress behavior on rigid disk, 135–138 fluorine contamination, 314–317 forces SOM theory, 370–372 stress in solids and, 77–79 stress vs., 76 formulae, of vector/tensor calculus, 361–367 Fourier’s law of heat conduction, 98, 101 four-point bend test, 33–36 fracture mechanics, 155–186 back-of-the-envelope calculations, 180–181 beam-bending test, 43 blister test, 31 critical intrinsic surface fracture energy, 53–54 decohesion number approach, 174–180 elementary computational methods, 163 improperly cured film and, 317 nickel on glass problem, 183–185 overview of, 155–159 polyimide on glass-ceramic problem, 181–183 strain energy approach, 159–161 stressed pin, in pin-to-board interconnect technology, 325 stress intensity factor approach, 161–163 surface fracture energy, 197, 214, 217 thin coating on rigid disk, 163–174 433 full elastic-plastic analysis, see elastic-plastic analysis fully quantitative peel test, see peel test, fully quantitative fundamental adhesion, G Gaussian elimination, 347 Gauss’s law, 286–287 GC (glass-ceramic) polyimide on, 181–183 thermoelastic properties of, 179 glass dynamic modulus test for, 61–65 laser spallation test, 50–51 problem of nickel on, 183–185 stresses in glassware, 249–250 thermoelastic properties of, 179 gradient of vector, 359–360 gradient operator, 355–356 grain boundary effects, metal coatings, 250–251 gravitational loading, 77 Green’s strain, 93 H heat flux vector, 97 holographic interferometry, 265–269 homogeneous isotropic materials constitutive behavior of, 95 examples of simple deformations, 99, 102–106 field equations for, 100–101 overview of, 96–99 Hooke’s law beam-bending problems and, 115, 371–372 deformation and strain and, 89, 106 fully quantitative peel test, 200 uniaxial tension and, 108 humidity/moisture contamination effect on adhesion, 311 fluorine as cause of moisture sensitivity, 314–316 surface acoustic wave experiments and, 67–68 testing sensitivity of peel strength to, 190 hydrostatic stress, 77, 86 I identities, vector, 355, 361–367 identity matrix, 344–345 impact methods, 409 434 Adhesion Measurement Methods: Theory and Practice indentation debonding test, 17–21 index of refraction, 288 indicial notation advantages of, 340 divergence operator, 357 gradient of vector, 359–360 gradient operator, 356 manipulating tensor arrays, 345 matrix inverse, 351 matrix/tensor multiplication, 349 matrix transformations, 352 product of matrix with vector, 350 tensor/matrix scalar product, 350 tensor operations, 344 vector operations, 340–342 working with stress tensor through, 81 infinitesimal strain measure, 104–106 infinite stress problems, fracture mechanics, 156–157 initiation energy, 38 ink coatings, tape peel test on, 12–13 interface adhesion, 41 interferometers holographic interferometry, 265–269 laser interferometry, 258 overview of, 52 internal energy, strain, 141–142 internal friction, 64–65, 409 internal stress level, 48–49 isotropic materials, see homogeneous isotropic materialsisland blister test, 28–30 J J integral, 146–151 conservation of energy theorem, 146–147 example usage of, 150–151 overview of, 149–150 path-independent integrals and, 147–149 K KE (kinetic energy), 139–141, 141 kernel function, in boundary element method, 135 Kronecker symbol, 345 L lab balance, peel test equipment, 189–190 Lagrangian formulation, 90 Lamé equations, 131 laminate structures, driving force formulae for, 385–388 Lap Shear test, 409–411 laser beam, measuring coating and film stresses, 258 laser holographic, measuring coating and film stresses, 265–269 laser-induced decohesion spectroscopy (LIDS), useful applications of, 55–56 laser interferometry, measuring coating and film stresses, 258 laser spallation test, 49–56 lattice mismatch, metal coatings, 250–251 LIDS (laser-induced decohesion spectroscopy), 54–56 loading/unloading beam-bending and, 116 centrifugal loading test, 405–406 decohesion model of Suo and Hutchinson, 177–178 elastic, 224–225 elastic-plastic, 226–231 gravitational, 77 self-loading systems, 138, 142 shear force balanced with downward load, 124–125 long range microscope, optical measurement of deflection, 257–258 Lorentz force, 59–60 M magnetic fields, see electromagnetic test magnetic methods, stress measurement, 297–299 magnetoelastic parameter (MP), 298 magnetostriction, 297, 299 mappings, deformation and strain, 89–90 mass elements, of solids, 77 material law, for substances, 93–99 materials adhesion engineering, 3–5 electromagnetic test and, 60 properties of selected substances, 377–381 matrix notation advantages of, 339 gradient of vector, 359–360 manipulating tensor arrays, 345 matrix inverse, 351 matrix/tensor multiplication, 348–349 matrix transformations, 351–352 product of matrix with vector, 349–350 simple deformation example of, 101 stress in solids and, 80–81, 83 tensor/matrix scalar product, 350 tensor operations, 343–344 vector operations, 340–342 Index matrix/tensor multiplication, 347–349 maximum principal stress, 83–84 Maxwell's equations, 281–285 Maxwell's theory of photoelastic effect, 290 MELT (modified edge liftoff test), 46–47 membrane equation, 109–110 mesh generation, automatic, 329 metals dynamic modulus test for, 61–65 elastic-plastic peeling for soft metals, 213–217 laser spallation test, 50–51 peel test for metal strip, 208–209 stress measurement for metal coatings, 250–251 stress measurements for metal films, 255–256 microelectronic devices Brazil nut test for, 41 dynamic modulus test for, 63, 65 electromagnetic tests for, 60 pin testing on, 16–17 self-loading test advantages, 48–49 thermal expansion behaviors in, 112 micromilling techniques, 189 microscopy, measuring coating and film stresses, 257 microstrip test, 47–48 mixed formulation, 130, 133–134 mode mixity, peel test, 8–9 modified edge liftoff test (MELT), 46–47 moisture, see humidity/moisture moment curvature diagram, 223 moment M, beam mechanics, 116 moment of inertia, beam mechanics, 116 motion in solids, 87–89 multiplication, matrix/tensor, 347–349 Mylar peel strip, 211–212 N Newtonian particle mechanics, 81 Newton's law, 138–140, 146–147 nickel on glass problem, 183–185 thermoelastic properties of, 179 nomenclature adhesion measurement, deformation and strain process, 90, 93 nondestructive methods, 60–61 nondestructive methods, of adhesion measurement, 60–65 defined, dynamic modulus test, 61–65 435 references and commentary on, 396 surface acoustic waves (SAWs) test, 65–69 nonlinear effects, 91 nonlinear problems, 135 numerical methods, continuum theory, 134–135 O operations special tensor, 344–347 tensor, 342–344 vector, 340–342 vector, in cylindrical coordinates, 364–365 vector, in spherical coordinates, 366–367 vector calculus, 355–360 optical measurement of deflection, 257, 258 P paint coatings, pull test for, 14–15 path-independent integrals, 147–149 peel force, vs peel angle, 208 peel roller test, peel test, 187–197 in action, 190–193 advanced, 193–194 advantages/disadvantages of, 10–11 applying to contamination sensitivity case, 312–314 deformation calorimetry, 194–197 equipment, 189–190 overview of, 8–9, 187–188 recommendations, 11 references, 395–396, 414–420 sample preparation, 188–189 tape, 11–14 thermodynamics of, 194 peel test, fully quantitative, Bikerman approach to elastic analysis, 199–203 case study of elastic peeling, 225–226 case study of elastic plastic loading and unloading, 227–231 case study of elastic plastic peeling/unloading, 226–227 earliest work on, 198–199 elastic-plastic analysis, 210–212, 210–213 elastic-plastic peeling for soft metals, 213–217 elastic-plastic theory for soft metals, 213–217 full elastic-plastic analysis, 217–225, see elastic-plastic analysis, full Kaelble approach to elastic analysis, 203–209 Spies approach to elastic analysis, 198–199 436 Adhesion Measurement Methods: Theory and Practice work of Bikerman, 199–203 work of Kaelble, 203–209 work of Yurkenka, 209–210 Yurenka approach to elastic analysis, 209–210 peninsular blister test, 28 PET (polyethylene terephthalate) films, 13, 23 photoelastic method, measuring coating and film stresses, 280–295, 302 photolithography, 189 piezoelectric coupling, in surface acoustic waves test, 65–69 pin testing with pull test, 16–17 with topple beam test, 42–43 pin-to-board interconnect technology, 326 plane strain, 86 plane stress overcoming limitations of SOM theory, 119–120 principle of, 85–86 plastic, loading/unloading, 224–225 Poisson ratio homogeneous isotropic materials and, 96 properties of common materials, 377–380 triaxial tension and, 111–112 uniaxial tension and, 108 polar decomposition theorem, 91 polariscope, 289 polarization direction, of sound waves, 278 poly(amic) acid, 181 polyethylene terephthalate (PET) film, 13, 23 polyimides biaxial tension and, 110 on ceramic substrates, 317 delamination of polymide coating, 317–318 on glass-ceramics, 181–183 peel energy for aluminum with, 196 peel testing in action, 190–193 self-loading test for, 49 stress measurements, 322–325 surface acoustic wave experiment for, 66–67 thermoelastic properties of, 179 polymers constitutive behavior of, 95–96 material properties of, 379–380 stresses in, 250 potential energy, strain, 139–140 practical adhesion, principal stress states, 83–84 pulley, peel test equipment, 189 pullout test, 422–423 pull test advantages/disadvantages of, 15–17 comparing topple beam test to, 42 overview of, 14–15, 242–245 recommendations, 17 references, 420–422 for stressed pin, in pin-to-board interconnect technology, 325 push out test, 423 Q qualitative results blister test, 31–32 indentation debonding test advantages, 19 pull test, 16–17 tape peel test, 11–14 quantitative results; see also peel test, fully quantitative blister test, 31–32 defined, elementary peel testing, 193 indentation debonding test, 19–20 laser spallation test, 55 pull test, 16–17 self-loading test, 48–49 tape peel test, 11–12 working ten times harder for, 49 quantum mechanics, 75 R radial displacement, thin coating on rigid disk calculations, 169 radius of curvature, in peel testing, 210–211 Raman spectroscopy, 299–300 Rayleigh wave method, 280 Redux adhesive, 198 reed samples, see dynamic modulus test refractory materials indentation debonding test, 19 laser spallation test, 55–56 material properties of, 380 residual stress polyimide on glass-ceramic and, 181–183 Self-Loading test references, 423 strain energy principles and, 141–142 rigid substrates indentation debonding test for, 19 stress behavior of flexible coatings on, 135–138 thin coating on, 163–174 rigid translation deformation, 99, 101 rolling drum technique, 198 Index S salt bath test, 13 SAWs (surface acoustic waves) test, 65–69 scalar field, 339 scalar product matrix/tensor multiplication, 348 matrix with vector, 349–350 tensor/matrix, 350 vector operations for, 340–341 scalars, 337–339 Scotch tape, 395 scratch test, 233–241 with acoustic spectroscopy, 23–24 advantages/disadvantages of, 26–27 attempts at quantifying, 24–25 overview of, 20–22, 231–233 recommendations, 27 testing coating/substrate hardness, 25–26 threshold adhesion failure and, 22–23 screw drive, peel test equipment, 189 secular equation, eigenvalue problem, 354 self-loading systems delamination problems as, 138 residual stress mechanisms leading to, 142 self-loading tests, 44–49 semi-inverse method, in mixed formulation, 134 shear (mode II) loads, peel test, 8–9 shear stress, 133, 338 shear thickening, 94 shear thinning, 94 shock waves, in laser spallation test, 49 silane adhesion promoters, testing, 190–193 silicone oil, as contaminant affecting adhesion, simple rotation deformation, 103–105 simple stretching deformation, 105–106 simulation, modeling delamination of improperly cured film, 320–321 skimming longitudinal waves, for surface stress measurement, 279–280 slider box, peel test equipment, 189 small-scale yielding assumption, fracture mechanics, 159 solids, stresses in, 397–398 SOM (Strength of Materials) theory, 369–375 basic ideas of, 112–113 basic quantities of, 371–372 equations for bending of simple beams, 114–118, 372–375 notion of static equilibrium, 370 overcoming limitations of, 118–121 overview of, 370–375 sound waves 437 in air, 277 measuring stress distribution with, 272 polarization direction of, 278 SPATE (stress pattern analysis by thermal emission), coating and film stresses, measuring, 301–302 spectral theorem, 352–354 spectroscopy, 23 spherical coordinates, vector operators, 366–367 stability, crack, 161 stability maps, 333 static equilibrium, SOM theory of, 370–372 statistical analysis, pull test data, 17 steel, surface acoustic wave experiment for, 66–67 stiffness ratio, Suo and Hutchinson decohesion model, 175–176 Stokes' theorem, 361 strain Cauchy's strain tensor, 93 connecting stress to, 93–99 deformation and, 89–93 Euler's strain, 93 peel test of, 215–216 rates, 55–56, 60 relief methods, 294–297 uniaxial tension and, 107–108 strain energy elastic, 138–146 fracture and delamination problems and, 159–161 improperly cured film case study, 321 release rate, 180 stress intensity factor approach vs., 161–162 Suo and Hutchinson decohesion model, 175–177 strain field defined, 152 deformation and strain process, 92, 100 path-independent integrals and, 148 strain energy principles and, 145 Strength of Materials theory, see SOM (Strength of Materials) theory stress in coatings and films, see coating and film stresses elasticity field equations, 132–133 formulation, 130 function in beam bending, 121–123 function in thin coatings on rigid disks, 165–168 stressed pin, in pin-to-board interconnect technology, 325–332 stress, in solids behavior of flexible coating on rigid disk, 135–138 438 Adhesion Measurement Methods: Theory and Practice concept of, 77–83 connecting to strain, 93–99 equation of motion, 86–89 references, 397–398 special stress states, 83–86 stress singularities in, 156–158 stress field beam bending and, 123 concept of stress in solids, 78 defined, 152 J integral and, 149–150 strain energy principles and, 145 stress formulation in elasticity field equations, 133 St Venant's principle and, 85 stress intensity factors calculating decohesion number, 179–180 decohesion model of Suo and Hutchinson, 175–177 overview of, 161–163 polyimide on glass-ceramic, 181–183 stress pattern analysis by thermal emission (SPATE), 301–302 stress tensor indicial notation for working with, 81 matrices for working with, 80–81 stress in solids and, 78–79 stress states, 83–86 St Venant's principle, 84–85 stress testing beam-bending test and, 43 wedge tests and, 42 strip chart recorder, peel test equipment, 189–190 St Venant's principle, 84–85, 133–134 substrates brittle, 183–185 ceramic, 317 copper, 17–18, 41 peel test for flexible coatings on rigid, 8–9 rigid, 19, 135–138, 163–174 Z factor for substrate penetration, 386 surface acoustic waves test, see SAWs (surface acoustic waves) test surface cracking, Z factor for, 385–387 surface fracture energy defined, 214 determining for coating/substrate under study, 217 peel test data and, 197 surface-skimming SH waves, 280 surface stress, 279–280 suspended membrane measurement, 265–269 symmetric arrays, 344 T TAF (threshold adhesion failure), 22–23 tape peel test, 11–14 tapered double cantilevered beam test, 33, 37–40 Taylor's theorem, 373 temperature affect on microelectronic multilevel structures, 112 biaxial tension and, 109 continuum theory summary of, 152 deformation calorimeter using uniform, 194 electromagnetic tests and, 58–59 Fourier's equation for, 101 homogeneous isotropic materials and, 96–99 solving field equations assuming constant, 130 stress behavior of flexible coatings on rigid disks and, 136 triaxial tension and, 111 uniaxial tension and, 107 tensile (mode 1) loads, peel test, 8–9 tensile force, as result of beam-bending, 114–115 tensile testing experiments, 84–85 tensors defined, 342 matrix scalar product and, 350 matrix/tensor multiplication, 347–349 notation for, 80–81 operations, 342–344 special operations for, 344–347 useful identities and formulae for calculus, 361–366 theorems continuum theory, see continuum theory vector calculus, 360–366 thermal cycling, peel test, 191–193 thermal stress, 51 thermal tests, 428 thermodynamics deformation calorimeter using laws of, 195 fracture and delamination and, 159–161 homogeneous isotropic materials and, 96–99 of peel test, 194 thermoplastic recording film, 265 thixotropic behavior, 94 three-point bend test, 32–34 threshold adhesion failure (TAF), 22–23 through-thickness measurement, 279 topple beam test comparing to other beam-bending tests, 33 overview of, 42–43 torque beam mechanics and, 114–115 SOM theory of, 370–372 T peel test, Index trace, of array, 345 traction vectors, 80 transpose of array, 344 triaxial tension, 110–112 two-dimensional stress states, 85–86 two-dimensional vector, 339 U ultrasonic measurement, of stress, 272–280 acoustic wave experiments, 277 acoustoelastic constants and, 276 Rayleigh wave method, 280 sound waves and, 277–279 stress distribution equations, 272–275 surface-skimming SH waves, 280 surface stress using skimming longitudinal waves, 279–280 through-thickness, 279 uniaxial tension case, 84–85, 107–108 Unislide assembly, 189–190, 190–191 unit normal, specifying in continuum theory, 78 universal peel diagram, 229 unloading, see loading/unloading V vector calculus, 355–360 basic theorems, 360–361 curl operator, 357–359 divergence operator, 356–357 gradient of a vector, 359–360 gradient operator, 355–356 notes, 367–368 useful identities and formulae of, 361–366 vector identities, 355 vector notation advantages of, 339 matrix/tensor multiplication, 347–348 product of matrix with vector, 349 tensor/matrix scalar product, 350 tensor operations, 342–343 vector operations, 340–342 vectors, 337–354 absolute magnitude of, 341 addition, 340 defined, 339–340 439 eigenvalue problem and spectral theorem, 352–354 fields, 89–90, 338 gradient of, 359–360 identities, 355 matrix inverse, 351 matrix transformations, 351–352 matrix/vector product, 349–350 notation for, 80–81 operations, 340–342 overview of, 337–339 simple scalars defined, 339 special tensors and operations, 344–347 tensor/matrix multiplication, 347–349 tensor/matrix scalar product, 350 tensor operations, 342–344 vector product, 341–342 Velcro fasteners, velocity gradient, strain energy, 138–139, 142–143 vertical deflection, 117 vibrational resonance method, 260–265 W weak singularity, 157 wedge spallation, 26 wedge test comparing to other beam-bending tests, 33 overview of, 41–42 Weibull analysis adhesion testing, 242–243, 245 pull test and, 16–17 X x-rays, measuring coating and film stresses, 269–272 Y Young's modulus, 96, 377–380 Z Z factors, 385–388