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Proceedings of a Workshop on Materials State Awareness Session II: What Is Materials State Awareness? AN INTEGRATED VIEW OF MATERIALS STATE AWARENESS R. Bruce Thompson, Iowa State University Materials state awareness seeks to estimate the remaining lifetime of individual systems or structures or components, the heart of condition-based maintenance strategies. In principle, such estimates should be based on a knowledge of the initial state, damage or failure processes, operational environment, and nondestructive evaluation (NDE) assessment of state at various points in the lifetime. Achieving this goal requires the integration of information from a variety of disciplines, including the mechanics of materials, materials science, engineering mechanics, and NDE engineering. Data interpretation and analysis will also require a focused effort, relying on the integration of statistical concepts with the engineering functions as well. Included in this overview of some of the issues associated with engineering integration is a discussion of some fundamental differences in the structure of the data that would be obtained in depot and field inspections as opposed to those from onboard sensors, and the need to deal with missing data, uncertainty, and variability in the process of estimating state from field-generated information. It is suggested that Bayesian approaches, which are designed to provide strategies to combine new data with existing knowledge or expertise, provide an appealing framework for this integration by virtue of being able to handle the wide diversity of inputs. Some early efforts in the NDE community to use such approaches are reviewed; at the time (early 1980s) they were considered fairly academic. However, the major advances in simulation tools for NDE and damage processes as well as in computational capability that have occurred in the intervening 25 years suggest that the NDE community should re-examine these approaches.
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Proceedings of a Workshop on Materials State Awareness NONDESTRUCTIVE PHYSICAL PROPERTY MEASUREMENTS TO ESTABLISH MATERIALS STATE AWARENESS David L. Olson, Colorado School of Mines The commonality of advanced NDE techniques occurs at the electronic level. All of the NDE techniques assess the electronic structure of materials and perturbations in the structure due to crystallinity, defects, microstructural phases and their features, manufacturing and processing, and service-induced strains. Electronic, magnetic, and elastic properties have all been correlated to the fundamental electronic properties of the material. The Role of the Electron in Solid State Hume-Rothery, Darken and Gurry, Gschneider, and Waber,1 on a diagram, correlated the elemental electronegativity and the atomic radius to the degree of solubility of a solute in a solid solvent. This correlation was the first attempt to introduce the role of the electron to define the material state. Engel2 and Brewer3 further developed the methods to predict elemental crystal structures, terminal solubilities, and the phase fields of intermetallic phases. Brewer drew from concepts of spectroscopy and chemical bonding in introducing the electron promotion energy to establish a hybrid elemental electronic structure. This hybrid structure correlates electronic and crystal structures, such as dns (bcc), dnsp (hcp), dnsp2 (fcc), and dnsp3 (dc). Miedema and Chelikowsky,4 by using a model based on the Wigner-Seitz cell, related the enthalpy of formation of a specific phase to the elemental work function and the bulk modulus/molar volume. The work function suggests the role of the electron in property predictions, and the bulk modulus suggests the connection to elastic property measurements. This method is able to predict interfacial properties and behavior. Mott and Jones and others5 introduced the wave mechanics concepts allowing for the establishment of the electronic band theory, Fermi energy, and Brillouin zones. The use of the 1 W. Hume-Rothery. 1967. Factors Affecting the Stability of Metallic Phases. Pp. 3-23 in Phase Stability of Metals and Alloys. New York: McGraw-Hill; J.T. Waber, K. Gschneider, Jr., A.C. Larson, and M.Y. Prince. 1963. Prediction of Solid Solubility in Metallic Alloys. Transactions of the Metallurgical Society of AIME 227: 717-723; K.A. Gschneider, Jr. 1979. L.S. (Larry) Darken’s Contribution to the Theory of Alloy Formation and Where We Are Today. Pp. 1-39 in Theory of Alloy Phase Formation. Warrendale, Pa.: TMS-AIME. 2 N. Engel. 1964. Metallic Lattice Considered as Electron Concentration Phases. Transactions of ASM 57: 611-619. 3 L. Brewer. 1994. Calculation of Phase Diagrams of the Actinides. Journal of Alloys and Compounds 213/214: 132-137; L. Brewer. 1970. Thermodynamics and Alloy Behavior of the BCC and FCC Phases of Plutonium and Thorium in Plutonium and Other Actinides. Pp. 650-658 in TMS Nuclear Metallurgy Series, Vol 17. Warrendale, Pa.: TMS-AIME. 4 A.H. Miedema, R. Boom, and F.R. deBoer. 1975. Simple Rules for Alloying in Crystal Structures and Chemical Bonding in Inorganic Chemistry. The Netherlands: North Holland Publishing; J.R. Chelikowsky. 1979. Solid Solubilities in Divalent Alloys. Physical Review B 19(1): 686. 5 N.F. Mott and H. Jones. 1936. The Theory of the Properties of Metals and Alloys. London: Oxford University Press; J.M. Ziman. 1963. Electrons in Metals: A Short Guide to the Fermi Surface. London: Taylor and Francis, Ltd; C. Kittel. 1963. Introduction to Solid State Physics. New York: Wiley; R.E. Watson and L.H. Bennett. 1978. Transition Metals: d-band Hybridation, Electronegativities, and Structural Stability of Intermetallic Components. Physical Review B 18(12): 6439-6449; L.H. Bennett and R.E. Watson. 1979. Parameters in Semi-Empirical Theories of Alloy Phase Formation. Proceedings of the AIME International Annual Meeting. New Orleans; R.H. Bube. 1992. Electrons in Solids, 3rd Edition. New York: Academic Press; J.C. Phillips. 1979. From Wigner-Seitz to Miedema to ? Pp. 330-343 in Theory of Alloy Phase Formation, Warrendale, Pa.: TMS-AIME.
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Proceedings of a Workshop on Materials State Awareness free electron model for a metal can be extended to consider electron-lattice potential interactions through the introduction of the effective mass of the electron. The effective mass of the electron, me, is derived to be: (1) where ħ is the Planck constant divided by 2π. The effective mass describes the shape of the Fermi energy surface in situations at the Fermi energy level where the band filling is subject to electron-lattice potential interaction. The second derivative factor allows electronic property measurements to be useful, sensitive NDE microstructure and alloy stability assessment tools. When the Fermi energy surface contacts the Brillouin zone boundary, which represents an energy band gap that exists when the electron energy has a wave vector that will be diffracted, the conditions for a phase transformation occur. After the Fermi energy surface contacts the Brillouin zone boundary, it quickly fills higher energy states during further alloy additions, thus rapidly increasing the effective mass of the electron. The lattice will select a different crystal structure, thus a new Brillouin zone, which can continue filling the electronic states, allowing for lower energy filling. This situation is the electronic explanation for phase transformations. Recognizing that the phase compositional field on a phase diagram is defined by the chemical potential of a species between two phases, the chemical potential of the electron in one phase is equal to the chemical potential of the electron in the second phase. It is also known that the chemical potential of the electron is defined as the Fermi energy at absolute zero. From the free electron model, the Fermi energy is directly related to the conduction electron concentration. Dooley et al.6 used these concepts of phase equilibrium with the Brewer values of the e/a for specific phases and calculated the phase diagram for the Pu-Ga system, which has respectable correlation to experimentally determined phase diagrams.7 The utility of using the effective mass of the electron, me, to understand the state of the microstructure can be seen by considering the total energy, E, of an electron in a solid, based on wave mechanics; then: (2) where k is the electronic wave vector, and V is the potential that the nearly free electron is experiencing from the lattice. If the information of the potential of electron-lattice interactions, V, is incorporated into the factor m, then the total energy of electron in the lattice can be expressed in terms of effective mass me as: (3) 6 D.E. Dooley, D.L. Olson, G.R. Edwards, and F. E.Gibbs. 2001. Development of an Electronic Phase Diagram and the Production of Plutonium Alloy Phase Stability Using Electronic Properties. Journal of Physics-Condensed Matter 13: 8677-8696. 7 L. Brewer. 1994. Calculation of Phase Diagrams of the Actinides. Journal of Alloys and Compounds 213/214: 132-137; L. Brewer. 1970. Thermodynamics and Alloy Behavior of the BCC and FCC Phases of Plutonium and Thorium. Pp. 650-658 in TMS Nuclear Metallurgy Series, Vol 17. Warrendale, Pa.: TMS-AIME.
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Proceedings of a Workshop on Materials State Awareness These localized potentials represent the structural contributions that disturb the periodic lattice (Block function), such as dislocations, grain boundaries, areas of lattice strain, and phase changes. The me concept is very sensitive to changes in alloy composition, lattice strain, and susceptibility of a phase transition allowing for electric conductivity and thermoelectric power (TEP) coefficient measurements as materials state assessment tools. The TEP coefficient is a measure of the electron configurational entropy in the filling of the electronic bands of the metal or alloy and can be expressed as: (4) where kB is the Boltzmann’s constant.8 If the lattice experiences compressive or tensile stresses due to solute additions, residual strains, radiation damage, and so forth, then the electronic overlap of d and f orbitals between lattice atoms will cause both changes in the reciprocal lattice and, thus, the size and shape of the bands. Also, the change in the electronic concentration causes a relocation of the Fermi energy level in the band. The me at the Fermi energy is extremely sensitive to changes in the electronic band structures due to the (d2 E/dk2) factor. Electronic properties, such as TEP coefficients, resistivity, and induced resistivity measurements, have demonstrated correlation to solute and phase content, a potential phase transformation, and even residual strain. Retained austenite in transformation-induced plasticity steels have been accurately determined by using TEP measurements. Woodyatt et al.9 developed phase computation (PHACOMP), an analytical practice, with criteria to determine if an alloy is susceptible to sigma phase formation. Sigma phase is a detrimental microconstituent that can form in high-temperature superalloys used in high-performance turbine engines. The electron vacancy (unfilled states of the d-band), NV, is estimated and used to correlate to the criteria for the formation of sigma phase. If NV is greater than 2.49, sigma phase is likely to form. (5) Further efforts have developed a more fundamental-based model, known as New PHACOMP, to predict more accurately the phase boundary for sigma phase formation.10 This quantum mechanical calculation gives a more specific elemental contribution to the d-band electron filling. If it is possible to calculate whether a specific alloy composition is susceptible for sigma phase formation by an electronic computation and correlation, then it should be possible to measure the electronic property state for the susceptibility of sigma phase formation. 8 A. Sommerfeld and H. Bethe. 1933. Elektronentheorie der Metalle. Pp. 333-622 in Handbuch der Physik 24: 2. Berlin: Springer. 9 L.R. Woodyatt, C.T. Sims, and H.M. Beltram. 1966. Prediction of Sigma-Type Phase Occurrence from Compositions in Austenitic Superalloys. Transactions of the Metallurgical Society of AIME 235(4): 519-527. 10 M. Morinaga, N. Yukawa, H. Adachi, and H. Ezaki. 1984. New PHACOMP and Its Applications to Alloy Design. Pp. 523-532 in Superalloys. Metals Park, Ohio: ASM; M. Morinaga, N. Yukawa, H. Adachi, and H. Ezaki. 1984. Alloying Effect on the Electronic Structure of Ni3Al(γ′). Journal of the Physical Society of Japan 53(2): 653-663; M.J. Cieslak, G.A. Knorovsky, J.J. Headley, and A.D. Romig, Jr. 1986. The Use of New PHACOMP in Understanding the Solidification Microstructure of Nickel Base Alloy Weld Metal. Metallurgical Transactions 17A(12): 2107-2116.
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Proceedings of a Workshop on Materials State Awareness Available Physical Property Measurements X-ray fluorescence spectroscopy offers a rapid NDE chemical compositional analysis for elements in the condensed matter. Elastic analysis, in its many forms, is advancing rapidly to reach beyond just the determination of the number, size, and morphology of defects in the solid. Elastic waves perturb the atomic positioning, but also the electron density throughout the perturbed lattice. This electronic-phononic exchange in both directions can be seen with the use of elastic waves generated by either piezoelectric transducers or electromagnetic acoustic transducers (EMATs). The elastic moduli are a function of the electron density of the elements.11 Through the use of spaced, properly calibrated EMATs, the speed of sound can assess the temperature in a material. Balashchenkov and Livanov12 have correlated the elastic behavior to the electronic structure in an expression that connects the speed of sound to the TEP value when performing nondestructive measurements of impurities in solids, indicating the relationship between various physical property measurements. Magnetic analysis can detect phase changes and even prephase transformations, such as Guinier-Preston zones or γ′ ordered-structure formation.13 Magnetic analysis has been used to assess the hydrogen content in hydrogen storage materials and should also be able to measure residual strain in ferrous alloys.14 The Use of Frequency and Amplitude Modulations By implementing a full range of wave-perturbing frequencies, and with knowledge of the depth factor, wavelengths can be used at all levels of microstructural scale, from nano to millimeter, to assess atomic-to-grain structure, size, and morphology. The interplay between wave perturbations and the matter (and the reverse) will become an even more valuable assessment protocol. Both frequency and amplitude modulation can be applied to this wave analysis. With instrumentation, various combinations of harmonics between the perturbation wave and the analyzed wave may be employed to assist in signal recognition analysis. The use of wave analysis, whether electronic, magnetic, or elastic, offers the new capabilities to assess the material without using a calibration standard. Magnetic Barkhausen and magnetic acoustic emissions analyses assess the elastic emission resulting from the transporting of the magnetic domain wall through ferromagnetic 11 Seung-Am Cho. 1977. Engel-Brewer Theory and Related Physical Properties of Hume-Rothery's Class-I Metals. Acta Metallurgica 25:1085-1094; J.J. Gilman. 2003. Chapter 12, Bulk Modulus. Pp. 110-141 in Electronic Basis of the Strength of Materials. Cambridge, U.K.: Cambridge University Press. 12 K.D. Balashchenkov and D.V. Livanov. 1997. Effect of Impurities on Thermoelectric Power Due to Phonon Drag. Journal of Experimental and Theoretical Physics 84(6): 1221-1224. 13 K.A. Lindahl, D.L. Olson, and J.U. Trefny. 1996. Alloy Phase Analysis from Measurements of Bulk Magnetic Properties. Metallurgical and Materials Transactions 27: 2958-2965. 14 Y.D. Park et al. 2003. Characterization and Prediction of Hydrogen Absorption Behavior for AB5 Type Hydrogen Storage Alloys by Using Electronic Measurement. Pp. 69-75 in Proceedings of the 6th International Conference on New Energy Systems and Conversions, Pusan, Korea; A.N. Lasseigne-Jackson, J.E. Jackson, D.L. Olson, and B. Mishra. 2007. Development of Electromagnetic Techniques for Hydrogen Content Assessment in Coated Linepipe Steel. Pp. 1159-1166 in Review of Quantitative Nondestructive Evaluation, Vol. 26. D.O. Thompson and D.E. Chimenti, eds. Melville, N.Y.: American Institute of Physics.
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Proceedings of a Workshop on Materials State Awareness materials.15 The elastic emission results from the unpinning events of the block wall from nonperiodic sites in the lattice. By varying the frequency of the eddy current source, which perturbs and oscillates the domain wall, one can identify specific frequencies that are more pronounced in unpinning specific structural lattice irregularities, and these frequencies can be used to identify the microstructural state of the ferrous material. By scanning frequencies, the evolution of the many carbide types in 2¼ Cr–Mo steel resulting from high-temperature services can be assessed, and the results can assist in the determination of remaining service life. The Need for Multiple Measurements The significant difficulty of using a single physical measurement to characterize material microstructure, composition, or other properties is that the measurements are dependent on numerous independent variables. Electronic property measurements are dependent on at least three independent electronic properties. For a physical property measurement to assess the material state requires reference to materials standards, requiring calibration measurements to hold most of the physical and compositional variables constant by comparing measured values to this calibrated material’s standard. The necessary advancement in use of physical measurements to assess materials is through the use and correlation of sufficient different physical measurements to experience all of the independent material variables. This case is similar to the algebraic problem of having sufficient equations for the unknowns. The use of a combination of magnetic and elastic property measurements on the same material, and with the same thermomechanical history, offers a practice to achieve sufficient correlatable information to assess the material without the use of materials standards. Also, the use of property measurements, based on wave analysis (electromagnetic and elastic waves), allows measurements to be made at different frequencies that interact with different specific microstructural details. The use of the same physical measurements at different frequencies can offer independent information to allow correlation to the material’s independent variables. Likewise, amplitude modulation also allows wave analysis to offer more insight to the determination of material properties, microstructure, and behavior. The aging kinetics of maraging steels involves precipitation of metastable phases (Ni3[Ti,Mo]) followed by the formation of stable phases (Fe2[Mo,Ti]) and austenite with continued composition changes in the highly alloyed matrix. Also, high residual strains caused by the semicoherent precipitates and reduction in the dislocation and point defect densities have offered a number of investigators a family of alloys providing an opportunity to examine the concept of fully characterizing a material using multiple nondestructive evaluations. The literature describes much nondestructive testing of maraging 250 steels, which includes resistivity, eddy currents, magnetic properties (magnetic saturation and magnetic Barkhausen emission [MBE] remote monitoring systems), ultrasonic wave velocities, TEP, x-ray diffraction (full-width half maximum as an indication of residual strains and phase composition) and x-ray fluorescence (phase composition).16 15 K.V. Rajkumar, S. Vaidyanathan, A. Kumar, T. Jayakumar, B. Raj, and K.K. Ray. 2007. Characterization of Aging-induced Microstructural Changes in M250 Maraging Steel Using Magnetic Parameters. Journal of Magnetism and Magnetic Materials 312: 359-365; F.G. Caballero, A. García-Junceda, C. Capdevila, and C. García de Andre. 2005. Precipitation of M23C6 Carbides: Thermoelectric Power Measurements. Scripta Materialia 52: 501-505. 16 M. Morinaga, N. Yukawa, H. Adachi, and H. Ezaki. 1984. Alloying Effect on the Electronic Structure of Ni3Al(γ′). Journal of the Physical Society of Japan 53(2): 653-663; M.J. Cieslak, G.A. Knorovsky, J.J. Headley, and A.D. Romig, Jr. 1986.
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Proceedings of a Workshop on Materials State Awareness The Need for a Microstructural Rule As with materials phase analysis, the phase rule determines the least number of intrinsic properties, the degrees of freedom (F), to define the number of phases. A microstructural rule is needed to determine the specific number of intrinsic property measurements needed to fully characterize a microstructure. The microstructure rule is given as: (6) where C is the number of components and P is the number of phases, the “2” recognizes pressure and temperature, and an additional M term addresses the need for measurements to express microstructural constituents’ concentrations, sizes, and morphologies. A microstructural rule is needed to identify the minimum number of intrinsic property measurements required to fully characterize the material. Consider the example of the two-phase, α + Fe3C, region of the iron-carbon system. This region can be represented by various morphologies such as pearlite, Bainite, or as spherical carbides in a ferrite matrix. All three satisfy the same phase rule count of phases, but additional property measurements are needed to distinguish the specific microstructural features. The effort to establish a quantitative scheme to determine M will have to draw on rules from phase equilibrium, phase transformation, metallography, petrology, and topology. The Use of New PHACOMP in Understanding the Solidification Microstructure of Nickel Base Alloy Weld Metal. Metallurgical Transactions 17A(12): 2107-2116; Seung-Am Cho. 1977. Engel-Brewer Theory and Related Physical Properties of Hume-Rothery's Class-I Metals. Acta Metallurgica 25:1085-1094; J.J. Gilman. 2003. Chapter 12, Bulk Modulus. Pp. 110-141 in Electronic Basis of the Strength of Materials. Cambridge, U.K.: Cambridge University Press; K.D. Balashchenkov and D.V. Livanov. 1997. Effect of Impurities on Thermoelectric Power Due to Phonon Drag. Journal of Experimental and Theoretical Physics 84(6): 1221-1224; K.A. Lindahl, D.L. Olson, and J.U. Trefny. 1996. Alloy Phase Analysis from Measurements of Bulk Magnetic Properties. Metallurgical and Materials Transactions 27: 2958-2965; Y.D. Park et al. 2003. Characterization and Prediction of Hydrogen Absorption Behavior for AB5 Type Hydrogen Storage Alloys by Using Electronic Measurement. Pp. 69-75 in Proceedings of the 6th International Conference on New Energy Systems and Conversions, Pusan, Korea; A.N. Lasseigne-Jackson, J.E. Jackson, D.L. Olson, and B. Mishra. 2007. Development of Electromagnetic Techniques for Hydrogen Content Assessment in Coated Linepipe Steel. Pp. 1159-1166 in Review of Quantitative Nondestructive Evaluation, Vol. 26, D.O. Thompson and D.E. Chimenti, eds. Melville, N.Y.: American Institute of Physics; K.V. Rajkumar, S. Vaidyanathan, A. Kumar, T. Jayakumar, B. Raj, and K.K. Ray. 2007. Characterization of Aging-induced Microstructural Changes in M250 Maraging Steel Using Magnetic Parameters. Journal of Magnetism and Magnetic Materials 312: 359-365; F.G. Caballero, A. García-Junceda, C. Capdevila, and C. García de Andre. 2005. Precipitation of M23C6 Carbides: Thermoelectric Power Measurements. Scripta Materialia 52: 501-505; M.N. Rao. 2006. Progress in Understanding the Metallurgy of 18% Nickel Maraging Steels. International Journal of Materials Research (formely Z. Metallkd.) 97(11): 1594-1607; R. Tewari, S. Mazumder, I.S. Batra, G.K. Dey, and S. Banerjee. 2000. Precipitation in 18 wt% Ni Maraging Steel of Grade 350. Acta Materialia. 48: 1187-1200; K.V. Rajkumar, S. Vaidyanathan, A. Kumar, T. Jayakumar, B. Raj, and K.K. Ray. 2007. Characterization of Aging-Induced Microstructural Changes in M250 Maraging Steel Using Magnetic Parameters. Journal of Magnetism and Magnetic Materials 312: 359-365; K.V. Rajkumar, A. Kumar, T. Jayakumar, B. Raj, and K.K. Ray. 2007. Characterization of Aging Behavior in M250 Grade Maraging Steel Using Ultrasonic Measurements. Metals and Materials Transactions 38A: 236-243; Y. Snir, M. Pinkas, Y. Gelbstein, O. Yeheskel, and A. Landau. 2007. Applying TEP Measurements to Assess the Aging Stage of a Maraging 250 Steel, 34th Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE2007), July 23-27, 2007.
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Proceedings of a Workshop on Materials State Awareness The Need for Generation II Materials Science Processed materials consist of compositional, microstructural, and property gradients that require modifications in the materials science fundamentals to describe the nonuniform materials behavior, such as aging, phase stability, and the defect initiation. This is so especially in materials that depend on nanostructural features. When lattice dimensions in the nano-to-millimeter range are necessary to describe the material, then nonlinear thermodynamics and kinetics need to be used to accurately describe the system.17 Cahn and Hilliard18 describe the thermodynamics on the nonuniform systems, Hart19 has addressed the nonuniform strain issues, and Tu20 described the need for application of nonlinear terms in the expressions describing the evolution of nanoscale thin films. Advanced composite theory will need to describe the electronic charge gradient across the bonding interfaces based on electronic concepts. These bonding interfaces, which will be considered as junctions with electronic gradients described by the Debye lengths, will use electronic and elastic NDE tools to assess the amount of remaining service life. The expressions for describing lattice behavior and the response of the lattice to perturbations will require additional nonlinear terms. The influence of these nonlinear effects on NDE assessment needs to be investigated, and the analytical materials science practices need to be developed to allow interpretation of the micro (nano)-structural state of many advanced and high-performance materials now being used or that will be used by the United States Air Force. Outlook With the use of the proper combination of independent NDE measurements, it is possible to accurately evaluate the microstructure and properties of materials. The fundamental limitations of correlating microstructure and properties to NDE measurements result from both the numerous independent variables that each of these properties has and the number of intrinsic property measurements necessary to characterize the number of phases and the microstructural features. Different electronic, magnetic, and elastic measurement combinations offer complementary insights into materials properties, and practices for their selection need to be developed for the appropriate applications. This advanced integration of physical property and phenomena measurements will result in new opportunities for the NDE community and the development of new analytical measurement equipment and practices. 17 F.G. Yost. 1997. Growing Understanding on Nonlinear Effects in Materials Science. Journal of Materials 49(12): 29. 18 J.W. Cahn and J.E. Hilliard. 1958. Free Energy of a Non-Uniform System, I: Interfacial Free Energy. Journal of Chemical Physics 28: 258; J.W. Cahn and J.E. Hilliard. 1959. Free Energy of a Non-Uniform System, II: Thermodynamic Basis. Journal of Chemical Physics 30: 1121-1124; M. Hillert. 1961. A Solid-Solution Model for Inhomogenous System. Acta Metallica 9: 525-535; A. Novick-Cohen and L.A. Segel. 1985. Non-Linear Aspects of the Cahn-Hilliard Equation. Physica D. 10: 277-298.; M.F. Ashby. 1970. The Deformation of Plastically Non-Homogenous Materials. Philosophical Magazine 21(170): 399-424. 19 E.W. Hart. 1959. Thermodynamics of Inhomogeneous Systems. Physical Review 113: 412-416. 20 K.N. Tu. 1985. Interdiffusion in Thin Films. Annual Review of Materials Science 15: 147-176.
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Proceedings of a Workshop on Materials State Awareness MODELING AND SENSING MECHANICAL DEGRADATION IN METALS AND COMPOSITES W.A. Curtin, Brown University The detection of cracks in structural components poses significant technological challenges as the necessary scale for detection decreases. The detection of precursors to cracks remains largely a long-term goal. Nonetheless, modeling of the material behavior at micro- or nanoscales can provide insight into what the precursors actually are, how they evolve, and what methods of detection might be feasible. Here, recent progress in the modeling of damage evolution in metals and carbon-fiber-reinforced polymer composites is discussed. In metals, discrete dislocation models are being applied to model fatigue crack growth emanating from precracked inclusion particles. While these models show the role of both size and particle type in the growth of micron-sized fatigue cracks and on dislocation distributions around the cracks, such models are still far from providing the information needed for designing detection methodologies. In contrast, in carbon-fiber-reinforced polymer composites the use of electrical resistance changes owing to evolving distributed damage is emerging as a promising approach to couple mechanical degradation and prognosis. Here, a coupled electromechanical model to predict resistance versus applied loading and/or applied cycles is presented, and predictions from both analytical and simulation studies show that electrical resistance changes can (1) be far larger than stiffness changes, (2) provide evidence of internal damage early in life, and (3) be sensitive to anomalous load spikes. While this modeling has yet to be extended fully to evaluate detection methodologies, statistical features, and sensitivity versus probed volume, the results to date represent a firm foundation on which systems for materials state awareness and prognosis can be built. VIRTUAL TESTS: MAKING THE MOST OF EXPERIMENTAL KNOWLEDGE Brian Cox, Teledyne Scientific Taking advantage of major recent advances in computational methods and the conceptual representation of failure mechanisms, the modeling community is building increasingly realistic models of damage evolution in structural composites. The goal of virtual tests, in which most (but not all) real experimental tests can be replaced by high-fidelity computer simulation, appears to be reachable. The payoff in reduced cycle time and costs for designing and certifying composite structures is very attractive; and the possibility also arises of considering material configurations that are too complex to certify by purely empirical methods. However, major challenges remain, the foremost being the formal linking of the many disciplines that must be involved in creating a functioning virtual test. Far more than being merely a computational simulation, a virtual test must be a system of hierarchical models, engineering tests, and specialized laboratory experiments, organized to address the assurance of fidelity by applications of information science, model-based statistical analysis, and decision theory. The virtual test must be structured so that it can function usefully at current levels of knowledge, while
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Proceedings of a Workshop on Materials State Awareness continually evolving as new theories and experimental methods enable more refined depictions of damage. To achieve the first generation of a virtual test system, special attention must be paid to unresolved questions relating to the linking of theory and experiment: how can one ensure that damage models address all important mechanisms, how can the materials properties embedded in the models be calibrated, and what constitutes sufficient validation of model predictions? The virtual test definition must include real tests that are designed in such a way as to be rich in the information needed to inform models and model-based analyses of the tests that are required to mine the information. But to date these compelling issues have been greatly underserved by both the modeling and experimental communities. Model-based analysis of tests has been undertaken only in terms of very simple (linear or continuum) engineering concepts; information-rich tests for more complex damage mechanisms have not been defined; and in fact the information in which experiments need to be rich has not been stated. Specific challenges in designing experiments for informing virtual tests and some promising experimental methods are summarized.