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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials APPENDIX C Performance OVERVIEW Research in the performance of materials cuts broadly across the entire field of materials science and engineering. Performance-related research ranges from understanding the microstructural response of interfaces between complex solids to predicting lifetimes for structural materials subject to stress or corrosion. Progress in these areas depends on tools and perspectives drawn from all of traditional materials science and engineering plus related parts of chemistry, physics, mathematics, and engineering. Scientists and engineers should strive to broaden both their technical perspectives and their professional interactions in approaching problems in this field. Those responsible for funding in materials science and engineering, especially in the area of performance, which cuts across an unusually wide variety of disciplines, should deal with the field as a whole, recognizing and fostering opportunities for new fundamental advances across a broad front. Computational modeling of the complex processes involved in synthesis, fabrication, deformation, degradation, and failure of materials is becoming a central tool in research on performance. The increasing power of computers, coupled with new theoretical developments, now makes it possible to develop quantitative methods for solving some of the major problems in this field. In particular, accurate codes may become available to aid in the microstructural design of complex materials such as composites, or for making reliable predictions of the lifetimes of structural materials in service. Research leading to such developments should be strongly encouraged. Research in processing, manufacturing, and fabrication of materials should
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials be more fully integrated with research on performance and with engineering design of components or structures. Industry-university collaboration should be strengthened. This is a particularly difficult challenge because much of the industrial base that traditionally has supported research in the performance of materials is in poor health. Industrial areas to which special attention should be paid in this regard include fossil and nuclear power technology, energy resource extraction, surface transportation, and the metals industry. THE BROAD SCOPE OF RESEARCH IN THE PERFORMANCE OF STRUCTURAL MATERIALS Research in the performance of materials seeks to predict and improve the way materials behave in service. The materials may be metals, ceramics, polymers, or any of the various alloys or composites that may be formed by combining such constituents. The example of performance research chosen here for detailed discussion is that of structural materials. One wants to know how such materials respond to stresses caused by service loading, mechanical contacts, or temperature variations; how they react to hostile, corrosive environments; and how they undergo internal degradation, e.g., by diffusive processes. The crucial issues are strength, reliability, durability, life prediction, and life extension. Such issues are relevant not just for the materials that are used in large structures or machines but also for those that form the structural elements in electronic, magnetic, or optical devices. Research in performance involves all the conventional inputs that contribute to understanding relations between the structure of materials and their mechanical (and often chemical and electronic) response properties. It also involves understanding the means of manipulating structures to achieve desired properties and learning how properties, together with operating conditions, determine lifetimes. Here, structure refers not only to atomic structure of constituents and to the atomic bonding between phases, but also to structure at a variety of more macroscopic levels of organization that prove essential to understanding the strength of materials and their failure in service. These macroscopic structures include grains, preexisting cracks or pores, precipitates and inclusions that may contribute to strengthening but may also introduce cracks or voids, fibers embedded in matrices, and surface films or coatings. Thus the relevant background for performance research includes not only the quantum mechanical concepts essential to understand matter at the atomic scale, and the thermodynamic, chemical, and kinetic concepts needed for understanding structural transformations, but also the more macroscopic concepts of deformation and transport that are relevant to processes that occur on the larger than atomic scales of materials microstructure. (The application
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials of mechanical principles at such scales, to understand strength, deformation, degradation, damage, and failure processes, is commonly called “micromechanics.”) Further, since performance research addresses materials in service, its scope includes engineering disciplines such as structural analysis, fracture mechanics, materials forming processes, nondestructive evaluation, tribology, electrochemistry, and corrosion. We see therefore that the scope of performance research is unusually broad. Few of its currently active researchers and advanced practitioners are involved in the entire spectrum, and fewer yet have received formal education in that breadth. Yet it is evident that many of the most challenging problems in the area call for individuals who can reach well beyond the conventional disciplinary boundaries of contributory fields such as engineering mechanics, metallurgy, polymer chemistry, and solid-state physics. In short, research in performance is particularly an area in which national needs and priorities must be addressed by the materials science and engineering community as a whole. NEEDS AND INSTITUTIONAL ISSUES Some general needs and opportunities for research in the performance of materials are presented below. Technical and Scientific Requirements Improved instrumentation and experimental techniques. These are needed to characterize microstructures and, especially, to clarify the dynamics of the complex microstructural mechanisms by which materials deform, degrade, and fracture. They are also needed to detect and characterize defects developed in processing, manufacturing, and fabrication, and to trace the evolution of defects in service applications. Better theoretical understanding of performance-related properties and phenomena, and improved capabilities for quantitative analysis and modeling. This need exists at all levels including the electronic and atomic, micromechanical, and macroscopic engineering domains. The goals are both improved fundamental understanding and the provision of a basis for more enlightened empiricism. Design of materials microstructures for optimized performance. Advanced microstructural design relies on progress in the two categories just mentioned. It will be carried out best at laboratories where new ideas regarding relations between microstructure and performance may be investigated in collaboration with innovative research in synthesis and processing. Improved methods for prediction and assurance of lifetime in service.
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials Techniques for predicting performance of materials should be based on fundamental understanding of degradation and failure processes, on rational test procedures, and on improved nondestructive evaluation technology to detect and characterize cracking or damage in service. For new components or structures, these methodologies should be part of an integrated engineering process involving not only design to meet performance requirements but also the concomitant modeling of the processing, manufacturing, or fabrication steps necessary to bring a material to service. It may be noted that these needs require, for their fulfillment, work across a range of materials science and engineering activities that often stretches beyond traditional disciplines. The work goes hand in hand with characterization, synthesis, processing, analysis and modeling, and engineering design. Education Neither the current status of education in materials science and engineering nor the priorities for funding are fully suitable for meeting needs in the performance area. For example, individuals active in this area have generally had education in core materials science and engineering, in a mechanics-related engineering field, or, to a lesser extent, in physics or chemistry. The core materials programs sometimes lack emphasis on the theoretical background and techniques of quantitative modeling underlying performance research. Those from mechanics-related engineering programs often have minimal exposure to structure-property relations, techniques of manipulating microstructures, and materials phenomena at atomic or molecular scales. Those educated in physics are usually without exposure to core concepts in performance research such as the mechanics of strength and failure processes, and those in chemistry often consider structure-property relations only in terms of small molecules or, at most, highly ordered crystals, rather than in terms of the multiplicity of solid-solid interfaces pervading most useful materials. These lacks are to some extent inevitable, but it is essential that increasing numbers of capable students be encouraged to bridge traditional areas. They will find much productive work at the interfaces. SCIENTIFIC AND TECHNICAL ISSUES The basic scientific issues addressed by research in the performance of structural materials are strength, deformability, chemical degradation, and fracture. The goals are to predict, control, and improve the integrity of materials in service. In the following paragraphs, these issues are discussed from a scientific and technical point of view. The discussion is organized
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials according to the length scales—from atomistic to macroscopic—that characterize the underlying phenomena. Atomic Scales Atomistic studies of strength, fracture, and chemical reactions are becoming increasingly important in optimizing the performance of materials. For example, modern metallic and ceramic structural materials, as well as composites and artificially structured devices, typically contain large numbers of interfaces separating grains or phases. Fracture at such interfaces, which is frequently influenced by local segregation of solutes and of environmentally introduced impurities such as hydrogen, is often critical in limiting toughness. New fundamental approaches to alloy design, e.g., identification of favorable trace elements that will improve interfacial toughness, should follow from basic understanding of the atomistics of interfacial fracture. One example, so far understood only empirically, is that the polycrystalline-ordered Ni3Al alloy normally fractures easily along grain boundaries, but may be made ductile by addition of trace boron atoms, which, apparently, segregate at the boundaries in such a way as to strengthen them. An opposite example is the weakening of quenched and tempered martensitic steels by grain-boundary segregation of trace elements such as phosphorus, sulfur, tin, antimony, and, especially, hydrogen. Analysis and modeling at the atomic scale should be useful in two primary ways. The first is by providing accurate, quantum mechanical calculations of material properties (interfacial energies, solute binding energies, dislocation core configurations and energies, and so on), which are needed in continuum theories of deformation or fracture but which are not easily or accurately measured. Dramatic improvements in our ability to make such calculations have been achieved in recent years, and the impact of these developments is only now beginning to be felt. The second way in which atomic-scale modeling is becoming useful is in exploring the dynamics of complex, many-atom processes. Such calculations necessarily involve departures from rigorous quantum mechanical principles, for example, the use of pair potentials or a modern improvement like the “embedded atom method.” Examples of processes for which dynamic modeling is currently being attempted include fracture at a crack tip, chemical bond formation during separation of fracture surfaces, the motion of dislocations, interaction of glide and grain-boundary dislocations, nucleation of martensitic transformations, and entanglements of long-chain molecules during deformation and crazing of polymeric materials.
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials Micromechanics of Strength and Fracture Studies of fracture by electron microscopy reveal that the behavior of crack tips is influenced by microstructure at scales well above atomic (e.g., grains, inclusions, and fibers) and often involves, at least in metallic and nonglassy polymeric materials, substantial amounts of local plastic flow. The study of these processes will be aided, often in critical ways, by what is learned atomistically. Nevertheless, such studies depend principally on the largely independent theoretical framework of solid continuum mechanics, specifically, crack theory, dislocation theory, and the constitutive descriptions of plastic, viscoelastic, or viscoplastic flow. Studies in this latter domain will be critical in designing microstructures to optimize the performance of materials. The domain of “micromechanics” is thus the study of processes that occur in solids on length scales roughly of the order of microns. These scales are much larger than atomic, thus justifying the use of continuum theories, but they are much smaller than the bulk scales ultimately of interest in engineering design. The important problems are to understand processes pertaining to strength and fracture in heterogeneous microstructures. The conceptual starting point for research in micromechanics is the idea of micron-sized defects that, ultimately, may lead to macroscopic failure of solid objects. These defects are produced in many ways. Sometimes microcracks or cavities are introduced into newly formed materials by synthesis and processing; sometimes they are generated during deformation in secondary processing, manufacturing, fabrication, or service. In metallic systems, nucleation of precipitates typically is accompanied by extensive plastic strain. In ceramics, nucleation of new phases may be activated at incompletely sintered zones or by local stresses generated by elastic modulus or thermal expansion mismatch. Suitable theories to explain the separate effects of macroscopic stress and inelastic strain on nucleation do not exist. At high temperatures, stress-assisted and transport-assisted cavity nucleation becomes possible. This process occurs along interfaces, often at the sites of inclusions along grain boundaries, and provides the cavities that enlarge to failure in the high-temperature creep rupture of metals and ceramics. Here, too, there are problems in explaining observed behavior in that stresses predicted for nucleation according to the standard model of vacancy condensation generally exceed stress levels inferred experimentally. Once nucleated, the growth to linkage of microcracks or cavities, causing final fracture, is usually an extremely complex process in multiphase alloys and composite materials. It can also be complex in single-phase solids. The complexity induced by microstructural alterations can frequently be beneficial, and progress toward the understanding of complex fracture processes can pay handsomely in improved properties of materials.
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials Toughened Ceramics One example of recent progress in micromechanics is the toughening of ceramics. Ceramics normally are extremely brittle, and yet many are attractive for applications because of their strength at high temperatures (e.g., for heat engines), low thermal conductivity, low density, hardness (for cutting tools), usually low coefficient of friction, and corrosion resistance (for coatings). Routes to toughening of ceramics have been discovered empirically but are now to some extent explained theoretically and are currently being exploited in materials development. These routes include stress-induced phase transformations within initially constrained inclusions (e.g., partially stabilized zirconia), the introduction of ductile metallic inclusions (cermets) that can attract and pin macrocracks, and whisker inclusions that can slide in relation to the matrix and bridge the crack surfaces. Ductile Rupture Another example of the use of micromechanics is in studying the mechanisms that lead to rupture in metals used for structural purposes. Generally, such metals are chosen for their ductility. They are thought to fracture by the nucleation of cavities that grow by ductile deformation. Currently promising approaches to understanding the growth to coalescence of these cavities are based on models of continuum plasticity. The key problem is to understand the overall deformation of a porous solid whose material elements obey nonlinear elastic-plastic constitutive relations. Of interest is the growth of such voids to coalescence with their neighbors and, especially, the local instabilities in deformation between pairs or among clusters of voids, which can lead rapidly to macroscopic fracture. Ductile-Brittle Transition Some classes of metallic alloys, including the carbon steels used extensively in large structural applications, show transitions from ductile response to low-energy cleavage with decrease of temperature, increase of loading rate, or long-term exposure to neutron irradiation. While such transitions have been known and characterized experimentally for many years, their fundamental explanation is incomplete. The factors that induce embrittlement are also those that increase the resistance to plastic flow, and some degree of understanding has been obtained on this basis. For example, increased strength causes increased stress ahead of a crack or a sharp notch. This stress acts to nucleate running cracks at brittle phases, such as carbides in steel, and also makes it possible for the crack to continue in a brittle cleavage mode across the adjoining metallic grains. However, what is still poorly
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials understood despite impressive recent advances in theoretical modeling is how the strain rate and temperature dependence of plastic flow, together with specific loading or brittle phase crack-nucleation conditions, govern whether a potentially cleavable lattice will in fact sustain such a brittle cracking mode. Deformational Instabilities and Pattern Formation At somewhat more macroscopic levels in the analysis of ductile materials, problems arise in understanding the instabilities and patterns that occur in large plastic deformations. An important example is the onset of shear localization. Sometimes this phenomenon is triggered by incipient cavitation at inclusions, but it may also result from an intrinsic instability of the multidislocation motion itself. Shear localization frequently leads to profuse voidage within the shear zone and to ductile rupture. Some important theoretical advances have been made in modeling such localization phenomena, e.g., as instabilities in nonlinear elastic-plastic or viscoplastic behavior. However, even within this approach, there does not yet exist a suitable method for analyzing shear localization in strongly nonhomogeneous deformation fields such as those that exist at the tips of macroscopic cracks. Shear localization strongly limits ductility. In some high-strength alloys it takes place at macroscopic crack tips and leads to low-energy zigzag fracture paths, consisting of one shear localization-induced rupture followed by another. On the microscale, these fractures show extreme ductility; macroscopically, they are extremely brittle in character. Also, while fracture by ductile void growth to coalescence can lead to substantial macroscopic strain at fracture, the actual strain at fracture is often sharply reduced by localization. For example, it is common that well before voids generated from large impurity inclusions grow to coalescence with one another, localized shear bands develop between them and abruptly terminate the process by triggering profuse voidage from families of smaller precipitates within the band. In addition, there is evidence from studies of hydrogen in localization-prone steels that hydrogen can enhance flow localization. This phenomenon too lacks suitable theoretical explanation, but it is important as a mechanism of hydrogen embrittlement other than by the direct degradation of cohesion along interfaces. Other types of pattern formation for which present understanding is inadequate include the development of patchy slip textures, where active slip systems vary substantially from region to region of a crystal under nominally identical stresses. In cyclic plastic deformation, patterns of “persistent slip bands” are often observed to take up most of the macroscopic straining. Such bands lead to stress concentrations at material surfaces and are important mechanisms for fatigue crack nucleation.
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials Contact and Wear Modern phenomenological descriptions of wear in sliding and rolling contact postulate microstructural mechanisms that are similar to some of those just discussed in connection with strength and fracture. The study of friction and wear is a major part of tribology (which also includes lubrication and machine dynamics). While traditionally studied independently of other work on the micromechanics of strength and fracture, the same basic concepts and experimental techniques have proven essential. For example, repetitive rolling or sliding contact in ductile systems results in repetitive plastic shear parallel to the contact plane in subsurface material. This leads to localized shear, crack nucleation, and, ultimately, the flaking-off of wear particles. Neither the microstructural alterations caused by wear nor the basis for environmental sensitivity of these processes is well understood at present. Progress in this area should lead not only to better design of wear-resistant structural materials but also to better understanding of wear inhibition by surface coating or ion implantation. In brittle systems, sliding contact produces arrays of microcracks, which ultimately join to form wear particles. Similar processes occur in erosion. They too involve complex mechanisms that are not well understood at present. Polymers Many ductile polymeric materials exhibit phenomena analogous to those observed in metallic systems. For example, failure during ongoing deformation is known to be caused by nucleation, growth, and coalescence of voids. Instabilities such as shear localization are also observed. Fractures in ductile systems such as polyethylene often are preceded by the formation of extensive “craze” zones in which the entangled molecules, initially without preferred orientations, form extended zones of fibrils oriented parallel to the direction of maximum stress. Significant improvements of toughness of brittle glassy polymers such as polystyrene and polymethyl methacrylate have been achieved by microstructural manipulation, particularly by blending them with elastomeric second phases, which arrest incipient crazes. Polymers are being used increasingly in structural applications as matrices for composites, as adhesive joints, and, in some cases, as strong materials (such as aromatic polyamide polymers) that can be used themselves as fiber-reinforcing phases, e.g., in concrete. In order to assess the performance of such composites, it will be important to understand the relatively slow processes that control the degradation of the polymeric components, for example, viscous flow, moisture uptake, and radiation-induced molecular rearrangements. In summary, improved fundamental understanding of micromechanical
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials properties is going to be needed in order to design at the microstructural level new materials that will meet advanced standards of performance. The class of materials for which rational microstructural design looks promising is remarkably broad. It includes very fine grained single-phase materials, dispersion-strengthened solids, intermetallic compounds, toughened ceramics, polymer alloys and blends, composite materials of all types, thin films, and layered solids. It also includes high-performance concretes with relatively impermeable and hence degradation-resistant pore structures. There is clearly a large amount of work to be done. Crack Growth, Degradation, Damage, and Life Prediction The domain of macromechanics includes processes that can be described on macroscopic length scales, that is, scales comparable to the sizes of the devices or structures whose performance is being evaluated. Some topics in research on the performance of materials that lie in this domain are discussed below. Fatigue Most service conditions involve time-dependent stresses. Often the most critical questions for evaluation of performance and lifetime relate to the behavior of materials exposed to cyclic loading. Here, just as in the topics discussed in the section “Micromechanics of Strength and Fracture,” there is no shortage of complexity. The basic mechanism of fatigue crack growth is an irreversible process in which the crack tip opens under increasing load but does not return fully to its original configuration when the load is released. It turns out that the extent of crack tip opening and the degree to which it can be reversed by closure slip and rewelding are sensitive to the environment. Further, the loading actually sensed at the crack tip differs from that for an idealized crack with traction-free surfaces because the crack walls near the tip come into mechanical contact with each other during the part of the cycle when the load is decreasing. Closure is promoted by protrusions left on the fracture surface by deformation markings from prior cycles and by irregularities of the fracture path. Further, the chemically reacted state of the newly formed fracture surface, i.e., an oxidized or corroded layer, also affects the geometry of the surfaces and the tendency for closure. Careful experimentation has shown that this picture of crack closure can explain qualitatively the observed dependence of growth rates on load level, crack depth, and external environment in the sense that growth per cycle correlates with the range of near-tip loading over which there is no crack closure. However, a basis is still lacking for fundamental prediction of crack growth rates or for identification of microstructural alterations that might
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials improve fatigue resistance. Also, the methodology for accurate prediction of lifetime in service remains incomplete because of our still limited understanding of crack nucleation and crack growth in the short crack regime where crack depths are comparable to or only a few times larger than microstructural sizes such as grain diameters. Corrosion and Environmentally Assisted Cracking Environmental chemistry strongly influences crack tip mechanisms in both fatigue and sustained-load growth (e.g., stress corrosion cracking). The mechanisms are varied, and our understanding of them is highly incomplete. They include the hydration of silicon-oxygen bonds of silica glasses in moist environments; the successive formation and rupture of oxide films at crack tips, usually along grain boundaries, in many metallic systems; and, as in the high-strength steels, the evolution of hydrogen in aqueous surface reactions, which promotes hydrogen embrittlement. Nearly all service applications of materials in hostile environments involve large fluctuations of loading. As a result, in many applications, it is necessary to predict life on time scales well beyond those that can reasonably be covered by testing. A critical focus for research is on understanding crack growth and other forms of damage in conditions involving interactive fatigue-corrosion or fatigue-creep-corrosion. To a first approximation, pure fatigue crack growth is determined by the number of load cycles but not by their rate of occurrence. Interactive growth rates, on the other hand, are not accurately described as a simple sum of pure fatigue and sustained load rates. It will be essential for progress in developing reliable methods for life prediction that the physical basis of these interactions be clarified. The goal is to provide sound predictions of lifetimes extending, say, 10 to 30 years from short-time tests. In addition to modeling crack tip separation processes, studies in this area should include the modeling of transport, fluid flow, and electrochemical potential in cracks under steady and oscillating loading. Oxidation Research on oxidation should address the critical conditions for transitions between protective film formation and internal oxidation. An important issue is the healing of breaks in a protective scale, which may limit the high-temperature applications of intermetallics such as Ti3Al. Protective coatings are used for high-temperature oxidation resistance, and research is needed on the mechanisms and kinetics of the breakdown of diffusion barriers between alloys and such coatings. Transport-related limits to performance also arise with integrated circuits.
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials These occur as electrotransport, thermal diffusion, and strain-induced transport, and include diffusional phase transformations at ohmic contacts. Macromechanics of Crack Growth Other research of critical importance to the prediction of lifetime in service involves the macroscopic mechanics of crack growth and other types of damage, especially under conditions extending beyond those of linear elastic, quasi-static fracture mechanics. Major progress has been made in recent years on the elastic-plastic continuum mechanics of crack tip fields and on the characterization of resistance to quasi-static ductile crack growth. However, ductile crack tip response to complex load histories, as in low-cycle fatigue, as well as crack surface closure effects, remains poorly understood from the standpoint of predictive modeling. Another important area of continuing research is the unsteady dynamics of crack growth and crack arrest. This area includes the viscoplastic dynamics of cracking in ductile solids, a problem that is critical for understanding ductile-to-brittle transitions. It also includes problems such as the arrest of cracks nucleated in more brittle portions of structures, for example, in the radiation-embrittled region near the inner wall of a reactor pressure vessel. Other problems in the forefront of current research include subcritical crack growth in the high-temperature creep range. There, stress relaxations and redistributions following load transients, as well as the effects on the crack tip of transient creep and stress alterations induced by the crack motion itself, must be understood in order to provide a suitable framework for life prediction. Related issues arise in a form that is still virtually unconfronted in cyclic loading, for example, in creep-fatigue interactions. Distributed Damage While macroscopic fracture mechanics has developed according to the concept of a single dominant crack, there are circumstances when a more realistic picture is that of a broadly distributed damage zone. Here, damage refers to a multitude of microcracks or cavities such as occurs, for example, in creep rupture by broadly distributed cavitation. Also, failure of composites under cyclic fatigue loadings typically involves a large number of local cracks, whether in the matrix phase or as isolated fiber breaks, which degrade properties but join together as a throughgoing crack only in the final phase of fracture. A suitable mechanics of damage states needs to be developed, rooted in studies of the micromechanics of failure as discussed earlier, but suitable as a basis for engineering analysis of response to complex stress states and temperature histories in service applications. Situations intermediate to that of broadly distributed damage and of a single dominant crack
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Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials are frequently encountered. For example, many successfully designed composites and brittle materials such as concrete fracture under rising load with an extensive damage zone at the crack tip. Typically, the macrocrack surfaces remain bridged by incompletely pulled out fibers, or by frictionally restrained aggregate particles, and this provides a significant contribution to material toughness. At present, empirical relations are used in life prediction studies to describe the rates of growth of cracks or accumulation of damage in terms of load history, temperature, and environment. The complexity of these problems dictates that such empirical procedures will remain prominently in use, but an achievable goal for research is the provision of a more enlightened basis for them. For example, research in macroscopic fracture mechanics in the nonlinear range has identified parameters that, in certain defined circumstances, characterize the severity of deformation near the crack tip and hence serve as the loading variable in terms of which crack growth rate should be characterized in empirical studies. Current approaches to ductile tearingmode cracking and elevated-temperature creep crack growth provide examples. Also, simple theoretical models of creep deformation and cavity growth, over a broad range of stresses and temperatures, lead to maps of deformation and fracture mechanisms. These maps subdivide the stress and temperature plane into regimes in which one mechanism or another (e.g., diffusive creep versus dislocation creep, diffusive cavity growth versus plastically assisted cavity growth) is dominant. The map concept provides a caution that empirically based relations will, likewise, have limited domains in which they accurately describe deformation, and the maps themselves suggest where to look for those limits. Nondestructive Evaluation The aim of fracture mechanics is to predict the growth to failure of cracks or other damage in materials. To be effective for predicting lifetimes, such work should go hand in hand with nondestructive evaluation of materials and structures for defects. Here, research challenges occur in sensor technology for making the necessary measurements, sometimes under hostile conditions and with limited access. Also, research is needed on the quantification of nondestructive evaluation signals so that the information about the state of the material provided by such techniques can be used with confidence in estimating lifetimes.
Representative terms from entire chapter: