Macroscopic cracks in bulk silicon are generally considered to be immune to fatigue. Here, evidence for pronounced fracture-related fatigue damage in cyclic contact loading of (001) monocrystalline silicon with hard spheres of millimeter-scale radius is presented. The periodic indentation field generates ring cracks around the contact, which proliferate with continued cycling. Copious debris in the form of slabs and particulates is ejected from within the crack walls onto the specimen surface. Continued ejection leads ultimately to large-scale surface removal. The fatigue damage progressively degrades the material strength, more rapidly at higher contact load. Implications concerning the function of silicon devices, including microelectro-mechanical systems, will be briefly discussed.

A study is made of top-surface cracks induced in brittle trilayers by cyclic indentation with a hard sphere in water. The trilayers consist of an external brittle layer (veneer) fused to an inner stiff and hard ceramic support layer (core), in turn adhesively bonded to a thick compliant base (substrate). These structures are meant to simulate essential aspects of dental crowns, but their applicability extends to a range of engineering coating systems. The study follows on from like studies of brittle monoliths and brittle-plate/soft-substrate bilayers. Competing fracture modes in the outer brittle layer remain the same as before: outer and inner cone cracks and radial cracks, all of which form in the near-contact zone and propagate downward toward the veneer/core interface. Inner cone cracks and radial cracks are especially dangerous because of their relatively steep descent through the outer layer as well as enhanced susceptibility to mechanical fatigue. Experiments are conducted on model glass/alumina/polycarbonate systems, using video cameras to record the fracture evolution in the transparent glass layer in situ during testing. Each fracture mode can lead to failure, depending on the maximum contact load and other variables (plate thickness, sphere radius). The potentially beneficial role of a stiff intervening core is discussed, along with potentially deleterious side effects of residual thermal-expansion-mismatch stresses.

A preceding study of the competition between fracture modes in monolithic brittle materials in cyclic loading with curved indenters in liquid environments is here extended to brittle layers on compliant substrates. The fracture modes include outer and inner cone cracks and radial cracks that initiate from the near-contact zone and penetrate downward. Outer cone cracks are driven by stresses from superposed Hertzian and plate flexure fields; inner cone cracks also grow within these fields but are augmented by mechanical driving forces from hydraulic pumping into the crack fissures. Radial cracks are augmented by mechanical driving forces from developing quasiplasticity zones beneath the indenter. Basically, the crack-growth rates are governed by a crack velocity relation. However, the hydraulic and quasiplastic mechanical forces can cumulate in intensity with each cycle, strongly enhancing fatigue. Plate flexure generates compressive stresses at the top surface of the brittle layer, somewhat inhibiting the initiation, and tensile stresses at the lower surface, strongly enhancing the far-field propagation. The tensile stresses promote instability in the crack propagation, resulting in through-thickness penetration (failure). Experiments on a model bilayer system consisting of glass plates bonded to thick polycarbonate bases are presented as an illustrative case study. In situ observations of the crack evolution from initial growth to failure reveal that each fracture mode can dominate under certain test conditions, depending on plate thickness, maximum load, and sphere radius. Implications concerning the failure of practical layer systems, notably dental crowns, are discussed.

A study was made of radial crack evolution in curved brittle layers on compliant support substrates. Three-dimensional boundary element analysis was used to compute the stepwise growth of radial cracks that initiate at the bottom surfaces of glass on polymeric support layers, from initiation to final failure. The algorithm calculates reconstituted displacement fields in the near-tip region of the extending cracks, enabling direct evaluation of stress-intensity factors. Available experimental data on the same material systems with prescribed surface curvatures were used to validate the essential features of the predicted crack evolution, particularly the stability conditions prior to ultimate failure. It was shown that the critical loads to failure diminish with increasing surface curvature. Generalization of the ensuing fracture mechanics to include alternative brittle-layer/polymer-substrate systems enabled an explicit expression for the critical load to failure in terms of material properties and layer thicknesses. Implications concerning practical layer systems, particularly dental crowns, are briefly discussed.

The competition between fracture modes in monolithic brittle materials loaded in cyclic contact in aqueous environments with curved indenters is examined. Three main modes are identified: conventional outer cone cracks, which form outside the maximum contact; inner cone cracks, which form within the contact; and median–radial cracking, which form below the contact. Relations describing short-crack initiation and long-crack propagation stages as a function of number of cycles, based on slow crack growth within the Hertzian field, are presented. Superposed mechanical driving forces—hydraulic pumping in the case of inner cone cracks and quasiplasticity in the case of median–radials—are recognized as critically important modifying elements in the initial and intermediate crack growth. Ultimately, at large numbers of cycles, the cracks enter the far field and tend asymptotically to a simple, common relation for center-loaded pennylike configurations driven by slow crack growth. Crack growth data illustrating each mode are obtained for thick soda-lime glass plates indented with tungsten carbide spheres in cyclic loading in water, for a range of maximum contact loads and sphere radii. Generally in the glass, outer cone cracks form first but are subsequently outgrown in depth as cycling proceeds by inner cones and, especially, radial cracks. The latter two crack types are considered especially dangerous in biomechanical applications (dental crowns, hip replacements) where ceramic layers of finite thickness are used as load-bearing components. The roles of test variables (contact load, sphere radius) and material properties (hardness, modulus, toughness) in determining the relative importance of each fracture mode are discussed.

Strength properties of silicon substrates containing dense oxide and nitride surface films are investigated using nanoindentations to introduce small flaws of predetermined scale. The indentation flaws provide favored sites for failure in subsequent flexure loading, even in the subthreshold region for indentations without visible corner cracking, confirming that microflaws generated within the indentation zone act as effective crack sources in the substrate. Deposition of the oxide films increases the strength while the nitride films diminish it at any given indentation load. The strength shifts are attributed primarily to the presence of residual compressive stress in the oxide, tensile stress in the nitride. A fracture mechanics formulation based on a previous analysis for monolithic substrates is here adapted to allow for a superposed crack closing or opening stress-intensity factor term associated with the residual stresses. Allowance is also made in the mechanics for the influence of the film on effective hardness and modulus of the substrate. The formulation accounts for the basic strength shifts and enables evaluation of the magnitude of the residual stresses. The results quantify the susceptibility of basic device materials to damage from small-scale contacts and impacts.

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

The fundamentally changing nature of fracture in brittle coatings on compliant substrates with diminishing coating thickness is examined. Attention is focused on cracking induced by concentrated loading with a spherical indenter at the top surface. It is shown that the fracture mode undergoes transitions, from top-surface ring cracking around the contact (“thick-coating” region) to bottom-surface radial cracking at the lower ceramic surface (“intermediate” region) and, finally, back to surface ring cracking (“thin-coating” region). These transitions reflect a progressively changing stress field in the layer structures and highlight the differences in failure mechanism that may be anticipated at the large- and small-scale levels. Simple fracture relations are derived for each mode, expressing critical loads in terms of coating thickness relative to contact or sphere radius, coating strength and coating/substrate modulus mismatch. Data from finite element simulations and contact experiments on model ceramic/polymer bilayer systems are used to validate the basic elements of the analytical relations and to quantify deviations. Implications of the transitional behavior in relation to the strength of brittle coating/film systems are discussed.

Silicon is a principal material in submicrometer-scale devices. Components in such devices are subject to intense local stress concentrations from nanoscale contacts during function. Questions arise as to the fundamental nature and extent of any strength-degrading damage incurred at such contacts on otherwise pristine surfaces. Here, a simple bilayer test procedure is adapted to probe the strengths of selected areas of silicon surfaces after nanoindentation with a Berkovich diamond. Analogous tests on silicate glass surfaces are used as a control. The strengths increase with diminishing contact penetration in both materials, even below thresholds for visible cracking at the impression corners. However, the strength levels in the subthreshold region are much lower in the silicon, indicating exceptionally high brittleness and vulnerability to small-scale damage in this material. The results have important implications in the design of devices with silicon components.

A perspective on the issue of scale in the fracture and deformation properties of ordinarily brittle covalent–ionic solids (ceramics) is presented. Characteristic scaling dimensions for nanomechanical properties of this class of solids are identified—specimen size or layer thickness, microstructural scale, and contact dimension. Transitions in mechanical damage processes occur as the characteristic dimensions diminish from the macroscale to the submicroscale. Such transitions generally preclude unconditional extrapolations of macroscopic-scale fracture and deformation laws into the nanomechanics region. Strength of brittle solids tends to increase while toughness tends to decrease as the scaling dimensions diminish. The nature of flaws that control strength in the submicroscale region also undergoes fundamental changes—even flaws without well-developed microcracks can be deleterious to strength.

The role of a compliant adhesive interlayer in determining critical conditions for radial fracture at the undersurfaces of brittle coatings bonded to substrates of dissimilar materials is investigated. Semi-empirical relations for the critical loads are derived by treating the adhesive as part of an effective substrate, thereby reducing the problem to that of a bilayer. A finite-element analysis of a model silicon/epoxy/glass system is used to evaluate adjustable parameters in the analytical relations. In situ experimental observations of crack initiation on the same material system are used to verify these relations. The critical loads depend sensitively on the adhesive thickness and modulus. Delamination at the interface in poorly bonded specimens greatly reduces the critical loads. This analysis affords a basis for predicting the prospective fracture resistance of brittle coatings joined by adhesives.

In this article, we review recent advances in the understanding and analysis of damage initiation and evolution in laminate structures with brittle outerlayers and compliant sublayers in concentrated loading. The relevance of such damage to lifetime-limiting failures of engineering and biomechanical layer systems is emphasized. We describe the results of contact studies on monolayer, bilayer, trilayer, and multilayer test specimens that enable simple elucidation of fundamental damage mechanics and yet simulate essential function in a wide range of practical structures. Damage processes are observed using post mortem (“bonded-interface”) sectioning and direct in situ viewing during loading. The observations reveal a competition between damage modes in the brittle outerlayers—cone cracks or quasiplasticity at the top (near-contact) surfaces and laterally extending radial cracks at the lower surfaces. In metal or polymeric support layers, yield or viscoelasticity can become limiting factors. Analytical relations for the critical loads to initiate each damage mode are presented in terms of key system variables: geometrical (layer thickness and indenter radius); material (elastic modulus, strength and toughness of brittle components, hardness of deformable components). Such relations provide a sound physical basis for the design of brittle layer systems with optimal damage thresholds. Other elements of the damage process—damage evolution to failure, crack kinetics (and fatigue), flaw statistics, and complex (tangential) loading—are also considered.

Fracture and deformation in model brittle-outerlayer/metal-core/polymer-substrate trilayer systems in concentrated loading are studied. Model systems for experimental study are fabricated from glass microscope slides glued with epoxy adhesive onto steel and aluminum sheets, and the resulting laminates glued onto polycarbonate substrate bases. Critical loads to initiate two basic fracture modes in the glass layers—cone cracks at the top surfaces and radial cracks at the undersurfaces—are measured as a function of metal thickness by in situ observation through the glass side walls. Finite element modeling (FEM) is used to quantify these competing fracture modes. The more damaging radial fracture mode is attributed to flexure of the glass layers on soft underlayers. Although much of this flexure can be eliminated by removing the soft adhesive interlayer between glass and metal, yield in the metal limits the potential increases in critical load for radial cracking. Trilayer systems consisting of porcelain fused to Co-, Pd- and Au-alloy core support layers relevant to dental crowns are then analyzed by FEM. The hardness (especially) and elastic modulus of the metal are identified as the primary controlling material parameters, with modulus and strength of the brittle layer as supplemental parameters. Guidelines for improving metal-based crownlike layer structures are thereby developed via optimization of metal properties and relative layer thicknesses.

A preceding study of contact damage in a bilayer system consisting of a porcelain coating on a stiff Pd-alloy substrate is here expanded to investigate the role of substrate modulus and hardness. Bilayers are made by fusing the same dental porcelain onto Co-, Pd-, and Au-alloy metal bases. Indentations are made on the porcelain surfaces using spheres of radii 2.38 and 3.98 mm. Critical loads to initiate cone fracture at the top surface of the porcelain and yield in the substrate below the contact are measured as a function of porcelain thickness. Radial cracks form at the lower surface of the coating once the substrate yield is well developed. By virtue of its controlling role in the metal yield process, substrate hardness is revealed to be a key material parameter—substrate modulus plays a secondary role. A simple elasticitybased analysis for predetermining critical loads for a given brittle/plastic bilayer system is presented.

Contact-induced fracture modes in trilayers consisting of a brittle bilayer coating on a soft substrate were investigated. Experiments were performed on model transparent glass/sapphire/polycarbonate structures bonded with epoxy adhesive, to enable in situ observation during the contact. Individual layer surfaces were preferentially abraded to introduce uniform flaw states and so allowed each crack type to be studied separately and controllably. Fracture occurred by cone cracking at the glass top surface or by radial cracking at the glass or sapphire bottom surfaces. Critical loads for each crack type were measured, for fixed glass thickness and several specified sapphire thicknesses. Finite element modeling (FEM) was used to evaluate the critical load data for radial cracking, using as essential input material parameters evaluated from characterization tests on constituent materials and supplemental glass/polymer and sapphirse/polymer bilayer structures. The FEM calculations demonstrated pronounced stress transfer from the applied contact to the underlying sapphire layer, explaining a tendency for preferred fracture of this relatively stiff component. Factors affecting the design of optimal trilayer structures for maximum fracture resistance of practical layer systems were considered.

The role of elastic mismatch in determining critical conditions for indentation fracture in brittle coatings on substrates of unlike modulus was investigated. A model transparent trilayer system, consisting of a glass coating layer bonded to a thick substrate of different glass or polymer by a thin layer of epoxy adhesive, facilitated in situ observations of crack initiation and propagation. A tungsten carbide sphere was used to load the layer system. Abrasion flaws were introduced into the top and bottom glass coating surfaces to control the flaw populations and to predetermine the origins of fracture: cone cracks occurred at abraded top surfaces, radial cracks at abraded bottom surfaces. Analytical relations for the critical loads are presented for each crack system in terms of elastic modulus mismatch, indenter and coating dimensions, and material fracture parameters. Implications concerning materials selection for resistance to crack initiation are considered.

An analysis is made of contact damage in brittle coatings on metal substrates, using a case study of a dental porcelain coating of thickness between 0.1 and 1 mm fused onto a Pd alloy base, with spherical indenter of radii 2.38 and 3.98 mm. At large coating thicknesses (>300 μm), the first damage takes the form of surface-initiated transverse cone cracks outside the contact. At small coating thicknesses (<300 μm), the first damage occurs as yield in the substrate, with attendant formation of subsurface transverse median cracks in the coating. At high loads and thin coatings, both forms of transverse cracking occur, along with subsequent delamination of the ceramic/metal interface, signalling impending failure. Conditions for avoiding such transverse cracking are considered in terms of minimum coating thicknesses and maximum sustainable contact loads. General implications concerning the design of brittle coating systems for optimum damage resistance are considered, with special reference to dental crowns.

A thermal wave methodology for monitoring the thermal conduction of ceramic coatings with accumulating mechanical damage is described. Tests are conducted on a model alumina coating containing laminar defect intralayers. Controlled subsurface damage introduced with a spherical indenter is observed using a presectioned specimen. Microcrack damage accumulates progressively with increasing contact load and number of cycles. Associated changes in thermal diffusivity, specifically in the through-thickness direction, are imaged and quantified point-by-point using laser-generated thermal waves. The effective thermal resistance of the coating increases with crack density, up to the point of failure.

Thermal waves are used to image damage accumulation digitally beneath Hertzian contacts in ceramics. Alumina ceramics over a range of grain size 3–48 μm are used in a case study. The nature of the images changes with increasing alumina grain size, reflecting a transition in damage mode from well-defined cone fracture in the finer-grain materials to distributed subsurface microfracture in the coarser-grain materials. Quantitative determinations of microcrack densities are evaluated in the latter case by deconvoluting thermal diffusivities from the image data. These determinations confirm the grain-size dependence of degree of damage predicted by fracture mechanics models. Potential advantages and disadvantages of thermal waves as a route to damage characterization in ceramic systems are discussed.

A new philosophy for tailoring layer composites for damage resistance is developed, specifically for alumina-based ceramics. The underlying key to the approach is microstructural control in the adjacent layers, alternating a traditional homogeneous fine-grain alumina (layer A) for hardness and wear resistance with a heterogeneous alumina : calcium-hexaluminate composite (layer C) for toughness and crack dispersion, with strong bonding between the interlayers. Two trilayer sequences, ACA and CAC, are investigated. Hertzian indentation tests are used to demonstrate the capacity of the trilayers to absorb damage. In the constituent materials, the indentation responses are fundamentally different: ideally brittle in material A, with classical cone cracking outside the contact; quasi-plastic in material C, with distributed microdamage beneath the contact. In the ACA laminates, shallow cone cracks form in the outer A layer, together with a partial microdamage zone in the inner C layer. A feature of the cone cracking is that it is substantially shallower than in the bulk A specimens and does not penetrate to the underlayer, even when the applied load is increased. This indicates that the subsurface microdamage absorbs significant energy from the applied loads, and thereby “shields” the surface cone crack. Comparative tests on CAC laminates show a constrained microdamage zone in the outer C layer, with no cone crack, again indicating some kind of shielding. Importantly, interlayer delamination plays no role in either layer configuration; the mechanism of damage control is by crack suppression rather than by deflection. Implications for the design of synergistic microstructures for damage-resistant laminates are considered.