In this Part I of a two-part study of Hertzian indentation in silicon nitride we characterize irreversible contact damage as a function of microstructure. Three controlled silicon nitride microstructures are examined, representing a progression toward greater long-crack toughness: fine (F), bimodal with predominantly equiaxed ␣ grains; medium (M), bimodal with mostly  grains of intermediate size; and coarse (C), with almost exclusively elongated  grains. An effect of increasing the microstructural heterogeneity in this sequence is to suppress ring cracking around the indenter, ultimately to a degree beyond that expected from increased toughness alone. Along with the crack suppression is a parallel tendency to enhanced damage accumulation beneath the indenter, such that the contact in the coarsest microstructure is predominantly quasi-plastic. The characterization of damage includes the following: determination of indentation stress-strain curves, to measure the level of quasi-plasticity; measurement of threshold loads for the initiation of ring cracking and subsurface yield, to quantify the competing damage processes; and measurement of characteristic dimensions of the ensuing cracks and deformation zones in their well-developed stages. These quantitative results are considered in terms of formal contact mechanics, along with finite element modeling to generate the essentially elastic-plastic fields in the different silicon nitride structures. This contact mechanics description serves also as the basis for subsequent analysis of strength degradation in Part II. Implications concerning microstructural design of silicon nitride ceramics for specific applications, notably bearings, are considered.
Natural teeth (enamel/dentin) and most restorations are essentially layered structures. This study examines the hypothesis that coating thickness and coating/substrate mismatch are key factors in the determination of contact-induced damage in clinically relevant bilayer composites. Accordingly, we study crack patterns in two model "coating/substrate" bilayer systems conceived to simulate crown and tooth structures, at opposite extremes of elastic/plastic mismatch: porcelain on glass-infiltrated alumina ("soft/hard"); and glass-ceramic on resin composite ("hard/soft"). Hertzian contacts are used to investigate the evolution of fracture damage in the coating layers, as functions of contact load and coating thickness. The crack patterns differ radically in the two bilayer systems: In the porcelain coatings, cone cracks initiate at the coating top surface; in the glass-ceramic coatings, cone cracks again initiate at the top surface, but additional, upward-extending transverse cracks initiate at the internal coating/substrate interface, with the latter dominant. The substrate is thereby shown to have a profound influence on the damage evolution to ultimate failure in the bilayer systems. However, the cracks are highly stabilized in both systems, with wide ranges between the loads to initiate first cracking and to cause final failure, implying damage-tolerant structures. Finite element modeling is used to evaluate the tensile stresses responsible for the different crack types. The clinical relevance of these observations is considered.
A model of strength degradation for ceramics subject to damage from contact with hard spheres is developed. Primary attention is focused on tough ceramics with heterogeneous microstructures which deform in a quasi‐plastic mode. Brief consideration is also given to ideally brittle ceramics which form classical ring cracks, as a comparative baseline. Strength vs indentation load data from two microstructurally controlled ceramics, silicon nitride and a micaceous glass‐ceramic, illustrate distinctive strength degradation responses: in fine‐grain (F) form, ideally brittle failure from ring cracks, with abrupt strength loss at the critical load for crack initiation followed by a slow falloff at increasing load; in coarse‐grain (C) form, failure from within the quasi‐plastic zone, with continuous strength loss beyond a load well above that for the onset of yield, and with even slower falloff. Failure in the latter materials occurs from contact‐induced microdamage flaws with two essential elements: an inner closed shear crack with frictional sliding faces (“shear fault”), which forms within the confining compression–shear contact field; an outer annular, kinked crack that initiates at the fault edges (“wing crack”), and that extends in tensile local mode. The critical fault–crack is modeled as a virtual crack, with the residual field from the inner fault stabilizing the net driving force on the outer wing crack during ensuing tensile loading. Finite element modeling is used to evaluate the nonlinear elastic–plastic contact fields, and to provide a relationship between residual shear fault stress and contact load. The model accounts for the essential qualitative and quantitative features of the strength–load data, with provision for catastrophic degradation at high fault densities and extreme loads by microcrack coalescence. The model also contains the ingredients for analysis of contact fatigue, via attrition of the frictional tractions on the residual fault.
An analysis of transverse cracks induced in brittle coatings on soft substrates by spherical indenters is developed. The transverse cracks are essentially axisymmetric and geometrically conelike, with variant forms dependent on the location of initiation: outer cracks that initiate at the top surface outside the contact and propagate downward; inner cracks that initiate at the coating/substrate interface beneath the contact and propagate upward; intermediate cracks that initiate within the coating and propagate in both directions. Bilayers consisting of hard silicon nitride (coating) on a composite underlayer of silicon nitride with boron nitride platelets (substrate), with strong interfacial bonding to minimize delamination, are used as a model test system for Hertzian testing. Test variables investigated are contact load, coating/substrate elastic-plastic mismatch (controlled by substrate boron nitride content), and coating thickness. Initiation of the transverse coating cracks occurs at lower critical loads, and shifts from the surface to the interface, with increasing elastic-plastic mismatch and decreasing coating thickness. This shift is accompanied by increasing quasi-plasticity in the substrate. Once initiated, the cracks pop in and arrest within the coating, becoming highly stabilized and insensitive to further increases in contact load, or even to coating toughness. A finite element analysis of the stress fields in the loaded layer systems enables a direct correlation between the damage patterns and the stress distributions: between the transverse cracks and the tensile (and compressive) stresses; and between the subsurface yield zones and the shear stresses. Implications of these conclusions concerning the design of coating systems for damage tolerance are discussed.
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