Edwin R. Fuller

Equilibrium penny-like cracks in indentation fracture

A study is made of the mechanics of two basic types of indentation fracture, cone cracks (“blunt” indenters) and median cracks (“sharp” indenters). The common feature which forms the central theme in this work is that both crack types, in their well-developed stages of growth, may be regarded as essentially “penny-like”. On this basis a universal similarity relation is derived for equilibrium crack dimension as a function of indentation load. Experimental measurements confirm the general form of this relation. A more detailed fracture mechanics analysis is then given, to account for additional, contact variables evident in the data. Notwithstanding certain analytical limitations, the study serves as a useful basis for investigating a wide range of contact-related problems, both fundamental and applied, in brittle solids.

Measurement of thin-layer surface stresses by indentation fracture

A model is developed for evaluating stresses in the surfaces of brittle materials from changes in indentation crack dimensions. The underlying basis of the model is a stress intensity formulation incorporating the solution for a penny-like crack system subjected to a constant stress over a relatively thin surface layer. Results from a previous study of surface damage in proton-irradiated glass are used to illustrate the scope of the method. The indentation fracture analysis also provides some fresh insight into the susceptibility of brittle surfaces to spontaneous cracking. Implications of the study concerning the potential effect of surface stresses on mechanical properties, such as strength, erosion and wear, are briefly discussed.

Residual stresses in thermal barrier coatings: effects of interface asperity curvature:height and oxide thickness

The effects of curvature and height of the interface asperity on residual thermal stresses in a plasma-sprayed thermal barrier coating were numerically simulated. In the tip region of a convex asperity, the residual stress normal to the interface, sy is tensile in the ceramic top coat and increases with both curvature and height of the asperity. However, this residual tensile stress is lower for a periodic array of asperities than for an isolated asperity. The effects of thickness of the thermally grown oxide at the top coat‐bond coat interface on residual thermal stresses were also numerically simulated. In the tip region of a convex asperity, sy in the ceramic top coat is tensile for a thin oxide but becomes compressive for a thick oxide. In the tip region of a concave asperity, sy in the ceramic top coat is compressive for a thin oxide and becomes less compressive for a thick oxide. The physical meaning of the above trend was qualitatively interpreted using an analytical model of three concentric circles. Published by Elsevier Science S.A.

Micro-mechanical aspects of asperity-controlled friction in fiber-toughened ceramic composites

The role of friction as an energy dissipation mechanism is an important aspect of fiber toughening of ceramic materials. The toughening contribution from the work done during fiber/matrix debonding is usually much smaller than that dissipated during frictional sliding of the fiber. The longer the total sliding distance, the more significant the frictional contribution. Friction in most theoretical treatments of composite toughening is characterized by Coulombic friction between the sliding fiber and matrix without regard to the microstructural aspects of interface. Recent microscopical observations indicate the importance of roughness on frictional behavior of the interfaces. In this paper, the authors confirm the empirical observations and address a few fundamental aspects of the role of asperities of developing a micro-mechanical model for interfacial friction.

Damage evolution during microcracking of brittle solids

Microcracking due to thermal expansion and elastic anisotropy is examined via computer simulations with a microstructural-based finite element model. Random polycrystalline microstructures are generated via Monte Carlo Potts-model simulations. Microcrack formation and propagation due to thermal expansion anisotropy is investigated in these microstructures using a Griffith-type failure criterion in a microstructural-based finite element model called OOF. Effects of the grain size distribution on the accumulation of microcrack damage, as well as on the threshold for microcrack initiation, are analysed. Damage evolution is rationalised by statistical considerations, i.e. damage accumulation is correlated with the statistical distributions of microstructural parameters.

Numerical methods for computing interfacial mean curvature

A procedure is described for computing the mean curvature along condensed phase interfaces in two or three dimensions, without knowledge of the spatial derivatives of the interface. For any point P on the interface, the method consists of computing the portion of volume enclosed by a small template sphere, centered on P, that lies on one side of the interface. That portion of the template volume is shown to be linear in the mean curvature of the surface, relative to the phase lying on the opposite side of the interface, to within terms that can usually be made negligible. An analogous procedure is described in two dimensions. Application of the procedure to compute the mean curvature along a digitized surface is demonstrated. A burning algorithm can be included to improve computational accuracy for interfaces having sharp curvature fluctuations. A minor extension of the method allows computation of the orientation of an interfacial element relative to a fixed reference frame.

Analytical and numerical analyses for two-dimensional stress transfer

Abstract Both analytical modeling and numerical simulations were performed to analyze the stress transfer in platelet-reinforced composites in a two-dimensional sense. In the two-dimensional model, an embedded elongated plate bonded to a matrix along its long edges was considered. The system was subjected to both tensile loading parallel to the plate’s long edges and residual thermal stresses. The ends of the plate can be debonded from or bonded to the matrix during loading, and both cases were considered in the analysis. Good agreement was obtained between the present analytical and numerical solutions. However, better agreement between analytical and numerical models was obtained for the case of bonded ends than for debonded ends.

Atomic modelling of chemical interactions at crack tips

Abstract A simple atomic model for incorporating the effects of chemically-assisted fracture is described. Development of the model is in two parts, which can be formulated independently: lt]o li](i) the crack itself is represented by two elastic semi-infinte chains of atoms, linked transversely by stretchable bonds (quasi-one-dimensional representation); li](ii) the chemical interaction, which takes place at the crack tip atoms, is represented by a classical reaction between two diatomic molecules. While clearly oversimplistic in relation to real structural materials, the approach offers insight into the actual mechanisms of crack-tip chemistry. In particular, the factors which contribute to the generalised force on the crack-tip bond (viz. the applied load, the lattice, and the cohesive force itself) are clearly identified, and conclusions may be drawn in a quite general way about the prospective response of alternative crack systems. The mechanisms of chemically-assisted crack growth under either equilibrium or kinetic conditions are contained naturally in the formalism. Although explicitly set up along the lines of an ideally brittle crystalline cleavage, the model may well be extended to traditionally more complex crack configurations, e.g. as in glasses and metals.

Fracture of a textured anisotropic ceramic

The role of crystallographic texture in determining the fracture behavior of a highly anisotropic ceramic, iron titanate, has been examined. By exploiting the anisotropy in its single crystal magnetic susceptibility, crystallographically textured and untextured iron titanate microstructures were formed by gelcasting in the presence and absence of a strong magnetic field, respectively. The magnetic field-assisted processing imparted a fiber-like texture to the processed ceramic material in which the crystallographic b-axes of the grains aligned parallel to the applied field. Triaxial residual stress and lattice parameter measurements showed that both the untextured and textured materials had undergone significant stress–relaxation, presumably due to spontaneous microcracking. Further, ‘aggregates’ of non-textured material were discovered within textured material that led to a population of meso-scale cracks (meso-cracks) in the microstructure oriented normal to the direction of alignment. Both crack populations were examined using a finite element simulation and confirmed by small angle neutron scattering measurements, and for meso-cracks, by X-ray tomography. Bend strength and R-curve behavior were evaluated as a function of texture and orientation in the magnetically processed materials. Strengths remained within 20% of that of the control material, except for one orientation, for which the strength decreased with increasing degree of texture due to favorably oriented meso-cracks. The R-curve behavior was highly anisotropic, with the peak fracture toughness of the magnetically processed material ranging from approximately equal to 2.5 times that of the control material. Additionally, the peak fracture toughness of each orientation increased with the degree of texture. Anisotropic fracture properties were related to interactions between the test crack and the population of meso-cracks.

Surface-Roughness Induced Residual Stresses in Thermal Barrier Coatings: Computer Simulations

Adherence of plasma-sprayed thermal barrier coatings (TBCs) during deposition is strongly dependent on a rough metallic bond-coat surface topology. However, the resultant interfacial asperities modify the residual stresses that develop in the coating system due to thermal expansion differences, and other misfit strains, and generate stresses that can induce progressive fracture and eventual spallation of the ceramic coating. For a flat interface, the principal residual stress is parallel to the interface, as the stress normal to the interface is zero. However, the residual stress normal to the interface becomes non-zero, when the interface has the required interlocking morphology. In the present study, an actual microstructure of a plasma-sprayed TBC system was numerically simulated and analyzed with a recently developed, object-oriented finite element analysis program, OOF, to give an estimate of the localized residual stresses in a TBC system. Additionally, model TBC microstructures were examined to evaluate the manner in which the topology of interfacial asperities influences residual stresses. Results are present for several scenarios of modifying interfacial roughness.