Elastic/Plastic Indentation Damage in Ceramics: The Median/Radial Crack System

Abstract

A theory for describing the evolution of the medianhadial crack system in the far field of sharp-indenter contacts is developed. Analysis is based on a model in which the complex elastic/plastic field beneath the indenter is resolved into elastic and residual components. The elastic component, being reversible, assumes a secondary role in the fracture process: although it does enhance downward (median) extension during the loading halfcycle, it suppresses surface (radial) extension to the extent that significant growth continues during unloading. The residual component accordingly provides the primary driving force for the crack configuration in the final stages of evolution, where the crack tends to near-half-penny geometry. On the hypothesis that the origin of the irreversible field lies in the accommodation of an expanding plastic hardness impression by the surrounding elastic matrix, the ensuing fracture mechanics relations for equilibrium crack growth are found to involve the ratio hardness-to-modulus as well as toughness. Observations of crack evolution in soda-lime glass provide a suitable calibration of indentation coefficients in these relations. The calibrated equations are then demonstrated to be capable of predicting the widely variable median and radial growth characteristics observed in other ceramic materials. The theory is shown to have a vital bearing on important practical areas of ceramics evaluation, including toughness and strength.

Solid particle erosion mechanisms of protective coatings for aerospace applications

“…One such relationship is the H/E ratio which has been shown by Leyland and Matthews [19] to be descriptive of several mechanical contact situations related to tribological processes. In fact, it can be found in several of the models proposed to calculate fracture toughness by sharp probe indentation, most notably in the work by Lawn and coworkers [20][21][22]. It has also been shown to be an indicator of surface resistance to sliding wear [23,24] of coated surfaces, and to be an important predictor of the amount of energy dissipated through plastic deformation during indentation [25,26].…”

“…[71] elaborated on this approach and developed analytical expressions that predict these transitions in material behavior. They based their work on the analytical indentation models proposed by Wiederhorn and Lawn [72] for cone cracks, Lawn et al [20] for the median/radial crack system and Marshall et al [21] for the lateral crack system. They expressed the transition thresholds as critical velocities (V crit ) for a given particle size at which transition will occur.…”

“…We then evaluated fracture toughness using the equation developed by Lawn et al [20] and Anstis et al [22]:…”

Dependence of crystalline, ferroelectric and fracture toughness on annealing in Pb(Zr0.52Ti0.48)O3 thin films deposited by metal organic decomposition

“…Using the equation given by Lawn et al 12 for the fracture toughness of brittle materials, the fracture toughness of the ceramic thin film/coating investigated in the present study may be given as follows: (1) where E f is the elastic modulus of the thin film, H f hardness of the thin film, W the normal load and C r the radial crack length on the surface of thin film. Generally, electric charges are produced during the indentation of ferroelectric thin film and consequently the fracture toughness of PZT thin film is affected.…”

“…The variation of remanent polarization and coercive field with annealing temperature was analyzed in P-V hysteresis loops obtained by RT66A standard ferroelectric analyzer. The crack patterns of PZT thin films in indentation in relation to annealing temperature and the indentation load were examined and the fracture toughness of PZT thin film was measured by the indentation model proposed by Lawn et al [12][13] . The fracture pattern diagram is described as a function of the indentation load and the annealing temperature.…”