R Curves from Compliance and Optical Crack-Length Measurements

High-toughness, high-strength ceramics, such as self-reinforced Si3N4, derive their superior mechanical properties from microstructures that promote very steeply rising R curves. Furthermore, accurately evaluating the R curve at the earliest stages of crack growth is necessary for correctly understanding, and predicting, the mechanical behavior. Compliance- and optical-based methods for evaluating the crack length, and R curve, at the early stages of crack extension from machined notches are discussed. The earliest stages of crack growth are missed during measurements of the crack length by optical observations due to the nonuniform extension of the crack front during initial crack extension. The most accurate method of evaluating the crack length over all amounts of crack extension is from compliance measurements analyzed by solving a system of equations that incorporates both the effects of the notch and the changes in compliance with the development of bridging tractions. Such a method is computationally expensive, but for materials with steeply rising R curves, simply applying the linear-elastic compliance evaluation, which only accounts for the notch, but not the bridging tractions, gives a result within about 1%. At longer crack extensions, such an approximation method will incur significant errors; however, at this stage, optical measurements can provide accurate assessments of crack length and enable an accurate assessment of the R curve.