R -curve measurements in PSZ ceramics
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I. INTRODUCTION
The large values of fracture toughness quoted for transformation-toughened ceramics such as MgOdoped zirconia (PSZ) are pertinent at crack-size scales the order of 1 mm or greater.1 Toughness values that correspond to shorter cracks can be much lower as a consequence of /?-curve behavior, wherein toughness decreases as crack-size scale decreases.1"3 This has significant implication for structural design and applications using these ceramics.4"6 Measurement of i?-curves in ceramic materials, particularly in systems such as transformation-toughened zirconia, has become an important part of their mechanical-property characterization. In the work reported here, indentation-bend methods have been applied to this problem for PSZ. i?-curve behavior in PSZ has been measured using conventional techniques, for example, compliance of a notched beam during loading-unloading cycles.7 The instantaneous load and crack length are used to compute the fracture toughness pertaining to a given crack size. Marshall6 obtained an i?-curve using direct measurements of crack size for "intrinsic" cracks pre-existing or self-nucleated on the tensile surface during bending of a polished bar. While these techniques can determine i?-curves, they are not simple in terms of the experimental procedure or equipment needed. The difficulties in manually loading and unloading the beam are discussed in Ref. 7. Furthermore, calibration is required to generate the compliance-crack size relations. In addition, the precracks are nucleated from a notch, the effect of which on the i?-curve is not well understood. The direct measurement of intrinsic surface cracks requires a sophisticated optical system for in situ observation during bend-loading. A recent study by Marshall and Swain8 compared incurves obtained from surface-crack measurements and the compliance technique for PSZ. Systematic differences were noted, with the .R-curve from the compliance tests being steeper and above that for the direct 1490
http://journals.cambridge.org
J. Mater. Res., Vol. 5, No. 7, Jul 1990
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surface-crack measurements. The difference was pronounced at the shorter crack sizes, with the difference decreasing with increasing crack size. This was attributed to the localized transformation of favorably oriented grains on the tensile face of the bend bar. It was argued that the dilatational component of the transformation will lead to surface-crack nucleation during bend tests. Furthermore, the transformation zone produced will act as a localized residual-stress driving force, similar to indentation plastic zones. The "microstructural" crack driving force Km can be assumed to have the form4 Q
(1)
where Q is proportional to transformation-induced residual force and c is crack size. Equation (1) follows from the fracture-mechanics condition for equilibrium extension of a point-loaded circular crack. Marshall and Swain8 show that equivalent crack driving forces obtain for a transformation zone size that is approximately one-and-one-half ti
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