R, curve behaviour

Lamicq etal. (1986) reported that the bending strength of water-quenched woven SiC/SiC (CVI) specimens decreased slightly in the quench range A T = 300-750°C, and then remained unchanged up to A T= 1200°C. The composite also seemed to exhibit a steep R-curve behaviour. 

Figure 4.9 R-curve behaviour of Mg-partially stabilised zirconia (Mg-PSZ) compared to that of alumina (Bleise and Steinbrech, 1994 Inghels, Heuer and Steinbrech, 1990). ( With permission by John Wiley and Sons.)...

Danzer et al. have discussed the influence of other types of flaw populations (e.g. of bimodal distributions) on strength [I I, 12]. In these cases the Weibull modulus might depend on the applied load amplitude and on the size of the specimen. Then the determination of a design stress in the usual way may become problematic. A stress and size dependent modulus occurs for materials with an R-curve behaviour [11] and may also be caused by internal stress fields [ 11 ]. 

Additionally, the insitu-reinforced silicon nitride materials exhibit an increased Weibull modulus [86]. This has two reasons firstly, the concentration of the large, strength-limiting grains is so high that the defect size has a narrow size distribution and secondly, these materials exhibit pronounced R-curve behaviour, which makes the material tolerant of larger cracks. The high thermal shock resistance of these materials also seems to be connected with this fact [30]. 

Nakano K, Kamiya A, Yamauchi S, Kobayashi T, Fracture toughness of carbon fibre reinforced ceramic composites, Japan Fine Ceramics Center, Fracture Mechanics of Ceramics 9. Composites, R-Curve Behaviour and Fatigue, Bradt RC, Hasselman DPH, Munz D, Sakai M, Shevchenko VY eds., Proc 5th Int Symp, Nagoya, 15-17 Jul 1991, Fracture Mechanics of Ceramics, Plenum, 9, 123-132, 1992. 

R-Curve. R is the crack resistance force, which for many ceramics increases as the crack propagates. This is termed R-curve behaviour, but the shape of the curve R vs a/W is not a characteristic of the material, but depends also on the test conditions. a/W is the crack length a, normalized for a specimen height W. 

Implications of cracks surface contact are observed also on a larger scale in the crack wake. The crack bridging yields formation of a new side path behind the actual tip of a segmentation crack. Obviously the tortuous crack surfaces provide sufficient contact bridging to shield the apparent crack tip, a toughening mechanism frequently observed in ceramics with R-curve behaviour . 

Thus it seems premature to further quantify the measured R-curve behaviour and to describe the toughening effect in a model. Yet an important conclusion can be drawn from the present study. Tailoring plasma sprayed TBCs with low crack resistance for segmentation cracks and high delamination resistance should focus on a reduction of the density of inter-splat mieroeraeks. Variation of the spraying parameters has the potential to systematieally ehange APS-TBCs with respect to the ratio of inter- and intra-splat defects in the lamellar microstructure. 

F. Deuerler, R. Knehans, R.W. Steinbrech, Testing methods of R curve behaviour of AI2O3, Journal de Physique, 1986, Cl 617 621... 

---