74 2 Brittle and Ductile Fracture centrations as much as several orders of magnitude higher than that in the grain interior [160.The most dangerous impurities segregating in bcc iron and steels are phosphorus,tin and antimony.For example,the disintegra- tion of the rotor at the Hinkley Point Power Station turbine generator in 1969 was caused by 50%of phosphorus segregated at grain boundaries of the 3Crl/2Mo low-alloy steel containing a few tenths of a percent of phosphorus in the bulk 161. Brittle intercrystalline (intergranular)decohesion caused by impurity seg- regation exhibits relatively high microroughness of fracture surfaces.More- over,the secondary cracks identifying the splitting of the main crack front are often observed preferentially at triple points.Both these phenomena lead to the so-called geometrically induced shielding (GIS)of the crack tip that has a favourable effect on decreasing the local stress intensity factor,thereby increasing the fracture toughness.This kind of shielding is one of the so- called extrinsic components of fracture toughness that can be considered as a possible toughening mechanism in the research and technology of advanced materials. In the next subsections,the theory of GIS and its practical application to an improvement of fracture toughness of brittle materials is outlined. 2.1.1 Geometrically Induced Crack Tip Shielding Crack front interactions with secondary-phase particles or grain (phase) boundaries in the matrix structure cause deflections of the crack front from the straight growth direction resulting in the microscopic tortuosity of cracks. As already mentioned,such waviness combined with crack branching (split- ting)is a natural property of intergranular cracks in metals as well as ce- ramics.In general,the tortuosity induces a local mixed-mode I+II+III at the crack front even when only a pure remote mode I loading is applied. In order to describe the crack stability under mixed-mode loading,various LEFM-based criteria were proposed(see,e.g.,[162-164).Several of the most frequently used mixed-mode criteria can be found in Appendix B,where con- ditions of their validity are also briefly described.When selecting a suitable criterion one should note that an unstable brittle fracture in metallic mate- rials is usually preceded by a stable corrosion and/or fatigue crack growth to some critical crack size.During such growth the crack always turns per- pendicularly to the direction of maximal principal stress,i.e.,to the opening mode I loading.This physically corresponds to minimization of both the crack closure (see Chapter 3 for more details)and the friction so that the rough crack flanks behind the tortuous crack front do not experience any significant sliding contact.Because the crack-wake friction is responsible for somewhat higher fracture toughness values measured under remote sliding modes II and III when compared to those under mode I [164],one can consider an approx-74 2 Brittle and Ductile Fracture centrations as much as several orders of magnitude higher than that in the grain interior [160]. The most dangerous impurities segregating in bcc iron and steels are phosphorus, tin and antimony. For example, the disintegra￾tion of the rotor at the Hinkley Point Power Station turbine generator in 1969 was caused by 50% of phosphorus segregated at grain boundaries of the 3Cr1/2Mo low-alloy steel containing a few tenths of a percent of phosphorus in the bulk [161]. Brittle intercrystalline (intergranular) decohesion caused by impurity seg￾regation exhibits relatively high microroughness of fracture surfaces. More￾over, the secondary cracks identifying the splitting of the main crack front are often observed preferentially at triple points. Both these phenomena lead to the so-called geometrically induced shielding (GIS) of the crack tip that has a favourable effect on decreasing the local stress intensity factor, thereby increasing the fracture toughness. This kind of shielding is one of the so￾called extrinsic components of fracture toughness that can be considered as a possible toughening mechanism in the research and technology of advanced materials. In the next subsections, the theory of GIS and its practical application to an improvement of fracture toughness of brittle materials is outlined. 2.1.1 Geometrically Induced Crack Tip Shielding Crack front interactions with secondary–phase particles or grain (phase) boundaries in the matrix structure cause deflections of the crack front from the straight growth direction resulting in the microscopic tortuosity of cracks. As already mentioned, such waviness combined with crack branching (split￾ting) is a natural property of intergranular cracks in metals as well as ce￾ramics. In general, the tortuosity induces a local mixed-mode I+II+III at the crack front even when only a pure remote mode I loading is applied. In order to describe the crack stability under mixed-mode loading, various LEFM-based criteria were proposed (see, e.g., [162–164]). Several of the most frequently used mixed-mode criteria can be found in Appendix B, where con￾ditions of their validity are also briefly described. When selecting a suitable criterion one should note that an unstable brittle fracture in metallic mate￾rials is usually preceded by a stable corrosion and/or fatigue crack growth to some critical crack size. During such growth the crack always turns per￾pendicularly to the direction of maximal principal stress, i.e., to the opening mode I loading. This physically corresponds to minimization of both the crack closure (see Chapter 3 for more details) and the friction so that the rough crack flanks behind the tortuous crack front do not experience any significant sliding contact. Because the crack-wake friction is responsible for somewhat higher fracture toughness values measured under remote sliding modes II and III when compared to those under mode I [164], one can consider an approx-