2.1 Brittle Fracture 75 imate equality KIe KIe KIle along tortuous crack fronts of remote mode I cracks.Moreover,first unstable pop-ins at these fronts follow,most probably,the local planes of already pre-cracked facets.Consequently,the simplest stability criterion Geff=GI+GII+GIII, can be accepted,where Gef is the effective crack driving force.An almost equivalent relation is often used in terms of stress intensity factors: Kg=V好+K+一k (2.7) For example,in the case of a long straight crack with an elementary kinked tip,it simply reads Kef cos2(0/2)KI, (2.8) where 6 is the kink angle.One can clearly see that Kef KI for 6>0. This inequality generally holds for any spatially complex crack front.Hence, the local stress intensity Kef at such a front is always lower than the re- mote Kr-factor applied to a straight(smooth)crack of the same macroscopic length.The geometrically induced shielding(GIS)effect belongs,according to Ritchie [165],to so-called extrinsic shielding mechanisms.The resistance to crack propagation in fracture and fatigue has,in general,many compo- nents that can be divided into two main categories:intrinsic and extrinsic toughening.The first mechanism represents the inherent matrix resistance in terms of the atomic bond strength or the global rigidity,strength and duc- tility.Appropriate modifications to both the chemical composition and the heat treatment are typical technological ways to improve the intrinsic fracture toughness.On the other hand,processes like kinking,meandering or branch- ing of the crack front,induced mostly by microstructural heterogeneities, belong typically to the extrinsic toughening mechanisms.They reduce the crack driving force and,apparently,increase the intrinsic resistance to crack growth.Thus,the measured fracture toughness can be expressed as a sum of the intrinsic toughness and extrinsic components: Ke=KIei+∑Kie (2.9) The standardized procedure for calculation of Ki-values [166 assumes a planar crack with a straight front and,therefore,does not take the extrinsic shielding effect associated with the crack microgeometry into account.Hence, surprisingly high Kre-values might be measured,particularly for materials with coarse microstructures and highly tortuous cracks.General expressions for GIS contributions in both brittle and quasi-brittle fracture were derived in [167,168]by following the approach first introduced by Faber and Evans 169.In the case of brittle fracture2.1 Brittle Fracture 75 imate equality KIc ≈ KIIc ≈ KIIIc along tortuous crack fronts of remote mode I cracks. Moreover, first unstable pop-ins at these fronts follow, most probably, the local planes of already pre-cracked facets. Consequently, the simplest stability criterion Geff = GI + GII + GIII , can be accepted, where Geff is the effective crack driving force. An almost equivalent relation is often used in terms of stress intensity factors: Keff = K2 I + K2 II + 1 1 − ν K2 III . (2.7) For example, in the case of a long straight crack with an elementary kinked tip, it simply reads Keff = cos2(θ/2)KI , (2.8) where θ is the kink angle. One can clearly see that Keff < KI for θ > 0. This inequality generally holds for any spatially complex crack front. Hence, the local stress intensity Keff at such a front is always lower than the re￾mote KI -factor applied to a straight (smooth) crack of the same macroscopic length. The geometrically induced shielding (GIS) effect belongs, according to Ritchie [165], to so-called extrinsic shielding mechanisms. The resistance to crack propagation in fracture and fatigue has, in general, many compo￾nents that can be divided into two main categories: intrinsic and extrinsic toughening. The first mechanism represents the inherent matrix resistance in terms of the atomic bond strength or the global rigidity, strength and duc￾tility. Appropriate modifications to both the chemical composition and the heat treatment are typical technological ways to improve the intrinsic fracture toughness. On the other hand, processes like kinking, meandering or branch￾ing of the crack front, induced mostly by microstructural heterogeneities, belong typically to the extrinsic toughening mechanisms. They reduce the crack driving force and, apparently, increase the intrinsic resistance to crack growth. Thus, the measured fracture toughness can be expressed as a sum of the intrinsic toughness and extrinsic components: KIc = KIci +KIce. (2.9) The standardized procedure for calculation of KIc-values [166] assumes a planar crack with a straight front and, therefore, does not take the extrinsic shielding effect associated with the crack microgeometry into account. Hence, surprisingly high KIc-values might be measured, particularly for materials with coarse microstructures and highly tortuous cracks. General expressions for GIS contributions in both brittle and quasi-brittle fracture were derived in [167, 168] by following the approach first introduced by Faber and Evans [169]. In the case of brittle fracture