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H. Askes et alii, Frattura ed Integrità Strutturale, 25 (2013) 87-93; DOI: 10.3221/IGF-ESIS.25.13 87 Special Issue: Characterization of Crack Tip Stress Field Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics Harm Askes, Luca Susmel Department of Civil and Structural Engineering, The University of Sheffield, Sheffield S1 3JD, United Kingdom A BSTRACT . According to Gradient Mechanics (GM), stress fields have to be determined by directly incorporating into the stress analysis a length scale which that takes into account the material microstructural features. This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longer singular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both the geometry of the cracked component being assessed and the value of the material length scale, the magnitude of the corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by taking full advantage of those computational methods specifically devised to numerically implement gradient elasticity. In the present investigation, it is first shown that GM’s length scale can directly be estimated from the material ultimate tensile strength and the plane strain fracture toughness through the critical distance value calculated according to the Theory of Critical Distances. Next, by post-processing a large number of experimental results taken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linear- elastic crack tip stresses can successfully be used to model the transition from the short- to the long-crack regime under Mode I static loading. K EYWORDS . Length scale; Gradient elasticity; Theory of Critical Distances; Static breakage; Ceramics. I NTRODUCTION ertainly Linear Elastic Fracture Mechanics (LEFM) as formalised by Griffith, Irwin and others represents a ground-breaking point of no return in the field of fracture and strength of engineering materials, this holding true not only from a scientific, but also from an industrial point of view. What we have achieved in sectors such as, for instance, transportation and energy production would have been impossible without the LEFM based design theories. As to the accuracy and reliability of LEFM, in 1964 Irwin affirms [1]: “… linear elastic fracture mechanics already provides a rather complete set of mathematical tools. Additional experimental observations rather than additional methods of analysis are now the primary need for practical applications” . Examination of the state of the art suggests that, as far as brittle failures are concerned, the international scientific community has taken the above statement literally: over the last five decades a big effort has been made mainly to experimentally extend the use of the LEFM concepts to different materials/loading conditions, rather than to develop new theoretical approaches, LEFM being treated as a kind of untouchable “religion”. By challenging Irwin’s belief, the present paper aims to show that gradient-enriched linear-elastic crack/notch tip stresses can directly be used to predict the detrimental effect of cracks on the overall static strength of engineering ceramics, the microstructural features of the assessed material being explicitly taken into account through the critical distance calculated according to the Theory of Critical Distances (TCD). This has the potential to represent an important step forward in the way cracked/notched components are designed against static loading. C