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H. Askes et alii, Frattura ed Integrità Strutturale, 25 (2013) 87-93 ; DOI: 10.3221/IGF-ESIS.25.13 90 already been explained in great detail elsewhere [17, 18], in what follows just its fundamental steps are summarised briefly. In order to coherently link l to L, according to Neuber’s structural volume concept [19], the initial hypothesis is formed that the process zone defining the overall strength of the investigated cracked material is circular in bi-dimensional situations and spherical in tri-dimensional bodies, its radius being equal to L [20]. Given a generic material point having coordinates (X, Y), nonlocal stresses  nl at this point can directly be derived from the local stresses  determined at those points having coordinates (X+x,Y+y) that are in the vicinity of the point at which the non-local stresses themselves are evaluated, i.e.:   nl 2 2 2 2 1 (X, Y) H L x y (X x, Y y) dy dx L               (9) In the above equation H is the Heaviside function where H(s)=1 when s>0 and H(s)=0 otherwise, s being a generic variable. Observing that factor  L 2 is used for normalisation reasons, the local stresses expanded in a Taylor series at the material point having coordinates (X, Y) take on the following value:   nl 2 2 2 2 1 H L x y x y dy dx L x y                             (10) By so doing, the stresses and their derivatives are evaluated at point (X, Y) and, therefore, they can be taken out of the integral. If the terms in the integral are rewritten according to polar coordinates  and r, where x=r · cos  and y=r · sin  , the right-hand side of Eq. (10) can be elaborated. For instance, the second derivative terms is found to be:   2 L 2 2 2 2 2 2 2 2 2 1 1 1 2 2 8 2 2 2 2 2 0 0 1 1 H L x y x dy dx r cos r dr d L L x L x x                            (11) According to Eq. (11), it easy to observe that all terms with odd powers of x or y cancel. After some straightforward algebra, one obtains: nl 2 2 1 8 L         (12) Finally, by using the explicit-to-implicit transition as formalised by Peerlings et al. [20], Eq. (12) can be rearranged as follows: nl 2 2 nl 1 8 L         (13) Eq. (9), which is the starting point of the reasoning summarised above, represents a link between the AM [10] and gradient elasticity as formalised by Aifantis and co-workers [3-5], so that, if the terms of order L 4 and higher are ignored, the the l vs. L relationship can explicitly be written as: 2 2 1 L 8    L 2 2   (14) G RADIENT ENRICHED TIP STRESSES TO ESTIMATE STATIC STRENGTH OF CRACKED CERAMICS n order to check the accuracy of gradient enriched tip stresses in estimating the static strength of cracked engineering ceramics under Mode I static loading a number of experimental results were selected from the technical literature, the mechanical properties of the investigated materials being summarised in Tab 1. Such results were generated by testing cracked samples having different geometries which include: controlled surface flaws, surface scratches, large pores, and sharp notches. The selected experimental results are summarised in the normalised Kitagawa-Takashi diagram plotting the ratio between the nominal gross stress resulting in static breakage,  th , and the material ultimate tensile strength,  UTS , against a normalised equivalent length calculated as F 2 a/L, where F is the LEFM shape factor and a the crack length. The main advantage of the above schematisation is that experimental results generated by testing samples having shape factor different from unity can directly be compared to the case of a central crack in an infinite plate loaded in tension (for which F is invariably equal to 1). I