13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Figure 1. a) Palmqvist cracks configuration; b) crack parameters for Vickers indenter; c) crack parameters for Berkovich indenter. where P is the maximum indentation load, c is the crack length (Fig. 1), E is the elastic modulus and H is the hardness. The parameters k and n are empirical constants equal to 0.016 ±0.004 and 0.5, respectively. Other studies [4] determined k = 0.0098 and n = 3/2. For Palmqvist cracks configuration, where the cracked areas are represented by semicircles of diameter equal to the crack length measured from an impression corner (Fig. 1a), many expressions have been developed to calculate KC. Niihara et al. [5] proposed the following expression: a l P H E K k 2 5 C = (2) where a is the half-diagonal of the indentation impression, l is the crack length and k was determined as 0.0089 (Fig. 1b). Laugier [6] proposed an alternative expression for Palmqvist cracks: 3 2 2 3 1 2 C V c P H E l a K x = (3) where xV was determined as 0.015. However, the applicability of these equations encounters three basic difficulties. First, all these equations are semi-empirical as there is no theoretical basis behind these expressions. Second, it is necessary to obtain a particular pattern of cracks (Fig. 1a) and to know the morphology of the cracks in the plane parallel to the loading direction in order to implement the Eqs. (1)-(3). Third, all these equations were developed for ceramic materials and for the symmetrical Vickers indentations (Fig. 1b). Therefore, they are not valid for the asymmetrical Berkovich indentations. Some efforts have been made to obtain similar equations to those described above but properly modified for Berkovich indentations [7] (Fig. 1c). Combining the model proposed by Laugier [6] and the Ouchterlony´s radial cracking modification factors [8], fracture toughness can be determined according to Eq. (4).
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