Issue34

L. Marsavina et alii, Frattura ed Integrità Strutturale, 34 (2015) 387-396; DOI: 10.3221/IGF-ESIS.34.43 390 Maximum Energy Release Rate criterion (Gmax) Hussain et al. [19] postulate that the crack propagation initiates when the Energy Release Rate G reaches a critical value G Ic and expressed the energy release rate G in terms of stress intensity factors of initial crack:      2 ' Ic c Ic K G G E (8) with E’=E Young's modulus for plane stress, and E'=E/(1-  2 ) for plane strain. The crack initiation angle could be found by solving Eq. (9) from Tab. 3, while the functional relationship between K I , K II and K Ic is represented by eq. (10). Equivalent Stress Intensity Factor criterion (ESIF) Richard [20, 21] proposed a generalized fracture criterion, based on the equivalent stress intensity factor K eq , which is defined as:       2 2 1 4 2 2 I eq I II K K K K (11) with  = K Ic / K IIc . Crack starts to propagate when K eq reaches the fracture toughness of the material K Ic . For the crack initiation angle Richard proposed an empirical expression (12), which represents a correlation with a considerable number of experiments. Condition Mathematical formulation Crack initiation angle                       2 0 0 155.5 83.4 II II c I II I II K K K K K K (12)   , , I II Ic F K K K       2 2 1 4 2 2 I I II Ic K K K K (13) Table 4 : The ESIF criterion. M ATERIALS AND METHODS Materials rack propagation studies were performed on rigid PUR foams having a closed cell microstructure. Three foam densities, manufactured by NECUMER GmbH (Germany), were investigated 100 kg/m 3 (NECURON 100), 145 kg/m 3 (NECURON 160) and 300 kg/m 3 (NECURON 301). A statistical analysis of the foams microstructure is presented in [14]. The main properties provided by the manufacturer are listed in Tab. 5, [22]. According to the manufacturer the main applications of these foams are test models, draw dies, large volume models, back filling of moulds and patterns, and substructure for hard styling clay. Property Units of measure NECURON 100 160 301 Density kg/m 3 100 145 300 Temperature resistance 0 C 120 120 65 Compressive strength MPa 2 3 5 Flexural strength MPa 1.5 2.5 6 Table 5 : Material properties according to manufacturer [22] (approximate values). C