Issue34

L. Marsavina et alii, Frattura ed Integrità Strutturale, 34 (2015) 387-396; DOI: 10.3221/IGF-ESIS.34.43 388 and loading rate. Their results show that the value of fracture toughness obtained in FPB loading configuration is higher with a factor of 2 comparing with those obtained on TPB. Only few studies present the mixed mode fracture of polymeric foams, and only for PVC foams. Hallsttröm and Grenestedt [12] investigated mixed mode fracture of cracks and wedge shaped notches in expanded PVC foams. Different types of specimens made of Divinycell H100 were investigated and the non singular T-stress was considered in formulation of fracture criteria. It was concluded that for predominantly mode II the use of T-stress improved the facture predictions. Three different densities of PVC foams were investigated using a Compact Tensile Specimen with Arcan fixtures to produce mixed mode conditions, [13]. The ratio between mode II and mode I fracture toughness K IIc /K Ic was found to be between 0.4 and 0.65 depending on foam density. For mixed mode loading the Richard fracture criterion gives better predictions of fracture limit and crack initiation angle. Marsavina el. al. [14, 15] and Linul et al. [16] presented results mixed mode fracture toughness of PUR foams. They highlighted that the foam density is the major factor influencing fracture toughness, loading speed and loading direction having minor influence. The anisotropy of the foam was explained trough the cellular topology of foams. However, the crack initiation angle is less investigated [13, 15, 16]. Present study assessed the theoretical fracture criteria for crack initiation angle in PUR foam materials under mixed mode loading, using an asymmetric semi-circular bend and single edge crack specimens. A NALYTICAL MODELS FOR CRACK PROPAGATION he fracture initiation for a crack in-plane mixed mode conditions is described by:  The angle of crack initiation  c ,  A critical combination of stress intensity factors ( K I and K II ) and fracture toughness ( K Ic ) in the form:    , , 0 I II Ic F K K K (1) The four most used fracture criterion are summarized below. Maximum Tensile Stress criterion (MTS) Erdogan and Sih [17] criterion, based on maximum tensile stress, consider that crack initiation starts radially from the crack tip at an angle    c perpendicular to the maximum tensile circumferential tensile stress   ,max . The crack propagation becomes unstable when   ,max reaches a critical value  cr , which is a material parameter at a radius r :       ,max 2 Ic cr K r (2) The equation for crack initiation angle and the relationship between Stress Intensity Factors (SIF's) K I , K II and fracture toughness K Ic for MTS criterion are presented in Tab. 1. Condition Mathematical formulation Crack initiation angle               2 2 2 2 2 3 8 arccos 9 II I I II c I II K K K K K K (3)   , , I II Ic F K K K            2 3 cos cos sin 2 2 2 c c I II c Ic K K K (4) Table 1 : The MTS criterion. Minimum Strain Energy Density criterion (SED) Sih [18] postulated that the fracture occurs in the direction where the strain energy density S is minimum, at a critical distance r 0 :     2 1 8 cr Ic S K (5) T