numero25

C. J. Christopher, Frattura ed Integrità Strutturale, 25 (2013) 161-166; DOI: 10.3221/IGF-ESIS.25.23 162 Figure 1 : Schematic idealisations of forces acting at the interface of the plastic enclave and the surrounding elastic material, where F A is the Mode I applied force generating the crack tip stress field usually characterized by K I , F B is the additional applied force induced by Mode II loading, F T represents the force due to the T-stress shown in this example as positive, F S is the interfacial shear force between the elastic and plastic zones, F C and F P together create the shielding effect. F P is the force generated by the constraint of compatibility on the plastically deformed material and F C is the contact force between the flanks of the crack generated by the interference of the plastic zones along the flanks [1]. The present work extends the CJP model to deal with the case of mixed Mode I and Mode II loading and thus opens up enhanced possibilities for testing it on inclined cracks in metallic specimens. This extension requires the addition of only one new force parameter to the model, shown as F B in Fig. 1, i.e. an anti-symmetric shear force on either side of the crack. T HE CJP MODEL UNDER BIAXIAL ( MODE I AND MODE II) LOADING he CJP Model [1] is defined as: 1 3 1 3 0 2 2 2 2 y x xy 2i Az z z C B ln(z) z Dz z z ln(z) E               (1) The extension to the model was obtained by making the coefficients A and B complex and making the assumptions B i A r A i3   , B B B r i i   , D E 0   . 1 3 1 3 0 2 2 2 2 y x xy r i r i 2i (A i3B )z iB )z z Cz Dz z z ln(z ( ) B ln(z) E                 (2) The elastic stress fields near the crack tip are given by: Forces on plastic field Forces on elastic field Maximum applied load Minimum applied load F S F S F S F S F S F S F S F S F Ay F Ay F Ay F Ay F Ax F Ax F Py F Py F Px F Px F Py F Py F C F C F C F C F T F T F T F T F T F T Notational boundary of  plastically deformed material Closed crack with flank contact F T Open crack  F T T