13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 2.1. Crack Relative Displacement Factor evaluation from experimental measurement The experimental evaluation of CRDFs has been performed from the experimental measurements by DIC. The displacement data output by the DIC method are typically affected by experimental noise. It proves quite difficult to accurately analyze stress and strain fields from raw displacement data; moreover, real deformation fields of the crack tip and its location are difficult to obtain with precision from DIC [5-7, 11-14]. Consequently, the crack tip parameters predicted directly using raw experimental displacement data are inaccurate [5-7]. An adjustment procedure has thus been derived to avoid these difficulties. Then, once the experimental displacement has been calculated, the adjustment procedure based on a nonlinear iterative Newton-Raphson is performed between the Williams' series forms (1) and the experimental data. By taking measurement boundary conditions (e.g. specimen geometry and symmetry, crack orientation) into account, this adjustment procedure is also able to consider a rigid body motion, crack tip localization and its orientation as unknowns. These parameters are then used to adjust the displacement fields. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = 骣 ÷ ç ÷ = 鬃 + 鬃 + - ç ÷ ç桫 骣 ÷ ç ÷ = 鬃 + 鬃 + + ç ÷ ç桫 å å / 2 / 2 1 1 2 1 2 1 / 2 / 2 2 1 2 2 1 1 , , , , N N u A r f A r g T R x u A r l A r z T R x c c c c c c c c c c c c c c k j k j k j k j (1) Where: ( ) ( ) 骣 骣 骣 骣 鼢 鼢 珑 珑 = 鬃 - ? ? + - 鬃 桫 桫 桫 桫 骣 骣 骣 骣 鼢 鼢 珑 珑 = - 鬃 ? ? ? + - 鬃 桫 桫 桫 桫 骣ç = 鬃 çççè cos cos 2 1 cos 2 2 2 2 2 ( 1) sin sin 2 1 sin 2 2 2 2 2 sin 2 f g l c c c c c c c c c c k j j j c c c c c k j j j c k j ( ) ( ) 骣 骣 骣 鼢 鼢 珑 + ? ? + - 鬃 骣 骣 骣 骣 鼢 鼢 珑 珑 = 鬃 - ? ? + - 鬃 桫 桫 桫 桫 sin 2 1 sin 2 2 2 2 cos cos 2 1 cos 2 2 2 2 2 z c c c c c c c j j c c c c c k j j j (2) The adjusted experimental field now allows defining a physical and local interpretation. The kinematic state of crack lips can in fact be identified using Crack Relative Displacement Factor ( ) Ke a (CRDF) [5-9], which denote the relative opening and shear displacements of crack lips. Thanks to developments offered by Dubois, the kinematic state in the crack tip vicinity can be defined using Crack Relative Displacement Factors (CRDFs). At a very short distance x from the crack tip, the relative opening displacement 1 [u] and shear displacement 2 [u] are defined as follows (see Figure 2): ( ) ( ) 轾 轾 = ? 犏 犏 臌 鬃 臌 2 1 1 2 2 2 u K and u K e e x x p p (3) By combining Eqs. (1) with (3), we can now provide, in the crack tip vicinity, a mathematical interpretation of CRDF, such that: ( ) ( ) ( ) ( ) = 鬃 + 鬃 = 鬃 + 鬃 1 1 1 1 2 2 2 1 2 2 1 2 K A and K A e e k p k p (4)
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