PSI - Issue 28

Mohamed Ali Bouaziz et al. / Procedia Structural Integrity 28 (2020) 393–402 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The propagation steps disappeared, thereby resulting in a gradual propagation. In this way, the enhanced FE-based method measured the crack growth in a more precise way and was less sensitive to the propagation discretization. 4. Experimental calculation of J -integral The J -integral is a measure of the energy release rate in a cracked medium and is expressed in the form of a contour integral (Rice 1968)      ds J w dy t u (2) where  is a contour surrounding the crack tip, w the strain energy density, t the traction defined with the outward normal along  , u the displacement vector, and s the curvilinear abscissa along  . The J -integral can be obtained experimentally (Becker et al. 2012; Catalanotti et al. 2010; Yoneyama et al. 2014). For example, to evaluate the J -integral in a composite material, Catalanotti et al. (2010) proposed a formulation derived from Rice’s work (Rice 1968). The integral is calculated using displacement, strain and stress data with a rectangular contour enclosing the crack tip              ds n J T T u σ n σ ε 1 (3) where   σ is the average stress vector,   ε the corresponding strains,   n the contour normal, 1 n the contour normal in the crack direction (Figure 5), and   1 x   u the displacement gradient. The energy release rate (here equal to J ) was computed point-by-point along each edge of the contour. Such formulation may prove suitable for 3D printed materials.        x                x 1 2 1

Fig. 5. Contour used for the calculation of the J-integral

The J -integral was then assessed from the sum of all discrete contributions of each subset center of the DIC analysis. The µ-SENT sample was fabricated by a succession of +45° and -45° layers. The average stresses were computed from the transformed stiffness matrices of the +45° and -45° plies,      45 Q and      45 Q respectively, as     45 45 ε σ Q Q   . The derivative of the displacement field was expressed as

2 1

  

  

    

 

  