Issue 47

M.F. Funari et alii, Frattura ed Integrità Strutturale, 47 (2019) 277-293; DOI: 10.3221/IGF-ESIS.47.21 283 transformation rules defined by Eq.s (7)-(8). In the present paper, more emphasis is given to the numeric procedure implemented to simulate the crack growth in the core, since the one related to the core/skin interfaces can be recovered in previous author’s works [21, 22, 25]. From the numerical point of view, the crack growth is achieved by evaluating the interfacial variables on a small region containing the crack tip. In the proposed model, the J -integral methodology is used to evaluate on a contour enclosing the tip, in which a high number of elements is introduced to ensure accuracy in the prediction of the fracture variables. During the crack growth, such region is moved rigidly, avoiding mesh distortions in the crack tip region. Moreover, the boundaries affected by the crack advance are enforced to have the same displacements of the structure, leaving unaffected the shape of the cracked faces. This task is achieved by introducing two nodes close to the region adjoining the crack tip, which are stretched as far as the angle variation predicted by Eq.(10). 3 is lower than a fixed angle tolerance value. Once tolerance condition is satisfied, a new definition of the computational nodes, driven by the new value of crack propagation angle, is required. During the crack growth, mesh movements of the computational nodes produce distortions in the grid points, which are eliminated by the use of a re-meshing algorithm. This is able to reconstruct a new regular mesh discretization, transferring the nodal variables from the distorted to the new computational points. The procedure is recalled by means of a mesh quality parameter, which controls the allowable distortion in each element. Governing equations as well as the steps referred to above are formulated by using a customized FE subroutine in the framework of COMSOL Multiphysics software [26]. The algorithm was developed by means of script files implemented in a MATLAB® environment, which manage the parameters and the results required by the iterative procedure. In particular, the following steps are implemented in the user subroutine: 0) Read the input data: geometry, material, mesh discretization and load configuration; 1) Evaluate fracture variables and crack angle of propagation (Eq.(10).3); 2) Check crack growth conditions (Eq.(11)); 3) Solve incremental Structural and ALE problem; 4) Check tolerance conditions for the angle variation or mesh quality; 5) If the angle variation or mesh quality tolerance are satisfied, proceed to the crack growth, else employ re-meshing algorithm. The proposed procedure is quite general and can be solved either in a static or dynamic frameworks, taking into account the time dependent effects produced by the inertial characteristics of the structure and the boundary motion involved by debonding phenomena. Since the governing equations are essentially nonlinear, an incremental-iterative procedure has been adopted to evaluate the current solution. F RACTURE PROPERTIES OF FOAMS n this section, the fracture toughness of a commercially available core foam under mode I is evaluated by three point bending tests on Semi-Circular Bending (SCB) specimens. Mode II is analysed on Asymmetric Semi-Circular Bend (ASCB) specimens. Ayatollahi et al. [27] proved that the ASCB loading scheme is able to generate all range of mixed fracture modes in fragile construction materials, including a pure mode II fracture condition. The method was used by Marsavina et al. [28, 29] for PVC foams. The experimental determination of fracture properties of the core is instrumental to the implementation of the numerical simulations that follow in the paper. Experimental Setup The experimental tests were performed using a Tinius Olsen testing machine equipped with a 5 kN load cell and an appropriate bending rig. All specimens were cut from 20 mm Divinycell H100 panels in the two main directions using a Denford CNC router with a 0.1 mm resolution equipped with a 3 mm drill bit. Although the numerical cutting procedure included the mid-span sample notching, the natural crack was initiated by sliding a fresh razor across the notch root. The samples were uniformly sprayed with several coats of white paint. Subsequently a stream of black paint was applied as to obtain a random b/w speckle pattern, the ideal reference system for Digital Image Correlation (DIC) purpose [30]. Fig. 4 shows the two load conditions taken in consideration. Three samples were tested according to each scheme, accounting for a total of six specimens. All samples had identical geometrical properties: the radius, R , of the semi-circular samples was 80 mm, whereas the length of the notch, a , was 40 mm. I