13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 2. When a short crack grows in a layer of matrix and meets a fibre, a high level load is needed to overcome this energy barrier. It first deviates a little into the interface or in the matrix before entering in the fibre; 3. When the crack grows in a layer of fibre and meets the matrix, it deviates slightly in the matrix before penetrating into the matrix. As the matrix strength is much lower than that of the fibre, the remote load drops significantly; 4. As the transversal main crack grows and becomes longer, the length of its deviations into the interfaces increases when it meets a fibre; 5. We can remark that the interface debonding acts as a crack arrestor as described in previous studies [3]. When the crack propagates in an interface, the crack tip mode mixity varies from mode I toward mode II. Its growth requires more and more energy according to the interface fracture criterion (Equation 15); As a result of the interface debonding, the final fracture surfaces take a stair form as observed in previous experimental studies [22-23]. 0 100 200 300 400 500 600 700 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 0,009 E11 Σ11(MPa) (c) (d) Figure 3: Global response (a) and fracture patterns at the beginning (b), the middle (c) and the end (d) of the failure process of the basic cell under uniaxial tension 5: Discussions and concluding remarks In this work, we have established a non-local fracture model and resolved it by using the Fast Fourier Transforms (FFT). The maximal stress criterion was adapted by means of the non-local concept in order to describe the fracture in brittle and quasi-brittle materials. The non-local model enables the predicted damage to be independent of the grid size. Moreover, the proposed model is equivalent to the Griffith-Irwin criterion when a macro-crack is formed. Consequently, the proposed fracture model is capable to predict crack initiation as well as crack growth. Comparisons with analytical results on pure mode-I cracks show that the proposed approach is highly efficient and accurate.
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