Issue 50

F. Larbi Chaht et alii, Frattura ed Integrità Strutturale, 50 (2019) 331-341; DOI: 10.3221/IGF-ESIS.50.28 332 Several researchers have studied the effect of the stacking sequence on the behavior of composite structures such as Mokhtari [6] and the use of stratified composite with change in ply thicknesses Mokhtari [7]. These techniques have been expanded by the use of strengthening or repair patch by Ait Kaci [8]and Benzaama [9]. In the damage the models are implemented on formulations of solid type Donado [10], and more often of the shell type, these two-dimensional elements Peter Linde [11] with a geometrically zero thickness are used for problems of thickness and displacement more or they can greatly reduce the calculation time Elangovan [12].But in the case where the shear deformation occurs in structures with a larger thickness, we must opt for the use of solid elements which give results that can't be obtained by shell elements Yong Guo [13]. on which rests a good accuracy. The Hashin criterion Barberon [14] seen improvements in its prediction ability through the quadratic interaction criterion between the different tractions; that of the fiber and the matrix acting on the plane of damage until the introduction of the criteria which distinguish between the tension and the compression of fiber and the matrix, and this by using a quadratic interaction between stress invariants. According to the researchers, the latter is not always appropriate in the case of matrix or fiber compression, and which does not take into account the effects of shear in the plane which significantly reduces the compressive strength of a composite layer. This prompted several researchers to propose modifications to the Hashin criteria in order to improve their predictive abilities Carlos [15]. We use this Hashin damage criterion for unidirectional fiber composites: This is a criterion that interacts with more than one stress component to evaluate different fracture modes. This criterion was originally developed for unidirectional polymer composites, and other types of non-polymeric laminates. Failure indices for the Hashin criteria are related to fiber and die failures and involve four failure modes. The maximum stress criteria are used for the transverse normal stress component that respond to three- dimensional problems. Notches are inevitable in the design of structures. This is the problematic of our work because are the areas where the initiation and the propagation of the cracks will take place. This approach, which can practically be difficult to achieve, is approved by the numerical results and can also be a solution to other problems in composite structures. The originality of our work is the improvement of the resistance of a composite structure notched by modifications both geometric and others whose parameters of the material in use is the criterion of Haschin. This objective will take place if the architecture parameters of the composite are optimized because the competition between the reduction of thickness and the increase of the volume fraction of the fibers amply show results which are highly evaluative by their parameters. H ASHING CRITERIA AND INPUT PARAMETER he growth prediction and the damage trajectory are implemented by an intra-laminar damage criterion that is implemented in the standard Abaqus calculation code [16]. The input data for the Hashin criteria given in the tables are longitudinal tensile and compressive strengths, transverse tensile and compressive strengths, and longitudinal and transverse shear strengths. All resistance values are assumed to be positive Sokolinsky [17]. In this criterion of damage there is no inter-laminar propagation path, no separation or existence of the interface but the damage is continuous in the structure by degradation of rigidity or by removal of the elements of the structure. Several modes of damage can occur such as the breaking of the fiber and that of the matrix in tension and in compression. In most of cases these modes occur simultaneously, hence the importance of opting for the Hashin criterion which introduces six criteria for initiation of tension and compression damage for fiber and matrix and at the interface level. This is to predict the multimodal phenomenon of composite damage. The Hashin criteria used are quadratic, not because of their mechanical behavior may be the fit of the curve Pederson [18]. These criteria of damage have the following general forms: 1. Tensile fiber failure for σ 11 ≥ 0 2 2 2 12 13 11 2 12 1 failure 1 no failure T X S                 (1) 2. Compressive fiber failure for σ 11 < 0 2 11 1 failure 1 no failure C X             (2) T