Issue 49

M. Tashkinov et alii, Frattura ed Integrità Strutturale, 49 (2019) 396-411; DOI: 10.3221/IGF-ESIS.49.39 397 When analyzing the mechanical behavior of polymer composite structures, an important task is to create numerical models that allow to reproduce the deformation behavior of the structure not only in the elastic zone, but also after the onset of the development of internal defects and subsequent failure process. To obtain more accurate numerical results it is necessary to take into account both the structural features of the laminated composites (distribution of epoxy between plies, presence of epoxy “pockets” and internal defects) and a number of mechanisms that cause the occurrence and progression of the defect, implemented in the form of appropriate criteria and fracture models. In addition, interaction of microstructural elements plays a key role in the propagation of fracture processes in composites. Accordingly, besides the development of defects arising at the scale level of the composite ply, it is necessary to model the effect of damage accumulation at the micro-scale level. The most common types of fracture in laminated composites are fiber rupture, matrix cracking and delamination [1–3]. The traditional approach when creating failure models of composites is to use the failure criteria on a scale of a ply. These criteria compare the stress state in a ply with the strength characteristics or allowable deformation of the material and are defined in the local coordinate system. At present, a large number of fracture criteria have been developed for composite materials that take into account these mechanisms to some extent and which depend on a different sets of critical constants [4–8]. The foundations for the development of strength criteria for the composites were laid in the works of Hill [9], Tsai [10] and others, who formulated the criteria on the basis of the relations between the components of the stress tensor. More sophisticated criteria based on a set of different possible failure modes, including, separately, matrix and fibers failure, were initially proposed, by Hashin [11,12], Puck [13] and Chang [14]. In order to take into account the structural defects, the approaches of continuum damage mechanics (CDM) are used, according to which after the failure criterion in a ply is met, the material with defects is replaced by a fictious continuous material without defects, but with lowered elastic properties [15]. To simulate the growth of delamination, approaches of the fracture mechanics are used. Since laminated composites demonstrate brittle behavior, linear elastic fracture mechanics (LEFM) are used to model delamination, one of the common approaches of which is the virtual crack closure technique (VCCT) ) [16–20]. The essence of the method in application to the finite element approach lies in the separation of the nodes of the finite element mesh located on the initially connected surfaces of the plies when specified fracture criterion is fulfilled. For the same model of composite structure, the use of different fracture theories can lead to significant differences in the results of evaluation of its mechanical response. When creating models of structures made of laminated composites in order to take into account all the basic mechanisms of failure it is necessary to (i) to create a laminated geometric ply-by- ply model of the composite material; (ii) analyze the state of contact between the plies on the basis of approaches of fracture mechanics that allow to numerically implement the process of separation of plies; (iii) evaluate the strength characteristics and damage accumulation in the ply not only by using its effective properties, but also by establishing its relation to the analysis of local fields in microstructural components. This work is aimed at studying the influence of damage accumulation processes and changes in the stiffness properties in the woven ply of a polymer composite material on the development of delamination in laminated polymer composites structures. An L-shaped specimen subject to load leading to delamination and, at the same time, accumulation of defects and damage in the plies, is investigated. The method of estimation of microstructural parameters as well as physical and mechanical properties of the composite material is based on a multi-scale mathematical model taking into account the geometry of the material, anisotropy of physical and mechanical properties of the plies and mechanical properties of the matrix. The virtual crack closure technique (VCCT) with the application of the Benzeggagh-Kenane (BK) criterion is used for modelling the propagating delamination. The assessment of plies damage is based on two criteria: a multicomponent criterion, which uses the simplest fracture indicators for various components of the stress tensor, and more complex Hashin criterion [12], taking into account the analysis of local microstructural fields. The numerical results of modeling of the mechanical behavior of the specimen using different criteria are compared and the relationship between the processes of delamination and damage accumulation in plies is studied. M ULTI - SCALE MODEL OF FRACTURE IN LAMINATED COMPOSITES Virtual crack closure technique ccording to the concept of this technique, the energy released by the expansion of the crack at a certain distance is equal to the energy required to close the crack at the same distance. In the framework of the finite element simulation, this energy can be calculated from the nodal forces at the delamination front and the corresponding A