Issue 39

M.A. Tashkinov, Frattura ed Integrità Strutturale, 39 (2017) 248-262; DOI: 10.3221/IGF-ESIS.39.23 249 In most cases, only prediction of initiation of fracture is not sufficient because the local failure does not necessarily lead to the loss of the bearing capacity of structure due to stress redistribution between the components of the material [1]. It is necessary to understand underpinning mechanisms of the process at each scale level to be able to create reliable models of failure of composites. Constituents of composites are described by phenomenological approaches. Their strength characteristics can be described in terms of traditional theories or determined experimentally. During the processes of manufacturing and exploitation of composite materials, their microstructure on the ply scale may be subject to various structural changes, contributing to development of the failure processes. These include matrix cracking, fiber breakage or bending, potentially accompanied by delamination between matrix and fibers, as well as between the plies [1-4]. Delamination is one of the most commonly occurring types of defects in composites, it is defined as separation of plies with forming of voids and growing of cracks, oriented by normal to the ply [5]. It may be caused by local geometric nonuniformities that appeared in the manufacturing process and results in out-of-plane loads. Also, debonding can be caused by differences between the properties of the constituents of the composite, which leads to emergence of interlaminar stresses. Cracking of the matrix, which occurred during the deformation process, gives the same effect. Another cause of interlaminar stresses and, consequently, delamination, may be the influence of temperature and humidity. Finally, the different types of operating loads, such as prolonged static and cyclic loading as well as impact effects, can directly or indirectly cause the appearance of defects in the form of deboning and delamination [6-8]. Whatever the original cause of the formation of the delamination is, its development can lead to premature decrease of structures’ resource, and in some cases, even cause catastrophic loss of load-bearing capacity. Understanding influence of the defects on the properties of composite structures is necessary for the prediction of their durability. In this regard, urgent problem is development of models describing the delamination process as well as development of the initiation of damage in composites. This work is devoted to investigation of numerical models for processes of delamination nucleation and development in laminate composite materials, numerical modeling of these processes depending on the initial parameters of the defect, as well as studying of the influence of the defect on the strength characteristics of the materials. Currently, many approaches had been developed for creation of mathematical models of the mechanical behavior of composites considering the start of fracture process and its further development. There are two main groups: approaches based on the theory of strength, and approaches based on fracture mechanics [9]. Approaches related to the first group use strength criteria to determine the moment of the first ply failure in the laminate. Such criteria may include various parameters, such as the value of the stress tensor components, material characteristics, strain, force, displacement and others. The foundations for the development of strength criteria for the composites were laid in the works of Hill [10], Tsai [11] 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 separating of the matrix and fibers failure, were proposed by Hashin [12, 13], Puck [14], Chang [15] and were developed in the works of other authors [9]. Theories that are able to describe development of existing damage had been developed within the framework of fracture mechanics. At the same time, usually the classical theories do not say anything about the origin of the defect. One of the most widely used models are based on monitoring of the rate of deformation energy released during the propagation of the defect, and its comparison with a threshold value of the strain energy release rate for the particular material [9]. To determine the energy release rate, a number of techniques, implemented with the finite element methods (FEM), have been developed [16-18]. Over the past decades many models and analytical tools for modeling of debonding processes were created using modifications and combinations of the approaches outlined above. Detailed reviews of works in this area are given, for example, in [1] and [6]. In this paper a practical analysis of models of delamination growth will be carried out, involving the virtual crack closure technique as well as the progressive failure analysis using a range of failure criteria. F INITE ELEMENT MODELING OF DELAMINATION IN COMPOSITES Virtual crack closure technique (VCCT) ccording to the concept of this approach, the energy released during the crack expansion onto a certain distance is equal to the energy required to close the crack at the same distance [17, 19, 20]. The energy expended to the crack closure is calculated from the coupling of values of the strength at the crack tip and displacement during movement of the crack tip: A