Multiscale approaches for failure analyses of composite materials

Abstract

Fiber-reinforced composite materials are being increasingly adopted in place of metallic elements in many structural applications of civil, automotive and aeronautical engineering, owing to their high stiffness-to-weight and strengthto- weight ratios, resistance to environmental deterioration and ability to form complex shapes. However, in many practical situations, composite materials experience different kinds of failure during their manufacturing processes and/or in-services, especially for laminate configurations, where damage phenomena are rather complex, involving both intralaminar mechanisms (e.g. matrix cracking, fiber splitting and interface debonding between fiber and matrix) and interlaminar mechanisms (e.g. delamination between plies). These damage mechanisms, which take place at the microscopic scale in conjunction with eventual contact interaction between crack faces, strongly influence the macroscopic structural behavior of composites, leading to a highly nonlinear post-peak response associated with a gradual loss of stiffness prior to failure. As a consequence, a proper failure analysis of a composite material subjected to such microstructural evolution should require a numerical model able to completely describe all its microscopic details; however fully microscopic models are not pursued in practice due to their large computational cost. To overcome this problem, homogenization techniques have increasingly gained in importance, based on either classical micromechanical or periodic homogenization approaches; if combined each other, these models are able to deal with both periodic and nonperiodic (e.g. random) composite microstructures. According to these approaches, also referred to as sequential multiscale methods, a “one-way” bottom-up coupling is established between the microscopic and macroscopic problems. As a consequence, such methods are efficient in determining the macroscopic behavior of composites in terms of stiffness and strength, but have a limited predictive capability for problems involving damage phenomena. To overcome these limitations, two classes of multiscale methods have been proposed in the literature: computational homogenization schemes and concurrent multilevel approaches. Computational homogenization approaches, also referred to as semiconcurrent approaches, are very efficient in many practical cases, also for only locally periodic composites, especially when implemented in a finite element setting, as in the FE2 method. The key idea of such approaches is to associate a microscopic boundary value problem with each integration point of the macroscopic boundary value problem, after discretizing the underlying microstructure. The macrostrain provides the boundary data for each microscopic problem (macro-to-micro transition or localization step). The set of all microscale problems is then solved and the results are passed back to the macroscopic problem in terms of overall stress field and tangent operator (micro-tomacro transition or homogenization step). Localization and homogenization steps are carried out within an incremental-iterative nested solution scheme, thus the two-scale coupling remains of a weak type. On the other hand, concurrent multiscale methods abandon the concept of scale transition in favor of the concept of scale embedding, according to which models at different scales coexist in adjacent regions of the domain. Such methods can be regarded as falling within the class of domain decomposition methods, since the numerical model describing the composite structure is decomposed into fine- and coarse-scale submodels, which are simultaneously solved, thus establishing a strong “two-way” coupling between different resolutions. The present thesis aims to develop a novel multiscale computational strategy for performing complete failure analyses of composite materials starting from crack initiation events, which usually occur at the microscopic level, up to the formation of macroscopic cracks, subjected to propagation and coalescence phenomena. To this end, two alternative models have been proposed, belonging to the classes of semiconcurrent and concurrent multiscale models, respectively. Firstly, a novel computational homogenization scheme is described, able to perform macroscopic failure analyses of fiber-reinforced composites incorporating the microstructural evolution effects due to crack initiation and subsequent crack propagation process. A two-scale approach is used, in which coupling between the two scales is obtained by using a unit cell model with evolving microstructure due to mixed-mode crack initiation and propagation at fiber/matrix interface. The method allows local failure quantities (fiber/matrix interfacial stresses, energy release and mode mixity for an interface crack) to be accurately obtained in an arbitrary cell from the results of the macroscale analysis, and, consequently, crack initiation and propagation at fiber/matrix interface to be predicted. Crack initiation at fiber/matrix interface is simulated by using a coupled stress and energy failure criterion, whereas crack propagation is analyzed by means of a mode mixity dependent fracture criterion taking advantage of a generalization of the J-integral technique in conjunction with a component separation method for computing energy release rate and mode mixity. The evolving homogenized constitutive response of the composite solid is determined in the context of deformation-driven microstructures, based on the crack length control scheme able to deal with unstable branches of the equilibrium path, such as snap-back and snap-through events; moreover, the micro-to-macro transition is performed by adopting periodic boundary conditions, based on the assumed local periodicity of the composite. The second approach proposed in this thesis consists in a novel concurrent multiscale model able to perform complete failure analyses of fiber-reinforced composite materials, by using a non-overlapping domain decomposition method in a finite element tearing and interconnecting (FETI) framework in combination with an adaptive strategy able to continuously update the finescale subdomain around a propagating macroscopic crack. The continuity at the micro-macro interface, characterized by nonmatching meshes, is enforced by means of Lagrange multipliers. When modeling fracture phenomena in composites, the competition between fiber/matrix interface debonding and kinking phenomena from and towards the matrix is accounted for, whereas continuous matrix cracking is described by using a shape optimization strategy, based on a novel moving mesh approach. A key point of the proposed approach is adaptivity, introduced into the numerical model by a heuristic zoom-in criterion, allowing to push the micro-macro interface far enough to avoid the strong influence of spurious effects due to interface nonmatching meshes on the structural response. It is worth noting that this heuristic zoomin criterion is uniquely based on geometric considerations. Numerical calculations have been performed by using both the proposed approaches, with reference to complete failure analyses of fiber-reinforced composite structures subjected to different global boundary conditions, involving both uniform and non-uniform macroscopic gradients. The validity of the proposed multiscale models has been assessed by comparing such numerical results with those obtained by means of a direct numerical simulation, considered as a reference solution. Numerical results have shown a good accuracy, especially for the proposed concurrent multiscale approach; moreover, this model has been proved to be more suitable for handling problems involving damage percolation in large composite structures and, at the same time, managing boundary layer effects