ABSTRACT of the Doctoral Thesis
For structural analysis of laminated fiber reinforced polymer composites, a reliable constitutive model is required which describes the intra-ply behavior of the embedded plies. As it is desired to exploit the potential of laminated composites, also the response beyond elasticity has to be accounted for in such a model. Motivated by this fact, a constitutive model for the nonlinear intra-ply behavior is developed, implemented, and applied in the present work. In the formulation of this constitutive model, two major types of effects which both lead to pronounced non-linearity are distinguished as being motivated from experimental observations. These effects are stiffness degradation and unrecoverable strain accumulation.
Stiffness degradation is attributed to microscopic brittle matrix cracking, fiber/matrix debonding, as well as progressive fiber failure. Such phenomena are expected to lead to a decreased stiffness primarily, and, accordingly, respective strains are taken to be recoverable after unloading. Stiffness degradation is modeled via continuum damage mechanics, whereby the ply material behavior is featured by the behavior of an appropriate fictitious material. This way, the anisotropic effect of brittle damage is incorporated. The formulation for damage evolution consists of two different approaches. The first approach deals with stiffness degradation due to widespread, evenly distributed matrix dominated phenomena. Respective damage evolution equations are related to the material exertion predicted by recourse to Puck's failure surface. Here damage accumulation is accompanied by slight strain hardening. The second approach for damage evolution deals with stiffness degradation triggered by localized matrix dominated as well as fiber dominated phenomena. Respective damage evolution equations are formulated with respect to elastic strains. Here damage accumulation causes strain softening.
Unrecoverable strain accumulation is associated to the formation of microscopic areas with inelastically deformed matrix material. Respective strains are referred to as plastic strains since their evolution is described by two modeled plasticity mechanisms. These mechanisms treat the evolution of plastic in-plane shear strains and the evolution of plastic normal strains of the ply. The presented approach leads to a multi-surface formulation and is able to capture the ductile portion of the behavior of fiber reinforced polymer plies.
The development of the constitutive model aims at the analysis of laminated, thin-walled structures as for example used in many applications of aeronautics. Since the Finite Element Method is a state-of-the-art tool for structural analyses, the constitutive law is implemented as user defined material routine for the commercial Finite Element package ABAUQS/Standard. In this context also the material Jacobian matrix is derived. Furthermore, viscous regularization to alleviate convergence problems as well as a method to alleviate the well-known mesh dependency in the strain softening regime are addressed.
In order to asses the predictive capabilities of the proposed constitutive model, nonlinear Finite Element simulations are conducted. Thereby different material systems, various laminate layups, complex loading scenarios, and structural responses are considered. The predictions are discussed in detail and compared to experimental results. The agreement between predictions and experimental results is shown to be good.
The proposed constitutive model offers some outstanding features concerning the simulation of laminated composites. Firstly, residual deformations are predicted which is very unlike to many other available models. Secondly, the laminate stiffness affected by anisotropic brittle damage is captured. Finally, the behavior of components in the proximity of the load carrying capacity can be simulated since strain softening is modeled as well. All the mentioned phenomena are incorporated within a single constitutive model, which is easy to calibrate and readily implemented within the Finite Element Method.