Micro scale numerical modeling of the fatigue behavior of fiber reinforced polymers

Kurzfassung

Due to a lack of knowledge and robustness in current design processes regarding the fatigue behavior of composites, a “no-damage-growth” certification requirement is imposed on composite aerospace structures. This leads to strain limitations which thwart the lightweight potential of fiber reinforced composite materials. Numerous material models in all degrees of complexity---ranging from straight-forward fatigue life models to discrete crack or delamination growth approaches---try to capture the fatigue behavior mechanically, yet fail to predict the behavior for other than the investigated load case, material, or layup. One weak point is usually the damage initiation criterion which is often empirical of inherent, i.e. the presence of a pre-crack is required. The numerous approaches show that the damage mechanisms are complex and their cause is not too well understood. Part of the problem is the complex matrix (polymer) behavior which shows time/frequency dependencies, i.e. needs to be modeled viscoelastically or viscoplastically. For cyclic loading, this frequency dependency along with other parameters such as several load levels, layups and materials need to be investigated experimentally to have a sound experimental basis which is often not feasible and thus limits the applicability of the material model. The pure amount of material models indicates a need for detailed damage mechanism research, i.e. the underlying effects of fatigue damage need to be investigated. Fatigue damage tends to start very early and propagates until final failure. The mechanisms are similar to static loading and include fiber/matrix-de-bonding, transverse cracks, delamination, fiber breakage and many others. Damage like fiber/matrix-de-bonding initiates at the micro-scale and at multiple locations until further degradation coalesces these sites into a transverse crack. When a transverse crack hits a ply interface of an adjacent layer, a delamination site is likely to be initiated. Modeling these effects on a structural level, i.e. the macro scale, requires an inaccurate “smoothing” of the actual damage cause to the homogeneous unidirectional layer or even the whole layup. Therefore, a micro scale approach to fatigue investigations is reasonable. For a detailed investigation of the initiation and propagation of micro scale fatigue damage, a representative volume element (RVE) is used. The 3D RVE is created automatically using a model generator which has been implemented using the Python scripting interface of ABAQUS. A graphical user interface lets the user set a fiber volume fraction and relevant material and geometric data. Periodic boundary conditions are applied by means of equation constraints and three reference points whose degrees of freedom are equivalent to the full 3x3 macro displacement gradient. While the fibers are modeled linearly elastic without damage, the matrix material is viscoelastic. The damage rate dD/dN, where D is the scalar damage variable and N the number of cycles, of a matrix material point is updated depending on its accumulated viscoelastic hysteresis energy and two material constants determined in neat resin cyclic loading experiments. For the sake of numerical efficiency, an adaptive cycle jump algorithm is implemented to overcome the necessity of a cycle-by-cycle analysis. To be able to account for weak and strong fiber-matrix-interface properties, the material data can be adjusted for a discrete layer of elements around the fibers. Despite the straight-forward modeling and material damage approach, first results show a good qualitative agreement with micrograph images of cyclic loading specimens from the literature with respect to the damage initiation and propagation behavior. This indicates that hysteretic effects caused by the viscoelastic/-plastic polymer material provide a meaningful physical measure for the damage modeling of composite materials not only on the micro scale but also on a structural level.