W. Van Paepegem

A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites

Abstract During the last decades, fibre-reinforced composites have been established as competitive materials for naval, automotive and aerospace industry. However, the fatigue behaviour of fibre-reinforced composites is so diverse and complex that present knowledge is far from complete. Two commonly used approaches to model fatigue damage are the residual stiffness and the residual strength approach. In this paper, the change in the modulus of elasticity due to fatigue damage is studied for uni-axial bending. The proposed modelling approach is new in two ways: (i) the damage growth rate—a measure for stiffness loss—is expressed by two separate terms representing the initiation and propagation phase of damage respectively, (ii) a static failure criterion is modified to represent the decreasing reserve to ultimate static strength. In that way this coupled approach of residual stiffness and strength is capable of simulating the three stages of stiffness degradation: initial decline, gradual reduction and final failure, as well as the stress redistribution due to the loss of stiffness in the damaged zones. The model has been applied to displacement-controlled bending fatigue experiments of plain woven glass/epoxy specimens.

Effects of Load Sequence and Block Loading on the Fatigue Response of Fiber-Reinforced Composites

The vast majority of fatigue loading experiments are constant-amplitude tests, although this type of fatigue loading is hardly present in real in-service fatigue loading conditions. However, due to the expensive and time-consuming nature of variable-amplitude experiments, their effect is often assessed by performing block loading experiments with various low-high and high-low sequences. In this article, the effects of load sequence and block loading on the fatigue damage development in fiber-reinforced polymer composites is investigated. First it is shown that the opinions in the open literature on the damaging effect of low-high and high-low load sequences are divided. Next the effect of block loading on the bending fatigue behavior of composites is experimentally tested and numerically simulated with a newly developed fatigue damage model. Finally, numerical simulations show that the transitions from low to high stress levels are the most damaging, and that the number of transitions and their relative importance in particular determine which block loading sequence (low-high or high-low) is the most devastating.

Experimental set-up for and numerical modelling of bending fatigue experiments on plain woven glass/epoxy composites

In general fatigue of fibre-reinforced composite materials is a quite complex phenomenon, and a large research effort is being spent on it today. Due to deficiencies in the current life prediction methodologies for these materials, composite structures are often overdesigned: large factors of safety are adopted and extensive prototype-testing is required to allow for an acceptable life time prediction. This paper presents an investigation of the fatigue performance of plain woven glass/epoxy composite materials and of the numerical modelling of these composites’ behaviour under fatigue. First the experimental setup which has been developed for bending fatigue experiments, is discussed. The materials used are plain woven glass/epoxy specimens in two configurations: [#0o]8 and [#45o]8. Experiments show that these two specimen types, although being made of the same material, have a quite different damage behaviour and that the stiffness degradation follows a different path. Next a numerical model is presented which allows one to describe the degradation behaviour of the composite specimen during its fatigue life. This model has been implemented in a mathematical software package (Mathcad TM ) and proves to be a useful tool to study the fatigue degradation behaviour of composite materials.

Coupled Residual Stiffness and Strength Model for Fatigue of Fibre-reinforced Composite Materials

The fatigue behaviour of fibre-reinforced composite materials is complex and present knowledge is far from complete. Several classes of models attempt to predict the fatigue life and/or fatigue degradation of fibre-reinforced composites. Two major classes are the residual stiffness models and the residual strength models. This paper presents a phenomenological residual stiffness model which predicts the stiffness degradation as well as final failure of the composite component. The reserve to failure has been evaluated by means of a modified use of the Tsai-Wu static failure criterion. The fatigue damage model has been applied to displacement-controlled bending fatigue experiments of plain woven glass/epoxy specimens. The damage and stress (re)distribution, as well as the force-cycle history have been simulated and compared to experimental results. Due to the consistent integration of continuum damage mechanics and the residual stiffness approach, the implementation of the fatigue model in a commercial finite element code has been possible, which allows for an accurate simulation of the successive damage states during fatigue life.

Application of digital phase-shift shadow Moiré to micro deformation measurements of curved surfaces

The shortcomings of conventional shadow Moire topography have in the past been improved by means of the phase-shift method which enhances the sensitivity and allows to process the fringe patterns automatically. This paper presents a digital implementation of the phase-shifting process, which requires only one image to be taken. The grating lines, projected onto the deformed object surface, are captured directly with a digital camera. Next the reference grating is superimposed numerically onto the projected grating lines. Then a number of phase-shifts are performed taking into account the non-linearities in the expression for the height-dependent intensity field. Experimental results prove that these non-linearities can considerably affect the micro deformation measurements of curved surfaces. The proposed method is very efficient and eliminates all causes of erroneous measurements due to the miscalibration of phase-stepping devices.

Finite element approach for modelling fatigue damage in fibre-reinforced composite materials

Today, a lot of research is dedicated to the fatigue behaviour of fibre-reinforced composite materials, due to their increasing use in all sorts of applications. These materials have a quite good rating as regards to life time in fatigue, but the same does not apply to the number of cycles to initial damage nor to the evolution of damage. Composite materials are inhomogeneous and anisotropic, and their behaviour is more complicated than that of homogeneous and isotropic materials such as metals. A new finite element approach is proposed in order to deal with two conflicting demands: (i) due to the gradual stiffness degradation of a fibre-reinforced composite material under fatigue, stresses are continuously redistributed across the structure and as a consequence the simulation should follow the complete path of successive damage states; (ii) the finite element simulation should be fast and computationally efficient to meet the economic needs. The authors have adopted a cycle jump approach which allows to calculate a set of fatigue loading cycles at deliberately chosen intervals and to account for the effect of the fatigue loading cycles in between in an accurate manner. The finite element simulations are compared against the results of fatigue experiments on plain woven glass/epoxy specimens with a [#45°]8 stacking sequence.

Fatigue degradation modelling of plain woven glass/epoxy composites

Due to their anisotropic and inhomogeneous nature, the fatigue behaviour of fibre-reinforced composite materials is complicated and since many years a large research effort is being spent on this problem. Despite these efforts, fatigue design of fibre-reinforced composites still has to rely mostly on expensive time-consuming fatigue experiments and large safety factors have to be adopted. In this paper, a combined experimental/numerical investigation of the fatigue behaviour of plain woven glass/epoxy composites is presented. Bending fatigue tests were used to yield the experimental data. With the aid of an advanced phase-shift shadow Moire technique, an out-of-plane displacement profile during fatigue life of the composite specimens was recorded at a number of intervals, as well as the bending force history. A residual stiffness model, which describes the fatigue damage behaviour of the composite material, was adopted. Next, a new finite element approach was developed to implement the fatigue damage model in a commercial finite element code that proves to be capable of simulating the observed experimental results.

Response of FBGs in Microstructured and Bow Tie Fibers Embedded in Laminated Composite

Fiber Bragg gratings in bow tie fiber and highly birefringent microstructured optical fiber are embedded in a carbon fiber reinforced epoxy. The Bragg peak wavelength shifts of the embedded gratings are measured under controlled bending, transversal loading, and thermal cycling of the composite sample. We obtain similar axial and transversal strain sensitivities for the two embedded fiber types. We also highlight the low temperature dependence of the Bragg peak separation of the microstructured fibers, which is an important advantage for this application. The results show the feasibility of using microstructured fibers in structural integrity monitoring.

Modelling damage and permanent strain in fibre-reinforced composites under in-plane fatigue loading

Abstract The vast majority of the fatigue models for fibre-reinforced composites is limited to one-dimensional loading conditions. Due to the heterogeneous and anisotropic nature of composites, the extension of these models towards multi-axial fatigue loading conditions is not straightforward. This paper presents a phenomenological residual stiffness model that predicts the stiffness degradation and (possible) permanent strain in fibre-reinforced polymers under in-plane fatigue loading. The model takes into account the actual stress state in each material point and does not make any assumptions about geometry or boundary conditions of the fatigue loaded specimen. As the presented model has been developed within a larger research programme, the emphasis in this paper lies on the theoretical modelling framework, rather than on an in-depth validation of the model which would require much more detail about the close feedback between experimental data and finite element simulations. Therefore the development of the stress–strain-damage relationships and the damage growth rate equations is explained thoroughly and a few finite element results are presented for plain woven glass/epoxy composites.

A PIV-based method for estimating slamming loads during water entry of rigid bodies

Hydrodynamic impact of bodies onto the water surface is a problem of great importance in the design of off-shore and naval structures (wave energy converters, off-shore platforms, high-speed boats, etc). Classical measurement techniques, namely pressure sensors, present major drawbacks in the determination of impact loads because of their intrusive nature. In this paper, we propose a method to determine the impact loads on rigid bodies during water entry, based on high-speed particle image velocimetry. The method consists of two steps: firstly, an automated procedure is developed to determine the velocity field from high-speed images during water impact. Secondly, the unsteady pressure field is estimated from the velocity fields, using a Poisson-based solver. The method is validated on a rigid wedge slamming experiment and the results are compared with results from computational fluid dynamics simulations (performed with the software LS-Dyna) and from the literature.