A fatigue damage model for epoxy resin and its application to fiber reinforced plastics

Kurzfassung

Introduction Epoxy resins feature good mechanical properties and a high adhesiveness to many substrates which makes them a widely used candidate as matrix material for fiber reinforced plastics (FRP) and as structural adhesive [1], e.g. for wind rotor blade applications [2]. Within these applications, epoxy resins are exposed to mechanical loading including cyclic loading conditions. The gradual property degradation of FRP under cyclic loading is related to the successive fatigue degradation of the epoxy matrix [3]. Also, for adhesively bonded joints, the fatigue damage behavior of the epoxy adhesive is crucial, as cracks initiating in the adhesive tend to propagate into the adherends [4]. Thus, understanding the fatigue phenomena of epoxy and developing reliable methods for prediction are key aspects for designing robust FRP structures and composite joints. Methods This contribution presents a stress-based progressive fatigue damage model for epoxy considering the non-linearity and the tension/compression-asymmetry of the constitutive material behavior [5] as well as the mean stress effect of the fatigue behavior [6]. The law by Palmgren [7] and Miner [8] is used to consider variable loading amplitudes and a property degradation law, active after damage initiation, enables to account for stress redistributions occurring within the matrix of FRP. SN curves obtained from uniaxial cyclic loading with different stress ratios are used for model calibration (Figure 1). Arbitrary multiaxial stress states are assessed by transferring them to equivalent uniaxial stresses using a procedure based on a pressure-dependent failure criterion [9]. The progressive fatigue damage model is implemented as user-defined material subroutine within the Fortran library MCODAC [10] to be available within Finite Element Modelling software. For assessment and validation, the model is applied in a micro-scale modelling framework for predicting fatigue behavior of unidirectional FRP subjected to cyclic tension, compression and shear loading. Doing this, the morphology of the composite’s micro-scale, consisting of carbon fibers distributed within the epoxy matrix, is modelled by a Representative Volume Element (RVE) with hexagonal fiber packing and periodic boundary conditions. Results The fatigue damage model of the pure epoxy in conjunction with the RVE approach yields to a qualitatively good prediction of the FRP’s fatigue behavior with respect to the mean stress effect and to the crack patterns observed under different loading conditions. However, the model overestimates the fatigue life for higher stress levels and underestimates for lower stress levels (Figure 2). Conclusion The application of the developed progressive fatigue damage model for pure epoxy resin is demonstrated for predicting the fatigue behavior of unidirectional FRP. From the deviations observed between model prediction and fatigue test data for unidirectional FRP, the following suggestions for improvement of the model are derived: - Implement a pressure-dependent visco-plastic constitutive model to account for plasticity effects which may accumulate over fatigue life. - Replace the linear constant life diagram – currently used to capture the mean stress effect – with a non-linear approach to mitigate the fatigue life underestimation at lower stress levels [6]. - Address challenges concerning the transfer of multiaxial stress states into equivalent uniaxial stresses, for instance by following an energy-based approach. References [1] F. Jin, X. Li, S. Park. Synthesis and application of epoxy resins: A review. 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