PSI - Issue 19

Marc J.W. Kanters et al. / Procedia Structural Integrity 19 (2019) 698–710 Marc Kanters et al./ Structural Integrity Procedia 00 (2019) 000–000

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Accurate modelling of short fiber reinforced plastics requires a valid representation for any microstructure. This is achieved by representing composite orientation tensor by a set of pseudo-grains having a fixed orientation and a given weight computed such that the weighted average of all fixed orientations equals the orientation tensor [Doghri2005], as illustrated in Figure 3. The behavior of a composite is then obtained in two steps. First, the behavior of each pseudo grain is computed from the matrix and fiber behavior via mean-field homogenization. Second, the composite behavior is obtained from averaging the behavior of all pseudo-grains [Doghri2005a]. The Digimat fatigue approach uses a stress-based version of the Tsai-Hill 3D transversely isotropic criterion, applied at the pseudo-grain level. As such, the three failure parameters (the axial tensile strength, the in-plane tensile strength and transverse shear strength) are defined at a level where the microstructure is well known, the pseudo-grain, and its values can be a function of lifetime, allowing an evolution of the failure envelope. Few stress – lifetime curves with different microstructure (at least three), allow determination of the fatigue failure indicator parameters. Digimat deals with mean stress sensitivity by scaling the stress tensor amplitude, using a factor that depends on the local stress ratio. The Digimat material model for lifetime prediction is calibrated in three steps, as illustrated in Figure 4: I) the calibration of an elastic model capturing anisotropic stiffness for any microstructure, II) the calibration of a fatigue model to predict lifetime for any microstructure, stress amplitude and load ratio, and III) the enrichment of the model lifetime prediction via the calibration of post-processing parameters capturing the sensitivity to stress concentration.

Figure 4: Overview of the workflow for material model calibration within Digimat.

4. Results and discussion 4.1. Calibration of the material model

4.1.1. Anisotropic stress-strain curves and model fit The stress field that serves as basis for the lifetime evaluation is calculated with an anisotropic linear elastic material model. This model is calibrated on the stiffness measured on specimens milled at various orientations from an injection moulded plate. Further input for the model is related to the material’s microstructure: glass fiber content, effective glass fiber aspect ratio, and the glass fiber orientation distribution across the specimen thickness (based on micro-CT data, see Figure 1). Next, the known glass fiber properties (Young’s modulus, Poisson’s ratio and density) are considered. To complete the material model, the linear elastic properties of the thermoplastic polymer matrix are fitted. The model prediction and experimental results are compared in Figure 5.