Micromechanical modeling of the progressive failure in short glass-fiber reinforced thermoplastics

(eng) Thermoplastics reinforced with short glass fibers are increasingly used in many industrial applications due to their attractive mechanical properties, rapid processing and relatively low manufacturing cost. Injection molding is a widely used process for the production of reinforced parts with complex shapes. However, the concentration and the orientation of the fibers vary from one point to the other. This induces a strong heterogeneity throughout the material, making the prediction of its behavior and rupture a nontrivial task. Multi-scale or micro-macro approaches have been proposed in the literature in order to take into consideration the influence of the microstructure on the macroscopic properties. Among them, Mean-Field Homogenization predicts with satisfying accuracy the macroscopic response and to a lesser extent the per-phase responses. In this work, a new approach for modeling the behavior of thermoplastics reinforced with short glass-fibers has been developed. The constitutive law is based on an elastic-plastic formulation. The micro-macro transition is achieved in two steps using a Mori-Tanaka (MT) scheme and a Voigt scheme (or also a selfconsistent scheme) while integrating phenomenological failure laws. One essential concept in this modeling approach is the Pseudograin (PG) unit. A PG is defined as a fictitious subregion of the microsctructure where all fibers are aligned and share the same aspect ratio. Failure models are applied at the PG level. An incremental MT model is then used to predict the phase averages of the stresses and strains in each PG. Once average responses are computed, a failure procedure is applied at each PG to predict its state of degradation. Finally, the overall average response is computed using a second homogenization rule. Two models have been developed based with different treatments of damage. The first one is called the "First Pseudograin Failure" model in which failure criteria are used to predict the PG failure. The second one is the "First Pseudograin Damage" model in which continuum damage mechanics is adopted to predict the progressive degradation of a PG. Thus, the implemented methods account for the damage within the PGs. It can also be used for non-proportional loadings cases and can be extended to rate-dependent behavior. An extensive validation of the predictions against experimental data is conducted for short glass-fiber reinforced polyamide 6,6.