A new constitutive equation to predict the nonlinear behavior of short fiber reinforced composite materials

Organic sheets and short fiber-reinforced composite materials as well as the components made of their combination, i.e., hybrid components, play a significant role in the automotive industry. Producing conventional thermoset-based composite materials have difficulties such as their improper automatic production procedure, major scrap rate, and high production price. The new generation of thermoplastic-based composites show advantages over thermoset-based composites such as their volume production capability, lower production prices, formability, and recyclability. Therefore, the thermoplastics seem to be a proper replacement for the conventional thermosets. Organic sheets made of glass fibers with a thermoplastic matrix and usually delivered as an unfinished production to exert final procedure such as thermoforming or over injection to achieve the final component. In addition to organic sheets, short fiber reinforced thermoplastics are increasingly used in automotive industry, mostly using mold flow process, which offers a high design freedom and faster volume production procedure. Combining short fiber reinforced composite materials and organic sheets reaches the hybrid components which show excellent mechanical performance in comparison to their remarkably lower weight. This research begins with the production of the hybrid composite component which is supposed to be used for the load-bearing parts in the light vehicles. The production procedure, as well as the constituents decompositions, are explained. Even though the hybrid components are made by two different technologies, i.e., back-injected and compression molding, but since our main objective is to simulate the injected elements, then the compression molding procedure will be skipped in the numerical simulations. In the next step, the 3-point bending experiments are performed on the hybrid component in both direction and different loading rates. The configuration of the test is explained in detail. The components demonstrate different response under different loading rates and various boundary conditions which is widely discussed in this work. According to the experimental results, the hybrid component under 3-point bending test does not show a high degree of nonlinearity before damage. Therefore, to simulate the back-injected hybrid component under bending, we introduce a linear elastic model including a damage model. The proposed model is described and a rate-sensitive damage model, as well as the integration schemes, are introduced for either of the implicit and explicit solvers. The torsion test is prepared for the back-injected-made hybrid component which from the very beginning demonstrates a high degree of nonlinearity. The nonlinear behavior of the component is related to its elasto-plastic response, and it is our main concern in the current research. The short fiber-reinforced composites can be considered as transversely-isotropic materials. Thus, to catch the plasticity induced nonlinearity, we introduce an elastic-plastic model and the post-plasticity damage model. The model is founded on the representation theory of the basic invariants of the anisotropic materials. The associated constitutive equations for transversely isotropic materials are proposed. This work comprises the representation of the general constitutive equations, an introduction to the representation theory and the elastic constitutive equations for transversely isotropic materials. Since we deal with the non-metallic materials, then the elasto-plastic model must be non-associated which requires a potential function be defined besides of a yield function. These requirements, as well as the proper invariants for the transversely isotropic materials, are discussed and introduced. Having defined the basic requirements of an elasto-plasticity model, we introduce the elasto-plasticity model. Since the numerical integration scheme requires a general definition of the model, then it is formulated in a general continuum mechanics fashion. Also, to deal with the rate-dependent behavior of the hybrid component under bending, a simple model is introduced. A Continuum Damage Model (CDM) is proposed for the post elasticity damage phenomenon. A damage model for degradation of the transversely isotropic material after reaching the saturation stress is developed based on the CDM concept. The so-called non-local damage model is described as well. The numerical implementation and the integration schemes are discussed which include the description of the backward Euler and the explicit integration algorithms. In the last step, the numerical and experimental results are given and discussed. The bending test for the hybrid components are performed under quasi-static and the velocity of 127 mm/sec loading conditions. Other than ambient condition, the quasi-static bending experiment is performed for the components preheated by 90 degree Celsius, and the results are available. The numerical results for the quasi-static and dynamic 3-point bending are given, respectively. The elasto-plasticity plus the damage after plasticity models’ numerical results are presented and validated by the results taken from [1] for the basic tensile and compression test results of PA6GF60. The numerical and experimental results for the back-injected-made hybrid component under torsion are presented.