Micro-mechanical modeling of continuous glass reinforced isotactic polypropylene: Influence of strain rate and temperature

Thermoplastic composites have become attractive for many engineering applications due to advantages such as high specific strength, short processing cycles and low cost at high volume production. Within this class of materials, continuous fiber reinforced, unidirectional glass/isotactic polypropylene (G/iPP) is one of the strongest competitors thanks to the balance between its good mechanical properties and low manufacturing cost. To expand its applications in load bearing structures, the ability to predict the mechanical performance under anticipated conditions is essential.

Structural components composed of continuous fiber reinforced G/iPP composites can be exposed to various loading and environmental conditions such as load application rates, loading angles and temperatures. As a result of load and temperature dependent nature of their polymer constituents, both the stress-strain response as well as the failure kinetics of G/iPP structures may be affected. Accurate numerical models that can simulate the materials response over a wide range of loading rates and temperatures conditions in a virtual environment would reduce the extensive experimental cost and time to understand the effects of each condition on its mechanical response and failure. Such models also enable investigation of complex, local failure phenomena that are difficult to observe in the experiments. The main goal of this thesis to provide a numerical tool that allows prediction of the mechanical response of continuous fiber reinforced, UD G/iPP composites at different temperatures, strain rates and loading angles by means of a micro-mechanical approach.

The first step towards this objective was to obtain an accurate mathematical description of the stress-strain response of iPP over a large range of strain rates [10−5, 10−1] s−1 and temperatures [5 – 75°C]. This was achieved by extending the Eindhoven Glassy Polymer (EGP -) model to three processes, each with their own deformation kinetics and time-dependence. These contributions can be assigned to deformations within the amorphous and crystalline phases of iPP. A methodology was developed to determine the model parameters in a straight forward manner.

Secondly, a micro-mechanical tool was developed based on the three-process EGP model to represent the mechanical response of iPP in a representative volume element (RVE) scheme. Realistic RVEs were generated from microscopic images of cross-sections of the composite material. To determine the appropriate image size to be an RVE, the micro-structural irregularity of unidirectional G/iPP composite was investigated on microscopy images in terms of its averaged fiber volume fraction, local fiber volume fraction and the nearest neighbourhood distances. An appropriate size was determined as 250 μm for the material under consideration, providing a good representation of both the fiber irregularity and the mechanical response of the actual material.

Next, the obtained constitutive relation was combined with realistic RVEs to perform simulations over a range of strain rates, temperatures and loading angles. As microscopic analysis revealed a good adhesion between fibers and matrix, the micromechanical simulations could be performed assuming perfect adhesion. Micro-mechanical simulations were subsequently employed to get insight in the possible causes of failure at various loading conditions.

Simulations for different loading angles could be performed using the same RVEs by use of a novel method to apply the boundary conditions at the desired loading angle. This method was applied for the first time in large deformations. For a loading angle of 90°, i.e. transverse to the fibers, the simulated stress-strain responses at temperatures of 23°C, 50°C and 90°C are in a good agreement with the experiments. Moreover, also the stress-strain responses under a tensile loading with angles 20°, 30° and 45° with respect to the fiber direction are predicted well. For smaller angles such as 15° and 10°, the strain hardening response was over predicted due to the significant rotation of the fibers during deformation.

Finally, the micro-mechanical model was employed to study the local stress and deformation fields in the composite at the point of macroscopic failure. Two separate failure modes were observed in the uniaxial tensile experiments performed on unidirectional G/iPP composites. The first one is pre-yield failure, which is typically observed at 23°C and 50°C for the investigated strain rates at large loading angles. The failure mode changes to macroscopic plastic failure with decreasing strain rate, increasing temperature or decreasing loading angle.

In the case of pre-yield failure, the hydrostatic stress level appeared to be the main cause. At higher temperatures, or lower loading angles, the magnitude of hydrostatic stress decreases and macroscopic plasticity is observed in the composites’ response. Failure after large macroscopic plastic deformation appears to be controlled by the local equivalent plastic strain. At a loading angle of 45°, the hydrostatic stress still appears to have a minor role.

In conclusion, the present thesis provides a micro-mechanical tool that can effectively simulate the mechanical response of continuous fiber reinforced, unidirectional G/iPP composites over a wide range of strain rates, temperatures and loading angles based on an accurate polymer constitutive model and a realistic RVE scheme with a novel method for the appropriate loading conditions.