Analysis of the viscoelastic deformation behaviour of continuous fibre-reinforced polymers subjected to the automotive painting process

Abstract

The automotive industry has developed an interest in manufacturing structural parts from continuous fibre-reinforced polymers because legislation is becoming more strict on the permissible CO₂ emission of newly produced vehicles. Additional requirements on the level of recyclability has raised the question if composite materials with a thermoplastic matrix in particular can be utilised in the body structure. From the perspective of cost sensitivity, the conventional automotive manufacturing chain has to remain as it is and requires the body structure to pass through the automotive paint shop and subjects all structural elements to significant hygrothermal loading. The objective of this research is to analyse the deformation behaviour of continuous fibre-reinforced thermoplastics subjected to hygrothermal loading characteristic for the automotive painting process.

Studying the theory behind viscoelastic problems revealed that numerical solutions to the integral form of the linear viscoelastic constitutive equations often pose a problem regarding computational memory usage because of the importance of strain history. Utilising a recursive formulation of the constitutive equations eliminated this problem and identified the required material parameters for the numerical model. Thermal expansion, hygroscopic shrinkage, polymer-chemical effects, and stress relaxation were the four phenomena that governed the deformation. Measurements with a dilatometer, a micrometer, and an analytical scale yielded quantitative results about hygrothermal expansion. Thermogravimetric analysis provided information on the moisture diffusion and dynamic mechanical analysis quantified the stress relaxation behaviour. Quasi-static tensile tests confirmed the linearity of the viscoelasticity and digital image correlation supplied the major Poisson’s ratio.

A finite element model has been developed that implements hygrothermal expansion and takes into account orthotropic linear viscoelastic behaviour by means of a material user subroutine. Adopting a sequential uncoupled simulation approach allowed the prediction of heat transfer, moisture diffusion, and stress distribution. A semi-numerical simulation approach enabled the calculation of the expansion of symmetric balanced laminates through classical laminate theory whilst taking into account the time- and temperature-dependency of the mechanical properties computed with a micromechanical model created for special orthotropic laminae. Sensitivity studies justified the usage of one-dimensional heat transfer- and moisture diffusion simulations. Moreover, mesh- and time step convergence studies revealed the sensitivity of the simulation to these parameters.

Dilatometer experiments with dry- and moisture saturated multi-directional specimens confirmed the correct calculation of hygrothermal expansion. Increasing in complexity, measuring the out-of-plane deformation of a clamped unidirectional tensile specimen subjected to a temperature profile that resembles the most severe thermal loading found in the automotive painting process confirmed a satisfactory agreement between the numerical results and the experimental data. Geometric compensation for the thermal expansion of the fixture and choosing graphite as construction material kept the thermal expansion of the fixture to a minimum. Components with the geometry of the roof bow that is currently in series production for the BMW 7 Series were manufactured by a thermoforming method to allow validation of the simulation with complex geometry. A proper agreement between the predicted deformation behaviour by the semi-numerical simulation and the optical measurements of the dry- and moisture saturated roof bows with various multi-directional lay-ups validated the functioning of the developed simulation.