Addressing the transportation industry megatrends to improve fuel efficiency and reduce carbon emissions, lightweight polymer composites are replacing heavier metal counterparts in automotive, aerospace, and commercial vehicle applications.
Polymer composites also offer design flexibility, easy fabrication, and parts consolidation. As transportation industry engineers faced with stringent safety requirements and dynamic applications adopt polymer composite solutions, accurate material models are required to predict behavior and failure.
Over-molding continuous fiber reinforced preforms with short glass reinforced polyamide (PA) 6,6 nylon may be used in lightweight door reinforcement beams to protect from side impact. Engineers from DuPont manufactured a demonstration beam by compression molding a woven fabric reinforced nylon sheet, followed by over-molding a short fiber reinforced nylon polymer.
Short fiber composites modeling
Short fiber reinforced composite plaques are manufactured by injection molding thermoplastic polymer compounded with short glass fiber into a mold. Dog-bone shaped tensile coupons are cut from the plaque at three different angles, 0°, 45°, and 90°, with respect to the primary flow direction.
Accurate representation of fiber orientation is essential in developing an anisotropic material model for short glass reinforced materials. The orientation is estimated by duplicating the injection molding process with a mold filling analysis using Moldflow, an Autodesk mold filling simulation software product. The resulting fiber orientation distribution is mapped onto the 3-D structural mesh of the dog-bone specimen.
To check the accuracy of the fiber orientation predicted by the mold filling simulation software, an experimental determination of the fiber orientation at the center of the plaque was done by extracting the orientation from tomography images taken through the thickness.
A comparison was made at the plaque's center, between experimentally determined 2nd order orientation tensor values and those predicted by the mold filling simulation. This comparison showed reasonably good agreement, lending confidence to the application of the mold filling simulation to predict the fiber orientation values for the entire plaque.
Two phases, glass fiber and PA 6,6 matrix, were considered in the multi-scale material modeling. An elastic model was used to describe glass fiber behavior, while an elasto-viscoplastic (EVP) model was selected to represent PA 6,6 matrix behavior.
Researchers determined the elastoplastic (EP) matrix parameters from quasi-static test data, by importing the 0° and 90° test data into an e-Xstream Engineering Digimat MX module and using its reverse engineering (RE) optimization algorithm to determine the EP matrix parameters, such as yield stress, hardening modulus, and exponent. The calibrated EP matrix model and the elastic fiber model were then imported into a Digimat MF module to calculate the composite quasi-static stress-strain curves. The calculated model results were in good agreement with the test data measured at three angles.
After all EVP parameters were determined, two viscoplastic (VP) models were imported into the MF module to simulate the material's response when subjected to loading at different speeds and angles. High strain rate tensile data at 0° and 90° were selected for RE of the VP model parameters.
Both models captured the VP effects, but the current yield Norton model computed greater tangent stiffness at stress saturation and high strain rates, while the Prandtl model calculated greater tangent stiffness when the material enters into the plastic region. The current yield Norton model was selected for further development of failure model based on this overall comparison.
A 3-D finite element model was created using Abaqus to simulate high strain rate tensile tests. The predicted material response was softer than the test data, which suggested a mismatch of microstructure definition between numerical analysis and test specimens. One major factor leading to the discrepancy was the rough agreement between orientation from mold filling simulation and actual measured data. Further study of the mold filling analysis is needed to develop a more accurate model.
The strain-based failure model predicted early failure in all cases, while the stress-based failure model underestimated the failure at highest strain rate for all three angles, and tended to over predict at lower strain rates for 0˚ and 90˚. This may relate to how the orientation is defined during the RE and/or details of the Digimat algorithm for hybridization and failure indicator development.
Overall, the model was able to capture key features of the orthotropic rate dependent behavior of short fiber composites by taking account of microstructure, fiber orientation, and mechanical behavior per phase. Further study and improvements in these algorithms may lead to improvements between the model predictions and test data.
Woven fabric composites modeling
Glass woven fabric composites are composed of three layers of 2-2 fabric sheet (2 yarns in warp and 2 yarns in weft) and PA 6,6 matrix. Specimens are cut from the sheet at angle of 0°, 45°, and 90° with respect to the warp direction.
The orientation of 2-2 woven fabric, which is a balanced weave, is approximated in the material model by two unidirectional tapes oriented in the 0° and 90° directions. Because 0° and 90° tensile behavior is dominated by the fiber and 45° tensile behavior is dominated by the matrix, the stiffness in 0°/90° is much higher than the stiffness in 45°.
In addition, viscoelastic effect is observed in 0°/90° test specimens, while VP is observed in 45° test specimens. The model presented here assumes a simple elastic model for fiber phase and EVP model for matrix phase. So the model behavior at composites level is EVP and the viscoelastic feature is not included. Since the balanced weave makes the behavior in 0° and 90° similar, only 0° data are used for model development and CAE validation.
Like the modeling procedure for short fiber composites, an EP model for woven fabric composites was developed first.
Based on the observation of different behavior in 0°/90° and 45°, maximum principal stress failure was defined for fiber and maximum principal strain failure was defined for matrix. A strain rate dependent failure model was built initially. Using the RE feature in the MX module, matrix failure strain at each strain rate was calculated using 45° curve and fiber failure stress at each strain rate was calculated using 0° curve. The calibrated EVP model was implemented in the MF module to simulate rate dependent composite response at all three angles.
The model captured rate dependent effect at 45° very well, but EVP model of matrix had no influence on response at 0°/90°, which is dominated by fiber. All calculated curves at 0°/90° are superimposed and represent stiffness at strain rate of 15/s. Although the rate dependent failure model worked well in the MF module, there is strain rate oscillation in the explicit FE model causing unexpected early failure. So both strain- and stress-based strengths are modeled as independent of strain rate. Finally, the stress failure value at 15/s for the 0° data and the strain failure value at 28/s for the 45°data data were selected for fiber stress strength and matrix strain strength.
A shell finite element model with the actual size of woven fabric composites coupon was created. Constraints were applied on both ends to represent clamped boundary condition in experiment. One end was fixed and the other end was moved at a constant velocity in length direction. The developed EVP model with failure for woven fabric composite was assigned to the specimen.
Since the viscoelastic effect was not included in the model, the rate dependent behavior at 0° was not captured. However, the model results had a good agreement with the measured data for all speeds at 45°. Moreover, the predicted failure represents the high rate failure very well in both directions.
Structural FEA of over-molded beam
An over-molded beam manufactured using DuPont’s hybrid material technology was composed of a compression molded woven laminate layer over-molded with a short fiber reinforced thermoplastic. An FE model was generated based on actual geometry with the beam length of 730 mm and width of 140 mm. Two layers of shell elements sharing the same nodes were employed to represent laminate layer and injection over-molded layer. The total beam thickness was 3 mm with a half thickness for each layer.
The predicted stiffness of both models matched the measured data well. The model with strain failure for short fiber composites predicted failure when the force reached about 5800 N. Thereafter, the beam continued to carry load until the final failure at about 6600 N. A deeper examination of the failure between the initial and final failure indicated the initial load drop was caused by failure of the short fiber composite layer. After this initial failure the woven fiber composite layer continued to carry load up until it failed.
The model with stress failure predicted failure at 7900 N, which corresponded well with the maximum force reached in the test. When stress failure model was used for the short fiber composite layer, failure in this layer was delayed, resulting in a delayed onset of the global beam failure.
High compression stress and a strong stress gradient are found localized in the contact area, causing global failure. Better model prediction can be achieved by reducing stress gradient localization by using a finer mesh and/or redefining the failure model to allow for different tension and compression failure criterion, as well as damage evolution after failure.
This article is based on SAE International technical paper 2014-01-0961 by Alan R. Wedgewood, Patrick Granowicz, and Zhenyu Zhang, DuPont.