Multiscale Simulation of Unidirectional Carbon Fiber Reinforced Polymer Strength

A MultiMechanics White Paper

Finite element (FE) Analysis has become increasingly important for mechanical design and the development of new advanced materials. Being able to predict structural performance accurately and efficiently can circumvent the extensive time and cost of repetitive and rigorous material testing. 

However, with fiber reinforced polymers (FRPs), the assumption of homogeneity as well as the generalization of a material based on global properties does not sufficiently describe the material close to failure.

The key to accurately predicting component failure is to realistically capture microstructural damage under complex multiaxial loads while simultaneously relaying the material response to the part level. This is possible through TRUE multiscale analysis (similar to FE^2) but with a drastic reduction in computational cost) and in this paper, is applied to a specific FRP, unidirectional (UD) carbon fiber reinforced polymer (CFRP). 

The first study demonstrates the benefit of stochastic variance at the microstructure length scale. Multiple representative volume elements (RVEs) are created with varying fiber volume fraction (FVF), slight fiber misalignment, and the fiber strength following the Weibull statistical distribution. These different RVEs are applied to a coupon, tested in longitudinal tension. Multiple runs of this multiscale model result in varying strengths and moduli due to the stochastic nature of the model. These results are compared against the experimental results this model is based on, showing good agreement. 

The second study uses a different RVE (representing the same UD CFRP), integrated in a model of a laminate with multiple plies in different orientations. The RVE’s constituent material properties (fiber, matrix, and fiber-matrix interface properties) are designated using only standard lamina level data. After the RVE is calibrated, three different laminate models for each material are run with the results showing stress-strain curve and strength of the coupon. These results are well aligned within the experimental data publicly available through the National Institute for Aviation Research (NIAR), demonstrating the accuracy of failure prediction using multiscale simulation.

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