Study of uncertainty in the application of the micromechanical enhancement method to predict failure initiation of fiber composites

Alvaro Jesus Mendoza-Jasso, Purdue University

Abstract

Failure initiation of carbon fiber reinforced polymer matrix composites and the uncertainty measurement of the model used to predict this phenomenon are the central topics in this work. To begin, an open hole off axis specimen in tension was modeled with finite element software. The FE model replicated the geometry, material properties and boundary conditions of tests performed on real composite coupons so that experimental data were available to compare to model predictions. The coupon was not modeled explicitly, i.e., it was not represented with the fibers embedded in the matrix. Instead, it was modeled as a monolithic material with homogeneous mechanical properties. The resultant average strain field in the homogeneous coupon in tension was de-homogenized with the MME so that the average strain fields were localized. The volumetric and deviatoric strain invariants were calculated following the de-homogenization or enhancement. De-homogenization was taken one step further: randomness in fiber distribution was considered in order to model the dispersion of the fibers in the composite. The implementation of random fiber distribution aimed to replicate the variability in mechanical properties and mechanical behavior that characterizes the composite. With the strain invariants calculated after consideration of fiber distribution randomness, locations with high values of strain invariants were identified with contour plots of the coupon. The largest values of strain invariants were located at the hole surface in a very specific interval. Thousands of simulations with the post-processing of FE data allowed the definition of a failure angle distribution that agreed well with the experiments in as much as 75%. An investigation on the capability of SIFT and MME when they were used to predict failure initiation and failure location in the open hole off axis coupon was carried out. Predictions' validation of the failure angle interval was performed with the use of Bayesian methods. Bayesian approaches' core characteristic is that they allow update of existent data's statistics as new data arise. The resource used is known as the Bayes' factor. We consider the experimental data as the existent data. Model predictions were considered as the update to the experiments. The Bayes' metric calculated from model predictions and experimental data gave a good indication that the experiments support the predictions performed with the model. Finally, a more general validation of SIFT and MME was elaborated using also the Bayes' factor. In this case, 9-fibers finite element models were used to represent explicitly the composite material. These simulations were taken as a representation of experimental data. A unidirectional tensile deformation was applied to the 3-cells by 3-cells model and the resulting strains were used directly to calculate the strain invariant at failure with no use of MME, since the model represented explicitly the material. The MME method was also applied by finding the dependency of the deviatoric strain invariant with the fiber volume fraction randomness and with the applied strain, including the effect of thermomechanical strains. Thermoresidual strains were found to cause non-linear response of the deviatoric strain invariant. Specifically, a quadratic relationship was found between the invariant and the volume fraction that corresponded to the value of the applied strain in tension simulated with the explicit FE model. This quadratic relationship was evaluated thousands of times with the random generated volume fraction distribution. Hence, the random volume fraction distribution generated a random strain invariant distribution. Validation of this new data calculated with MME was performed similarly to the case of the open hole geometry. In this case, the deviatoric strain invariant distribution derived from the explicit finite element model was taken as the existent data, the experimental data. The distribution calculated with MME for the thousands of realizations with the quadratic relationship was considered the update to the experiments. The Bayes' factor was calculated by proceeding similarly as before. Once more, the Bayes' metric gave an indication of the high reliability attainable when SIFT-MME is used to predict composite failure initiation. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Koslowski, Purdue University.

Subject Area

Mechanical engineering|Materials science

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