Fragmentation Prediction for a Brittle Ceramic: An Integrated Two-Scale Model Approach
A new implementation of a multi-scale fragmentation model is introduced that combines existing independent macro and micro-scale models into a single material model within the Library of Advanced Materials for Engineering (LAME) that can be used directly by the finite element structural mechanics code SIERRA/SM, developed at Sandia National Laboratories. The implementation not only joins existing independent fragmentation models into a single framework, but also enables further development by virtue of being integrated into SIERRA/SM. Integration with a finite element structural mechanics code for a true two-way coupling of the fragmentation models that were previously independent. Hereafter, the prior implementation will be referred to as the sequentially applied fragmentation model. In contrast, the newly developed model will be called the integrated two-scale model. The sequentially applied fragmentation model consists of two independent models applied sequentially to account for the macro-scale and microscale fragmentation. The macro-scale fragmentation behavior is calculated using an elastic gradient damage explicit material model developed to model fracture in brittle materials. The micro-scale fragmentation model is an implementation of the 1D cohesive-zone model developed by Zhou, et al. The micro-scale model is implemented by post-processing the macro-scale data that provides initial conditions for the 1D analysis. The micro-scale model is necessary to predict the resulting fragment size distribution at length scales inaccessible to the finite element based macro-scale model. The full range of fragmentation behavior is then predicted by combining the results from the two independent models. The sequentially applied fragmentation model was used to predict the fragments that result from impact loading of a brittle material, which in that case was a ceramic cylinder of commercial UO{sub 2} nuclear fuel. Understanding the fragmentation behavior of such materials is important for evaluating the risk of airborne particulate release under impact loading scenarios. This work will verify the implementation of the integrated two-scale model using the same experiment modeled by the existing sequentially applied model. The purpose of this manuscript is to introduce the new integrated two-scale fragmentation model and validate the implementation against the existing sequentially applied model for a specific case of impact loading of a brittle material. This validation case will not fully utilize the benefits of having the model integrated into the finite element code as a material model. Rather, this study will demonstrate consistency between the two fragmentation models to ensure that the success of the sequentially applied model will be duplicated by the integrated two-scale approach. Once validated, further development of the model can be made by utilizing the integration into the finite element code to create a fully two-way coupled fragmentation model that will be extended to include higher fidelity models.