Stochastic Analysis of Dynamic Quasibrittle Fracture
Impact resistance is a critical design consideration for many defense structures. Direct experimental investigation of structural impact resistance is often limited to certain structural geometries and sizes due to the constraints of the test set-ups. Therefore, one has to rely on numerical modeling. Modern defense structures are often made of brittle heterogenous (quasibrittle) materials such as engineering ceramics and composite materials. One of the salient features of quasibrittle materials is that they generally exhibit a strain-softening behavior. This leads to the spurious mesh sensitivity in finite element (FE) calculations, which severely limits the prediction capability of the FE models. Furthermore, for quasibrittle materials, both material microstructure and local material properties are also subjected to significant variability. Therefore, the resulting structural response under impact loading is highly stochastic. Developing a predictive stochastic numerical model is of paramount importance for reliability-based design of quasibrittle structures under impact loading.
This research aims to develop a novel multiscale numerical model for probabilistic analysis of quasibrittle structures under impact. The proposed model will be anchored by a stochastic FE model, where the probability distribution functions of the relevant material properties will be determined by a rate-dependent finite weakest link model and a stochastic micromechanical model. The finite weakest link model will statistically represent the damage localization mechanism and naturally involve the length scales associated with the stochastic material damage process. Consequently, the weakest link model will be able to correctly capture the dependence of the probability distribution functions of the material properties on the finite element mesh size, which is essential for mitigating the spurious mesh sensitivity for the stochastic FE simulations of dynamic quasibrittle fracture. The finite weakest link model will be further calibrated and validated through a stochastic micromechanical model, which can explicitly represent the random grain sizes, pre-existing flaws and fracture properties of grain boundaries. Therefore, through this multiscale model, the variability of the material properties for the FE model will be physically related to the random microstruc- tural features as well as the random fracture properties at the micro-scale. This research will use silicon carbide (SiC) structures as a model system. The proposed numerical model will be calibrated and validated by a set of impact tests on SiC beams in collaboration with the Impact Physics Branch at the Army Research Laboratory (ARL).
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