Size Effect on the Fracture Properties of Nuclear Graphite

The objective of this study was to investigate the size effect on the fracture properties (fracture toughness, tensile and flexural strengths, and their statistical characteristics) of nuclear graphite through numerical modeling. The continuum damage mechanics (CDM) model was used to simulate the fracture of nuclear graphite under different loading conditions. The damage behavior of nuclear graphite was considered through a traction-separation relationship. Three fracture tests were simulated—bars under tension, un-notched beams under three-point bending, and single-edge-notched beams under three-point bending—with each test including specimens of different sizes. The microstructural heterogeneity of nuclear graphite was modeled by assigning the elements with properties randomly created with a Weibull distribution. Using the maximum loads obtained from the simulated load-displacement curves, the strength and fracture toughness were predicted according to beam theory and fracture mechanics theory, respectively. Monte Carlo analyses were conducted to predict the statistical characteristics of the predicted fracture properties. The numerical predictions were compared with experiments, including those performed by the authors. Most of the predicted fracture properties showed size effects. For the range of specimen sizes considered, with an increase in specimen size, (1) the mean tensile strength remained almost constant, (2) the mean bend strength decreased, and (3) the fracture toughness increased. Besides the mean values, the variations of the fracture properties caused by the inherent heterogeneity of the material also showed a size effect: the smaller the specimen size, the bigger the scatter in the predicted values. These simulated results were mostly consistent with experimental data. By combining the effect of material damage and microstructural heterogeneity, one can correctly simulate the size effect seen in the fracture properties, the mean values and the variations, of nuclear graphite. This method can be used to understand the complex fracture behaviors of different nuclear graphite grades under different loading conditions.