Fig. 4

Simulation results from cohesive finite element model (CFEM) for LuPO₄ and Lu₂SiO₅ EBCs, and CMAS. Fracture patterns in the (a) LuPO₄ and (b) Lu₂SiO₅ microstructures through grains and along grain boundaries (c) The box plots show crack path fractions for EBCs. The J-integral values for (d) LuPO₄ and (e) Lu₂SiO₅ EBCs with evolving crack length. The variations in J-integral values for all the microstructures are shown as light-colored bands and their average is the dark-colored curve. Panel (f) compares fracture toughness (K_Ic) obtained from CFEM simulations with that of experimentally obtained values. The ‘*’ indicates similarity of the data from experiments and CFEM simulations based on two-sample t-test and Wilcoxon rank-sum test, see Supplementary Material for details.