Fig. 5

Simulation results from cohesive finite element model (CFEM) for 5% and 8% CMAS-penetrated LuPO₄ and Lu₂SiO₅ EBCs. Panels (a–d) Show fracture patterns in the 5% and 8% CMAS-penetrated LuPO₄ and Lu₂SiO₅ EBC microstructures respectively. The box plots in panel (e) shows crack path fractions for EBCs with CMAS penetration. The J-integral values for (f) LuPO₄ and (g) Lu₂SiO₅ with and without CMAS penetration are compared with that of the pure CMAS with evolving crack length. The variations in J-integral values for all the microstructures are shown as light-colored bands and their average is presented with the dark-colored curve. Panel (h) 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.