Effect of material parameters on thermal shock crack of ceramics calculated by phase-field method

Based on alumina ceramics, we employ the phase-field method to study the effects of thermal conductivity, specific heat, density, thermal expansion coefficient, Young's modulus, and fracture toughness on thermal shock cracks. The results show that increasing thermal conductivity and fracture toughness will reduce thermal shock damage. That is, the long crack length becomes shorter, or the crack density becomes smaller. However, increasing the thermal expansion coefficient and Young's modulus will increase thermal shock damage. It is consistent with the previous thermal shock theory. The effect of material parameters on crack propagation speed was also considered. In addition, we carried out a thermal shock test of the zirconia. The results of the phase-field calculation are the same as the thermal shock results of the zirconia. This paper verifies that the phase-field method is suitable for simulating thermal shock cracks in other ceramics

Additional file 1: of Controllable Growth of the Graphene from Millimeter-Sized Monolayer to Multilayer on Cu by Chemical Vapor Deposition

Supplementary information. Figure S1. (a) The TEM image shows the corner of the graphene domains. (b–e) Selected area electron diffraction (SAED) data for small regions indicated 1 to 4. These SAED data confirm the single-crystalline structure of the graphene domains as they have the same set of sixfold symmetric diffraction points. Figure S2. The optical microscopy images of the multilayer graphene with increasing size in the center region grown by decreasing hydrogen concentration and keeping the methane for constant (0.5 sccm CH4). (a) 38 sccm H2; (b) 29 sccm H2. Figure S3. The deconvolution of the 2D band of the (a) monolayer, (b) bilayer, (c) trilayer, and (d) tetralayer graphene with Lorentzians function as shown in Fig. 3a. Figure S4. The optical microscopy images of the multilayer graphene with non-Bernal stacking transferred to SiO2. Figure S5. The deconvolution of the 2D band of the (a) monolayer, (b) bilayer, (c) trilayer, and (d) tetralayer graphene with Lorentzians function as shown in Fig. 3b. Figure S6. The G (a) and 2D (b) peak position of the multilayer grahene with Bernal and non-Bernal stacking order as shown in Fig. 3a and b, respectively. Figure S7. The I2D/IG value of the multilayer graphene with Bernal and non-Bernal stacking order as shown in Fig. 3a and b, respectively. Figure S8. The typical EDS spectrum of the probe site on the nanoparticle and not on the nanoparticle. Figure S9. The optical microscopy images of the multilayer graphene growth with 32 sccm H2, 0.5 CH4 at different time. (a) 10 min, (b) 20 min, (c) 40 min. (DOC 6452 kb