Phase field modeling of diamond-silicon carbide ceramic composites with tertiary grain boundary phases

Modeling Deformation and Fracture of Boron-Based Ceramics with Nonuniform Grain and Phase Boundaries and Thermal-Residual Stress

“…The energy barrier  is obtained from the difference between the free energies of crystalline and amorphous phases. The preferred twinning system in a randomly oriented B 4 C grain is the one of among three possible basal twinning systems with the maximum Schmid factor, producing s and m [52]. Cleavage anisotropy α is prescribed similarly based on prior works [27,45,52], and χ = χ in (35) [40].…”

“…The choices of the regularization lengths l ξ and l η were analyzed in detail in a prior work on ceramic composites [52]; that discussion is now summarized. Here, the minimum acceptable length permitted by the mesh resolution and dimensions of the simulation domain [45,48] is assigned, with l ξ = l η for convenience.…”

“…In such nanoscale simulations, parameters correlate with molecular mechanics and take values of nm or smaller. Parametric studies with different regularization lengths for twinning, phase transformations, and fractures are reported in several prior works [26,45,52,55]. Generally, increasing the regularization length while holding the surface energy constant leads to a reduction in nucleation stress and peak strength, though the relative importance depends on the particular problem.…”

The diffuse interface phase‐field model for in situ interlayer phase formations in low‐temperature reaction bonding of alumina laminates—A theoretical and experimental comparison

“…The possible phase evolution, based on diffusion interface approach 20,21 and solution mass transport processes, 22,23 was modeled by a phase‐field model. The structure, orientation, and composition of microstructure grains were estimated by reduction in bulk energy, 24 decrease in interfacial energy, 25 and solid‐state phase transformations 26 . These diffusion interface domain interactions can be modeled by continuous variation in chemical profile within a limited zone, 27 the condition of materials flux, 25 and chemical potentials 26 .…”

Phase-field approaches to fracture in the 3rd millennium

“…The last five articles are devoted to extending the phase-field approximation beyond the setting of homogeneous linear elastic isotropic brittle materials, with the last three focusing on hydraulic fracture. Clayton et al (2022) put forth a phase-field model alongside a large set of simulations for the deformation, fracture, and deformation twinning of a twophase polycrystal bonded by grain boundaries with their own mechanical behavior. The model makes use of two order parameters, one to describe fracture, the other to describe twinning.…”