Prediction of crack nucleation and propagation in porous ceramics using the phase-field approach

Strength-based regularization length in phase field fracture

“…The last example highlights the interest of using a PF formulation with the same input parameters to assess failure in specimens made of the same material and containing either a singularity (V-notch) or a stress concentration (crack blunted by a hole) (Figure 8) (Abaza et al 2022). Two 2022) highlighted that using a classical PF implementation, two significantly different internal lengths had to be chosen in order to capture the crack initiation loading levels for these two configurations, which thus raises the question of which internal lengths should be chosen if we considered a specimen containing both a V-notch and a crack blunted by a hole.…”

“…The CC and PF approaches may somehow be related since they can be used in order to model the same fracture problems. Both approaches were for instance used for Hertzian indentation induced fracture (Strobl et al 2017;Strobl et al 2020), notched thin ply laminates fracture (Reinoso et al 2017) or notched specimens under bending (Abaza et al 2022). Based on the main idea proposed by Leguillon (2002), i.e., considering not only the material critical energy release rate but also its strength, Kumar et al (2020) recently proposed to revisit nucleation in the PF approach.…”

“…It was thus highlighted that for a given geometry and loading configuration, it is possible to identify ℓ c that corresponds to a given value of 𝜎 c (and vice-versa). Neverthless, Abaza et al (2022) recently observed that two significanly different internal lengths had to be identified to capture the initiation loading level predicted by the CC for two different ceramic specimens containing either a V-notch (identified ℓ c = 0.02 mm) or a crack blunted by a hole (identified ℓ c = 0.007 mm). Therefore, it is not straithforward to determine a unique internal length for a given material and it raised the question of which internal length should be chosen if the configuration under investigation contains both a V-notch and a crack blunted by a hole.…”

The effect of chemical vapor infiltration process parameters on flexural strength of porous α$\alpha$‐SiC: a numerical model

“…20,21 The void space inherent to porosity is in fact linked to damage directly in typical phase field descriptions of fracture. 22 Any step of the manufacturing process used to fabricate 𝛼-SiC ceramics is at least in part responsible for creating imperfections, especially pores. Because of this, the infiltration of matrix material has emerged as a necessary component of the manufacturing process as a subsequent porosity controlling mechanism.…”

“…Average 𝐿 2 norm of the difference in pore profile between grids with 𝑁 ∈[22, 158] and a grid with 𝑁 = 160. In all cases, Δ𝑡 CVI ∼ 𝑁 −2 , Δ𝑧 CVI = 𝐿∕(𝑁 − 1).…”