Investigation of microscale brittle fracture opening in diamond with olivine inclusion using advanced computational modelling

Diamond-hosted inclusions offer critical insights into Earth's interior, serving as tracers of entrapment pressure (P) and temperature (T) during diamond formation. These inclusions preserve residual pressures, crucial for reconstructing deep-Earth processes through geothermobarometry (Kohn et al., 2023; Rustioni et al., 2015). However, current models assume purely elastic post-entrapment behavior, overlooking mechanisms like brittle fractures and viscous deformation, potentially underestimating formation depths (Angel et al., 2022). This study models brittle fractures in diamond-hosted inclusions to refine geothermobarometric techniques.

Using Extended Finite Element Methods (XFEM) (Moës et al., 1999) and Phase-Field Modeling (PFM) (Wu, 2017), we analyzed the interplay between inclusion geometry, material properties, and fracture behavior. XFEM simulations revealed brittle fractures contribute marginally (~5–6%) to residual pressure relaxation, leaving pressures significantly higher (~0.76 GPa) than observed in natural systems (<0.5 GPa). These findings highlight limitations in brittle fracture assumptions and emphasize the influence of inclusion size and shape on stress concentration and fracture propagation (Puhan et al., 2024).

To address XFEM’s limitations, PFM simulations incorporating brittle and quasi-brittle fractures were implemented within an ABAQUS framework. Results showed geometric singularities, such as sharp edges in cuboidal inclusions, enhance pressure relaxation (~0.72 GPa), aligning better with experimental observations. Stress interactions in multi-inclusion systems demonstrated fracture coalescence as a key mechanism for additional relaxation. However, these effects remain insufficient to fully explain the lower residual pressures observed in natural systems.

This study explores the influence of inclusion size, fracture toughness, and material properties on fracture initiation and propagation. It identifies the need for additional mechanisms, such as fluid-mediated weakening, plastic deformation, and preexisting defects, to accurately capture the complexity of natural inclusion-host systems. By advancing numerical methodologies and addressing critical gaps in current models, this work provides a robust framework for refining geothermobarometric methods and deepening understanding of diamond formation and exhumation processes.

References

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