Fracture spacings of fiber inclusions in a ductile geological matrix and development of microboudins: 3D numerical modeling

Tensile fractures and resultant microboudinage structures of brittle fiber inclusions (e.g., tourmaline, piedmontite and amphibole) in the soft matrix of deforming minerals are of great significance for determining the finite strains and paleostresses of naturally deformed rocks. Using statistical strength theory, damage mechanics, and continuum mechanics, we have reproduced in a series of numerical models the sequential fractures of either homogeneous or heterogeneous fiber inclusions under axial tension in an elastoplastic matrix. The results clarify that: (1) The spacing between fractures in fibers is inversely proportional to the applied strain. As the applied strain increases, the fracture spacing systematically decreases as sequential fractures fill in until fracture saturation is reached. (2) As fiber length increases, the critical tensile strain for fracture saturation rises. For the same fiber diameter, saturation fracture spacing increases slightly with rising fiber length. For the same fiber length, however, saturation fracture spacing decreases significantly with lessening fiber diameter. Hence, fracture spacing at the saturation state depends on the volume fraction of fiber. (3) The rupture mode of fibers strongly depends on the non-uniform distribution of mechanical properties, which provides an effective approach for estimating the inhomogeneity of fibers by analyzing the formation of fractures. Furthermore, due to material heterogeneity, new fractures are unlikely to occur in the middle of existing adjacent fractures.