Modes of detachment at the inclusion–matrix interface

With the help of a 2D theoretical model, this paper analyses the modes of matrix detachment around a circular–elliptical rigid inclusion under pure and simple shear bulk deformations. Three modes of matrix detachment are possible: Mode 1—the matrix is displaced normal to the inclusion boundary, forming fissures at the interface; Mode 2—the matrix slips along the inclusion boundary without any separation; Mode 3—the detachment occurs by a combination of Modes 1 and 2. In order to determine the onset of detachment at any point on the coherent inclusion–matrix interface, the tensile and shear stresses were derived at that point, and compared with imposed critical values. Numerical simulations based on the theoretical model reveal that the three modes occur systematically along the inclusion–matrix interface, the geometrical dispositions of which depend on the aspect ratio (R) and orientation (φ) of the inclusion. In the case of circular inclusions, Mode 1 and Mode 2 domains are separated by a Mode 3 domain and the disposition shows an internal symmetry. On the other hand, it is asymmetrical when the inclusions are elliptical and oriented oblique to the bulk extension direction in pure shear and to the shear direction in simple shear. In simple shear, Mode 2 detachment with synthetic slip occurs dominantly when φ is less than 45° and greater than 135°. The results obtained from numerical models are complemented with observations in physical experiments. The paper also determines theoretically the critical stresses for detachment to occur as a function of R for different φ values, revealing that for a given mechanical strength of the inclusion–matrix interface, a particular mode of detachment can take place only when the aspect ratio crosses a threshold value.