Presented by:
Nikolai Gorbushin ESPCI ParisTech
Date:
Thursday 15th August 2019 - 14:00 to 14:30
Venue:
INI Seminar Room 1
Abstract:
Fracture mechanics serves both engineering and science in
various ways, such as studies of material integrity and physics of earthquakes.
Its main object is to analyse crack nucleation and growth depending on features
of a particular application. It is common to study cracks in homogeneous
materials, however analysis of cracks in bi-materials is important as well,
especially in modelling of frictional motion between solids at macro-scale and
inter-granular fracture in polycrystallines at micro-scale. The analysis of
fracture in dissimilar materials is the main topic of this research. We present
the analytical model of steady-state cracks in bi-material square lattices and
show its connection with associated macro-level fracture problem. We consider a semi-infinite crack propagating
along the interface between two mass-spring square lattices of different
properties. Assuming the linear interaction between lattice masses, we can
apply integral transforms and obtain the matrix Wiener-Hopf problem from
original equations of motion. In this particular case, the kernel matrix is
triangular which significantly simplifies the factorisation procedure and even
makes possible to reduce to the scalar Wiener-Hopf problem. The discreteness of
the problem, however, does not allow to derive factorisation analytically and
numerical factorisation was performed. We show that the problem discreteness
reveals microscopic radiation in form of decaying elastic waves emanating from
a crack tip. These waves are invisible at macro-scale but their energy
contributes to the global energy dissipation during the fracture process. We
also demonstrate effects of the material properties mismatch and link the
microscopic parameters with the macro-level fracture characteristics.
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