Fraunhofer IWM, Freiburg, Germany
Natural Sciences (Physics)
Simulation of a three point bending test of a silicon crystal. The upper cylinder is pushed downward in a path-controlled trajectory. On contact, the induced stresses on the upper and lower surface are discernible. Tensile stresses are color-coded in red and compressive stresses in blue. Eventually, brittle failure of the silicon crystal is initiated. The simulation was carried out using SimPARTIX.
Ceramics or glasses typically show brittle fracture behavior. Under tensile stresses these materials show an elastic behavior with reversible deformations. Above a certain tension threshold, however, these materials fail instantly with a complete relaxation of the applied stresses. The resulting breaking edge of crystalline materials is usually oriented along the crystal lattice structure showing smoothness at the atomic scale.
The fracture toughness of a brittle material is quantitatively described by a critical stress intensity factor. This quantity is an upper bound for the applied tension at the tip of an evolving crack. Once this bound is exceeded, brittle fracture occurs.
In SimPARTIX the mechanics of brittle fracture are modelled by the theory of peridynamics, which is a non-local extension of the classical continuum mechanic formalism. The mathematical structure of the peridynamic theory is well suited for the application in particle-based simulation techniques. Each single particle represents a finite volume of the work piece, which is connected to the neighboring particles by force bonds, whose stiffness represents the compressibility of the material. The fracture toughness of the material is then described by a critical limit of the deformation of the force bonds. If this limit is exceeded, brittle failure is initiated.
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